US F0308A Prestressed Concrete Bridges

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Design guide

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The Technical Department for Transport, Roads and Bridges Engineering and Road Safety (Service d'études techniques des routes et autoroutes - Sétra) is a technical department within the Ministry of Transport and Infrastructure. Its field of activities is the road, the transportation and the engineering structures.

The Sétra supports the public owner The Sétra supplies State agencies and local communities (counties, large cities and urban communities) with informations, methodologies and tools suited to the specificities of the networks in order to:

• improve the projects quality; • help with the asset management; • define, apply and evaluate the public policies; • guarantee the coherence of the road network and state of the art; • put forward the public interests, in particular within the framework of European standardization; • bring an expertise on complex projects.

The Sétra, producer of the state of the art Within a very large scale, beyond the road and engineering structures, in the field of transport, intermodality, sustainable development, the Sétra:

• takes into account the needs of project owners and prime contractors, managers and operators; • fosters the exchanges of experience; • evaluates technical progress and the scientific results; • develops knowledge and good practices through technical guides, softwares; • contributes to the training and information of the technical community.

The Sétra, a work in partnership • The Sétra associates all the players of the French road community to its action: operational services; research organizations; Scientific and Technical Network (Réseau Scientifique et Technique de l'Equipement – RST), in particular the Public Works Regional Engineering Offices (Centres d'études techniques de l'Equipement – CETE), companies and professional organizations; motorway concessionary operators; other organizations such as French Rail Network Company (Réseau Ferré de France – RFF) and French Waterways Network (Voies Navigables de France - VNF); Departments like the department for Ecology and Sustainable Development…

• The Sétra regularly exchanges its experience and projects with its foreign counterparts, through bilateral co-operations, presentations in conferences and congresses, by welcoming delegations, through missions and expertises in other countries. It takes part in the European standardization commissions and many authorities and international working groups. The Sétra is an organization for technical approval, as an EOTA member (European Organisation for Technical Approvals).

Design guide

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This document is the translation of the work " Ponts en bétonprécontraint construits par encorbellements successifs" publishedin June 2003 under the reference F0308.

Prestressed concrete bridges built using the cantilever method – Design guide

Authors This document was created by a working group consisting of:

Pierre Barras, CETE (Centre d’études Techniques et de l’équipement - Technical Engineering Center for Infrastructure) du Sud-Ouest / Bridges Civil Engineering Structures Division)

Daniel de Matteis, Sétra (Service d’études techniques des routes et autoroutes -Technical Center for Highways and motorways) / Large Bridges Division)

Jean-François Derais, Sétra / Large Bridges Division

Michel Duviard, Engineering and Design Department, Jean Muller International

Daniel Guillot, CETE de l’Ouest / Bridges Division

Jean-Michel Lacombe, DREIF (Direction régionale de l’équipement Ile de France – Ile de France Regional Public Works Directorate) / Bridges Group

Gilles Lacoste, Sétra / Methodology and Software Division

Daniel Lecointre, Sétra / Large Bridges Division

Virgile Ojeda, CETE Méditerranée / Bridges Division

Pierre Paillusseau, CETE du Sud-Ouest / Bridges Division

Jean-Marc Reinhard, CETE de Lyon / Bridges Division

The monographs, iconography, drawings and 3D images were produced by Stéphane Chevrot, Philippe Julien, Eric Lozinguez and Louis Resterrucci from the Sétra Large Bridges Division.

Photographic credits: Sétra / Gérard Forquet (Sétra Large Bridges Division)

Acknowledgements The authors would like to thank everyone who, through their help, comments and observations, contributed to the creation of this document, especially:

Mr. Aubin (Bouygues), Mr. Bataille (Semi), Mr. Boileau (DDE 31), Mr. Chaboud (DDE 974), Mr. Doan (SNCF), Mr. Duclos (Thales), Mr. Gaudin (SPIE), Mr. Gausset (EEG), Mr. Heusse (ERSEM), Mr. Kirschner (SECOA), Mr. Le Faucheur (Sétra), Mr. Mossot (Demathieu et Bard), Mr. Poineau (Sétra), Mr. Primault (Vinci), Mr. Ryckaert (SETEC), Mr.Thibaux (Eiffage TP), Mr.Treffot (DDE 67) and Mr. Xercavins (PX-DAM).

The “Les outils" Collection – Sétra page 4 septembre 2007


Table of contents AUTHORS 1

ACKNOWLEDGEMENTS 4

TABLE OF CONTENTS 5

FOREWORD 7

1 - BACKGROUND INFORMATION 8 1.1 - PREAMBLE 8 1.2 - TECHNICAL PROCESS 10 1.3 - FIELDS OF APPLICATION 11 1.4 - DEVELOPMENT OF THE CONSTRUCTION TECHNIQUE IN FRANCE 14 1.5 - MAJOR CIVIL ENGINEERING STRUCTURES RECENTLY CONSTRUCTED OUTSIDE OF FRANCE 19

2 - GENERAL DESIGN 21 2.1 - FIELD OF APPLICATION 21 2.2 - STATIC LONGITUDINAL DESIGN 21 2.3 - CHOOSING A CROSS-SECTION 30 2.4 - PRE-DESIGN OF A SIMPLE CROSS-SECTION 34 2.5 - BREAKDOWN INTO SEGMENTS 39 2.6 - MAIN RATIOS 41

3 - DESIGN AND VERIFICATION OF LONGITUDINAL CABLING 43 3.1 - CABLING PRINCIPLES 43 3.2 - STRESS CALCULATIONS 52 3.3 - VERIFICATIONS TO BE CARRIED OUT WITH REGARD TO NORMAL STRESSES 54

4 - TRANSVERSE AND LOCALIZED BEHAVIOUR 58 4.1 - VERIFICATION PRINCIPLES 58 4.2 - TRANSVERSE FLEXION 59 4.3 - GENERAL TANGENTIAL STRESSES 70 4.4 - SPECIFIC ELEMENTS 79 4.5 - LOCALIZED FORCES AND REINFORCEMENTS 81 4.6 - RULES TO COMBINE PASSIVE REINFORCEMENTS 85 4.7 - RECOMMENDED CONFIGURATIONS FOR REINFORCEMENTS 88

5 - CANTILEVER STABILITY 93 5.1 - PRINCIPLE OF CANTILEVER STABILITY 93 5.2 - STABILITY SYSTEMS FOR CANTILEVERS 94 5.3 - ACTIONS TO CONSIDERED 103 5.4 - COMBINATIONS OF ACTIONS DURING CONSTRUCTION 107 5.5 - VERIFICATION AND DIMENSIONING OF THE ANCHORING ELEMENTS 111 5.6 - VERIFICATIONS OF OTHER STABILIZATION METHODS 119

6 - CONSTRUCTION TECHNOLOGY 124 6.1 - CONSTRUCTION USING CAST-IN-SITU SEGMENTS 124 6.2 - CONSTRUCTION BY PREFABRICATED SEGMENTS 138

7 - ON SITE MONITORING 149 7.1 - BACKGROUND INFORMATION 149 7.2 - INSPECTION OF GEOMETRY 149 7.3 - INSPECTION OF TEMPORARY STRUCTURES 165

The “Les outils” collection – Sétra Page 5 septembre 2007


7.4 - INSPECTION OF CONCRETE 168 7.5 - INSPECTION OF FORMWORK 178 7.6 - INSPECTING THE REINFORCEMENTS 178 7.7 - INSPECTION OF PRESTRESSING 179 7.8 - OTHER IMPORTANT POINTS 190

8 - PATHOLOGIES AND REPAIRS 195 8.1 - HISTORY OF THE REGULATIONS 195 8.2 - PATHOLOGIES SPECIFIC TO THE CANTILEVER CONSTRUCTION TECHNIQUE 200 8.3 - MAIN REPAIR TECHNIQUES 205

9 - PROVISIONS TO FACILITATE MAINTENANCE 208 9.1 - GENERAL PRINCIPLES 208 9.2 - BRIDGE DECK 208 9.3 - PIERS 212 9.4 - ABUTMENTS 216

10 - RECOMMENDATIONS FOR THE CREATION OF A CONTRACTOR TENDER DOCUMENT 219

10.1 - NATURE OF THE TENDER ENQUIRY 219 10.2 - CREATION OF A CONTRACTOR TENDER DOCUMENT 219 10.3 - TENDER REGULATIONS 220 10.4 - TENDER DOCUMENT 221 10.5 - SPECIAL ADMINISTRATIVE CLAUSES 222 10.6 - SPECIAL TECHNICAL CLAUSES 224 10.7 - PRICE SCHEDULE 229

A1 DETERMINATION EXAMPLE 230 A1.0 – PURPOSE OF THIS APPENDIX 230 A1.1 - REMINDERS 230 A1.2 – SOURCE DATA 235 A1.3 – CANTILEVER PRESTRESSING DESIGN 240 A1.4 – PRESTRESSING DESIGN FOR THE CLOSING SEGMENT 243 A1.5 – EXTERNAL PRESTRESSING DESIGN 252

A2 MONOGRAPHS OF CAST-IN-SITU BRIDGES 264

A3 BIBLIOGRAPHY 291 A3-1 – OFFICIAL TEXTS 291 A3-2 – SÉTRA GUIDES, SÉTRA-LCPC, SÉTRA-SNCF 291 A3-3 – OTHER PUBLICATIONS 291 A3-4 - ARTICLES IN MISCELLANEOUS PUBLICATIONS 291 AFPC/AFGC PUBLICATIONS FOR FIB (FÉDÉRATION DE L’INDUSTRIE DU BÉTON-CONCRETE INDUSTRY FEDERATION) CONGRESSES 291 REVUE TRAVAUX 291 SÉTRA BULLETIN OUVRAGES D’ART 291 BULLETIN DES LABORATOIRES DES PONTS ET CHAUSSÉES 291 ANNALES DE L’ITBTP 291 TECHNIQUES DE L’INGÉNIEUR 291 PCI JOURNAL 291 REVUE L’INDUSTRIA ITALIANA DEL CEMENTO (IIC) 291



Foreword The cantilever method is the most widely used technique for the construction of large prestressed concrete bridges in France and throughout the world.

Since the beginning of the 1990s, concrete bridges built by this method have faced stiff competition in the medium-span category from composite bridges and, to a lesser extent, from concrete bridges erected by incremental launching. On the other hand, they are increasingly used for bridging large spans, as illustrated by the Tanus viaduct over the River Viaur, the Tulle viaduct on the A89 highway and the new bridge over the Rhine to the south of Strasbourg.

Intended for construction managers, consulting engineers and methods and project engineers, this guide provides a detailed review of these structures, their field of use and the technology used in their construction.

For this reason, this guide replaces Technical Bulletin No.7 and its supplementary information, published by Sétra (Service d’études techniques des routes et autoroutes - Technical Centre for Highways and Motorways in December 1972, which had become obsolete with regard to several important points such as calculation methods, prestressing design, the structure of form travelers and the management of delayed deformation.

Chapters 1, 2, 3, 5 and 6 of this guide cover certain points which are very specific to the cantilever method: the general design of the structures, the design and calculation of longitudinal cabling, the stability of cantilevers and construction technology.

Chapters 4, 7, 8, 9 and 10 are more generalized, respectively covering transverse flexion, site inspections, problems and their repair, precautions to be taken to facilitate maintenance, and finally, the contents of contractor tender documents. Although written with bridges constructed by the cantilever method in mind, the information in these chapters will also be useful for anyone involved in the design or construction of large civil engineering structures.

This guide is the outcome of a major collective effort and is another illustration of the expertise of French contractors, engineering firms and construction agencies in the field of civil engineering.

Emmanuel Bouchon

Head of the Large Bridges Division at Sétra.



1 - Background information This first chapter introduces the major principles concerning the construction of bridges by the cantilever method and its field of use. It also describes the history of the development of this method and of the applicable regulations from 1943 to the present day.

1.1 - Preamble The cantilever construction method is a very ancient technique, in which a structure is built component by component above ground level.

Since ancient times, this method has been used for the construction of arches in Europe (Fig. 1.1) and in South America (including the construction of Mayan arches), and for the building of wooden bridges (Fig. 1.2).

Fig. 1.1 – The “Treasure of Atreus”. Longitudinal section

Fig. 1.2 – Gallic wooden bridge

In the 19th and early 20th centuries, this method was applied to the construction of arched metal bridges, such as the Gabarit and Viaur viaducts, or lattice girder designs, such as the Forth Bridge, the Bénodet bridge or the old Pirmil bridge at Nantes (Fig. 1.3).



Fig. 1.3 – The old Pirmil bridge in Nantes Fig. 1.4 – The Normandie bridge

More recently, it has been used for the construction of cable-stayed bridges, such as the Saint-Nazaire bridge over the River Loire and the Normandie bridge over the Seine (Fig. 1.4).

As far as prestressed concrete is concerned, construction by the cantilever method mainly applies to bridges whose decks can be combined with straight or horizontally curving beams and which are built out from their piers, with cast-in-situ or prefabricated segments (Fig. 1.5 and 1.6). These types of bridges are the focus of this guide.

Fig. 1.5 – Bridge forming part of a continuous girder on single supports

Fig. 1.6 – Cantilever construction of prestressed concrete box-girder bridge decks with cast-in-situ segments on the left and prefabricated segments on the right

Many of the techniques used in this method are also employed in the construction of portal bridges with box girder decks, such as the Bonhomme bridge in the Morbihan region of Brittany, the Auray viaduct (Fig. 1.7) and the bridge over the River Truyère at Garabit.



Fig. 1.7 – Construction of the Auray portal bridge Fig. 1.8 – The cable-stayed bridge at Chalon-sur-Saône under construction

Finally, and although not strictly within the scope of this guide, it should be mentioned that the cantilever method is often used for the construction of cable-stayed bridges, such as the Iroise bridge over the River Elorn, near Brest and the Bourgogne bridge at Chalon-sur-Saône (Fig. 1.8) and also for concrete arched bridges such as the Roche Bernard bridge over the River Vilaine (Fig. 1.9) and the bridge over the River Rance.

Fig. 1.9 – The arched bridge of La Roche-Bernard under construction

1.2 - Technical process

1.2.1 - Description of the method

This construction method consists of erecting the majority of a bridge deck without falsework or scaffolding at ground level, by working in consecutive sections known as segments, each of which is cantilevered out from the preceding segment. After a segment is built, the prestressing tendons fixed to the extremities are tensioned,



firmly attaching them to the preceding segments and thus forming a self-supporting cantilever which serves as a support for the subsequent operations.

Construction is carried out:

• Symmetrically in general, either side of a pier in order to minimize the moments transmitted to this support during erection; the resulting double overhang is called a balanced cantilever (Fig. 1.10)

Fig. 1.10 – Symmetrical construction from a pier

• Sometimes asymmetrically on a single side of a balanced cantilever, when the other side is already joined to the adjacent span (Fig. 1.11)

Fig. 1.11 – Over-cantilevering construction

• More rarely from an abutment; in this case, the overturning moment exerted by the span is compensated for by an appropriately dimensioned counterweight which forms part of the deck itself (Fig. 1.12).

Fig. 1.12 – Construction by the cantilever method using counterweighted spans

Although it is possible to build an entire structure using the cantilever method, the majority of structures include cast-on-falsework sections at the extremities of the end spans.

1.2.2 - Association with other methods

Cantilever construction is often used in association with other methods such as:

• Construction on falsework, when parts of the structure are close to the ground and feature modest spans

• Construction by incremental launching, when the structure features a series of spans less than 65m in length, of constant depth, supporting a road whose geometry is compatible with this technique.

1.3 - Fields of application



1.3.1 - Background information

Spans of 80 to 150m are preferred for bridges with prestressed concrete box girder decks built by the cantilever method. However, this technique can be used for spans up to 200m in common widths without major problems. Above this size, the quantities of materials increase significantly, thus reducing the cost-effectiveness of the method.

The world record span for concrete bridges built by the cantilever method currently stands at 301 m and is held by the Stolma Bridge in Norway. This is closely followed by the Raftsundet Bridge in the Lofoten Islands, also in Norway, with a central span of 298m. Opened to traffic at the end of 1998, both of these bridges have central spans partially made from lightweight concrete. These bridges both surpassed the Brisbane Bridge in Australia, built in 1986, whose span of 260m had beaten the previous record of 240 m held by the Hamana Bridge in Japan, built in 1977.

For a long time, the Gennevilliers Bridge, built in 1976, held the French record for the longest span with its two spans of 172m. Following closely behind with spans of 172m and 144m was the Ottmarsheim Bridge, built over the Alsace canal in 1979 using concrete partly made from lightweight aggregates. With a single span of 190 m, the Tanus viaduct over the River Viaur in the Aveyron (Fig. 1.13) captured the record in 1998 before being relegated to second place in 2002 by the new bridge over the River Rhine, south of Strasbourg, whose central span measures 205m.

Fig. 1.13 - The Tanus viaduct



1.3.2 - Advantages and disadvantages of the method

Advantages

The cantilever construction method offers many advantages.

Firstly, the bridge decks are mostly built without any contact with the ground, making it possible to build structures over rivers subject to severe flooding or above very deep and rugged valleys.

This method can also be used to erect structures with very different geometries. Thus, in elevation, it is possible to design decks of a constant or variable depth. For the latter, parabolic, cubic or linear variations are all possible. The method is extremely forgiving with regard to the geometry of the road supported by the bridge because, in contrast to incremental launching and pushing techniques, any horizontal and vertical alignments can be built without difficulty.

Finally, construction using elements of 3 to 4 m in length is cost-effective in terms of the formwork tools required for the bridge deck, even if the spans are few in number and of different lengths. In the case of prefabricated segments, the small size of these components also helps to limit the weight of the elements to be assembled, thus reducing the cost of the installation equipment.

Disadvan tages

However, there are also certain drawbacks to the cantilever construction method.

For identical spans, bridges built using this method are much heavier than composite structures. They therefore need larger supports and foundations than those required for composite structures. Of course, this makes the cantilever method less attractive, especially when the foundation terrain is of mediocre quality or when the site is in an earthquake zone.

Another major disadvantage to this method is the large number of tasks which have to be carried out in situ, both for the casting of the deck and for the development of the access routes to the site. Although the number of these tasks is reduced when the segments are prefabricated, of course, they are nevertheless greater in number than for an incrementally launched concrete bridge. When the structure crosses traffic bearing routes, the frequency of these tasks may compromise the safety of travelers and/or of workers on the site. These routes must then be closed, which often poses major problems.

From an aesthetic point of view, bridges built by the cantilever method often have relatively thick decks, which can pose problems on certain sites. As a result, by breaking down their construction into small elements and multiple casting phases, there are more likely to be differences in color between two consecutive segments.

Spans

Type 35

70

90

120

150

200 300

- Bridges built using the cantilever

- Incrementally launched concrete bridges

- Composite beam bridges

- Composite box girder bridges

- Orthotropic slab box-section bridges

- Cables stays bridges

1.14 – Fields of application for different types of bridges

The area defined by the thickest line represents the most common field of application. It should be noted that suspension bridges are not included in this table, as they are primarily used for very wide spans.



1.3.3 - Competing techniques

Now, prestressed concrete box-girder bridges built using the cantilever method are designed for spans between 60 m and 300 m in length. This technique has to compete with a number of different solutions operating within this very wide range of spans.

For spans of less than 80 m, bridges built using the cantilever method are most commonly of a constant depth. They are in competition with girder bridges with a composite concrete and steel framework. If the geometry of the supported road is compatible, they also have to compete with incrementally-launched bridges made from prestressed concrete, which are economically viable for spans of between 35 and 70 m.

For spans of between 70m and 120m, bridges built by the cantilever method may be of constant or variable depth. They are in competition with girder bridges with a composite concrete and steel framework. For practical or aestetic reasons, composite concrete and steel box girder bridges or cable-stayed bridges are also often designed to cover this range of spans.

For spans of between 100 m and 200 m, bridges built using the cantilever method are almost always of variable depth and are in competition with composite or metal box girder bridges (beyond 140m) and cable-stayed bridges. Within this range of spans, presetressed concrete box girder solutions with lightweight metal webs may also prove to be economical.

1.4 - Development of the construction technique in France There now follows a short history of the development of the construction technique and the regulations for concrete bridges built using the cantilever method.

1.4.1 - 1946-1952

Construction using the cantilever method was used for the first time in France by Albert Caquot for the building of the Donzère and Bezons reinforced concrete bridges in 1953, using a form traveler suspended from a metal girder (Fig.1.15).

In Germany, Finsterwalder also used this technique for the construction of the Neckarsens and Baldunstein prestressed concrete bridges in 1950. It was then used for the construction of the Worms and Koblenz cantilever bridges in 1952, featuring a large span of 114 metres (using the form traveler technique).

In the same year, Nicolas Esquillan used a very similar technique with a form traveler suspended from a metal beam to build the La Voulte railroad bridge, consisting of several 60 m-wide portal spans.

It should be noted that at this time, there were no French design regulations concerning the cantilever construction method or even for prestressed concrete.

1.4.2 - 1953-1964

This period was marked by the introduction of regulations, the development of design methods, the improvement of the characteristics of prestressing reinforcements and the development of prestressing procedures.

During this period, the bridge-building techniques using the cantilever method improved considerably. As a result, we can refer to two distinct generations of bridges.



Firs t genera t ion br idges

The bridge decks of first generation structures were embedded on piers and even on abutments and featured hinges at mid-span.

Built in 1957 by GTM, the Chazey bridge over the River Ain was the first French bridge to be truly built by the cantilever method and the first in a series of major structures including the Beaucaire bridge over the River Rhône and the Savines bridge over the Serre-Ponçon reservoir dam in the Hautes-Alpes region. The Chazey and Beaucaire bridges suffered from prestressing defects and have since been demolished. The former was replaced by a new cantilever bridge in 1973 and the latter by a composite bridge in 1995.

Second genera t ion br idges

As the first generation bridges suffered from an excessive deformation of their cantilever elements after several years, due to an underestimation of the effects of concrete creep and shrinkage, a second generation of bridges was designed and built with continuous spans and therefore without hinges at mid-span.

Particularly noteworthy second generation bridges include:

• The bridges at Goncelin, over the River Isère and Lacroix-Falgarde over the Ariège, designed by the STUP (Société Technique pour l’Utilisation de la Précontrainte – Engineering Company for the Use of Prestressing). These were the first continuously rendered structures (1962)

• The Layrac bridge, over the River Garonne, designed by GTM

• The bridges of Choisy-le-Roi, near Paris, and Pierre-Bénite, near Lyons, built in 1965 by Campenon-Bernard, which were the first structures to use prefabricated segments and glued conjugated joints.

1.4.3 - 1965-1975

This was a period of enormous developments and constantly changing regulations. It began with the publication of the IP1 (Circular no. 44 of August 12 1965 relating to the provisional instruction for the use of prestressed concrete), and it finished with the publication of the Circular of April 2 1975, which brought an end to the second generation structures and paved the way for third generation bridges.

Fig. 1.15 – The Bezons bridge

The most notable bridges of the 1965-1975 period include:



• The Oléron bridge (1966), approximately 3,000m in length and built using prefabricated segments installed for the first time by a launching beam

• The Oissel bridge over the A13 highway: 700m long without an intermediate expansion joint (1970)

• The Calix viaduct in Caen, whose collapsed cantilever prompted the Sétra to define its rules for the stability of cantilevers which are still in force today (1975)

• The Saint-Cloud bridge (1974), on the outskirts of Paris, whose very wide (20.4 m) and slender deck (spans of 100m and a 1/30 slenderness ratio), had to be reinforced in 1990

• The Gennevilliers bridge over the River Seine near Paris, with a span of 172 m (1976)

• The bridge over the River Loire at Orléans (1976), whose box-girder deck featuring three webs with bar prestressing, had to be repaired in 1978 and 1987.

1.4.4 - 1975-1982

Bridges built during this period can be described as third generation bridges. Designed in accordance with the rules established by the Circular of April 2 1975, (including accounting for creep and thermal gradient), these structures were much better designed and did not suffer from the difficulties encountered with previous generations of bridges.

Worthy of note amongst the structures built of conventional concrete during this period are:

• The Mâcon bridge over the Saône, which was one of the first new-generation bridges (1977)

• The numerous interlaced viaducts of the Saint-Maurice interchange, between the A4 and A86 highways near Paris, built with prefabricated segments (1980)

• The Mathilde bridge near Rouen, whose central span includes an independent 115m long metal span, supported on a 30-m cantilevered girder made from prestressed concrete (1980).

Between 1975 and 1982, several bridges were also made from lightweight concrete, such as:

• The Tricastin bridge (1979), whose end spans and the beginnings of its central span are made from normal concrete, which acts as a counterweight and compensates for a highly unfavourable arrangement between the spans (25m – 142m – 25m) ;

• The Ottmarsheim bridge, which features a 172m lightweight concrete span (1980).

Two remarkable railroad structures were also built during this period:

• The crossing of the Seine at Nanterre via the railroad spur for the new town of Cergy-Pontoise (1977), which is a prestressed concrete structure of 1,390 m whose two viaducts of 229 m (48m, 85m, 48m, 48m) and 221.5m (48m, 85m, 48m, 40.5m) were built using the cantilever method

• The 400m long Viaduc de Commelles on the “conventional” Paris-Brussels and Paris-Lille lines, with a 4-web box-girder deck carrying four railroad lines and featuring main span of 45m (1980).



1.4.5 - 1983 to the present day

On the regulatory level, this period was characterized by the generalization of regulations concerning limit state calculations (BPEL 83 [Béton Précontraint par la méthode des Etats Limites – Limit State Prestressed Concrete Code], followed by BPEL 91 and finally BPEL 91 revised in 1999). The introduction of Quality Assurance and the development of french and european standardization also led to clear changes in the rules concerning the building of structures.

On the technological level, major progress was made in the design of major civil engineering structures made from prestressed concrete, due largely to the development of external prestressing.

The following structures are notable examples of traditional road bridges built during this period, although this is not an exhaustive list:

• The bridge over the River Loir at La Flèche, which was the first bridge to be built by the cantilever method and positioned by rotation (1983)

• The Pont à Mousson viaduct over the River Moselle, which was one of the first bridges to feature external prestressing

• The Sermenaz viaduct, near Lyons, with completely external galvanized prestressing

• The Île de Ré bridge (1988) whose deck consists of 3,000 m of prefabricated segments made from B60 category high-performance concrete

• The Arrêt-Darré viaduct, whose cantilevers were angled at the end of construction to follow the longitudinal profile (1988, [SER 90])

• The viaducts of Bourran, at Rodez, and La Rivière Saint-Denis, on Reunion Island, whose design features double-shelled piers (1991, [BOU 91], [BOU 94.1], [CON 91], [BOU 92] and [BOU 94.2])

• The Cheviré bridge, in Nantes, whose central span of 242 m includes an independent span of 162 m in length, consisting of a box-girder with an orthotropic deck plate (1991, [VIR 90 2], [VIR 91 2] and [VIR 94])

• The Arcins bridge, near Bordeaux, consisting of two parallel structures of 650 m in length made from prefabricated segments assembled by combination prestressing (1993, [ABE 91] and [ABE 94], Fig. 1.16)

• The construction of a parallel lane on the Gennevilliers bridge over the River Seine [CHA 94]

• The Piou and Rioulong viaducts on the A75 highway, whose cantilever segments are supported by metal struts (1995, [CRO 94] and [CIL 96], Fig. 1.17)

• The Viaduc de Rogerville on the A29, featuring two 680-m long decks made from prefabricated segments with innovative keyed expansion systems on certain spans (1996, [RIC 96], [JAC 96] and [JAC 98])

• The Tanus viaduct over the River Viaur, spanning 190 m and featuring a pier of over 100 m in height (1998, [BOU 94.3], [SER 98] and [GAC 98])

• The second Pont-Salomon viaduct, which represents one of the first applications of Eurocodes 1 and 2 (2000, [DAL 00] and [DEWOl]



• The viaducts of La Clidane (length: 132 m), La Barricade (length: 150 m) and Tulle (length: 180 m), supporting the A89 highway [LAC 02]

• The new bridge over the Rhine to the south of Strasbourg, which boasts a record single span structure of 205 m above the navigable channel of the Rhine (2002, [DEM 00], [DEM 01.1], [DEM 01.2], [DEM 01.3], [DEM 02]).

Fig. 1.16 – The Arcins bridge in Bordeaux Fig. 1.17 – The Piou viaduct

Particularly notable portal road bridges built using the cantilever method since 1983 include:

• The bridge over the Loch d’Auray, with an opening of 109 m between the base of the portal legs (1989, [VIR90.2], Fig. 1.18)

• The bridge over the River Truyère at Garabit, with an opening of 195 m between the base of the portal legs (1993, [GIL 93] and [CAN 94]).

Noteworthy railroad structures built since 1983 include several viaducts on the TGV high-speed Rhône-Alpes line (extension of the TGV Paris-South Eastern line to Valence) and of the TGV high-speed Méditerranée line, including:

For the TGV Rhône-Alpes high-speed line:

• The Costière viaduct, situated in the northern section of the eastern Lyons bypass: 1,725 m long in total, 900 m of which were built using successive cantilever segments with main spans of 88 m (1992).

For the TGV Méditerranée high-speed line:

• The Avignon viaduct over the River Rhône, whose two independent 1,500-m long decks were prefabricated (Fig. 1.19, [BOUS 98.1])

• The Vernègues viaduct, with a semi-circular transverse cross section. Measuring 1,210 m, this was built using a combination of the cantilever method and incremental launching techniques [BOUS 98.2]

• The 1,734-m long Ventabren viaduct, which relied upon incremental launching techniques, successive cantilever segment construction and a rotated installation.



Fig. 1.18 – The portal bridge over the Loch d’Auray

Fig. 1.19 –TGV high-speed railroad bridge over the Rhône at Avignon

Finally, a number of highly innovative road structures were also built during this period, including:

• The Sylans and Glacières viaducts over the A40. With respective lengths of 1,266 m and 214 m, both of these structures featured two parallel decks with triangulated concrete webs (1987, [BOU 90])

• The Corniche bridge at Dôle with corrugated webs, (1994, [COM 93], [LEB 94] and [REI 94])

• The three Boulonnais viaducts over the Al6 highway, whose decks are made of prefabricated segments with four triangulated metallic webs [MEU 98]

• The bridge over the Vecchio in Corsica, with open webs made of prefabricated triangular panels (1999, [PAU 98] and [PAU 00])

• The bridge over the Bras de la Plaine, on Reunion Island, whose single 260-m span is made from two pre-stressed slabs linked by a triangular tubular metal structure (2002, [CHU 02], Fig. 1.20).

1.5 - Major civil engineering structures recently constructed outside of France

In recent years, a very large number of bridges have been built using the cantilever method outside of France. The following list features some of the most important examples:

• Certain access viaducts to theVasco de Gama bridge in Lisbon, Portugal

• Access viaducts to the new Severn Bridge in Great Britain [COM 94] and [COM 96]

• Access viaducts to the Storebelt suspension bridge in Denmark

• The Stolma and Rafsundet bridges in Northern Norway

• The Houston canal bridge in the USA

• The Brisbane Bridge in Australia

• The Hamana bridge in Japan



• The new São João railroad bridge over the River Douro in Portugal

• The Medway Viaduct on the TGV high-speed rail line between the Channel Tunnel and London [POROl].

Although built using a slightly different method to that described in this guide, we should also make a special reference to extraordinary Confederation Bridge between the North American continent and Prince Edward Island in Canada, whose central section is made from forty 250-m long spans (Fig. 1.21, [BOI 96] and [COM 98]).

Fig. 1.20 – The bridge over the Bras de la Plaine Fig. 1.21 – Transportation of a prefabricated cantilever for the Confederation Bridge



2 - General design This chapter starts by covering the more general aspects of the design of bridges with box girder decks built by the cantilever method: layout of the supports, deck height variation law and choice of a cross-section.

It goes on to describe the more specific aspects of the project: design of a simple cross-section, layout of the segments and ratios of materials. The chapter only covers road bridges.

2.1 - Field of application As we have already seen in Chapter 1, the cantilever construction technique can be used to build a wide variety of prestressed concrete structures. Indeed:

• It is suitable for a very wide range of spans (from 40 to 200 m, or even 300 m)

• The supported road can have any type of geometry, both horizontally and vertically

• Between 60 and 100 m, the bridge deck can be of constant or variable depth

• This method can be used regardless of the natural characteristics of the gap to be bridged (large depth, steep slopes, very poor-quality soils, coastal site, etc.).

We shall cover each of these different points in detail during the course of this chapter. We shall also see how piers are positioned in the gap to be bridged, how the transverse structure of the deck is chosen and designed and how its formwork is accurately determined.

2.2 - Static longitudinal design

2.2.1 - Distribution of spans

Example o f a s t ruc ture cons i s t ing o f iden t i ca l can t i l evers

The simplest structures are made from main spans of identical length. This allows the construction of identical cantilevers, which simplifies the design of the erection and concrete casting equipment used and improves output.

The end spans are usually longer than a half-cantilever. The additional length, representing 10 to 20 percent of the length of the main spans, is usually built on falsework as this is generally the most economical method. It helps to balance out the moments in the different spans under operating loads and ensures positive support reactions on the abutments.



Fig. 2.1 – Distribution of spans for a simple bridge built by the cantilever method

Fig. 2.2 – Bridges with a combination of large spans in the river section and shorter spans on land

Fig. 2.3 – Bridge consisting of variable length spans according to the depth of the gap

Therefore, the most common structures consist of a series of equal spans flanked by end spans which are 60 to 70 percent of the length of the main spans.

Example o f a s t ruc ture made f rom can t i l ever s o f d i f f e ren t l eng ths

Gaps to be bridged often feature constraints that make it impossible to design a structure of the type we have just described. It then becomes necessary to build structures incorporating several different types of cantilevers.

The example in Figure 2.2 below shows a structure consisting of one or more large spans, as required by the need for a wide navigation channel, and a series of shorter – and thus more economical – spans crossing unnavigable flood zones.

The example in Figure 2.3 shows another structure featuring a large span in the deepest part of the valley to be crossed and shorter spans elsewhere.

In both of these cases, it should be emphasized that the transition from large to small spans is carried out via a span whose length is the mean of the two standard spans. It should also be noted that the end spans are 60% of the length of the adjacent standard spans.

Other examples

Certain special techniques may be used to circumvent these strict rules concerning the distribution of spans and the balancing of cantilevers. They include over-cantilevering, the use of counterweights and building out from a



counterweight span, etc. These techniques are described in Paragraph 2.2.4. Due to their cost, they are only used in very specific cases imposing the layout of piers (highly urbanized sites or the presence of railroad lines and canals) or when it is impossible or particularly costly to extend the bridge deck.

Nevertheless, for structures of a constant depth, it is possible to design unequal spans by shifting the joints (à valider pour "clavages"). It is then possible to shift certain piers slightly, which would otherwise be badly positioned (Fig. 2.4).

2.2.2 - Slenderness ratio and shape of the intrados

We shall now discuss the variation laws which determine the possible depth of the bridge deck, while mentioning the most economical solution for each range of spans.

With regard to the criteria concerning suitability for the site, it is very difficult to establish rules to dictate the most appropriate form for a given site. However, it should be noted that:

• If it is possible, a constant depth is well suited to geometrically complex structures: especially very curved bridges; the same applies to structures located in complex areas (urban sites, interchanges, etc.)

• A variable depth is generally quite well suited to deep valleys and large watercourses

• It is often a good idea to highlight certain sections of the gap by using spans of variable depths at its most outstanding sections.

2 .2 .2 .1 – Cons tant depth

When the main spans of a structure are less than 65/70 m long, bridge decks of a constant depth are generally the most economical, because the savings made by simplifying the formwork tools for the deck (form travelers or prefabrication units) and reinforcement for the deck are much greater than any possible savings in materials. In this case, the depth of the deck is between 1/20 and 1/25 of the maximum span. However, a minimum of 2.20 m is required for satisfactory movement inside the box girder.

Fig. 2.4 – Slight shifting δ of the piers for a structure of constant depth

(The shifting of the joints δ is thus double the value of δ)

For spans of above 100 m in length, the quantities of concrete and prestressing materials used increase significantly and the cost of a constant depth solution increases in comparison to a variable depth solution. For structures with very tall piers, which are sensitive to the effects of wind both in service and during construction, this phenomenon is even more noticeable as the surface area affected by the wind increases by approximately 25%.



In spite of the previous comments, the desire to create increasingly elegant and original structures has led to the design of structures with decks of a constant depth for spans well in excess of 90/100 m in recent years. For example, the unsuccessful concrete-based design for the Verrières viaduct featured a deck of a constant depth despite having a maximum span of 144 m.

Fig. 2.5 – Constant depth

2 .2 .2 .2 – Parabo l i ca l ly var iab le depth

In excess of 65 m/70 m, very large forces affect the cantilevers, requiring a large deck depth at piers which seems very excessive at the other sections of the span. It therefore becomes economically viable to build a deck of variable depth.

For these structures, the variation in depth between the crown and the pier is generally parabolic in form. The cantilever must be symmetrical in order to guarantee its stability during construction. The section of end span which is cast on falsework or built by over-cantilevering is always of a constant depth (the same depth as the crown).

In standard cases, the depth at the pier hp is between 1/16 and 1/18 of the length of the span in question. The depth at the crown is generally between 1/30 and 1/35 of this same distance, with a minimum of 2.20 m for ease of movement within the box girder.

h ch p

Fig. 2.6 – Parabolically variable depth

A statistical study carried out for the publication of this guide shows that the following formulas can be applied to a deck on simple supports:

On pier: 45

14 lhl

p

+=

At the crown: 7

19 lhl

c

+=

With l the length of the main span in meters.

This formula is applicable for any value of l included in the field of application for bridges built by the cantilever method.

2 .2 .2 .3 – Var iab le depth accord ing to o ther laws ( l inear , cub ic , e t c . )

In recent years, certain structures have been built with a cubic-type variation in deck depth. This solution, which slightly reduces the effects of selfweight, results in a somewhat more stretched appearance than a parabolic variation. However, this may pose problems due to insufficient depth in the quarter-span area, because the variation in depth may be unsuited to the distribution of bending moments and shear forces. As the curvature is



more pronounced near the piers, it is also important to ensure that the sideways thrust due to the compression of the lower slab is correctly accounted for.

Certain structures have also been designed featuring a linear variation in depth over 20 to 25% of the length of the main span, with the remainder of the spans being of a constant depth (Fig. 2.7). Although it is quite easy to implement, this solution is only used for modest spans. It is sometimes adopted for architectural reasons or to create a slightly greater clearance than that which is given by a parabolic intrados. It requires the presence of a cross beam at the level of the change in gradient, in order to take up the vertical component of the compression in the lower slab.

Fig. 2.7 – Linearly variable depth

2 .2 .2 .4 – Par t ly cons tant and par t ly var iab le depth

Designers often design structures with spans of very different lengths in response to the constraints imposed by the gap to be crossed. In such cases, it is possible to give the deck a variable depth in the large spans and a constant depth elsewhere (see the example in Figure 2.3). Clearly, for transition purposes, the depth of the large spans at the crown must be equal to the depth of the deck in the areas of constant depth, which often leads to the adoption of a deeper deck than is necessary.

2.2.3 - Support condit ions

We shall now describe the support conditions on piers possible for a bridge deck built using the cantilever method (simple supports, fixed support, etc.), along with the field of application for each of these solutions.

2 .2 .3 .1 – Br idge deck on s imple bear ings

The majority of bridges built by the cantilever method rest on simple bearings when in service, whereas during construction, they are embedded on piers using the cantilever stabilizing devices described in detail in Chapters 5 and 6.

Fig. 2.8 – Bridge deck on simple bearings

In most cases, elastomeric pot bearing devices are used for the permanent bearings. These are particularly suitable for bridges built by the cantilever method as they are extremely robust, compatible with very large vertical loads and compact. They are also available in several types – fixed models, models that slide one way and those that slide in multiple directions – thus absorbing the movements of the bridge deck at the end supports.

However, when the vertical forces are less than 7 MN per bearing, it is possible to use laminated rubber bearings. These are also used in earthquake zones, as they improve the distribution of horizontal forces between the supports.



2 .2 .3 .2 – Br idge deck embedded on p iers v ia re in forced concre te jo in t s

When the piers are very tall, it is often preferable to embed the bridge deck on top of the pier (Fig. 2.9). This solution was first used by Campenon Bernard in 1963 for the bridge over the Moulin à Poudre valley in Brest.

This technique offers the benefit of simplifying the bridge’s construction and service since no provisional cantilever stabilizing devices or bearings are used.

However, the piers and central span form a frame which is sensitive to the linear deformations of the deck under the effects of temperature, shrinkage and creep. If the piers are short and solid, their great rigidity causes moments and shear forces which they are not usually capable of withstanding. Therefore, this is only a viable solution for very tall structures on slender piers.

Fig. 2.9 – Bridge deck embedded on two hollow piers

In certain cases, rather than being hollow, the piers consist of two separate shafts with a gap of several metres, penetrating into the box girder (Fig. 2.10). The fixing in this situation is almost perfect as it uses the compressive and tensile stresses present in each of the shafts while remaining flexible with regard to horizontal movements, because each shaft only offers a low level of resistance to flexion. The Pont de Choisy-le-Roi over the River Seine was built according to this principle.

In general, this can prove to be an excellent solution in earthquake areas as it gives the structure a high level of longitudinal flexibility.

It was recently used for the construction of several structures such as the Tulle viaduct in which the upper part of the main piers is made from double shafts, both consisting of a box girder, and in the Rodez and La Rivière Saint-Denis viaducts in which the piers are made from two thin walls [BOU 91] and [BOU 92].

2 .2 .3 .3 – Br idge decks that are part ly embedded and part ly supported on s imple bear ings

Many structures have to bridge gaps with significant variations in depth. This requires piers of very different heights.

When the gap is crossed by a series of identical standard spans, and thus with identical cantilevers, the deck usually rests on simple bearings on all of the piers. This solution makes it possible to keep the structure very repetitive and therefore easy to construct.

When the gap is bridged by a structure featuring spans of different lengths, it is often advisable to embed the deck on top of the tallest piers and use simple bearings for the other piers. This technique was adopted for the viaduct over the River Viaur at Tanus [SER 98] and for the Pays de Tulle viaduct [LAC 02] over the A89 highway.



2 .2 .3 .4 – Br idge deck embedded on two rows o f bear ings on p iers ( for in format ion)

In the interests of thoroughness, we would like to mention that a third solution was used in the past and consisted of fitting two rows of laminated rubber bearings on top of each pier. This created a elastic fixed support for the deck on the pier.

The bridge connecting the French island of Oléron to the mainland and the Blois bridge over the River Loire were built according to this principle.

This solution is no longer in use today because, due to the bulkiness of the bearing devices, very wide pier heads were required and these were considered to be visually unattractive.

2.2.4 - Specif ic problems

2 .2 .4 .1 – Over-cant i l ever ing

The over-cantilevering technique consists of extending the length of one side of a cantilever by one or more segments, with the other side being already joined to the adjacent cantilever or to a cast-on-falsework section (Fig. 2.11). Therefore, this method can be used to extend one span in relation to the others.

Fig. 2.10 – Bridge deck embedded on two piers which are both made from two parallel walls

This technique seriously complicates the cantilever cable layout for the segments forming the extended cantilever. Indeed, as the rear anchorages of these tendons cannot be placed on the edge of the segments, they must be housed either inside anchor blocks within the box girder, thus complicating the formwork operations, or in a cross beam on top of the pier, which significantly lengthens these tendons. This technique must therefore be used sparingly: when using a form traveler to build the section of an end span which would usually be cast on falsework in a very steep-sided valley, for example.

2 .2 .4 .2 – Bu i ld ing out f rom a smal l cas t -on- fa l sework end span

A gap to be bridged sometimes features a very long and distinct central area (a river or a ravine etc.) in which it is impossible to erect any piers. In these situations, the designer may decide to design a normal structure with piers either side of the central area and end spans equal to 60 % of the length of the central span. If this approach produces end spans which are located very close to ground level, therefore being useless, it might be worth opting for two short end spans which are cast on falsework, with a deep cross-section to act as a counterweight. The central span would therefore be entirely constructed by over-cantilevering out from these two spans (Fig 2.12). The bridge over the River Est on Reunion Island is a good illustration of this method.

Another good example of this technique is provided by the Nantua viaduct. On this viaduct, it was impossible to build the far end of one of the end spans on falsework. Over-cantilevering out from the adjacent pier was also difficult given the length of this section, so the engineers decided to use the over-cantilevering technique from a small additional span built on falsework and situated on the adjacent slope. As this span was designed to be supported in the neighboring Chamoise tunnel, the engineers made this span as short as possible by giving it a very massive and thus very heavy cross-section, which was able to compensate for the imbalances.



This technique requires the development of a specific cabling arrangement. For the large span, this closely resembles traditional cantilever cabling, but in the counterweight spans it is very different, with numerous cables anchored in the cross beams on abutments or in the interior anchor blocks.

Fig. 2.11 – The over-cantilevering construction technique

It should be noted that large forces are transmitted to the counterweight. Therefore, it is essential to ensure that the forces are properly transmitted from the bottom for the counterweight box to its vertical walls and up to the cantilever tendons which are anchored there.

Fig. 2.12 – Cantilever construction out from counterweight spans

2 .2 .4 .3 – Counterweights on abutments

It is sometimes impossible to design sufficiently long end spans, i.e. at least 55% of the length of the adjacent span. In this situation, the weight of the segment on the abutment and the end cross beam in which the external tendons are anchored is not enough to counteract the support uplift under the effect of a rare load applied in the central span. To prevent this phenomenon, which would eventually lead to the failure of the expansion joint, the box girder can be filled with concrete poured during the second phase through hatches built into the upper slab. It is also possible to increase the thickness of the cross-section of the cast-on-falsework section of this span (Fig. 2.13).

For very short spans, when the support reactions on the abutments are still negative, it is possible to reverse the direction in which the bearings operate (Fig. 2.14) and to make the walls or posts of the abutments work in traction, as is the case for the Ottmarsheim and Beaumont-sur-Oise viaducts. However, this is a highly complex solution, which can lead to significant problems during the changing of bearings and it should only be adopted when all of the very severe installation constraints have been taken into consideration.

2 .2 .4 .4 - Hinges

Historically speaking, the first structures to be built using the cantilever method incorporated a crown hinge (Fig. 2.15).

The advantage of this solution was to create an isostatic structure in its permanent phase. Therefore, there were no barriers to stand in the way of deformations due to concrete shrinkage or creep or temperature variations, and there were no parasitic stresses.



However, it was difficult to adjust the hinges due to the fact that it is difficult to estimate the deformations affecting the cantilevers during construction. The differential height difference between the ends of two adjacent cantilevers could be compensated for by applying a vertical force, but a sudden change in level remained and this became more pronounced over time under the effect of delayed deformations due to creep. Furthermore, the hinges have a limited life span and there is a risk of seizure or blockage.

This solution also requires the presence of a expansion joint which is expensive to maintain.

As they are sources of major pathologies on these first structures to be built using the cantilever method, hinges are hardly ever used on modern bridges. They are only found on a few very long structures (e.g. the Cheviré bridge in Nantes, or the Île de Ré bridge etc.) to allow for expansion and/or to reduce the risk of damage to the structure in event of impacts from heavy ships. In all circumstances, they are no longer situated at the crowns of the spans.

Fig. 2.13 – End span with counterweight

Fig. 2.14 – Counterweighted end span with inverted bearing

Fig. 2.15 – Old structures with crown hinges

In this interests of thoroughness, we should also mention the devices used on the Rogerville viaduct on the A29 highway [UAC 98]. These devices, consisting of two metal beams parallel to the webs of the box girder, make it possible to fit expansion joints in the deck while transmitting shear forces and bending moments.

2 .2 .4 .5 – Use o f l i ghtwe ight concre te ( for in format ion)

In the 1980s, several large span structures were partially built from lightweight concrete as this reduced the selfweight of the bridge deck box girder.



Faced with stiff competition from other solutions (composite box girders, prestressed concrete box girders with lightweight metallic webs, etc.) this technique has virtually disappeared in France. On the other hand, as mentioned in Chapter 1, the two largest bridges in the world built by the cantilever method feature lightweight concrete sections in their central span.

2.3 - Choosing a cross-section


The large overhangs created in the construction phase require the use of a cross section with a high resistance to torsion. This is one of the reasons why designers opt for box girders. These cross-sections also feature a lower slab which lowers the centre of gravity and allows for efficient cabling on the pier. This is of paramount importance, as construction by the cantilever method produces very large negative moments.

There are several types of box girders. We shall now describe them and specify their fields of application.

2.3.2 - Simple monocellular box girders

For deck widths of less than 20 m, the most economical solution is almost always a box girder with two webs, featuring two solid slabs.

Upper slabs are made from reinforced concrete for widths of up to 15 or 16 m. For longer widths, they are often transversally prestressed using low-strength tendons. For example, there may be three or four waxed or lubricated T 15 single strands per metre or four 4T15S tendons per 3.50 to 4.00 metre segment.

This type of box girder is compatible with all of the deck depth variation laws (constant, parabolic, etc.).

Fig. 2.16 – Example of a simple monocellular box girder

2.3.3 - Monocellular box girders with r ibs or struts

For deck widths of between 18 and 25 m or more, the most common solution consists of a box girder with two webs, featuring a ribbed upper slab and a solid lower slab (Fig. 2.17).

One rib is used per standard segment, i.e. one every 3 to 4 m. In the narrowest structures, these ribs are made from reinforced concrete and they are of constant depth between the webs. When the decks are very wide, the ribs have a more elaborate geometry and are prestressed using medium-strength tendons (12T15 or 19T15).



The presence of ribs complicates the formwork for the deck and thus the construction of the segments. Before choosing a design for the transverse ribbing, it is therefore advisable to verify the resulting weight gain in comparison to a prestressed slab that is thicker but of constant depth. Furthermore, the external tendons must not strike the ribs near the cross beam on the pier. Recesses in the ribs are therefore created close to the piers or shorter ribs are used, thus allowing the tendons to pass freely.

As in the previous example, this form of box girder is compatible with all of the height variation laws.

For deck widths of between 18 and 25 m, it is also possible to design decks featuring a slab of constant longitudinal thickness without ribs, although this is often prestressed (Fig. 2.18). The webs are usually vertical and the steel or reinforced concrete struts are aligned under the cantilevers [GIL 96]. The struts may also be replaced by two acutely angled lateral concrete walls (Fig. 2.19).

These structures are aesthetically very pleasing. However, they are somewhat more difficult to construct than a box girder featuring an upper slab with ribs. Furthermore, they are restricted in application to structures of a constant depth. Indeed, if the depth of the box girder varies, the axes of the struts or the lateral walls must be distorted, which is extremely difficult and costly to carry out. Because of this, their use is restricted to structures with a maximum span of 80 to 90 m.

Fig. 2.17 – Example of a wide box girder with slab featuring prestressed rib stiffeners

Fig. 2.18 – Example of a wide box girder with struts



Fig. 2.19 – Example of a wide box girder with thin lateral walls

2.3.4 - Double-cel l box girders

For large widths, it is also possible to design a bridge deck consisting of two box girders connected by their internal cantilevers (Fig. 2.20).

In France, this solution is now rarely used on very wide structures. However, in other countries, it has recently been used on several occasions, including for the access viaducts built from prefabricated segments for the new bridge over the River Tage in Lisbon, and the viaducts for the second crossing of Severn estuary in England [COM 96]. It also remains widely used in Asia. It should be mentioned that this type of structure is particularly suitable for the construction of wide prefabricated bridge decks, as this involves the construction of two narrow decks side by side which are then fixed together transversally.

Nevertheless, controlling the creep-induced deformations in each of the box girders made from concrete of different ages remains a major problem during the construction of these structures. Furthermore, in the case of structures with skew lines of support or those featuring shifted piers for each box girder, the installation of the transverse prestressing is highly complex.

Like the simple monocellular box girders, double-cell box girders are compatible with all of the deck depth variation laws (constant, parabolic, linear, etc.).

2.3.5 - Monocellular box girders with three webs (for information)

For widths of between 15 and 20 m, it is possible to design box girders with three webs (Fig. 2.21).

In France, these structures are now very rarely used. Indeed:

• They are difficult and costly to build because two formwork cores must be used

• For the same cost, more aesthetically pleasing structures with struts or transverse ribs are often preferred

• Certain structures of this type have been affected by major pathologies, due to the difficulty of guaranteeing the even distribution of forces between the webs.



Fig. 2.20 – Example of a bridge deck consisting of two box girders joined together transversally

Fig. 2.21 – Older solution consisting of a box girder with three webs

These box girders are still constructed overseas and particularly in South-East Asia, where labour is cheaper. Furthermore, western companies have exported their equipment to these countries.

2.3.6 - Special transverse structures

A number of structures featuring highly original and innovative bridge decks were constructed in France during the 1990s.

First, we shall mention the Sylans and Glacières viaducts, constructed for the A40 highway near Nantua at the end of the 1980s. These viaducts feature two independent, different in height, prefabricated prestressed bridge decks, in which the conventional full webs are replaced by an ultra-lightweight concrete truss, as for the Bubiyan bridge in Kuwait.

Built in the 1990s to support the Al6 highway, the Boulonnais viaducts also feature bridge decks consisting of prefabricated segments with truss webs, which on this occasion are made from metal tubes [MEU 98].

The Corniche viaduct in Dôle, in the Jura region of France, also features a bridge deck with ultra-lightweight webs, but these are made from corrugated metal sheets [REI 94]. The fourth bridge with corrugated metal webs



to be built in France after the structures in Cognac, Charolles and the Parc Astérix, the Dôle viaduct was the first French bridge of this type to be built using the cantilever method.

The Vecchio viaduct, built in Corsica at the end of the 1990s, also has a highly original bridge deck, consisting of two parallel concrete slabs connected by triangular concrete elements acting as webs [PAU 00].

2.4 - Pre-design of a simple cross-section


In the following section, after a brief preamble on the subject of cabling, we shall examine the design of the different elements that make up a standard monocellular box girder. The figure below specifies the notations used:

Fig. 2.22 – Notations used

Fig. 2.23 – Tendons used on standard bridges

2.4.2 - Preamble concerning cabling

A detailed description of the longitudinal cabling used on bridges built using the cantilever method is given in Chapter 3, which is dedicated to longitudinal bending and primary cabling. At this stage of the guide, however, it is essential to provide some basic information about these tendons.



The cabling on standard modern structures consists of three types of tendons: cantilever tendons, internal continuity tendons, and external continuity tendons.

Cantilever tendons take up the negative moments, both during construction and when the bridge is in service. They are housed in the upper gussets. Their anchorages are often situated on the edge of the segments at the nodes between the webs and the upper slab.

Internal continuity tendons are designed to take up the positive moments that occur during construction due to site loads, the thermal gradient and delayed concrete deformations. In the end spans, they must also take up the weight of the cast-on-falsework sections. They are situated in the lower gussets of the box girder close to the webs and are anchored in anchor blocks.

External continuity tendons complement the internal prestressing, taking take up the operating loads and the weight of superstructures. They are situated between the webs and slabs, outside the standard section. They are anchored in massive cross beams on piers or abutments and are deflected via concrete beams called deviators.

2.4.3 - Upper slab

In a simple box girder, the webs are often situated at a quarter of the width of the box girder (C ≈ B / 4). The upper slab is solid and its thickness varies transversally in order to adapt to the transverse forces encountered.

The thickness of the upper slab at the end e1 depends on the retaining system used (see the Sétra technical guide for security barriers). It is a minimum of:

– 16 to 18 cm for a pedestrian parapet – 23 cm for a normal BN1 barrier – 24 cm for a normal BN4 barrier.

At the anchorage of the cantilever, the thickness e2 depends on the superstructures and the functional cross section. As an initial estimate for a reinforced concrete slab, we could use 1/7 to 1/8 of the width of the cantilever for e2, measured from the start of the gusset. This value can be reduced for prestressed concrete.

Its thickness at mid-span e4 is equal to D/25 or D/30, or even D/35 for very wide transversally prestressed box girders, with a minimum of 20 cm. At the fixed support point, the value e3 can be estimated at 0.10 meters +D/25 (with D representing the centre distance between the webs expressed in meters). In general, we also verify that: e3 > e2 – 0.10 m and e3 > 1.5 e4

In light of the preceding information, the mean thickness of the slab for a simple box girder amounts to between 22 and 26 cm, not including the gussets used for connecting to the webs of the box girder.

The transverse prestressing makes it possible to reduce the dimensions of e2, e3 and e4 by approximately 10% if there is sufficient space to house the cantilever tendons. It is important to pay particular attention to ensuring that the transverse tendons are properly covered and that they are correctly anchored at the ends of the slab, as the effectiveness of these operations can also determine the thickness of the end of the slab.

Ribbed slabs, of course, are thinner. Their thickness varies between 22 cm for a normal centre distance of 3 m to 3.50 m between ribs, and 10 cm for a much smaller centre distance. It also depends upon the construction method used for the segments (cast-in-situ or prefabricated).



2.4.4 - Thickness of the webs

2 .4 .4 .1 – Background in format ion

Box girder webs are usually angled because this arrangement facilitates the removal of formwork and reduces the width of the pier heads. Also, the external cladding of the webs is often of better quality when they are angled. The angle typically adopted varies between 10 and 30%.

Longitudinally, the webs are normally of constant thickness for bridges of variable depth and of variable thickness for decks of constant depth. When thickening is required near the piers, a sudden variation is built in (by benching and from the inside, of course) in order to facilitate the construction.

Vertically, the webs are almost always the same thickness throughout their entire height. For spans in excess of approximately 100 meters and in certain projects in which performance is maximized, the webs are sometimes thickened in proximity to the upper deck as the shear forces are greatest in this area.

Minimal th ickness o f webs in s tandard s i tua t ions

Usually, the cantilever tendons are anchored in the upper gusset or in a high-level anchor block. In this case, as the web is not breached by the tendons, its thickness can be reduced to the strict minimum needed to resist shear forces when the bridge is in service, while benefiting from the significant reduction in shear forces brought about by the raising of the external tendons. However, during the construction phase, there is virtually no reduction of the shear force, as the external tendons have not yet been tightened. The total thickness Ea of the two webs can be estimated at Ea = L/275 + l.25 x B/L – 0.125: a relation in which L is the main span and B is the width of the upper slab (with Ea, L and B expressed in meters).

Minimal th ickness o f webs in spec ia l s i tua t ions

It is sometimes desirable to pass the cantilever tendons down through the webs in order to increase the reduction in shear forces brought about by the prestressing. This becomes compulsory for very wide structures with large spans, in which the fixing of a single pair of tendons per segment is not sufficient.

In this case, the thickness of the webs must also conform to a certain number of conditions concerning the proper concreting and anchoring of the tendons on the edge of the segments:

– a > 2(e + 2d + V) + ∅g, with V = 7 cm minimum (concreting and vibration chute) – a > 2D with D being the cover thickness of the anchor plates given by the regulations for prestressing

systems according to the strength of the concrete. (As an initial estimate, we could state that D = 18 cm for 12T13 tendons and D = 20 cm for 12T15 cables)

– a > 3∅g with ∅g = 7 cm for 12T13 tendons and ∅g = 8 cm for 12T15 tendons.

Fig. 2.24 – Thickness of webs

It can also be added that shear force strength requires the conservation of an effective web thickness of Ea equal to 0.26 + L/500, with Ea and L in meters. This formula (somewhat less favorable than the previous formula for



short spans and relatively narrow box girders), gives good results for spans of between 70 and 170 m, and for deck widths of less than 15 m. This thickness must be increased for wider decks.

2.4.5 - Thickness of the lower slab

The thickness of the lower slab is minimal at the crown and maximal at the pier. The thickness variation laws according to the horizontal axis are either linear, parabolic or of the fourth degree. The latter variation law is used to maintain the minimum thickness of the slab over a large length and to save weight. Stepped variations in thickness, also known as “on demand” variations, are sometimes used. In the cast-on-falsework sections, the thickness of the lower slabs remains constant and is equal to that of the crown.

Minimum th ickness

In the central section of the spans, the lower slab must be as thin as possible (18 to 22 cm) in order to limit the selfweight of the box girder. For wide structures, transverse bending predominates and thickness tends to be in the region of 25 cm. In structures of an older design, this slab used to house continuity tendons which had to be protected against corrosion by a layer of concrete equal to at least half of the diameter of the duct. As the power of the tendons increased, this system finally resulted in cracking due to the distribution of the prestressing force to the area around the anchorages. Today, continuity tendons are housed in the lower gussets of the box girders and the cover thickness requirement specified above no longer applies to the slab. However, it is advisable to adjust the minimal thickness of the slab Ec in order to ensure that the upper layer of its transverse reinforcements do not come into contact with the ducts of prestressing in the gussets. It is also recommended that this thickness should not be less than one third of the thickness of the webs, so that the box girder can be considered to be impervious to transversal deformations.

2Ec d e≥ ∅ + + avec 18à 22cmEc ≥

Fig. 2.25 – Detail of the lower slab

Maximum th ickness

The thickness of the lower slab on the pier Ep is determined by the limitation of compression in the bottom fiber when the bridge is in service. This value, which is largely dependent on the span and widths of the slabs, varies between 35 and 80 cm or even more. It is advisable to adopt a safety margin for the maximum stress level in order to limit the redistributions due to creep.

For structures which vary in depth parabolically or cubically, the lower slab must also be transversally resistant to sideways thrust due to the combined effects of the compression of this slab and its curvature.

2.4.6 - Design of the upper gussets

The upper gussets must fulfil several functions which generally influence their dimensions:

• They thicken the slabs in areas subject to significant transverse forces

• Their funnel shape facilitates the concreting of the webs

• They house the cantilever tendons and ensure that their cover thickness



• They allow for the deflection of the cantilever tendons prior to their anchorages

• They thicken the nodes of the webs/upper slab, allowing them to absorb the forces due to the distribution of the cantilever tendons which are now almost always anchored at these nodes.

In cast-in-situ structures, prefabricated concrete blocks incorporating the anchorages for cantilever tendons are still sometimes used, as this system allows the tendons to be tightened a few hours after the segments have been cast. These blocks must therefore be situated in the webs/slab nodes and they may also influence the dimensions of the upper gussets.

Fig. 2.26 – Detail of the upper gussets

In light of the preceding points, the gussets are empirically designed and accounted for in the rough calculations and are only precisely established after the cantilever tendons and transverse reinforcements have been accurately calculated.

In conclusion, it should be noted that the internal shape of the gussets is always rectilinear, presenting an angle of between 30 and 45° to facilitate casting. On the other hand, their external form is often circular for purely aesthetic reasons.

2.4.7 - Design of the lower gussets

In addition to their mechanical role in which they act as a transition between the webs and the lower slab, the lower gussets must also house the internal continuity tendons (Fig. 2.27).

α

Fig. 2.27 – Detail of the lower gussets

The lower gussets are normally boxed in by the lower part of the central core of the formwork for the segment. They are angled at a slope of 40 to 45° in order to facilitate the flow of the concrete and prevent the formation of accumulations of pebbles or concreting defects. When the lower slab is wide, the angle of the gussets can drop as low as 15 or even 10° from the horizontal in order to improve the take-up of transverse bending forces. In these situations, the gussets are not cast in formwork but simply smoothed over during the concreting process.

As we have previously mentioned, the internal continuity tendons are anchored in the protruding anchor blocks, situated at the junction between the webs and the lower slab (Fig. 2.28). These anchor blocks are generally a little shorter than the standard segments. They are constructed at the same time as the rest of the segment.



Fig. 2.28 – Anchor blocks for internal continuity tendons

2.4.8 - Cross beams and deviators

Bridges built using the cantilever method incorporate major cross beams directly above the piers and abutments. Cross beams on piers play a particularly important role:

In the operating phase:

• By transmitting the shearing flows caused by shear force and torsion in the bridge deck from the webs and slabs to the bearings and piers

• By transmitting the vertical component of normal stress in the lower slab (Resal effect) to the bearings and piers (see 4.2.3.1 and 4.2.3.3)

• By taking up the local loads on the upper slab between the webs

• By providing anchorages for the external prestressing tendons distributing their forces

• By transmitting the vertical component of the external prestress tendons that are deviated inside the segments on piers to the bearings and piers (see 4.2.3.4).

During the construction phase:

• By transmitting the shearing flows caused by the the shear force and torsion of the bridge deck from the webs and slabs to the temporary bearings and piers

• By transmitting the vertical component of normal stress in the lower slab (Resal effect) to the temporary bearings and piers

• By taking up the forces caused by the cantilever stabilizing systems and transmitting them to the temporary bearings.

Concrete deviators situated in the different spans are used to deflect the external prestressing tendons (Fig. 2.29). These usually consist of a lower rectangular beam capped by two thin trapezoid walls.

2.5 - Breakdown into segments


We have already seen that the longitudinal geometry of the structure is dictated entirely by its mode of construction. This also influences its breakdown into segments (Fig. 2.30).



In the following section, we shall see how the lengths of different types of segments are determined. In certain specific situations, it should be noted that the breakdown into segments may also be conditioned or influenced by the need to have a uniform distribution of:

• The bridge deck’s transverse ribs or struts, if applicable

• Cornice elements with architectural design features that must be evenly matched to the BN4 posts.

The edges of the segments are usually perpendicular to the structure’s extrados, and thus to the longitudinal section, but vertical joints may also be used.

Fig. 2.29 – Deflection of the external tendons

Fig. 2.30 – Breakdown into segments

2.5.2 - Standard segments

Standard segments are of a constant length which varies between 2.50 m and 4 or even 5 m according to the structures.

For cast-in-situ segments, the most important selection criteria are the casting time and minimizing the number of construction cycles and thus the number of segments. This optimization policy can sometimes lead to the construction of segments of different lengths for the same half-cantilever. For example, in order to optimize the construction cycles, the segments for the new bridge over the River Rhine to the south of Strasbourg vary in length from 3.00 m close to the piers to 5.00 m in mid-span (at the design stage, the length was constant and equal to 3.25 m).

The main aim when determining the length of prefabricated segments is to reduce their weight. Indeed, as we shall see in Chapter 6, prefabricated segments must be moved using special equipment which obviously has a limited capacity. However, it should be noted that the shorter the segments, the harder it is to conform to the geometry of the cantilever.



At the preliminary design stage, it is common to calculate the length of the segments in such a way as to ensure that there is the same number of standard segments as there are pairs of cantilever tendons determined by the calculations. But this is only one option and it is often necessary to anchor two pairs of tendons per segment for very wide structures featuring large spans. As we have already established, the length of segments calculated in this way in the preliminary design may be modified during the construction surveys, in order to use form travelers built for a previous site or to reduce the number of segments and optimize the construction cycles.

Regardless of the method adopted, it can be considered that smaller cross sections have longer segments. Thus, segments of 2.5 to 3m are designed for very wide structures or bridges featuring large spans, and longer segments of 3 to 4 m can be used for narrow or short-span structures.

2.5.3 - Segments on piers

For cast-in-situ structures, the segment on pier (SOP) generally measures at least 8 m, in order to ensure that it is capable of supporting two form travelers during the construction of the first pair of segments. To support the installation of the pair of form travelers on the segment on pier, it must be twice as long as the standard segments plus an additional length of 50 centimeters to one meter.

The segment on pier represents a very large volume of concrete which can very rarely be constructed in a single phase. Furthermore, its formwork must be designed to resist the significant thrusts exerted by the fresh concrete. For cast-in-situ structures with a small number of piers, it may be beneficial to reduce the length of the SOP. In this case, the second segment of the first pair is constructed after the first form traveler has been moved. The cantilever is highly unbalanced before the installation of the second form traveler, but this is permissible given the small moment arms at this stage of the construction.

For prefabricated structures, the dimensions of the segment on pier are often incompatible with the capacity of the equipment used for transporting and installing the segments. The SOPs are therefore divided into two or three sections to be assembled by prestressing.

2.5.4 - Closing segments

The length of the closing segments varies considerably according to the technique used.

For cast-in-situ structures, the closing segments are slightly shorter in length than the standard segments because one of the form travelers is generally used for their construction. However, the closing segments must not be so short that it becomes difficult to dismantle the internal formwork from the form traveler. The closing segments require specific formwork, usually made from wood, which can be broken down into components small enough to be removed via a manhole. The length of the closing segments must also facilitate the overlapping of longitudinal reinforcements and the tightening of the last segments cantilever tendons. Therefore, their minimum length is approximately two meters.

For economic reasons, the closing of segments on prefabricated structures is carried out using the simplest possible system. This closure is thus reduced to its simplest form, not exceeding 15 to 20 cm in length. A joint of this length is made from non-reinforced concrete. Its shortness makes it impossible to tighten the cantilever tendons usually attached to the last standard segments. Therefore, temporary lashing provides the only form of prestressing before the jointing takes place.

2.6 - Main ratios The statistics for standard structures give the following ratios:

• Equivalent thickness: e = 0.4 + 0.0035 L

• (L being the length of the principal span of the structure in meters and e in meters)



• Longitudinal prestressing: 40 to 50 Kg/m3

• Transverse prestressing: 5 to 7 Kg/m² of deck

• Non-prestressed reinforcement bars:

– Without transverse prestressing: 130 to 170 Kg/m3 (*) – With transverse prestressing: 110 to 130 Kg/m3 (*)

The ratio of non-prestressed reinforcement bars is generally somewhat higher for prefabricated structures, because they often have a lower equivalent thickness than cast-in-situ structures and because reinforcements for temporary lashing and hoisting equipment must be added. (*) For non-prestressed reinforcement bars, the ratio is strongly dependent on the type and thickness of the upper slab (thick slab, ribbed slab, etc.), on the conditions imposed for the cumulation of distribution, shear and bending reinforcements and on the accepted value for the elastic limit of the reinforcement bars in the calculations (400 ou 500 MPa).



3 - Design and verification of longitudinal cabling This chapter covers the design and calculation-based verification of the longitudinal cabling for prestressed concrete bridges built using the cantilever method. Please note that the verification of tangential stress is covered in Chapter 4.

3.1 - Cabling principles The layout of the prestress tendons depends on the construction method used and on successive developments.

As mentioned in the previous chapter, different types of cables are used:

• Cantilever tendons: used for the assembly of consecutive segments

• Continuity tendons: designed to take up the forces resulting from all of the additional structures added to the structure after the construction of the cantilevers.

Until the mid-1980s, all of the pre-stressing on structures built using the cantilever method was situated inside the concrete.

Today, mixed prestressing technology, i.e featuring tendons both inside and outside the concrete, is used on a virtually automatic basis in France. For a structure with three spans, the following sequence of operations applies to the stressing of these different tendons:

• Tensioning of the cantilever tendons inside the concrete for assembly of the standard segments (Fig. 3.1)

Fig. 3.1 – Cantilever tendons

• Tensioning of the continuity tendons inside the concrete to secure the cast-on-falsework sections of the end spans to the two cantilevers (Fig. 3.2)

Fig. 3.2 – Internal continuity tendons on the end spans

• Tensioning of the continuity tendons inside the concrete at the crown of the main span in order to make the structure continuous (Fig. 3.3)



Fig. 3.3 – Internal continuity tendons on the central spans

• Stressing of the continuity tendons outside the concrete, stretching across one or two spans, in order to take up any additional loads (Fig. 3-4).

Fig. 3.4 – Externall continuity tendons on the end spans

3.1.1 - Canti lever prestressing

Cantilever tendons are designed:

• For the assembly of consecutive segments and to take up negative moments due to the selfweight of the cantilevers and site loads during the construction phase

• To help take up negative moments due to dead loads and imposed loads, along with the external continuity tendons when the bridge is in service.

These tendons are situated at the area of the upper axis of the bridge deck in order to act efficiently against negative moments. In virtually all cases, they are positioned inside the concrete in order to obtain the maximum effect.

3 .1 .1 .1 – Pr inc ip le o f cant i l ever t endons on o lder s t ruc tures ( for in format ion)

In older designs, these tendons were almost always deviated vertically at their extremities and their anchorages were positioned inside the webs. The main advantage of this arrangement was to reduce the shear force due to the angle of the tendons, which was particularly favourable in proximity to the piers.

However, this layout also had its disadvantages:

• The presence of tendons in the webs creates an obstacle during casting

• The bulkiness of the anchoring plates requires a large minimum web thickness (normally around 45 cm)

• In accordance with the french design regulations, the thickness of a web must be reduced by the thickness of a half to one cable duct for the calculation of shearing stresses, depending on the design rules used

• Cantilever tendons undergo significant angular deflections, which results in signicativ losses due to friction.



3 .1 .1 .2 – Pr inc ip le o f cant i l ever t endons on modern s tructures

In conventional modern designs, shear force is reduced by placing the continuity tendons on the outside of the concrete. Therefore, it is no longer necessary to drop the tendons down into the webs at their extremities, and they can be anchored directly in the upper nodes. The drawbacks of the old cantilever tendons systems are thus avoided.

For upper slabs of common widths (10 to 12 m), one tendon is anchored per web and per segment. For wider upper slabs, it may be necessary to anchor two cables per web and per segment. Likewise, it is possible to create a recess in the gusset gussetcorresponding to the size of the anchorages for the additional prestress tendons (cf. § 3.1.3.1). Because of this, the dimensions of the upper gusset gussets are directly related to the number and sizes of the tendon anchor plates and to the position of the cantilever tendon ducts.

3 .1 .1 .3 – Al ignment o f cant i l ever t endons on modern s tructures

Standard a l ignment

Cantilever tendons undergo vertical and horizontal deflections in the upper node. Whenever possible, the vertical deflections are dissociated from the horizontal deflections (Fig. 3.5).

Fig. 3.5 – Conventional cantilever tendons

The tendons must have a rectilinear alignment when they pass through the joints. In order to guarantee the correct assembly of the duct elements, the alignment of the cables in the passage through the joints is usually perpendicular to the formwork surface of the facing.

Comb layou t

The "comb" cable layout aligns tendons automatically, which simplifies their installation (Fig. 3-6). Indeed, such a layout:

• Always uses the same points of passage through the joints so that a single facing can be used



• Reduces the horizontal deflections and thus the losses by chafing

• Avoids having curved sections in line with joints

• Creates horizontal deflections throughout the exact length of the segment.

It is also apparent that the anchor plate is automatically angled on the axis of the web in one direction and then in the other.

Further information on “comb” cable layouts can be found in the article entitled "Practical design of cantilever tendons in bridges built by the balanced cantilever method” (FIP Symposium - London – September 1996).

Fig. 3.6 – Comb cantilever tendon layout: plan view and detail of gussets

On Figure above, we can observe the stress relating to the presence of stitching tendons on the support. The stresses relating to the recesses used for the attachment of the form travelers (cast-in-situ segments) and hoisting equipment (prefabricated segments) should also be mentioned.

It is also possible to position the anchor plates at the level of the gusset gussetand on the outside of the web reinforcements, to prevent the systematic cutting of the vertical stirrups in proximity to the tendon anchors. In this case, only the first tendons are anchored in line with the web: the following ones are anchored alternately on either side. This arrangement also makes it possible to attach two cables per web if necessary.

3 .1 .1 .4 – Spec i f i c des ign po int s

Number o f can t i l ever t endons

Two or four cables can be specified per segment. If, for the aforementioned reasons, we decide not to anchor the tendons in the webs and want to avoid increasing the size of the gusset gusset, the optimum number of tendons specified for the end of each segment is two (one tendon per web). This arrangement makes it possible to standardize the reinforcements for the segments.

Cabl ing o f the f ina l pa i r o f s egment s

During the construction of a cantilever, the most unfavourable situation generally occurs during the casting of the final pair of segments. The cantilever tendons anchored in this final pair of segments are not tensioned in the design phase and are therefore not required for the construction of the cantilever. Furthermore, experience shows that, because of the presence of the external continuity cables which span the entire length of the



structure, there are more cantilever tendons than needed when the bridge is in service. As a result, decks can be designed without the need to anchor cantilever tendons in the final pair of segments. This final pair then functions provisionally as reinforced concrete. This arrangement is commonly used for bridges with prefabricated segments in which the shortness of the closing segment (20 to 30 cm) makes it impossible to tension these tendons.

Cabl ing for s t ruc tures w i th pre fabr i ca ted segments

During the assembly process, lashing bars must be used to hold prefabricated segments in place parallel to the extrados until the cantilever tendon is tensioned. These bars hold the segment temporarily in place while exerting a minimal pressure of approximately 0.2 MPa on the adhesive in the segment joint. The segments are generally anchored in a staggered pattern on the vertical ribs built into the inner face of the webs, midway between the segment joints (Fig. 3.7).

Fig. 3.7 – Lashing principle for prefabricated segments

Cant i l ever t endons ou t s ide the concre te

For very large structures (span > approximately 120 m), a proportion of the cantilever tendons may be situated outside of the concrete in order to reduce the size of the upper gusset gussets and thus the dead loads

Angle o f the t endons

In order to reduce the shear stress in certain types of structures, it is possible to drop a proportion of the cantilever cables down into the webs (generally those of the first segments), according to a design similar to the layouts used in older structures (Fig. 3.8).

Fig. 3.8 – Cantilever tendons

These provisions are used for structures of variable depth in which the aim is to reduce the depth on the pier, and for structures of constant depth over 60 m in length.

“Extended can t i l ever” segments

As described in Chapter 2, in order to reduce the cast-on-falsework sections close to the abutments, or to build spans of different lengths, it may be necessary to construct one or more segments known as “extended cantilever segments” at a one end of the bridge only.

The cantilever is thus asymmetrical and the cantilever tendons anchored in these segments may be asymmetrical in relation to the pier. However, they must be anchored at a sufficient distance from the section on the pier in order to allow for the dispersion of the prestressing force within this section.



3.1.2 - Continuity prestressing

In general, continuity tendons are designed to take up all of the additional forces applied to the structure after the construction of the cantilevers.

In older designs, these tendons were all located inside the concrete. They were aligned in the lower slab at mid-span and were attached to the anchor blocks protruding over the slab, or raised in the webs and anchored inside recesses built into the extrados of the bridge deck. The large number of tendons meant that they had to be distributed throughout the entire width of the lower slab, which led to the development of major pathologies (see Chapter 8).

Today, continuity prestressing is generally mixed, i.e. consisting of tendons situated both inside and outside the concrete. This paragraph only concerns the use of mixed cables. For continuity tendons which are situated completely inside the concrete, the reader is advised to refer to SétraSétra Technical Bulletin No.7 published in 1972.

3 .1 .2 .1 – In terna l cont inu i ty cab les

Continuity tendons situated inside the concrete are strung across the central part of standard spans and inside the extremities of the end spans (Fig. 3.9 and 3.10).

Fig. 3.9 – Internal continuity tendons on end spans

Fig. 3.10 – Internal continuity tendons on standard spans

Designed to resist positive moments, these cables are situated inside the lower gusset gussets and are attached to the anchor blocks situated at the intersection of the web and lower slab (Fig. 3.11).

Fig. 3.11 –Anchor blocks for internal continuity tendons

They are often offset in relation to the top of the lower deck in order to standardize their alignment in the anchor block.



At the minimum, internal continuity prestressing is designed to be capable of taking up the shrinkage after grouting, thermal effects (thermal gradient and uniform temperature variation) and the reaction effects of the structure during the construction phases between the casting of the concrete fro the closing segment and the tensioning of the external continuity prestressing.

The attention of designers is drawn to the fact that, due to the effect of temperature variations, the provisional cantilever joints are liable to create significant forces in the bridge deck and supports, especially if the latter are rigid.

For the end spans, the internal continuity prestressing also has to take up the weight of the cast-on-falsework section.

3 .1 .2 .2 – Externa l cont inu i ty cab les

External continuity cables are designed to take up:

• Positive moments in the span due to dead loads (including shrinkage and the redistribution of forces due to creep) and imposed loads, in tandem with the internal continuity cables

• Negative moments on the pier due to dead loads and operating loads, in tandem with the cantilever cables.

In elevation, they are therefore situated close to the lower slab in mid-span (?) and close to the upper slab on supports. In order to account for construction tolerances, a distance of approximately 5cm must be allowed between the outside of the tendon ducts and the concrete of the segment slabs. This minimum distance will be also observed in relation to the top of the anchor blocks for the continuity tendons.

In a plan view, the external continuity cables are situated close to the webs. To take account of construction tolerances, a distance of approximately 5cm must also be allowed between the outside of the tendon sheaths and the concrete of the segment slabs and/or the anchor blocks. For curvilinear structures, it is necessary to recenter the tendons using additional deviators.

The tendons are deflected via the cross beams on piers and intermediate cross beams (deviators) on the spans, resultings in a polygonal alignment which is rectilinear per section. The deviators are generally situated between a third and a quarter of the way along the span (Fig. 3.12).

Fig. 3.12 – External continuity tendons on standard span

According to the length of the structure and the number of spans, they may be strung form one end of the deck to the other or overlapped across two or three consecutive spans, or even more. Considering the difficulties involved in the threading and grouting of curved tendons, they must be limited in length to approximately 200 m. This value may be slightly exceeded, especially in order to stretch a tendon across two spans of over 100 m in length. Longer curved tendons (e.g. 3 spans of 120 meters, i.e. 360 meters for 19T15 "super" tendons) have already been successfully tensioned.

These tendons may also stretch from span to span. In this case, they may be anchored in the deviator cross beams.



For example, for a symmetrical three-span structure, the following design allows for a precise adjustment of the prestressing in each span using two types of tendons (Fig. 3.13).

Fig. 3.13 – Different types of tendons used for optimizing the external cabling on a three-span bridge

In this example, the following numbers of tendons are used:

At the crown: 2 ne1 + ne2 = nc tendons

On the pier: ne1 + ne2 = np tendons

There must be a sufficient number of external tendons to prevent any structural deficiencies in the event of the breaking or removal of a tendon. However, too many tendons could risk overloading the box girder and lead to maintenance problems. In practice, there are often between three and five pairs of internal continuity tendons.

It is interesting to note that in a mixed cabling system, the external tendons play a major role in taking up the negative moments on the supports. This leads to a significant reduction in the number of cantilever tendons compared with older structures in which the cantilever tendons had to take up all of the negative moments.

If there are no problems of shear force, it is also possible to reduce the number of external tendons and to compensate for them in the central zones by using additional continuity tendons, which are more economical, as they are shorter.

3.1.3 - Miscellaneous construction provisions

3 .1 .3 .1 – Addi t iona l pres tress ing

Specific precautions must be taken at the design stage in order to overcome any deficiencies in the internal prestressing inside the concrete during the construction phase (excessive friction, inability to thread tendons, etc.). These provisions must be designed to compensate for a prestressing deficiency of between 5 and 10 % of the probable prestressing force Pm for the category in question. For example, it is possible to:

• Avoid using the full capacity of the anchor plates, thus making it possible to attach additional strands

• Build in empty ducts which could be used to insert one or more pairs of additional cables if necessary. Compulsory for cantilever tendons, these empty sheaths are also recommended for internal continuity cables. The layout of these empty ducts must allow tensioning to be carried out at any time during construction, either by making room in the gusset gusset for an anchor plate, or by positioning the duct in such a way as to allow the tendon to be anchored in an additional anchor block. The last of these provisions does not apply to prefabricated segments.

Unused empty ducts are injected at the end of the construction phase.



3 .1 .3 .2 – Replaceab i l i ty o f ex terna l pres tress ing

It must be possible to replace the external prestressing. More precisely, it must be possible to dismantle it without causing any damage to the structure apart from the possible destruction of the cable and its duct (cf. Circular of February 28 2001 “Conception de la précontrainte extérieure au béton" [Design of prestressing on the outside of the concrete]).

The general provisions for external prestressing, the products and materials used and their implementation are described in Chapter 7 of the supplement to the fascicule 65 A of the French CCTG (General Technical Clauses).

3 .1 .3 .3 – Recesses for addi t ion a l ex terna l pres tres s ing

Anchorages for additional prestressing and recesses in the deviators must be designed at outset in order to facilitate any necessary repairs or strengthening of the structure. The additional prestressing force must be equal to at least 20 % of the external continuity prestressing force determined during the construction of the bridge deck. In practice, at least one sheath per web is provided, allowing for the progressive replacement of all of the external continuity tendons.

3 .1 .3 .4 – Ant i -v ibra t ion sys tems for ex terna l pres tress ing

In order to prevent the development of resonance in the external tendons and avoid the risk of whip action in the event of an accident, the SétraSétra guide to external prestressing of February 1990 recommended the installation of intermediate tendon retention devices when the external part of the cable layout exceeds fifteen metres for a road structure and 10-12 meters for a railroad structure. Experience acquired in this field has shown that free lengths of approximately 25 m are acceptable. Acting as intermediate supports and helping to hold the ducts in place during their replacement, these devices must be rigid (Fig.3.14).

Fig. 3.14 – Anti-vibration devices for external tendons

3 .1 .3 .5 – Poss ib le geometr ica l conf l i c t s be tween long i tudina l t endons and o ther t endons

In the majority of bridges covered by this guide, cantilevers are stabilized by vertical prestressing cables housed in the segments on piers. As these tendons may conflict geometrically with the longitudinal prestressing, it is important to bear this in mind when determining the transversal positioning of the external and cantilever tendons.

A geometrical conflict is also possible in transversally prestressed bridge decks between the transverse tendons on the one hand, and the cantilever and external continuity tendons on the other (Fig. 3-15). In order to prevent this type of conflict, it is important to accurately define the position of the transverse prestressing and then to



determine the location of the longitudinal tendons. In general, it is advisable to place the transverse tendons in the first bed and the cantilever tendons in the second.

Fig. 3.15 – Example of the crossing of transverse / cantilever tendons

3.2 - Stress calculations


For the majority of the verifications, the stresses are calculated using an elastic model for the bridge deck.

The calculation must take account of the successive phases in the loading of the structure. Therefore, it is necessary to carry out a precise analysis of the construction phases and of the subsequent loading phases (consecutive concrete casting and stressing operations, in addition to the removal of formwork and the moving of form travelers, support transfers, adjustments, etc.).

3.2.2 - Selfweight of the bridge deck

As the form travelers are built from rigid metal components, the selfweight can be represented by a single nominal value calculated using the design drawings, as recommended by the BPEL 91, revised in 1999 and notwithstanding the Directives Communes (Common Guidelines) of 1979.

However, it is also important to account for the elements which are added to the bridge deck such as anchor blocks, diaphragms and deviators. Finally the selfweight of the bridge deck also depends on the weight of the ducts, tendons and grout used for the injection of the external prestressing.

Except under special circumstances, the unit mass of concrete is fixed at 2.5 t/m3.

If high or low density aggregates are used, the unit mass of the concrete γt , and of the bridge deck (prestressed and reinforced) is evaluated on the basis of the unit mass of the concrete alone γb, measured for a laboratory sample of concrete without reinforcements using the following formula:

( )γ γ ρ γt b b= + ×7,85

7,85 -



In which ρ is the total ratio of non-prestressed and prestressed reinforcement bars in t/m3 (a value of p = 0.2 t/m3

is generally adopted).

Fig. 3.16 – Site loads to be considered for construction phase verifications

Standard concrete based on basaltic aggregates and high-performance concrete have higher densities (allow around 50 kg/m3 more for HPC).

3.2.3 - Prestressing effects

For the verifications of longitudinal flexion, the prestressing can be represented by a single probable value Pm.

For large structures, specific precautions are taken (empty ducts, measurement of transmission factors, etc.) to ensure that the probable prestressing value Pm is properly obtained. In this case, values of k = 0.02 and k’ = 0.95 should be used for the Service Limit State calculations, in accordance with Article 4.10.1 of the BPEL 91, revised in 1999.

3.2.4 - Random site loads

During the construction of the cantilevers, random site loads must be considered when calculating the longitudinal flexion of the bridge deck (Fig. 3-16). These loads are:

• A distributed load QPRA1 of 200 N/m² over a half-cantilever, in standard cases

• A concentrated load QPRA2 of 100 kN applied at the end of the cantilever, representing the weight of the cable rollers, compressors and other equipment likely to be used on the structure.

3.2.5 - Delayed effects

Concrete shrinkage and creep in hyperstatic structures built according to flexible static plans gradually modifies the stresses and constraints that were initially calculated.

It is difficult to give a quantitative evaluation of this redistribution. For this, a computerized calculation is required, which takes account of the construction phases and the laws of behavior of the different materials (including the scientific creep test for concrete).

A calculation of this type will be performed at the design stage, in which certain construction phases may be grouped together.

Two compulsory calculations must be performed in the framework of the construction surveys:

• Firstly, an initial calculation of longitudinal flexion (A), is carried out according to the company’s provisional construction schedule, with coefficients of friction according to the type of prestressing used



• Secondly, after the complete construction of the bridge deck, and in order to determine the actual stress state of the structure in operation, a post-construction calculation (B) is performed according to the actual construction schedule, using the mean coefficient of friction measurements, and the actual mass of the segments for prefabricated structures.

Should significant changes be made to the work schedule, it is also necessary to perform a third calculation to take account of the rearranged work schedule. Any change of sequence of operations will be validated by a calculation.

Finally, while awaiting the implementation of the Eurocodes, whose materials laws are considered to be more realistic, another calculation can also be performed in order to determine the reverse deflections during construction, using a creep law that is more realistic than that of the BPEL (quicker). Nevertheless, it is recommended to perform a creep test in order to make sure that the concrete creep law does not differ from the theoretical model of behaviour that was adopted.

3.2.6 - Calculat ion programs

Several software programs have been designed by private or public engineering firms for bridge calculations including for structures built using the cantilever method.

Sétra has developed two programs designed for these types of calculations amongst others:

• STl software ;

• The PCP (Ponts Construits par Phases [Bridges Built in Phases]) system.

These programs are used for calculating three-dimensional or flat structures made from bar components and are intended for the design of civil engineering structures. They can account for prestressing reinforcements, construction phases and imposed road loads. The calculations are performed according to the Strength of Materials theory applied to elastic beams, in which each segment is normally represented by a beam element.

The calculation must closely follow all of the construction phases in order to consider the load application dates and the aging of the materials (shrinkage, creep and relaxation) between these different phases.

3.3 - Verifications to be carried out with regard to normal stresses

3.3.1 - Preamble

Paragraph 3-3 describes the verifications to be carried out with regard to normal stresses due to normal force.

These calculations must be performed at the Service Limit State and at the Ultimate Limit State, when the structure is under construction and in service.

Verifications to be carried out with regard to shearing stresses are covered in Chapter 4.

3.3.2 - Verif ication categories

Cast-in-situ structures are generally justified according to class II of the BPEL 91, revised in 1999.

Considering the absence of longitudinal reinforcement bars passing through the joints, decks made from prefabricated segments are generally verified longitudinally according to class I of the BPEL 91, revised in 1999. Article 3.1.43 of the BPEL 91, revised in 1999 also describes the possibility of verifications being made



in class II subject to the joints remaining fully compressed under Pm. In this case, in accordance with Article 6.1.32, the stressed zone must also be less than 5 cm in height.

The choice of verification category must be clearly stated in the STC (Special Technical Clauses).

3.3.3 - Verif ications in the construction phase

In general, verifications must be carried out during all phases of construction.

3 .3 .3 .1 – Ver i f i ca t ion o f cant i l ever pres tres s ing

In addition to the verifications specific to the static balance which are covered in Chapter 5 of this guide, SLS (Service Limit State) verifications must be performed at all phases of the construction of the cantilever in order to verify the prestressing of the bridge deck.

The loads to be used include the known site loads (form travelers etc.) and the random site loads defined in paragraph 3-2.4.F

For structures verified in class II, the comment in Article 6.1.23 of the BPEL 91, revised in 1999 can be applied and a tensile stress limit equal to ftj instead of 0.7ftj can therefore be considered in the coating section.

3 .3 .3 .2 – Ver i f i ca t ion o f in terna l cont inu i ty pres tress ing

The internal continuity prestressing inside the concrete is designed to take up shrinkage, creep and thermal effects (thermal gradient and uniform temperature variation) during the construction phase between the casting of the concrete for the closing segment and the tensioning of the external continuity prestressing.

The uniform temperature variation can be considered to be equal to +/- 10° C.

The positive thermal gradient can be considered to be equal to 8° C. A negative thermal gradient of 5° C must also be taken into account.

In the case of structures with prefabricated segments, it is also important to consider the launch beam and the low-bed semi-trailer. For structures verified in class II and considering the very short site design phase, the comment in Article 6.1.23 of the BPEL 91, revised in 1999, can be applied, and a tensile stress limit equal to ftj instead of 0.7ftj can be considered in the coating section.

3.3.4 - Verif ications at service l imit state (SLS) in service

The verifications must be carried out:

• Upon commissioning

• After all of the delayed losses and redistributions have occurred (e.g. after 50,000 days, this period may be considered to be “infinite”, even if all of the losses and redistributions have not occurred according to the laws of the BPEL)

• With or without thermal gradient effects.

3.3.5 - Verif ications at ult imate l imit state (ULS) in service

It is difficult to apply ULS coefficients to a structure built in phases. For the verification of longitudinal flexion in service, the following simplified method is proposed:



Given that:

• represents the empty states envelope (state upon commissioning, state after all losses) without weighting (this envelope was been used for SLS verifications)

• represents the state according to a new calculation performed by applying all of the dead loads at the same time (without prestressing)

• represents the effect of the imposed loads

The ULS combinations to be considered are:

[ ] + [ 0.35 ] -I- [ 1.5 ]

[ ] + [ 1.5 ]

With this method, the forces due to the prestress tendons have not been increased. Indeed, if we take:

P: to be the prestressing

G: to be the dead loads except for the prestressing [concrete (envelope before and after creep), equipment and asphalt]

Q: to be imposed loads

We can calculate the following:

P + 1.35 G + 1.5 Q and P + G + 1.5 Q

With this calculation method, which is considered to be unfavorable, the Ultimate Limit State is not generally a key factor with regard to longitudinal flexion.

3.3.6 - Dimensioning approach

The dimensioning of a prestressed concrete structure built by the cantilever method is performed at the Service Limit State. Structures dimensioned in this way are then verified at the Ultimate Limit State.

The dimensioning can be carried out according to the steps outlined below:

1 s t s tage : de te rmin ing the can t i l ever t endons

The cantilever cabling is dimensioned in the construction phase. It must take up the selfweight of the concrete in the cantilever and the site loads defined in paragraph 3-2 above.

If it is possible to choose the length of the standard segments, i.e. if the length of the form traveler is not imposed, it may be beneficial to choose a segment length and prestressing units that are compatible with the attachment of two tendons per segment. In this situation, it is necessary to test most common prestressing units and to choose the one that gives a conventional segment length, i.e of between three and four meters.



In most cases, the dimensioning of cantilever tendons takes account of the normal stresses in the upper axis of the section situated directly above the temporary blocks, at the moment of the casting of the final pair of segments, i.e. before the tensioning of any cantilever tendons that might be anchored in this segment.

In the case of the final pair of segments without cantilever tendons, the casting of the closing segment may be the critical phase.

2 n d s tage: de t e rmin ing the cont inu i t y t endons s i tua ted ins ide the concre te

The continuity cabling inside the concrete is dimensioned in the construction phase. It must take up the effect of the thermal gradient in the construction phase before the stressing of the continuity tendons situated outside the concrete in addition to the effect of the selfweight of the end spans. The internal continuity cabling must also take up some of the redistributed delayed forces.

In general, the same prestressing units are chosen for the internal continuity tendons and the cantilever tendons.

3 r d s tage : de te rmin ing the con t inu i t y t endons s i tua ted ou t s ide the concre te

These tendons are designed to take up the operating forces which are not absorbed by the two preceding families of tendons.

This cabling has two roles: • To keep the shear stress down to acceptable levels by reducing the shear force

• To keep the normal stress within acceptable levels.

Initally, it is important to concentrate on shear stresses and to discover which segments have permissible levels of shear stress without the reduction made by the external tendons. In this way, the location of the external prestressing deviator can be determined. This must be situated between a third and quarter of the way along the span (a third of the way along the span for variable thickness and a quarter for constant thickness). It should be noted that this method can only give an approximate alignment because the permissible shear stress depends on the normal stress, which is itself dependent on the prestressing that is used.

After obtaining an initial alignment, the focus can then be switched to the normal stresses in order to determine the intensity of the prestressing. As the number of external tendons is always the greatest on piers, an initial estimate of the dimensions of the tendons can determined by concentrating on the lower axis of the crown section and by considering that the redistributions of forces due to concrete creep create a tensile stress of approximately 2 MPa.

The final alignment can be obtained by making certain adjustments to these initial estimates such as: • Altering the length of the different tendons (the tendons may cross one, two or three spans)

• Moving the deviators on one or two segments.

If there are no shear force problems, it is also possible to reduce the number of external cables and to compensate for them by using additional internal continuity tendons in the central zones, which are more economical because they are much shorter.



4 - Transverse and localized behaviour This chapter covers the behavior of the bridge deck with regard to:

– Stresses (flexion and shear) arising from the transverse behavior of the bridge deck – Tangential effects originating from the general longitudinal flexion covered in this chapter, because it is

essential to combine them with localized effects when performing the detailed verifications and determining the reinforcements

– The distribution of localized forces – The forces in specific elements (segments on piers and deviators).

Although the majority of the points covered are not specific to bridges built by the cantilever method, we have decided to include them because they are not dealt with in any other guide. Furthermore, it is important to design the cross-sections of structures properly in the first place, rather than to rely on complex calculations to remedy any problems. Finally, this chapter describes how to accurately account for the forces in specific elements such as segments on piers, deviator segments, anchor blocks, etc.

4.1 - Verification principles Apart from general longitudinal flexion, the main points to be considered in the dimensioning of structures are:

• Transverse flexion

• Tangential effects

• Specific elements such as the segments on piers and on abutments

• Localized forces, caused mainly by the distribution of the anchoring forces.

It is then possible to determine the reinforcements for the cross-section in accordance with the different accumulated actions taking into account their concomitance.

In a structure of constant depth, the calculations for transverse flexion are performed in a standard section. In a structure of variable depth, they are generally performed in a section close to a pier and in the crown section. This makes it possible to account for the differences in behavior between two sections of contrasting height, with the taller section close to the pier being more flexible than the crown section.

For structures of constant depth characterized by a thickening of the lower slab close to piers, this variation is sufficiently localized that it is not normally necessary to perform a specific calculation in addition to the calculation for the standard section.

In a section of bridge deck, the main sections to be verified are:

• -The upper slab: at the base of the cantilever, at the gusset located on theinner side of the box-girder, and in the centre of the slab

• -The webs: at the level of the centre of gravity and at the upper and lower extremities

• -The lower slab: primarily at the base of the gusset.



Fig. 4.1 – Sections to be verified

4.2 - Transverse flexion

4.2.1 - Actions to be considered

When the structure is in service, the usual actions must be considered: selfweight of the structure, weight of the superstructures, weight of road traffic loads, any transverse prestressing, loads on the lower slab, etc.

In the construction phase, additional actions must be introduced in order to account for the forces developed in certain situations encountered on site. These forces include:

• The forces developed by some of the tie bars for the form travelers

• The weight of a launch beam on the section of bridge deck that has already been constructed

• The weight of a segment stored on the segment to be calculated: a situation encountered on certain prefabrication areas with insufficient storage space.

4.2.2 - Calculat ion of transverse stresses

It should be remembered that monocellular bridge decks represent the vast majority of structures built by the cantilever method. The methods described hereafter, and especially the "simplified" methods, apply to this type of structure. In the case of more complex structures, only sophisticated modeling techniques provide a satisfactory response to the problem posed.

Transverse forces can be calculated in different ways according to the type of deck in question:

• Using a 2D model

• Using a 3D model

• Using a finite element model.

4 .2 .2 .1 – Ca lcu la t ion wi th a 2D mode l (nomographs + f rame ca lcu la t ions )

For the upper slab, it is possible to use nomographs to calculate the forces, either by directly incorporating the statutory French loads (using Thénoz’ nomographs with loads from Fascicule 61 title II of the French CCTG, or more general methods (Pücher or Homberg), to which the loads from any regulations can be applied (e.g.



Eurocode 1) or even loads that are not specified by a particular regulation. The Thénoz and Pücher nomographs are only used for slabs of a constant thickness while the Homberg nomograph accounts for thickness variations.

For conventional structures (monocellular box girders), the forces are calculated using nomographs for double-embedded slabs for loads situated between the webs, and nomographs for embedded slabs for loads situated on the cantilevers. Next, the moments obtained at the embedded section are added at the upper nodes in a 2-D model representing a section of deck of a unitary length (Fig. 4.2).

This principle of a two-dimensional calculation supposes that:

• The bridge deck is of a locally constant section

• All of the sections are loaded in the same way.

Therefore, this calculation is completely valid for distributed loads such as selfweight or the fittings. For concentrated loads (road traffic loads), it is only an approximate calculation because on the one hand, the force is unevenly distributed along the fixed support and on the other, it does not represent the distribution of forces from the upper slab towards the webs and the lower slab. Calculations using finite elements have shown that this type of calculation is reasonably accurate for the upper slab when the webs are sufficiently rigid. This remains valid for the upper part of the webs, as there is not yet a significant distribution of forces in this area. However, this calculation is nowhere near as representative for the lower part of the box girder.

Fig. 4.2 – Principle of the calculation method using nomographs

[Sétra’s Bulletin Technique (Technical Bulletin) n° 1 and its Ouvrages d’art (Civil Engineering Structures) Bulletin n° 13 of November 1992 contain further details about this method.]

According to these calculations, the transverse moments acting in the box girder are:

• M nomograph + M frame for the upper central slab

• M frame in the webs and lower slab

• And M nomograph in the cantilevers, of course

Spec i f i c po in t s concern ing the mode l ing • The span of the central slab (for calculation by nomographs) is obtained by considering the point of

intersection of the intrados of the slab and a line angled at 45° from the origin of the gusset on the web (Fig. 4.3)



• For the introduction of the moments at the nodes of the frame, it is necessary to add the moment due to the shear force calculated at the theoretical edge of the slab, by multiplying it by the distance between this theoretical end fixing and the upper node situated on the centerline of the web (Fig. 4.3). This shear force is not given by the nomographs, but it is easy to calculate

• For stability, this model must include two supports. In order to avoid parasitic forces resulting from a blockage of the nodes in the model, it is necessary to free one of the supports transversally. These supports must be situated at the bottom of the webs (in the case of inclined webs), because the vertical reactions would then develop a horizontal component (of the normal force in the webs) which does not exist

• If we simply apply the fixed support reactions of the double-embedded slab at the upper nodes and place the frame supports in the lower nodes, a compression appears in the bars representing the webs, which does not exist in reality. In the interests of accuracy, it is essential to apply the opposite of the load applied (vertical force and torsion moment) to all of the bars of the model in the form of shear flows on each bar. This presupposes that the unitary flows due to a vertical load or a torsional moment have first been determined using a calculation program for the characteristics of hollow sections (Fig. 4.4). Of course, this type of calculation requires a balancing of the loads for each load situation. Then it is verified that the support reactions are zero

• However, in the majority of the cases (monocellular bridge deck with a moderate width and a moderate height), calculations can be simplified not applying this equivalent flow and neglecting the normal effort in the web. This approximation is justified by the weak difference with the reinforcement calculated with the previous method.

Fig. 4.3 – Relative positions of the forces calculated at the fixed support of the slab (for the nomographs) and of the upper node of the modeled frame to which the efforts are

applied

As the principle is obviously valid, this method can be extended to structures other than monocellular box girders. However, the fact of directly applying the fixed-end moments (with the nomographs giving a single value) presupposes that the structure and the forces are symmetrical.

Fig. 4.4 – Shear flows due to a vertical force in a monocellular box girder



For more complex structures (multi-cellular box girders), a common approach is to determine equivalent vertical loads giving the same moments in the middle of the slab and at the fixed support (uniformly distributed loads and knife-edge loads), which will then be moved transversally into different positions in order to obtain the maximum effects in the transverse structure.

As the frame effect in a structure of variable depth depends on the rigidity of the webs (according to their height and thickness), and to a lesser extent on the thickness of the lower slab, these calculations are almost always performed for the section on the pier on the one hand, and for section at the crown on the other, as mentioned in the preamble.

[For further information about these methods, refer to Analyse structurale des tabliers de ponts (Structural Analysis of Bridge Decks) by J.A. Calgaro, - Presse des Ponts et Chaussées 88].

4 .2 .2 .2 – Ca lcu la t ion us ing a 3D mode l

For conventional standard sections, the 2D model is usually adequate, in spite of its lack of precision in the lower areas of the webs and in the lower slab. Despite its complexity, a 3D model is not significantly more accurate.

On the other hand, for elements with non-standard sections, a 2D calculation is often too simplistic and unrealistic in terms of the actual distribution of forces. For example, this includes:

• Segments on piers (even for conventional box girders)

• Deviator segments for external cables (as above)

• Very wide monocellular box girders

• Box girders with transverse ribs

• Multicellular box girders

• Box girders with bracing.

Therefore, it is necessary to adopt another type of modeling (3D with bars or finite shell elements) which shows up local structural variations (ribs, thicker sections of webs, crossbeams on supports or deviator beams, etc.) or non-homogeneous behavior. Significant distorsions may be shown in the cross-section of multi-cellular bridge decks under the effects of both symmetrical and asymmetrical loads. The analysis of this three-dimensional phenomenon also requires 3D modeling (Fig. 4.5).



Fig. 4.5 –3D model of a multi-cellular box girder

Bas ic mode l ing recommendat ions

A 3D model is a beam grid system.

• According to the elements to be analysed (segments on supports or a standard sections of a complex structure), the longitudinal division can be varied in order to obtain an acceptable level of accuracy for the forces to be calculated:

In order to study the behaviour of a complex standard section, it is necessary to model a portion of bridge deck that is long for the forces not to be disturbed by the conditions at the extremities. It is advisable to divide the deck into sufficiently short sections, equal to approximately ¼ to ½ of the height, in order to obtain the correct local forces For a segment on pier, it is possible to take account of the longitudinal symmetry in order to halve the size of the model. In this case, it is necessary to be very careful to modelize conditions at the limits (the six degree of freedom of the nodes are not all embedded) to guarantee the representativity of the model. Furthermore, because on the one hand, we are using the bridge deck’s actual supports, and on the other hand, we are only interested in the forces in proximity to the crossbeam, we can also limit the length of the modeled portion to a few sections (Fig. 4.6), as the external actions originate primarily from the flows on the end section.

• In the other directions, the breakdown must remain consistent with that used in the longitudinal direction, which rapidly increases the size of the model.

• Each rod has its own specific characteristics (area, bending inertia) and the torsion inertia is considered to be equal to half of the bending inertia of the corresponding rectangular cross section (shell element - slabs, webs, but does not apply for stiffener, rib, …) in order to account for the distribution of forces in both directions of the beam grid.

• The strengthening pieces (segment on pier, deviator beams) modify the rods neutral axis. To determine the rod center of gravity and inertia, it is important to take account for the effective width of slab.

• The external forces are applied to the segment in the form of flows in the end sections of the model.It is therefore necessary that end sections should modelize the section of a standard segment.

• The loads applied to the section itself are balanced out by directly opposite flows (cf. § 4.2.2.1).



In this type of modeling, the forces given by the model are directly usable.

Fig. 4.6 – Modeling of a half-segment on pier using a 3D model

This method is more cumbersome than the 2D calculation method, but it gives a better representation of the direction of the forces, especially in proximity to the bearings or perpendicular to the deviators. On the other hand, due to the fact that it is impossible to generate elements automatically, 3D modeling is generally reserved for segments on supports or deviators.

4 .2 .2 .3 – Ca lcu la t ion us ing f in i t e she l l e l ements

As mentioned previously, a shell-type finite element calculation can be performed when the structure is not a traditional box girder, or for any other reason (better curracy for example).

These programs are extremely powerful and are capable of solving complex problems, but the engineer must have an excellent command of finite elements and a detailed analysis of both the structure itself and its modeling must be performed. Under no circumstances can they compensate for a poor initial design.

For detailed information about modeling and calculation methods, please refer to the "Emploi des éléments finis en génie civil" (Use of Finite Elements in Civil Engineering) documents published by the AFGC (Association française de génie civil - French Civil Engineering Association)].

Bas ic mode l ing recommendat ions

Several basic rules apply to this modeling:

• The conditions at the limits are very important, and the forces at the extremities of the model are completely disturbed. Consequently, it is necessary to model a sufficiently long portion in order to obtain a reasonably large undisturbed “usable” area. In general, it can be considered that the zone to be ignored corresponds to approximately 2 to 3 times the height of the section. For example, if an entire span is being modeled, it is extended by a segment of three times the height on each side (Fig. 4.7).

• In order to apply the general forces correctly, it is also necessary to extend the shell model with bars representing the deck itself, featuring the same cross-section characteristics.

• Of course, the segment of shells and bars are connected by an arrangement of rigid bars laid out in a “spider” configuration.



• The shape of the elements must not be too distended, in terms of their two-dimensional characteristics and their thickness. Thus, a maximum ratio of approximately 2 is recommended between the plan-view dimensions and the thickness, giving a shape similar to a rectangle, for which the ratio should also not exceed 2 (otherwise, use triangular elements). Consequently, the slabs and webs can be broken down into elements measuring approximately 0.50 m to 0.60 m in the plan view, with the crossbeams or deviators also having maximum thicknesses of 0.50 to 0.60 m

• It should be remembered that the results for finite elements are given at the centre of gravity of the element. The structure should therefore be broken down in such a way that the centres of gravity of the elements are situated in line with the correct cross sections: at the gussets for example. Otherwise, interpolations will have to be performed: a long manual operation that is a source of errors or inaccuracies

• The prestressing must be entered in the form of external forces. None of these forces should be omitted (anchoring forces and thrusts close to the deviations), because the system forms an independently balanced structure

• The dead loads are entered over the entire structure, including on the bars outside the shell segment

• Traffic loads: in order to perform an accurate calculation, after defining the calculation sections (in the transverse direction), it is possible to determine the lines of influence (or rather the surfaces of influence) of the efforts in question in these sections, which makes it possible to choose the positions of the loads in order to obtain the maximum effect required.

Fig. 4.7 – Breakdown of a bridge deck into finite shell elements

Furthermore, the designer’s attention is drawn to the fact that this method can be very cumbersome due to the need to move the imposed loads “manually” on the upper slab for certain finite elements programs which do not have an automatic load placement function.

In general, the forces given by the model are directy exploitable; however, the reinforced concrete elements, or “T” sections require a reconstitution of the forces on the section based upon the constraints for each element.

One of the main advantages of this method is that it gives an effective representation of the behaviour of the structure, both in the standard parts and in specific areas such as the segments on piers or deviators, and it also takes account of the interaction between the general effects and the local effects (general dispersion). This type of model must not be used to determine highly localized dispersion forces such as those in the first regularization prism or the radial tendon forces in the deviators, which we can continue to calculate manually.

Remarks

The shell finite elements are not adapted to model properly the massive parts of a segment on pier (cross-beam or anchorage block for example) ; it is then necessary to add offset rods or 3D finite elements, but which present other difficulties, such as determine the efforts and deduce the corresponding reinforcement (see also § 4.4.1). This method must be used in very specific cases and require a high level in modelling with 3D finite elements.



4.2.3 - Lateral thrust in curved or deviated compressed or stressed elements

4 .2 .3 .1 – Latera l thrus t s o f concre te in curved s labs

In bridge decks of variable depth, the longitudinal compression in the lower slab creates a lateral thrust (due to the curvature of the slab) which creates a transverse flexion of this slab.

This slab is embedded in the webs of the box girder, preferably using a gusset.

This is a cylindrical shell subjected to longitudinal compression stresses which can be considered to be uniform transversally to the structure.

This stress field causes a lateral thrust towards the top of the slab which is balanced out by the embedding of the slab in the webs and causes a transverse bending moment, which stresses the upper axis on the centerline of the slab and the lower axis in line with the fixed end in the web.

This moment varies throughout the length of the structure due to the longitudinal variations in the thickness of the slab and the extent of the stresses in the section. In a cross-section, the distribution of the fixed end moments in the webs and in the span also varies according to the relative stiffnesses of the slab and webs (with the upper slab generally being constant).

The lateral thrust in a given section of the structure of a unitary length is expressed per (transverse) meter of slab, by:

moymoyb R

eq σ=

with σb moy = mean stress in the lower slab for the segment in question

e = thickness of the lower slab in this segment

Rmoy = mean radius of the mean axis of the lower slab for the segment in question.



Fig. 4.8 – Vertical thrust of a curved slab – longitudinal section

Fig. 4.9 – Vertical thrust of a curved slab – transverse section

Note

In the case of a high curved lower slab (for example with a cubic depth variation), instability of this lower slab may occur under compression in the most curved zone. [See article from P. Faessel – Journée de l'AFPC April 1974 and M. Virlogeux – Annales de l'IBTP February 1981].

4 .2 .3 .2 – Radia l thrus t o f cont inu i ty tendons

The presence of prestress tendons in the lower slab causes a phenomenon of the same type but in the opposite direction. These tendons are tensioned in the second phase after the completion of the cantilevers, when the end or intermediate spans between consecutive cantilevers are closed. Two different situations are identified:

• Tendons in the curved slabs

• Construction irregularities.

The presence of tendons in the curved slabs generates similar forces to those described above, but in the opposite direction. However, these tendons are close to the centre of the span, an area of low slab compression: the action of these tendons is therefore preponderant. Furthermore, the presence of ducts reduces the strength of the section and thus increases the likelihood of the structure breaking along lines parallel to the ducts.

By calling f the linear force of the radial thrust of the tendon, this force is equal to RPf = with:

– P the prestressing force of the tendon – R radius of curvature



Furthermore, irregularities in the alignment of the ducts during construction, particularly in line with the segment joints, produce concentrated forces which can result in problems or even spalling in the lower slab. Indeed, if the radius of curvature becomes very small (producing an angular point), the force increases significantly amd can lead to the breaking of the slab.

It is thus highly inadvisable to place tendons in the lower slab of bridge decks of variable depth. Even for structures of constant depth, this arrangement is not recommended, because the segments are short and the large number of joints increases the risk of irregularities. In addition, the differential shrinkage can cause cracks near the tendon layouts which can lead to the corrosion of the tendon.

Note

The lateral thrust also exists when continuity tendons are placed in the gussets. However this phenomenon is less severe because the thickness of the concrete enables better distribution of the forces.

4 .2 .3 -3 – Latera l thrus t in a lower s lab perpendicu lar to an angular po int

In bridge decks of variable depth with linear gussets, localized lateral thrusts originate in the lower slab at the point of intersection of two rectilinear portions of lower slab subjected to longitudinal compression stresses.

The same applies directly above the supports when the slope of the slab suddenly changes.

The resultant is directed according to the bisector of the mean lines of the slab, giving a concentrated effort which results in strong localized stresses in the lower slab.

Fig. 4.10 – Forces perpendicular to angular points – longitudinal section

This is why it is essential to place a stiffener or crossbeam in this area in order to transfer the force towards the webs and to take up the transverse flexion of the slab.

On a support, a crossbeam is also needed to take up the torsion forces due to the asymmetrical loading of the bridge deck.

4 .2 .3 .4 – Thrus t perpendicu lar to a dev ia tor

External prestressing tendons are deviated in deviator crossbeams with a small radius of curvature. They thus develop large localized forces which must be taken up by these deviators. The principle is the same as above, with the radial thrust being directed according to the bisector of the tendons layouts.

In the case of a bridge deck with a high curvature in the horizontal plane, the horizontal component of this thrust is not negligeable.



Fig. 4.11 – Forces perpendicular to a prestressing deviator

4.2.4 - Forces due to thermal phenomena

Upper s lab

In addition to conventional flexion forces due to the thermal gradient, in certain cases it is advisable to consider the localized effects caused by a gradient operating between the two faces of the upper slab.

This gradient results in transverse flexion which is added to the other stresses. In the webs, the corresponding section of reinforcement is added to that which is determined by the general shear force.

The figure 4.12 represents the thermal gradient in a common concrete box-girder according to Eurocode 1 – Section 1.5. It shows that a thermal gradient exists in the upper slab.

For information only, we propose to consider a gradient of 10°C in the upper slab under the form of a linear gradient. The combination to use is the same as the one for general flexion : G + Wr + 0.5 Δθ.

Fig. 4.12 – Localized thermal gradient in the upper slab

Note

This gradient has some effect only in the case of multicellular box girders. It is not necessary to take it into account in the case of monocellular box girder.

Lower s lab

The lower slab requires generally few lateral reinforcements unless it is very wide. As concreting is made at the contact of the previous segment, the shrinkage can cause a longitudinal cracking. This phenomenon will be amplified with a high strength concrete, a wide lower slab or a cement with a high hydratation heat. Therefore, we advise to place a minimum reinforcement ratio equal to 10-4 fc of the lower slab section (with fc expressed in MPa). For example, it gives 0.4% for a C40/50 concrete.



4.2.5 - Verif ications of the sections

In the absence of transverse prestressing, the verification of the parts and the calculation of the reinforcements are carried out according to the instructions in the BAEL (Béton armé à l’état limite - Limit State Reinforced Concrete Code) 1991, revised in 1999. Cracking is generally considered to be detrimental.

When the transverse section is prestressed (upper slab), the verification of the parts and the determination of the prestressing bars and reinforcements are carried out according Class III in the BPEL (Limit State Prestressed Concrete Code) 1991, revised in 1999. But it is generally advised to increase the lateral prestressing because this latter is only determined by the condition of zero traction in concrete under dead loads while the imposed loads have a much bigger effect. The required amount of reinforcement would be high because the traffic loads would cause frequent and repetitive cracking. To limit the amount of reinforcements (it is necessary to enable a good concreting) and to limit the fatigue risk in these reinforcements or their corrosion, the class III rules have to be completed as followed :

For the sake of good design and to prevent excessive cracking, the upper slab must remain transversally compressed under a proportion of the imposed loads: for example, under the effects of the fatigue truck Bf (a single truck placed in the centerline of the slower lane), specified in the "Ponts métalliques et mixtes - résistance à la fatigue" (Metal and Composite Bridges – Resistance to Fatigue) guide published by Sétra/CTICM (Centre technique industriel de la construction métallique - Industrial Technical Centre for Steel Construction)/ SNCF (Société nationale de chemins de fer - French Railways). Such a choice has to be written in the Special Technical Clauses (STC). The contract can also impose the amount of transversal prestressing.

4.3 - General tangential stresses

4.3.1 - Verif ication principles

The verification of the bridge deck under tangential stresses consists of checking:

• Firstly, that the shear stresses are permissible at all points, in order to reduce the probability of cracking. Cracks caused by shear forces do not close up on their own like flexion cracks when the stress is reversed. Furthermore, failure due to shear forces is a brittle rather than a ductile phenomenon. This is why calculation methods always have a greater safety margin for shearing

• Secondly, that the non-prestressed reinforcement bars designed to take up the forces due to the concomitance of flexion and shear forces are properly positioned and dimensioned with regard to the statutory requirements (verification at the Service Limit State and the Ultimate Limit State). It should be remembered that verification at the service limit state is designed to control cracking and at the ultimate limit state the aim is to ensure safety by preventing brittle fractures.

4.3.2 - General design assumptions

Shear force calculations are carried out on sections of the beam perpendicular to the mean axis (Fig 4.13 where G1 and G2 are respectively the center of gravity of the vertical cross-sections and of the cross-section perpendicular to the mean axis.



Fig. 4.13 – Shear force on straight sections

To simplify, calculations of shear force are sometimes carried out on vertical sections, or more precisely, on sections perpendicular to the upper axis. This calculation is usually less favourable, although not always so, as the distribution of areas and stresses may reverse the phenomenon (cf. § 4.3.3).

The following actions must be considered:

• External loads (selfweight, fittings and imposed loads)

• Thermal gradient

• The redistribution of forces due to creep

• Prestressing (cf. § 4.3.2.2).

In addition, the Resal Effect must also be considered.

4 .3 .2 .1 - In f luence o f cons truct ion sequence o f operat ions

1) Segment on p i e r

The segment on pier is a large structure which is subjected to highly variable stresses during the construction of the bridge deck and when the structure is in service. Therefore, rather than just concentrating on the definitive situation, it is important to verify all of the major phases, from construction through to commissioning.

These major phases are:

• Imbalances during the construction of the cantilever, with the segment on pier being embedded (asymmetrical casting , detachment of form traveler)

• The transfer of supports after the grouting of closing segments

• The tensioning of the external prestressing in the segment on pier (maximum distribution forces)

• The service state (maximum flexion).



Fig. 4.14 – Traditional segment on pier

Fig. 4.15 – Segment on pier with double supports

Fig. 4.16 – Embedded segment on pier



2) S tandard segments

The major phases for standard segments are:

• The prestressing of the segment in question (maximum dispersion forces)

• The end of the construction of the cantilever (maximum prestressing in the section)

• The service state (maximum flexion).

4 .3 .2 .2 – Method used to account for pres tress ing

Tendons anchored at less than one regularization length from the section being studied create some distribution effects which add to the general effects (in particular shear force) provided by the design program. .Certain design programs include them just after their anchorage, other include them only at the other side of the segment.

Furthermore, the angle of the tendons in relation to the mean axis generally reduces the shear force according to the diagram 4.17. Therefore, it is important to be consistent when using the design program to account for the reduction of shear force due to the tendons in order to avoid counting the same force twice.

Fig. 4.17 – Diagram of the reduction of shear force due to the tendons

4 .3 .2 .3 – Br idge deck o f var iab le he ight

For structures of variable height, the mean axis presents an angular point directly above the support. Consequently, the support reaction is not equal to the sum of the shear forces to the right and left of this support, but the vertical component of the normal force in the section must be added to it.

4 .3 .2 .4 – Transverse morphology

The development of highways and urban structures has led to the construction of extremely wide structures.

Although the majority of structures are now mono-cellular box girders, multicellular structures are also sometimes used. These structures are more difficult to build and their complex transverse behavior, when not fully understood, may lead to problems in the webs (non-uniform distribution of shear forces, especially for box girders with three webs, as the central web takes up the most force). In particular, this type of section is sensitive to the distorsion (deformation of the cross-section) that appears under loads. 3D modeling is required to account for the transverse and longitudinal stiffnesses of the section.



Another solution that has been virtually abandoned in France is to construct structures with two box girders joined together by the upper slab. The main disadvantage of this method is the differential shrinkage which appears between concrete of different ages: between the concrete used for the box girders on the one hand and that used for the transverse grouting on the other. The creep leads to a transfer of loads :

• Vertically the parts built in the second phase leans against the first box girder

• The normal force of the part built in the second phase tends to go to the part built in the first phase.

However, this transfer of loads has only a moderate effect on the stresses.

Finally, the effective width of the upper slabs on very wide monocellular box girder structures (with or without struts and/or ribs) is reduced in relation to their total width (shear lag phenomenon). It is important to consider this when evaluating flexion stresses. For an initial approximation, this phenomenon can be accounted for according to the precepts of Article 5.4 of the BPEL, by limiting the effective width to 1/10th of the length of the span in question, on either side of the web (for a box girder with two webs, this makes it possible to reach a total effective width of b = total thickness of webs + 0.4 l. However, the presence of ribs improve the distribution of forces in the upper slab, in preventing the buckling of this slab ; it is therefore not necessary to reduce the effective width in such a structure.

It is recommended to concentrate the cantilever prestress tendons perpendicular to the webs so that they can directly take up the loads applied by the webs (by shearing). Furthermore, it is advisable to place a tendon at the end of each cantilever and position it so that it compresses the ends of the upper slab (see § 4.5.3 for further details).

Finally, the distribution of forces concentrated in this type of section is not compatible with the normal simplified rules and requires a specific study.

Fig. 4.18 – Example of a very wide bridge deck

4.3.3 - RESAL EFFECT

4 .3 .3 .1 – Bas ic pr inc ip les

In structures of variable depth, we usually see an adjustment of the shear force due to the fact that the mean fibre is inclined in relation to the slab: the compression in the slabs presents a component in the direction of the shear force.



Fig. 4.19 – Resal effect in the upper and lower slabs

A part of the shear force is balanced by the normal force in the slab.

The shear force is equal to V + ΔV.

ΔV is the correction of shear force by the Resal effect:

ΔV = -(α - ϕ) Nls + ϕNus

with:

ϕ the angle of the mean axis from the upper axis

α the angle of the lower slab in relation to the upper slab

Nls force (compression) of the lower slab

Nus force (compression) of the upper slab

According to the BPEL, the areas in question for the calculation of Nls and Nus are the slabs and gussets, excluding the webs.

As can be seen in the formula above, the upper slab exerts a Resal "counter-effect" in opposition to the effect in the lower slab. This is usually weak in proximity to the supports, as the compression of the upper slab is limited, whereas because the variation in height is the greatest in this area, there is a greater Resal effect due the lower slab. [For further details on theoretical methods, see the article by M.Virlogeux in the Annales de l’I.T.B.T.P, no. 391, February 1981].

4 .3 .3 .2 – Vert i ca l sec t ion ca lcu la t ions

With modern calculation methods, calculations are systematically performed on section perpendicular to the neutral axis. For the pre-design calculations, it is possible to perform calculations on vertical sections provided that:

• The extrados can be considered to be horizontal

• Shear forces are directed in the usual direction according to the cantilever, in contrast to what can happen in highly asymmetrical spans in which a reversal of the shear force can be observed.



In this case, the formula is simplified to:

ΔV = - Nls sin α with α being the angle of the lower slab from the horizontal

As mentioned previously, the vertical section calculation is less favorable. This is especially true close to the supports due to the steeper angle of the mean line, and less so in proximity to the crowns. The difference may be as much as 1 MPa in certain configurations.

4.3.4 - Shear reaction due to shearing force

For a traditional structure with two webs, the shear reaction caused by shearing force can be expressed by the following formula:

IybySV

nredm )(

)(=τ with

bn(y) Total width at the y ordinate

S(y) Static moment at the y ordinate (i.e. of the part situated above the transverse slice in relation to the line passing through the centre of gravity).

Vred Reduced shear force

I Inertia of the entire section

When the webs are angled, the width b is the straight width of the web in question and not its skewed width directly above the slice.

This formula supposes that there is no concentrated forces in the vicinity of the studied section. Additional steel reinforcement brought by the tendon anchorages are determined with the distribution calculations.

Fig. 4.20 – Shear reaction of angled webs

As for the value of the nominal width, in the event of there being a tendon in proximity to the joint (“internal” tendon), it should be remembered that the whole diameter of the duct shall be deduced from the width when it is not injected, or injected with a flexible product, and a half-diameter shall be deduced when it is injected with a cement grout (cf. BAEL Article 7.4.1).

4.3.5 - Torsion shear

The pure Saint-Venant torsion shear is equal to:



eT

T Ω=

2τ with

T moment of torsion;

Ω Area of tube defined by the middle surface of the box girder walls

e Thickness of the wall

This torsion is caused by asymmetrical loads (dead loads and especially imposed loads) and by any curvature of the bridge deck in the horizontal plane.

This shear is algebraically added to the shearing force calculated previously.

• This calculation obviously supposes that the section is undeformable, which is generally the case, as the structures feature deviators which act as stiffeners and have webs with approximately the same thickness as the slabs (with quite similar stiffnesses). This undeformability hypothesis can be considered if the length between stiffeners does not exceed 5 to 6 times the box girder width. Beyond, the box girder distorsion increases the difference of longitudinal flexion between the webs and can be expressed with an offset coefficient applied to the loads.In the case of a curved bridge which section is supposed undeformable as indicated above, the torsion induced by the curvature has to be taken account for at different stages:

• At the construction of the cantilever, for self-weight, the center of gravity of the arch portion is on the inner side of the curvature. As a result, the torsion effect tends to load the support on the inner side

• The fittings weight applies on the continuous structure, and generates a torsion opposed to that of the self-weight

• The external prestressing having a polygonal layout, generates a torsion which increases the load on the support on the inner side.

4.3.6 - Verif ication of the sections

The sections are verified according to Article 7.2 of the BPEL 1991, revised in 1999. The stresses σx, σt and τ calculated at any point of a section, must therefore satisfy the following inequalities at the service limit state:

For σx > 0

( ⎥⎦⎤

⎢⎣⎡ ++≤− txtjtjtx ff σσσστ

324,02 ) (no failure due to cracking)

( ) ( )⎥⎦⎤

⎢⎣⎡ ++−−≤− txtjtxcj

cj

tjtx ff

ff

σσσσσστ326,022 (no failure due to shearing and compression)

In the general situation in which σt = 0 (no vertical prestressing), we obtain:

⎥⎦⎤

⎢⎣⎡ +≤ xtjtj ff στ

324,02 and ( ) ⎥⎦

⎤⎢⎣⎡ +−≤ xtjxcj

cj

tj ffff

σστ326,022 with the first formula nearly always

predominating.



When the calculations are performed with the probable value of prestressing Pm, the limit stress τ must be multiplied by a coefficient k’. Special precautions must be taken with regard to structures built by the cantilever method due to their technical complexity. Consequently, a figure of 0.95 is usually adopted for this k’ coefficient (BPEL, Article 4.10.1).

The reinforcements are determined at the ultimate limit state (BPEL, Article 7.3.2):

utj

ureds

e

tn

t tgff

sbA βτ

γ ⎟⎟⎠

⎞⎜⎜⎝

⎛−≥

3. for reinforcements perpendicular to the mean axis.

Eurocode 2 (EN 1992 1.1 - Article 6.2) does not require verification at the service limit state. The procedure for calculating the non-prestressed reinforcements is similar to that laid down in the BPEL, with the contribution of the concrete accounted for in a similar way but with several additional refinements. As this document is still under development, we shall refer back to it when it is finally published.

4.3.7 - Active stirrups (for information)

This technique has sometimes been used to improve the shear resistance of webs. The only reason for its inclusion here is to remind readers of the drawbacks which led to its fall from grace:

• Considering the very short length of the prestressing tendons, their tension can differ considerably from the expected value due to the setting of anchorage wedges. Only certain types of active reinforcements can guarantee the correct tension (compression fittings, prestressing bars)

• The distribution of forces only occurs above a certain length - hence there is a lack of compression between the anchorages at the bottom of the web. Therefore, the shear force at the web/lower slab junction must be verified without taking account of this compression

• To guarantee the correct distribution of forces, it is necessary to bring the active stirrups very close together. These stirrups have to be inserted into the passive reinforcement of the web, thus complicating the concreting process

• Due to their design, these reinforcements emerge in the upper slab and are thus extremely sensitive to corrosion. It is thus necessary to use “offshore” types of protection techniques, which makes this a particularly costly solution (requiring sealed caps and ducts, for example)

• Finally, some of the vertical prestressing force is dissipated in localized areas of rigidity such as deviators or crossbeams (zones in which the greatest shear reaction is usually encountered reached).

4.3.8 – Tying the slabs into the webs

In order to prevent the fracturing of the vertical planes situated at the origin of the gussets (points S1, S2, I1, see Fig 4.1 at § 4.1) due to excessive shearforce, it is important to tie in the shear strain using transverse reinforcement bars. These bars are dimensioned in accordance with the instructions in Article 7.3,23 of the BPEL 91, revised in 1999. It is also important to verify the shear stresses at the service limit state as mentioned above (cf. § 4.3-6).



Fig. 4.21 – Tie bars to combat shear strain in the slab/web area

For the lower slab, a minimum level of transverse reinforcement is necessary to reduce cracking due to thermal shrinkage in the central area of the slab. A value of 0.5% seems to be sufficient under the most penalizing conditions (large width, HPC, etc. – see also § 4.2.4).

4.4 - Specific elements


4 .4 .1 .1 Genera l i t i e s

It should be remembered that the initial static design of these parts of structures often does not allow for the application of Strength of Materials principles for the wire frame beams at all points. It is thus important to verify that the morphology of the segment on pier is capable of withstanding the transmissions of internal forces (e.g. the subsequent anchoring of the external continuity prestressing, crossbeam for definitive or temporary bearings).

The verifications focus mainly on:

• The transmission of support reactions from the bearings (both temporary and permanent) towards the webs

• The take-up of torsion forces by the crossbeam

• The take-up of the lateral thrust of the lower slab by this same crossbeam for a variable height

• The distribution of the prestressing forces due to the tendons positioned in the segment on pier (SOP).

4 .4 .1 .2 – 3D mode l

As previously mentioned in § 4.2.2.2, a 3D model is generally used to model the segment on pier due to the presence of reinforcing elements (crossbeam, thicker sections of web, etc.) which completely modify its behavior in comparison to a standard section. This model is used to verify the first three points presented above.

4 .4 .1 .3 – S trut and t i e mode l

It is also possible to use a strut-and-tie model [cf. J. Schlaich - PCI Journal – May / June 1987] to verify this transmission of forces. The principle of this method is the following:

• Construction of a model composed of struts and ties which replace the actual stresses fields by straight elements and which concentrate the stress deviation in the nodes

• Calculation of the effort statically balanced in the rods of the truss-model



• Dimensioning of struts, ties and nodes.

The difficulty of this method is the construction of the model. The rods of the model have to be oriented according to the direction of the internal forces given by the Elasticity Theory. The usual method is the load path method. The model is linked to the rest of the structure where the stress are supposed to be regularly distributed and linearized (B zone as Bernoulli, cf Schlaich). The model is balanced with the force brought by this zone B. The stress diagram of this B zone is divided in such a way as to balance the concentrated forces by the corresponding zone with regularly distributed stress. The load paths have to link the two sides of the studied zone without crossing each other.

But it is sometimes difficult to determine the load path. It can require the use of a finite element model. This can be quite cumbersome.

The reader’s attention is drawn to the fact that although this method is very effective for use with any irregular parts of this type, it requires the engineer to have a very good understanding of structural behaviour. A poor choice of struts and ties could lead to an incorrect arrangement of reinforcement bars and the use of excessively or insufficiently large sections. The latter choice would be a much more serious problem.

Figure 4.22 below shows the behavior of the support crossbeam under the effect of the torsion of the box girder.

Fig. 4.22 Support crossbeam - transmission of torsion

As an example, the figure 4.22 represents the working of the crossbeam under the effect of the torsion transmitted by the box girder, for a common type of crossbeam ("V" shape). Other types of crossbeam can be considered : "A" shape, or strengthened frame.

4 .4 .1 .3 – Par t i cu lar po in t s

In the case of structures with high curvature, the bridge deck is subjected to torsion moments caused by the curvature, which results in significant shear reactions in the webs close to the piers. Obviously, the crossbeams on piers have to take up these additional forces (see also § 4.3.5).

The fourth point (distribution) is verified according to the usual principles (Appendix 4 of the BPEL). However, as the section is not constant (anchor blocks and thicker sections of web), it is necessary to make a choice between the sections in which the distribution of stresses is carried out. Considering the relatively large depth of the bridge deck in this area (especially in the case of structures of a variable depth), this distribution length generally includes the “standard” cross section of the bridge deck. It is on this section that we shall consider the stresses to be evenly distributed. On the other hand, when evaluating the shear stresses at the level of the transverse slices, it is reasonable to consider the actual section, i.e. including the additional thicknesses of the anchor blocks. This has hardly any effect on the reinforcement which depends primarily on force rather than stresses.



Fig. 4.23 – Section of a slice for distribution

Remark

To study the distribution of forces due to tendon anchorages in segments on piers, (or in segments on abutments), the upper slab has been sometimes considered as a beam supported by the web and the reinforcement calculated as a flexion reinforcement. This method was not satisfying since this "beam" is not a beam as a matter of fact because of the existence of the rest of the slab behind the element artificially isolated with length lr. The rebars will be placed at the opposite side of the anchorages where as the cracking phenomena always occur near the anchorages. This can lead to an incorrect arrangement of rebars and to severe problems in the structure. Anyway, it is advised to place some reinforcing bars in the opposite sides of the anchorage blocks to make it non brittle.

4.4.2 - Segments on abutments

Segments on abutments have to transfer much smaller forces to the supports than segments on piers. On the other hand, the distribution forces are much greater due to the fact that all of the external tendons are anchored in the same section. For this reason it is advised to place a transversal prestressing to reduce the passive reinforcement and make concreting easier. This prestressing enables also a cracking control.

The design principles are the same as for the segments on piers. As the height is constant, the phenomenon of lateral thrust due to the compression exerted by the lower slab does not exist.

The balance of the end strut will have to be studied very carefully. In general, it is sufficient to anchor two longitudinal tendons in the inferior angle above the support.

When concreting these segments, generally with a inner wood formwork, it is important not to wait too much before stripping not to obstruct the shrinkage.

Furthermore, it is necessary to stiffen the end of the upper slab under the pavement joint in order to take up the localized flexion forces at this edge under the effects of the moving loads.

4.5 - Localized forces and reinforcements

4.5.1 - Distr ibution of forces caused by the prestressing anchorages

In general, the distribution of prestressing is verified in accordance with the instructions in Appendix 4 of the BPEL 91, revised in 1999. However, as this article features several ambiguities or omissions, the following specific additions should be made – while awaiting modifications to this appendix.

As it currently stands, Eurocode 2 does not have a chapter about the distribution of concentrated loads.



4 .5 .1 .1 – Di s tr ibut ion in the hor izonta l p lane

For the regularization length, it must not be assumed that the bridge deck is simply “rotated” through 90°. This would give an excessive length, resulting firstly in very low shear forces and the use of insufficient reinforcements, and secondly, in these reinforcements being positioned too far from the point at which the forces are applied. It must be remembered that the cracks which are observed in examples of the distribution of concentrated efforts always appear near the anchorage. It is recommended to use half of the width of the bridge deck in the case of a box girder.

4 .5 .1 .2 – Cont inui ty t endon anchor b locks

Reinforcement bars for the anchor blocks are determined in accordance with the instructions in Appendix 4 § 2 of the BPEL 91, revised in 1999.

It should be remembered that it is highly inadvisable to situate anchor blocks or tendons inside the concrete in curved (cf. § 4.2.3-2) or even straight lower slabs, and that it is preferable to place them in line with the gussets at the junction with the web.

The transverse reinforcements in these anchor blocks must tie the blocks into the rest of the section.

The following reinforcements must be used:

• Reinforcement bars at the top of the anchor block in order to tie the block into the neighboring box girder wall (A1 reinforcements)

• Reinforcement bars taking up the radial thrust when the tendon deviates (A3 reinforcements)

• Tie bars for the rest of the anchor block (A2 reinforcements).

The aim of the calculations is to verify the safety at rupture for cracked concrete. However, in order to facilitate these calculations, the problem is compared with a non-cracked state, considering the anchoring force at the

service limit state and limiting the stress in the reinforcements to es f3

=σ 2

For the A1 reinforcements, the cross section is equal to : s

FAσ

2,01 = with F being the force at the anchorage.

This represents nearly all of the “surface” and “spalling” reinforcements described in the BPEL

For the A3 reinforcements, we simply use F sin α according to the deviation plane of the tendon; this value is normally around 0.2F.

Finally, for the A2 reinforcements, a maximum value of 0.2F is also used due to the fact that the prestressing force is directed towards the concrete and it thus exerts a component that is perpendicular to the “horizontal” calculation axis.

The areas of reinforcements in question must be the sum of the cross sections in both planes (horizontal and vertical). For example, two sections of reinforcements must be considered for A1 and the same applies to A2 and A3.

The reinforcement elastic stress shall be taken with its real value, because it is a ultimate limit state verification. For example, with fe=500 MPa for classical reinforcement Fe E 500 (no limitation to 400 MPa). Because the



excess of reinforcement leads to concreting difficulties, we have to be careful not to overdimension this zone. Furthermore, it is important to respect the concrete cover – not too small, not too high – to guarantee the concrete durability.

(For further details, see "bulletin Ouvrages d'Art" from Sétra n°11 from January 92 and comments and observations in n°12 from July 92 and n°14 from March 93.)]

Fig. 4.24 – Reinforcement of an anchor block

4 .5 .1 .3 – Trac t ion re in forcements

Traction reinforcements may be necessary to take up the traction due to the obstructed shortening of the concrete, behind the anchor blocks. These reinforcements are determined in accordance with the instructions given in Appendix 4 § 2.3 of the BPEL 91, revised in 1999, by limiting their length near to tendon.

4 .5 .1 .4 – Externa l t endons

The major characteristic of the external tendons is their great individual power which, added to the fact that the force is obviously applied outside the concrete, results in the need to ensure that such large forces are securely anchored. Mistakes in this area have sometimes led to complete failures which could have been avoided with a minimum of forethought at the design stage.

In the first place, it is a matter of common sense to position the anchorages for external tendons in the crossbeams as close as possible to the webs and slabs in order to transmit the forces as directly as possible towards the walls of the box girder. Transmission via compressed concrete struts is always the most efficient method.

Furthermore, it is essential to make the anchoring elements thick enough (in the longitudinal direction of the bridge deck) to ensure that they are capable of transmitting most of the force. A lack of thickness results in punching shear in the element in relation to the box girder tube which cannot be taken up by the reinforcements alone.

Finally, it is sometimes more appropriate to foresee a phasing which limits the dissymetry of tensioning forces, rather than thickening the anchorage blocks to resist an inappropriate intermediary phase.

4.5.2 - Shear keys of prefabricated segments

In prefabricated structures, the segments have multiple shear keys designed to transmit the shear force. The shear reaction is considered to be taken up over the shear keys cross-section according to the following formula:

στ += tjb f65,0 with



ftj characteristic tensile strength of the concrete

σ normal stress at the centre of gravity of the section

The shear keys alone have to take up the shear force before polymerization of the adhesive.

A conventional shear keys such as the one shown hereafter (cf. Fig. 4.25) can take up:

bV bad .10,0.τ= with b representing the width of the shear key (0.10 is the height of the keyshear (Vn+1)

In certain situations in which there is a rapid rate of assembly, several segments may be lashed before the first joint has had time to polymerize (up to four segments on the Ile de Ré bridge, for example). The number of shear keys required is calculated accordingly: it is considered that the shear force of n segments is taken up by the shear keys alone in the first section at the end of polymerization. Because some of the shear keys could break during stripping, it is necessary to foresee additional keys.

Once the adhesive has polymerized, the shear force is taken up throughout the entire height of the web, as for cast-in-situ structures.

It is essential that the shear keys leads to a web side, for the glue to evacuate when compressing the joint : for evident aesthetical reasons, we make the keys lead to the inner side of the box girder. Furthermore, shear keys have to be placed in the upper and lower slab to prevent the shifting of the slabs. Finally, in the case of variable height decks with vertical joints, these keys take up the the vertical component of the compression in the lower slab which slopes gradually towards the supports.

It is advised to compress the joint section with 0.2 MPa in order to spread the glue in all the section.

Fig. 4.25 – Prefabricated segment crowns

4.5.3 - Deformation of prefabricated segments

It has already been mentioned in paragraph 4.3.2.4, that extremely wide structures, which are becoming increasingly common, have specific behaviors and a reduced effective slab width. In the case of prefabricated segments, they suffer from a problem that increases with width, although this phenomenon is shared by all prefabricated structures: a transverse “banana-shaped” deformation occurs in the horizontal plane due to the thermal gradient between the segment in the process of hardening and the segment that has already been cast.



This causes the joints to open up when the segments are brought together and thus leads to a non-uniform distribution of the stresses (in the transverse direction), which can result in cracking at the ends of the joints. [For further information, refer to the article in the PCI journal - July-August 1995]. In certain extreme projects, an accumulated deformation of 24 mm can occur over a span of approximately 30 meters in length.

Fig. 4.26 – Deformation of prefabricated segments

4.6 - Rules to combine passive reinforcements The stresses to be taken into consideration for the calculation of non-prestressed reinforcements result from:

• Transverse flexion

• General shear force (including torsion). The tangential stresses accompanying the general or localized flexion stresses result in shear stresses which are added to the shear stresses due to distribution described hereafter

• Localized forces (reactions from the support system, application of the cantilever or continuity prestressing, forces due to the site loads or form travelers). The distribution of these forces in the structure gives rise to stresses which are added to the shear stresses described above.

The reinforcements include:

• A standard transverse reinforcement designed to take up the general shear force

• An additional reinforcement positioned in proximity to the concentrated efforts in order to take up the distribution of these forces.

It should be noted that the distribution forces are only high for the external tendons, firstly due to their high individual power, and secondly because several of them are placed in the same section (usually on a support). Cantilever tendons, like continuity tendons, are less powerful and it is rare to find more than one pair of them in the same section, which results in moderate distribution.

The following rules must be observed:

• The combination of shear force and torsion reinforcements is carried out according to Articles 7.6.54 of the BPEL 91, revised in 1999 and A.5.4.4 of the BAEL 91, revised in 1999



• The combination of dispersion and shear reinforcements is carried out according to Article 4 of Appendix 4 of the BPEL 1991, revised in 1999:

⎪⎩

⎪⎨

⎧

⎩⎨⎧

+

=

21

2

1

5,1min

maxAA

AA

Acis with A1 distribution reinforcements

A2 shear force and torsion reinforcements

• In the slabs, there is no combination of tie bar reinforcements with the transverse flexion reinforcements according to Article A.5.3.2 of the BAEL 91, revised in 1999. However when shear stress are close to limits or in the case of very important distribution stresses, we will apply the combination rules quoted below for webs (zone of anchorage at the end of deck for example).

Par t i cu lar case o f webs

In the webs, we shall place reinforcements with a total section of on the external side and on the internal side must be implemented in such a way that, using the following notation for the sections used to calculate the flexion reinforcements:

eA iA

Afl ext Flexion reinforcements, external side

Afl int Flexion reinforcements, internal side

the following formulas are observed:

int

2

2

cise f

cisi f

AA k A

AA k A

= +

= +

l ext

l

cis

Obviously, we have to take up the shear force on the one hand and flexion on the other hand i.e. place a minimum reinforcement of:

i eA A A A= + ≥

Pr inc ip le

Indeed, the combination of reinforcements must firstly take account of the non concomitance between the flexion forces. In a single horizontal section of web, a loading case giving flexion reinforcements on the external side of Afl ext will not give reinforcements on the internal side Afl int ≈ 0 (except in the case of incorrect dimensioning requiring the use of compression reinforcements). As a consequence, the reinforcements on the opposite side may take up the shear force, as this does not require a specific position in the section. Thus, it is not necessary for the areas of flexion and shear to be added up. [for further information on this theory, see the Article from D. Le Faucheur on this topic in the "bulletin Ouvrages d'Art" from Sétra n°41 October 2002].

Remarks

The coefficient k represents the part of additional reinforcement necessary to take up the shear force. It is equal

to : 2 sin cos3

u

bu u u

kf

τβ β

=



τu being the shear stress at Ultimate Limit State (ULS) and bu the angle of the strut associated with the shear force and limited to 30° (in case of casting in two phases, the value of bu is 45°). The ultimate compressive

strength of the concrete is equal to 0,85 fcbu

c

fθ γ

= .

fc is the characteristic compressive strength of concrete.

The theory quoted above use concomitant load cases. The complete study would be a useless complication. To simplify we can consider separately the characteristic combination for shear stress and the one for transversal flexion. It is then justified to take θ=0,85 (for short term loads). In this hypothesis, the coefficient k is equal to :

0,444 sin cosu

c u

kf

τ

uβ β=

It has to be noted that this is a ultimate limite state calculation. As a consequence, the reinforcements for flexion has to be calculated at ULS and not at Service Limit State (SLS) as it is the case for detrimental cracking. Otherwise it would be too severe and not coherent with the theory developped in this article.

This calculation principle is determining only for very thin webs. Indeed, the transversal flexion use a great part of its capacity and consequently it is necessary to complete the reinforcements to take up concurrently the shear force.

Similarly, it is necessary to consider consistent loading cases for the accumulation of reinforcements:

• If we consider the construction stages, maximum flexion is obtained when the bridge is in service, whereas distribution is lower due to the existence of a certain symmetry in the anchoring forces on supports, or due to losses of tension in the cables.

• Geometrically, for a cantilever tendon anchored in the height of the web, the transversal flexion is maximal at the top of the web where as the combination of general shear force and distribution force is under the anchorage (because shear stresses have the same sign under the anchorage and opposite sign above the anchorage).

Three zones can be distinguished for the reinforcements:

• Transverse reinforcements in the upper slab with tie bar reinforcements

• Transverse reinforcement of the webs with shearing and distribution force frames

• Transverse reinforcement of the lower slab with tie bar reinforcements.

Upper s lab

As mentioned above, the tie bar reinforcements must not be added to those determined by transverse flexion. In both cases, relatively large cross sections are obtained.

Webs

It is usually possible to limit the loading cases with regard to transverse flexion. A symmetrical loading case produces maximum flexion in the webs, whereas offset trucks produce maximum torsion and give a lower level of shear force.



Lower s lab

In the lower slab, transverse flexion forces are reduced due to the distribution of the imposed loads from the upper slab through the webs. In the case of very wide structures, attention should be focused on the relatively large tie bars between this slab and the web. This is the reason for the very long gussets which are usually used in this type of structure.

4.7 - Recommended configurations for reinforcements This is an appropriate point to offer instructions and advice with a view to obtaining reinforcements that are satisfactory in terms of the behavior of the structure and feasible to implement. Bridge decks built by the cantilever method consist of box girders whose components are quite thin and are thus subjected to significant stresses. It is important to use reinforcements which are properly designed and properly constructed.

Upper s lab

In general, it is preferable to position the transverse reinforcements (main bars with larger diameters) in the external layer and the longitudinal bars (secondary bars) in the internal layer.

When the slab is transversally prestressed by tendons, it is advisable to position them underneath the two previous layers, especially as this allows them to drop down inside the slab in accordance with bending moment, without being obstructed by longitudinal reinforcements.

In order to improve the casting quality of the slab and the webs, no more than two transverse reinforcements and one stirrup (i.e. three reinforcements in a plan view) should be placed side by side.

Given that it is common to find prestressing ducts in the upper slab, it is necessary to position duct supports sufficiently closely together in order to prevent the tendon from wobblingand make sure that there is no risk of the slab spalling once the tendons are stressed. The recommended spacing is approximately 0.50 m to 0.75 m. Furthermore, to avoid reinforcements deformation which could give an unsufficient reinforcement for the durability of the structure, it is necessary to place either some chair spacers between the two reinforcement layers, or some rectangular stirrups as it is the case in the lower slab (Fig 4.27 and Fig 4.29).

Fig. 4.27 – Reinforcement of the upper slab



Fig. 4.28 – Reinforcement of the upper gusset

Lower s lab

In proximity to the piers, the lower slab is submitted to very high compression. It is not recommended to use compressed reinforcements to take up this force if the slab is of insufficient thickness. Indeed, a spalling force appears at the ends of compressed bars, which weakens the overlapping areas and requires reinforcing with tie bars. Information concerning the precautions to be taken with compressed parts can be found in § A.8 of the BAEL 91, revised in 1999).

It is distinctly preferable to:

• Thicken the slab, being aware that the weight gain is small as the variation in thickness is generally parabolic and that this thickness is only apparent near the supports

• Or increase the compressive strength of the concrete in the bridge deck.

In all cases, the slab tends to delaminate due to compression, hence the need for tie bars. Consequently, it is strongly recommended to place reinforcement rectangular stirrups rather than concrete chairs within the slabs in order to support the upper layers. In addition, the rectangular stirrups add greater rigidity to the reinforcement and thus help to improve the cover of the reinforcement bars.

Fig. 4.29 – Reinforcement of the lower slab

Lower gusse t

An example of the reinforcement of the lower gusset is provided below. The tendon ducts must be supported by a special structure, which must be absolutely welded to the main reinforcement. Stiffness is necessary to prevent the ducts from shifting during the concreting under buoyancy, which could lead to very strong radial thrust when tensioning with disastrous consequences.



Fig. 4.30 – Reinforcement of the lower gusset

Webs

As for the slabs, the transverse reinforcements are positioned in the external layer. Considering the depth of the decks of bridges built by the cantilever method, it is very rare for the web reinforcements to be contructed in full rectangular stirrup. They generally consist of two overlapping parts.

It is essential to avoid overlaps along the walls, i.e. in the standard section of the web. There are two possible ways to resolve this problem:

• By using two L-shaped parts, which overlap in the full thickness of the upper and lower gussets

• Or by using large U-shaped part with a small U-shaped part as a top reinforcement, with the overlaps only occurring in the upper gusset (Fig. 4.31).



Fig. 4.31 – Webs reinforcement

The transverse reinforcements are joined by transverse rebars embedded inside the web, generally in the form of stirrups ending on one side in a hook and on the other in a simple angled return. For the sake of durability, it is better to place the hook on the external side of the bridge deck. The angled return should not be placed parallel to the wall; instead, it should be angled towards the inside of the bridge deck (Fig. 4.32). At least four stirrups should be used per square meter or two rectangular stirrups if this solution is used.

Longi tud ina l re in forcement

In the case of segments cast in situ, the longitudinal reinforcement cannot (save exception) respect the rules of alternated overlapping according to the Article 6.1.23 from BAEL, because of a problem of lack of space given the dimensions of the segment.

Fig. 4.32 – Reinforcements of webs



Phenomenon spec i f i c to mass i ve par t s

The segments on piers are massive parts for which it is advisable to carry out a specific analysis in order to evaluate the stresses due to thermal shrinkage during differential cooling in the body of the concrete after hydration of the cement. The temperatures rise in direct proportion to the volume and thickness of the cast concrete and its hydration heat. This analysis may lead to the development of an optimized sequence of operations for the segment on pier, taking account of the type of cement and any provisions that might be implemented in order to promote the regular and homogeneous cooling of the concrete. Whatever the circumstances, it is necessary to use crack control reinforcements capable of controlling any peripheral cracking in this structure. In addition, this rise in temperature does not only produce forces; it can also lead to internal chemical reactions within the concrete itself, known as sulfate reaction. These can cause severe problems in the structure of the bridge itself.

The risk of such reaction appears only for very large thickness, around one meter for example.

Fig. 4.33 – A large SOP



5 - Cantilever stability This chapter is entirely devoted to the problem of the stability of cantilevers in the construction phases. It successively covers the causes of instability, different stabilization solutions and finally, the verifications to be carried out.

5.1 - Principle of cantilever stability During the construction of segmental concrete bridges using the balanced cantilever method, it is necessary to guarantee the stability of the cantilever arms on their pier before they are joined to the neighbouring cantilever or to the cast-on-falsework section on the end span near to the abutments.

It is essential to prevent the cantilever from tipping on the pier crosshead. To evaluate this risk, two types of situations leading to imbalances must be considered:

• A temporary situation which occurs during construction when the cantilever is unbalanced due to the weight of a segment that is built or installed before its symmetrical counterpart is in place, asymmetrical site loads or a rising wind acting on one of the half-cantilever

• An accidental situation corresponding to the collapse of a form traveler or pre-cast segment.

Fig. 5.1 – Prefabricated cantilever under construction

In both cases, the combinations of actions to be used relate to the static equilibrium limit state.

Two families of combinations should be analysed: basic combinations corresponding to the first situation and accidental combinations corresponding to the second. In the first case, it is verified that the cantilever does not detach from its temporary supports; in the second case, a slight detachment is tolerated with a limited overstressing of the stressed reinforcements that are used to secure the cantilever to its pier.

It is also important to verify the strength of all of the mechanical components which contribute to the stability of the cantilever and of the whole pier and its foundations. This second verification relates to the strength ultimate limit state. For simplicity’s sake, the partial safety factors for the combinations used for this verification are identical to those used in the calculation of stability.



This chapter only provides general recommendations applicable to standard situations. Thus, the loads to be used and the combinations of actions to be analysed must be adapted according to the sequence of construction operations and the equipment used on site. Furthermore, for structures featuring large spans, built high up on exposed sites, an additional ten-year wind value must also be carried out. It should also be noted that the rules included in this chapter do not include construction errors or the failure to comply with construction procedures relating to the casting or assembly of segments or to the movement of form travelers or assembly equipment.

Before the construction of the first cantilever, the contractor must supply the site with accurate, dimensioned plans, showing all of the systems to be implemented along with their quality and tolerances. A specific procedure must describe all of the construction phases, specify the order of phases that must be observed and provide warnings about any dangerous events with a reasonable probability of occurrence. This procedure brings together the different design calculations and construction methods. Drafted by the site’s Organization and Methods Department, it must be approved by the engineering office and the site manager and must be read by everyone involved in the construction of the bridge deck, especially the site foremen and sub-foremen.

The operations laid down in this report cannot be modified without the prior permission of the author and of the engineering office which performed the stability verifications.

5.2 - Stability systems for cantilevers

5.2.1 - Different stabil ization methods for canti levers

To a large extent, the choice of the process used to stabilize the cantilevers depends on the general design of the structure (see Chapter 2). The span arrangement, the final support system and the design of the piers are obviously major considerations when choosing this system.

Six main solutions can be used to stabilize cantilevers on their piers. We shall now examine them in detail.

5 .2 .1 .1 – S t i t ch ing by pres tress ing

Stitching via prestress tendons is the most widely used method for stabilising cantilevers during the construction (Fig. 5.2). In principle, this is the most economical method for spans of less than 120 meters in length and whose relatively massive piers offer a large crosshead surface. The method consists of tensioning vertical reinforcements in order to secure the segment on pier to its supports.

Fig. 5.2 – Stability stitching by prestressing



During construction, the segment on pier rests on a set of temporary blocks on either side of the bridge bearing. The use of the definitive bearings during the construction of the cantilevers is not recommended because there is a significant risk of damage and, in any case, it is essential to adjust the bearings at the end of construction.

The stitching reinforcements are positioned at the side of the temporary blocks. Their upper anchorages are generally placed in temporary prefabricated anchor blocks, positioned on the upper slab, sometimes on a metal cross beam (Fig. 5.3). They then drop down through the segment on pier passing close to the webs, next to or inside the support crossbeam.

Fig. 5.3 – Section through the SOP with its stitching tendons

In the lower end, the tendons are either tied off inside the pier shaft or anchored in the usual way. In the latter case, the anchorages may be situated on the side of the foundations or in anchor blocks housed on the inside of the piers if they are hollow.

The stitching prestressing is generally centred on the centreline of the pier. In certain specific cases, it may be beneficial to reduce the number of tendons by offsetting them longitudinally. This applies:

• When a given direction of assembly or order of casting for the segments must be followed

• When the half-cantilevers are asymmetrical or made from different types of concrete.

In these specific cases, it is always important to check what would happen in the event of an error in the construction process.

For prefabricated structures, a longitudinal offsetting from the base of the incremental launching beam produces a similar effect (due to the support reaction caused by its weight and its anchoring tendons). In the case of curved cantilevers, it is also possible to offset the tendons transversally in order to balance out the torsion moment due to the curvature of the bridge deck.

Prestressing tendons are sometimes replaced by prestressing bars. However, this solution is not recommended, because, in the event of an incorrect alignment between the recesses built into the segment on pier and the pier crosshead, the bar may be subjected to parasitic flexion which could cause it to fail.

5 .2 .1 .2 – Temporary p i l ings

This method consists of increasing the center distance between the temporary support blocks by placing them on temporary metal or concrete pilings (Fig. 5.4). This is only feasible when the bridge deck is situated at a reasonable height above the ground (less than 15 meters or so).



Fig. 5.4 – Stabilization of a cantilever using temporary pilings

This method is used on terrestrial sites in the following situations:

• For total lengths in excess of 100 meters

• When the pier head dimensions are reduced, often for architectural reasons

• When the pier shafts do not have enough resistance to flexion to stabilize the cantilever on their own.

This is a viable solution for aquatic sites, provided that the pilings are supported on the foundation bulkhead for the pier.

The cantilever is usually stabilized by two pilings positioned symmetrically in relation to the pier. However, a cantilever may sometimes be stabilized by a single piling, especially when:

• The site is obliged to follow a fixed order of assembly or casting

• A difference in weight due to the geometry or to the use of lightweight concrete affects both of the half-cantilevers

• The structure is a portal bridge, as the portal legs cannot take up the vertical loads until the cantilevers are connected.

Vertical prestressing on pilings usually completes this system (Fig. 5.5). If a single piling is used, this prestressing is essential in order to prevent the side opposite the piling from tipping over.



Fig. 5.5 – Stability provided by a single piling

This prestressing may also be replaced by a counterweight placed on the same side as the piling (Fig. 5.6, [JAE 00]).

Fig. 5.6 – Cantilever stability by counterweight

For information, a variant also exists for prefabricated structures. This involves attaching the launch beam to one of the half-cantilevers via compression bracing in order to stabilize it.

5 .2 .1 .3 – Externa l tendons or t emporary s tay ing

Stitching tendons may be positioned outside the pier in order to increase their efficiency. In this case, they are anchored in the first cantilever segments and pass outside the pier shaft (Fig. 5.7). In the lower section, they are anchored on massive counterweights on land, or fixed to the pier foundations (especially on aquatic sites where the lower anchorages can be housed on the bulkhead). The tendons must be injected for adhesion to the foundations. They must be protected against corrosion and damage caused by impacts to their upper sections.

This method is especially used:

• For overall lengths of more than 100 meters

• When the dimensions of the pier head units are reduced and do not allow for a sufficient center distance between the stitching tendons (Fig. 5.8, [JAE 00]) ;



Fig. 5.7 – Cantilever stability by external tendons

Fig. 5.8 – Stability via tendons outside a pier with a small crossheadl

A genuine system of temporary staying can also be used to resist wind-related dynamic stresses for tall structures with large span lengths or more modest structures in windswept sites: Fig. 5.9 [BOU 94.3] and [GAC 98]). In this situation, the stays are anchored to a segment situated at a third or a quarter of the length of the half-cantilever in the upper section and to a counterweight block on the ground equipped with vertical ties or pilings working in traction. An efficient and economical anchorage can also be provided by attaching the stays to the foundations of neighbouring piers.

These stays are very effective at absorbing the rocking motion around a horizontal axis perpendicular to the centerline of the bridge deck. They supplement the fixed support or vertical stitching produced by the tendons on piers. The stays usually consist of external prestressing tendons at moderate tension (30% of the tendon’s maximum tension).

Fig. 5.9 – Staying of a cantilever on the Tanus bridge

Certain angled stays may also be used to limit the torsion of the pier under asymmetrical horizontal forces due to the action of wind on each half-cantilever (or under dynamic wind effects).

In addition, we should mention that it is sometimes better to stay the pier rather than the cantilever, especially for very tall structures that have a short total span (although this is quite a rare occurrence).

5 .1 .2 .4 – Closure o f the end span

If the structure has spans of very unequal lengths or very short end spans, it is possible to use the closure of the small spans to stabilize the adjacent half-cantilevers (Fig. 5.10). At the start of the construction of the half-cantilever, the structure must be stabilized using traditional methods. When the cantilever reaches the middle of the shorter span, the central connection segment is assembled. The longer span is then built by over-cantilevering, using the weight of the rear span to counteract the imbalance.



Fig. 5.10 – Closure of a rear span with counterweight and extended cantilever

5 .2 .1 .5 – Embedding on a p ier

When the cantilever is permanently embedded on its pier, the stability calculation is given by the strength calculations for the pier shaft and foundations (Fig. 5.11).

Fig. 5.11 – Embedding of the cantilever on the pier

Fig. 5.12 – Pier with double shafts

For structures subjected to very strong winds, additional stays are often necessary, requiring extra verifications under dynamic wind effects (see 5.2.1.3).



This solution is also required in the case of double pier shafts (Fig. 5.12).

5.2.2 - Design of pier head units

In the most common situations, the pier heads must be designed to receive the following components (Fig. 5.13):

• The permanent bearings, normally consisting of elastomeric pot bearings

• Stability blocks or temporary support blocks

• Stitching tendons

• Jacking points for cantilevers under construction or nearing completion, or for changing bearings

• Systems for inspecting and testing bearings in service

• Seismic stops for protection in the event of earthquakes or impacts from boats.

The size of the permanent bearings varies enormously according to the structures: from 0.50 x 0.50 m for structures with short overall spans to 1.10 x 1.10 m or more for structures with large spans.

Suppliers’ catalogues are useful for evaluating the surface area required for elastomeric pot bearings. These give the plan view dimensions according to the maximum reaction under rare combinations at the service limit state.

In the absence of such catalogues, it is possible to estimate the diameter of the pot bearing by considering that the elastomer stress reach 30 MPa under these same combinations. The dimensions of the plate can be estimated by considering that the stress on the concrete of the pier is limited to 0.6 fcj.

For modestly-sized structures in which the bridge deck rests on laminated rubber bearings, this surface area is calculated using a pressure of 13 to 15 MPa at the SLS under the same conditions as mentioned above.

In both cases, the minimum projecting ledge on the surface of the pier is 15 centimeters.

Fig. 5.13 – Diagram showing pier head design



Fig. 5.14 – Leveling and adjusting jacks and permanent bearing

The surface area of the temporary blocks is determined by calculating the stability of the cantilever (see paragraph 5.5.2). Solid blocks may also be replaced with sand boxes which can be removed without having to raise the bridge deck.

The jacks must be capable of raising the entire cantilever before the placement of the closing segment in order to insert the permanent bearings and change the bearings when the structure is in service.

However, for the changing of the bearings, it is possible to reuse the area of the crosshead that had previously been reserved for the temporary blocks. Therefore, the raising of the deck must only be considered in the construction phase. For information, 500-tonne jacks have a diameter of 40 centimeters. They must be placed on metal blocks (e.g. measuring 0.50 x 0.50 m) in order to limit the stress on the concrete to approximately 20 MPa. The limit stress values obviously depend on the compressive strength of the concrete in the pier head units. These are given in paragraph 5.5.2. It should also be noted that the clearance required between the underside of the bridge deck and the bearing base is approximately fifty centimeters for jacks with a capacity of 500 tonnes.

5.2.3 - Design of the segment on pier

From the outset, the design of the segments on piers and pier head units must incorporate the constraints associated with the cantilever stability systems. Indeed, stability systems which cross the segment on pier vertically (prestressing tendons or bars) interfere with the cantilever tendons situated in the upper gussets, the deviator tubes used to house the continuous external tendons and the dispersion reinforcements in the anchorages for the external tendons on the pier (Fig. 5.16).



Fig. 5.15 – Pier head unit on the Ile de Ré bridge

Fig. 5.16 – Stitching of a cast-in-situ segment on pier

It is also necessary to cross the highly reinforced areas of the lower slab, in light of the problems concerning the transmission of temporary and permanent support reactions towards the webs of the box girder.

In all cases, the stitching system shall be designed to transmit the forces towards the support blocks as directly as possible. In the upper part, the tendons must be anchored in thick areas.

The stitching tendons pass into the crossbeam on the pier if it is very thick or close to it and in proximity to the webs if it is thinner (Fig. 5.17). A system consisting of anchor blocks, a distribution beam and vertical uprights must also be envisaged for the transmission of the jacking force when the cantilever has been completed.



Fig. 5.17 – Adjustment of a prefabricated segment on pier

5.3 - Actions to considered The loads to be considered in this particular phase in the building of a cantilever correspond to loads in a construction situation. For this situation, the BPEL 91 distinguishes between dead loads (G), construction loads whose size and position are known (QPRC), random construction loads (QPRA) and finally, variable actions such as the wind (W) or a thermal gradient (Δθ). Accidental situations are also considered; these include dead loads, site loads and an accidental action (FA).

It should be noted that:

• The loads defined hereafter are not described in any statutory document; however, they represent the rules of good practice in the field and have been successfully used since 1975. Thus, it is essential to formalize these loads in the contract

• The proposed design methods depart from the rules for the creation of combinations in the Directives Communes sur le Calcul des Constructions (Common Guidelines for the Design of Constructions) of 1979 (DC 79). This must be specified in the Special Technical Clauses.

5.3.1 - Dead loads

The evaluation of dead loads, for this particular phase in the construction of the cantilever and for all of the construction and service phases for the structure, must be performed with the greatest of accuracy, while taking account of the precise geometry of the bridge decks and particularly of the crossbeams, deviators, anchor blocks and the other morphological characteristics of the structure.

The weight G of the cantilever is calculated using a unit weight γ of 24.5 KN/m3 according to the formwork plans (strictly speaking, the BPEL 91 fixes the concrete’s unit mass at 2.5 t/m3).

If high or low density aggregates are used, the measurement of the unit mass γt of the concrete used for the bridge deck (prestressed or reinforced) is based on the unit mass of ordinary concrete γb, using a laboratory sample of concrete without reinforcements using the following formula:



( )γ γ ρ γt b b= + ×7,85

7,85 -

with ρ = total ratio of stressed and non-prestressed reinforcements (in t/m3).

A figure of ρ = 0.18 at 0.22 t/m3 is normally used for bridges built by conventional cantilever segments. It should be noted that HPC is denser than traditional concrete. For this type of concrete, approximately 50 Kg/m3 should therefore be added to the aforementioned values.

The weight of a half-cantilever situated on the unbalanced side is increased by 2% (Gmax), whereas the weight of its corresponding half is decreased by 2% (Gmin).

For the rough calculations, simplified formulae can be used to calculate the weight of a cantilever. For example, if the depth of the bridge deck varies parabolically and the thickness of the lower slab varies in linear fashion, the approximate weight of the half-cantilever and the position of its centre of gravity can be determined using the following formulae (Krawsky’s formulae), with B1 designating the section on the pier and B0designating the crown section:

3l)B 2 (B P f01 γ+

=

)B 2 (B4l)B 5 (B d01

f01

+×+

=

with lf designating the length of the half-cantilever.

Fig. 5.18 – Evaluation of the weight of a half-cantilever

(NB: the selfweight of the half-cantilever calculated using this formula does not include the weight of the crossbeam on pier or the weight of the anchor blocks, deviators and ancillary parts situated on the span).

This simplified method allows for a manual approach, which can be used for the preliminary calculations for the structure. It is included here for illustrative purposes but it is not intended to replace precise calculations which remain indispensable.

For curved bridges, it is obviously important to consider the offsetting of the weight of the cantilever, which creates a transverse moment in the pier.

5.3.2 - Variable execution loads

The BPEL makes a distinction between site loads whose size and position are known, and random loads, for which a fixed allowance must be made.



5 .3 .2 .1 – Known s i t e loads

Known loads are loads whose weight and position can be specified in each phase of construction, e.g. launch beams, cranes used assembling segments, form travelers, etc. (Fig. 5.19). If there are significant uncertainties concerning weights or positions, maximum and minimum characteristic values are determined and applied in the most unfavorable way.

Fig. 5.19 – Example of known site loads

For cast-in-situ structures, this mainly concerns the weight of the form traveler, expressed as QPRC1, whose standard value varies between 0.30 and 0.90 MN according to the length of the segments and the width of the bridge deck. At the rough calculation stage, the weight of the form traveler is sometimes considered to be equal to half the weight of the heaviest segment. In reality, this weight is highly dependent on the system used to stiffen the form traveler under the weight of the fresh concrete. With complex systems featuring prestressing bars, the weight of the structural steel can be significantly reduced.

For prefabricated structures, known site loads mainly concern the reactions at the base of the launch beam during the installation of the segments.

In the calculations, these loads must be increased by + 6% on the side of the heavier half-cantilever or decreased by 4 % on the opposite side (QPRC1 max or QPRC1 min) according to the same principle as for the selfweight of the cantilevers.

5 .3 .2 .2 – Random s i t e loads

Random site loads (Fig. 5.20) correspond to the materials stored on the bridge deck (e.g. cable rolls), small equipment (e.g. compressors), staff and various climatic effects not considered elsewhere (rising pressure of wind under a half-cantilever).



Fig. 5.20 – Random site loads

The following loads are used to cover unknown site loads:

• An evenly distributed load (QPRA1) of 200 N/m²over a half-cantilever in standard situations (total span < 120 m). This load, which includes vertical wind force provided that the site is not exposed, is applied to the completed segments and the form traveler

• A concentrated load (QPRA2) of (50 + 5 b) kN applied to the end of the cantilever, at the far end of the last completed segment (b designates the width of the upper slab of the box girder expressed in meters); this load represents the weight of cable rolls, compressors, small equipment, etc.

These loads are arranged in such a way as to produce the most penalizing effect.

For structures with an overall span of over 120 meters, the intensities of the loads QPRA1 and QPRA2 must be calculated according to the equipment that is actually used on the site.

5 .3 .2 .3 – Vert i ca l w ind force

The load QPRA1 in the previous paragraph only includes the vertical wind force for structures with a total span of less than 120 meters.

For other structures, including those with more modest spans but which are exposed to frequent strong winds, for example in steep-sided valleys or in unstable areas where strong gusts of wind are common, it is important to consider an additional load.

The additional wind effect (Qw) is equivalent to a uniform load with an intensity of 100 to 200 N/m², depending on the characteristics of the site. It is essential to perform a specific study to analyze the nature of the site and the local climatic conditions before this load can be reduced for very large spans (over of 200 meters).

This distributed load applies in a vertical direction from the bottom to the top on the horizontal frontal area of a half-cantilever. Longitudinally, this force applies from the end of the form traveler to the row of temporary blocks situated on the same side (or, more simply, to the centerline of the pier). Transversally, the width of application is the width of the upper slab of the box girder.

Furthermore, in exceptional cases, (tall structures with a large overall span and relatively flexible piers), a dynamic study is essential in order to evaluate the behaviour of the cantilever on its pier and determine how to stabilize the cantilever before the closing segment has been completed (staying, compression bracing, etc.). This is covered in paragraph 5.4.3 of this chapter.



5 .3 .2 .4 – Hor izonta l wind force

Horizontal wind force only needs to be considered in particular cases: for tall structures in sites which are exposed to strong and irregular winds caused by the morphology of the site. Such places often include coastal or mountain valleys or sites exposed to winds that are renowned for their intensity.

In this case, we consider that one of the half-cantilevers is subjected to a uniform load of QWt. This load must be evaluated on an individual basis for each project. In general the load is derived from the CECM (Convention Européenne de la Construction Métallique – European Convention for Structural Steelwork) regulations. The intensity of this load depends particularly on the height of the bridge deck and the ruggedness of the site.

It should be noted that:

• For the calculation of the piers and the foundations, the whole of the cantilever and its pier should be loaded

• For very tall structures, the dynamic analysis prescribed in the previous paragraph must account for this horizontal wind force.

5.3.3 - Accidental actions

The collapse of all or a part of an empty form traveler or a prefabricated segment during the assembly process (FA) is allowed for by a dynamic increase coefficient of 2 in order to take account of the energy accumulated by the deformation of a half-cantilever affected by the fall. This amounts to reversing the direction of the weight the form traveler QPRC1MAX or of the last prefabricated segment on one of the half-cantilevers (Fig. 5.21).

Fig. 5.21 – Form traveler in the process of being moved

For a cast-in-situ structure, it is possible for any mobile load to collapse during one or more of the form traveler’s phases of movement. In the majority of cases, the calculations performed allow for the fact that the entire form traveler might fall. However, a lower value could be adopted if a specific analysis of the safety of the form traveler were to be carried out by the designers of this equipment at the start of the construction surveys (see Fascicule 65A of the French CCTG).

For prefabricated structures, it is possible for any part that is not lashed by prestressing to collapse during one or more phases of the assembly sequence.

5.4 - Combinations of actions during construction



Cantilevers must be verified with regard to:

• The ultimate limit state of static equilibrium, aiming to ensure the stability of the cantilevers on their pier

• The ultimate limit state of strength: for the different elements whose role is to provide stability and for the elements which are stressed during these phases, especially the pier head units, the piers and their foundations.

For each limit state, considering the nature of the actions, a distinction can be made between a temporary construction situation, relating to a verification under a fundamental combination, and an accidental situation, relating to a verification under an accidental combination.

During the construction surveys, these verifications must be systematically performed for the casting or assembly of every pair of segments.

As we have already mentioned, the rules described hereafter are not as strict as those in the 1979 Directives Communes sur le Calcul des Constructions (Common Guidelines for the Design of Constructions), according to which it would be necessary to apply a load factor of 1.1 to the the selfweight of one side and 0.9 to the selfweight of the other side. Therefore, it must be officially agreed in the Special Technical Clauses that these rules differ from the recommendations of the DC79, as they are not regulations in the legal sense of the term.

5.4.1 - Combinations in temporary construction situations (Type a)

For the verification of static equilibrium at ultimate limit states, the cantilever must not move from its temporary supports. If the cantilever is embedded on the pier, no static equilibrium verification is required, although the strength of the pier must be verified.

For the verification at ultimate limit states of strength, the different elements (blocks, tendons, pilings, temporary stays, etc.) and the supports and foundations are verified using partial coefficients of safety for the materials corresponding to the fundamental combination.

For cast-in-situ structures, the key phase at the pre-design level can be considered to be casting of the final pair of segments. It is assumed that both form travelers have been moved forward and that the casting of one of the two segments has been completed, whilst the casting of the other segment has not yet been performed, or the form traveler has been emptied due to a defect in the concrete.

Likewise, at the preliminary design phase for prefabricated structures, the cantilever is studied during the assembly of the final pair of segments. It is assumed that one of the two segments has been lashed to the end of the cantilever and has been released by the assembly equipment. The other segment has not yet been assembled.

The cantilever is therefore analysed with an imbalance of one segment.

It is essential to analyse this imbalance on a systematic basis, even if the sequence of assembly or construction operations calls for simultaneous operations. This is because:

• For a prefabricated structure, the perfect synchronization of operations cannot be guaranteed

• For a cast-in-situ structure, an incident during casting may lead to fresh concrete being emptied from one of the form travelers, even if casting is carried out simultaneously.

The following actions should therefore be studied:



For cas t - in - s i tu s t ruc tures (F ig . 5 .22 )

Combination A1: 1.1 (G max + G min) + 1.25 (QPRC1 max + QPRC1 min + QPRA1 + QPRA2 [+ QW])

Combination A2: 0.9 ((G max + G min) + 1.25 (QPRC1 max + QPRC1 min + QPRA1 + QPRA2 [+ Qw])

In these formulae, Qw refers to the additional wind action to be considered for structures with a total span length of more than 120 meters, or which are exposed to strong and frequent winds (see 5.3.2.3)

For pre fabr i ca ted s t ruc tures (F ig . 5 .23 )

Combination A1: 1.1 (G max + G min) + 1.25 (QPRC1 max + QPRC1 min + QPRA1 + QPRA2 [+ Qw])

Combination A2: 0.9 (G max + G min) + 1.25 (QPRC1 max + QPRC1 min + QPRA1 + QPRA2 [+ Qw])

The left-hand form traveler is empty

(n - 1 segments on left) The right-hand form traveler contains a segment

(n segments on the right)

Fig. 5.22 – Temporary construction situation to be considered for cast-in-situ structures

(n - 1 segments on left) (n segments on right)

Fig. 5.23 – Temporary construction situation to be considered for prefabricated structures

5.4.2 - Accidental construction combinations (Type b)

These combinaisons are used for verifications at ultimate limit states of strength under accidental combinations involving elements designed to provide the temporary fixed supports, and the supports and foundations supporting the cantilevers.

In an accidental situation, the structure must be capable of resisting the collapse of a form traveler (or of a segment in the case of a prefabricated structure).



In this case, the cantilever may be lifted off its temporary support blocks, but security is maintained by bringing the full capacities of the materials into play, e.g. in the case of temporary prestressing, the tendons could be overstressed.

For cas t - in - s i tu s t ruc tures (F ig . 5 .24 )

Combination B1: 1.1 (G max + G min) + FA + (QPRC1 max + QPRA1 + QPRA2)

Combination B2: 0.9 (G max + G min) + FA + (QPRC1 max + QPRA1 + QPRA2)

The left-hand form traveler is empty

(nv - 1 segments on the left) The left-hand form traveler contains a segment

(nv - 1 segments on the right)

Fig. 5.24 – Accidental situation to be considered for cast-in-situ structures

For pre fabr i ca ted s t ruc tures (F ig . 5 .25 )

Combination B1: 1.1 (G max + G min) + FA -+ (QPRC1 max + QPRC1 min + QPRA1 + QPRA2)

Combination B2: 0.9 (G max + G min) + FA + (QPRC1 max + QPRC1 min + QPRA1 + QPRA2)

(nv - 1 segments on the left) (nv segments on the right)

Fig. 5.25 – Accidental situation to be considered for prefabricated structures

5.4.3 - Specif ic rules for very tal l structures

Very tall structures are usually very sensitive to the action of the wind. Specific rules must be applied to them, not only to avoid penalizing them with an excessively high equivalent static pressure, but also to verify the behaviour of the cantilever under dynamic wind effects.

For large cantilevers, e.g. when the sum of the span length and of the height of the pier exceeds 180 meters, it is essential to perform a turbulent wind analysis at the ultimate limit state.

This specific dynamic analysis, which is carried out using one or more specialist wind effect programs (e.g. the French PCP program), is designed to assess the amplitude of the oscillations caused by wind turbulence on a flexible structure.



This calculation requires:

• A static description of the wind and its fluctuations (reference wind speed, ruggedness of the site, altitude, wind turbulence, etc.)

• A dynamic modal analysis of the structure, giving the deformities and durations of the fundamental modes of vibration in addition to the corresponding generalized masses

• The aerodynamic characteristics (drag, lift and moment coefficients) of the bridge deck and piers. (Some of these coefficients can by determined for simple shapes by applying the rules of Eurocode 1 – Actions du vent et de la neige sur les structures [Actions of wind and snow on structures]. Wind tunnel testing must be carried out for the others).

The accumulated static and dynamic effects are used to determine and verify the stresses in the concrete and the reinforcements for the pier shaft.

In the construction phase, the dynamic calculations are performed at the ultimate limit state only and by take account of the ten-year wind effect. In service, they are performed with a fifty-year wind at the ultimate limit state and also at the service limit state.

As the current regulations are quite limited with regard to this type of verification, the Special Technical Clauses must comprehensively describe the actions, the combinations of actions and the safety coefficients to be adopted.

The reader may also refer to the document entitled "Comportement au vent des ponts" (Behaviour of Bridges in Wind) published by the AFGC, in addition to the articles entitled "Pont de Tanus: Les études des effets du vent" (The Pont de Tanus: Wind Effect Analyses) [BOU 94.3] and "Le viaduc de Bourran à Rodez " (The Bourran Viaduct at Rodez [BOU 91] for additional details.

It is important to specify that the dynamic analysis of wind effects must be carried out at the design stage because it may raise questions about the design of the structure and also because the collection of data required for this calculation often takes quite a long time, which could cause problems with regard to the deadlines allowed for the construction surveys.

5.5 - Verification and dimensioning of the anchoring elements In this section, we shall specifically study the stability of cantilevers resting on two rows of temporary blocks and stitched onto their piers by two rows of tendons (Fig. 5.26). The verifications of the stabilizing elements for the other methods are presented in a more summary fashion in the following section.

For these calculations, the segment on pier is considered to be undeformable. The position of each block or temporary support includes an installation error of 5 centimeters (in the sense of a reduction in the space between these temporary supports).



Fig. 5.26 – System of stitching to a pier using tendons

5.5.1 - Calculat ing the number of cables

M and N are the stresses resulting from type A and B combinations. M and N are calculated for each of the four combinations A1, A2, B1 and B2. e is the distance between the centerlines of the two rows of temporary support blocks and d is the distance between one tendon and the opposite row of blocks (Fig. 5.27).

Firstly, we calculate the eccentricity of the resultant of forces M/N.

Fig. 5.27 – Geometry of the stitching system

In the event that M/N < e/2, there is no risk of the cantilever tipping over; in theory, this means that stitching tendons are not necessary; however, a minimum of two pairs of tendons are used for safety reasons (e.g. one pair of 12T15 tendons per row of blocks). We use:

2ia FeM

2NR +−= and 2ib F

eM

2NR ++=

With ( ) sp12F 0p2i ×σ×−×=

(force of a line of two tendons with p the % of losses)

( )pegprg0p f90,0,f80,0Min=σ

with fprg and fpeg the tensile strength and elastic limits and s the cross-section of the tendon.

The values of e and d are derived from the dimensions of the segment and the pier head unit. It is difficult to give advice with regard to the minimum values of e and d because they are highly dependent on the length of



the cantilever and the width of the box girder. Values of 3.00 to 3.50 m are common for e and d. This requires pier head units of between 4.50 and 5.00 m wide.

In the event that M/N > e/2, stitching tendons must be used to restore the balance of the cantilever. To calculate the number of tendons to be used, a distinction is made between type A and type B combinations.

5 .5 .1 .1 – Temporary cons truct ion s i tua t ion (A combinat ions )

The cantilever must not lift up. The prestressing must therefore compensate for the rising reaction force of block A under the action of M and N (Fig. 5.28).

0FeM

2NR ia ≥+−=

ib FeM

2NR ++=

with ( ) sp1nF 0pi ×σ×−×=

(force of n tendons of a line with p % of losses)

( )pegprg0p f90,0,f80,0Min=σ

with fprg and fpeg the tensile strength and elastic limits and s the cross-section of the tendon.

Fig. 5.28 – Forces in tendons and support reactions

Therefore, we have: ( ) 0pp12N

eM

snσ×−

⎟⎠⎞

⎜⎝⎛ −

=×

while still estimating the losses at p %.

5 .5 .1 .2 – Acc identa l s i tua t ion (B combinat ions )

Under the action of the resultant N and the moment M of the loads applied to the cantilever, the segment on pier remains in equilibrium due to the increase of the tendons tension ΔTg in a row of temporary supports and the compression Rb, of the blocks in the other row supports (Fig. 5.29).



Fig. 5.29 – Tipping of the cantilever with overtension of the tendons

The equilibrium of the forces applied to the segment on pier when it rotates at an angle of dα around a row of blocks and when the tendons lengthen or shorten, can be expressed in the following way:

ulgig FTFF ≤Δ+=

did TFF Δ+=

( )ded

TT

d

g

−=

Δ

Δ

( ) 0edFM2

NedF dg =−×++−×−

0NFFR dgb =−−−

Fg and Fd refer to the tensions in each line of tendons; Fi is their initial force, Fu1 is their limit tension at the ULS, with ΔTg and ΔTd being the variations in tension of each line of tendons (positive for a lengthening of the tendons). It should be noted that ΔTd is either negative or positive but less than ΔTg, according to the position of the blocks in relation to the tendons.

We obtain Fg and Fd according to Fu1 and Fi in the equations , and and they are carried over into . We also know that:

p

pegul

fsnF

γ××= and ( ) sp1nF 0pi ×σ×−×=

(with p being the % of losses) and:

γp = 1.00 for accidental combinations

fpeg already defined above

From this, we can determine the number of tendons n:

Kd

2eNMsn ×⎟

⎠

⎞⎜⎝

⎛ ×−=×



with s: cross-section of a tendon

and ( ) ( ) ( ) ( )[ ]22

p

peg0p edd

fdeed2p1K −+×

γ+−×−×σ×−= .

Next, the rotation of the cantilever must be verified in the event of an accident, under the effect of the stretching of the tendons. In fact, the longer the tendons, the greater will be the rotation.

The variation in tension in the line of tendons situated on the side of the rising force is equal to:

( ) 0pp

peg p1f

σ×−−γ

=σΔ

and the lengthening of the cables is equal to: sEσΔ

=ε

For tendons with a free length of L, the stretching ΔL can be evaluated at sE

L σΔ× . Therefore, the rotation of the

segment on pier is:

( )sEd

Ltan σΔ×=α

For very tall or highly flexible piers, it is necessary to add the rotation of the pier head unit under the effect of the unbalance moment M and the variations in tension of the stitching tendons.

If the designer considers the rotation of the cantilever to be too great, the response is to limit the increase of the tendons tension by establishing a reduction coefficient for the value of the ultimate force of the tendons Ful.

In standard situations in which losses are 20%, this stretching can reach approximately 3%, which corresponds to 6 centimeters for non-injected 20 meters cables. The calculation of rotation gives an angle of 1 degree for a tendon situated 3.50 meters from the opposite row of blocks: a value which is considered to be acceptable.

The designer’s attention is drawn to the fact that, as the cantilever stabilization tendons are temporary, they are not usually injected with cement grout. Consequently, if they are anchored at the foot of a very tall pier, their extensibility and therefore their elasticity are significant, which may cause dynamic effects that could aggravate the phenomenon during the rotation of the cantilever.

5.5.2 - Calculat ing the surface area of the blocks

We use the maximum number of tendons per row. The number given by the preceding calculations is rounded up to the next biggest even number, taking account of the need to place the bundles of tendons close to each web. Knowing the prestressing force applied by each group of tendons, we can now dimension the blocks in rows A and B.



Fig. 5.30 – Temporary blocks consisting of sand boxes

5 .5 .2 .1 – Normal cons truct ion s i tuat ion (A combinat ions )

The surface area of the blocks is such that they are compressed to fbu under the maximum reaction Rb,. As the concrete of the blocks and the pier crosshead is hooped, its characteristic strength under compression can be increased. Article A.8.4.23 of the BAEL 91 fixes this stress at:

⎟⎟⎠

⎞⎜⎜⎝

⎛×ρ×+×=

cj

etcjcf f

f21ff

with p representing the percentage of steel in the single hooped core, with an upper limit of 0.04.

For example, with 2% of hooping (a standard value), this gives approximately:

fcd = fc28 + 20 MPa

On the other hand, for blocks positioned on high and massive bearing blocks, the compressive stress in the concrete used for the bearing block is limited in order to avoid splitting the pier (Article A.8.4 and Appendix E.8 of the BAEL 91). The maximum value not to be exceeded is fclim, = K fbu with:

fbu Ultimate strength of the concrete at ULS b

cfbu

f85,0fγ×θ×

=

fc28 Characteristic strength of the concrete under compression

γb 1.50 for Type A combinations

θ 1.00 for loads with long duration of application

K aa

bb

aa

bb

= + − +⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥ −⎛

⎝⎜⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

≤1 3 43

1 43

1 43

3 30 0 0 0 ,



In order to obtain the critical value of 3.3 in the last formula, the support surface must have a large overhang in relation to the blocks. Such overhangs are rarely compatible with the dimensions of the pier head unit.

Fig. 5.31 – Plan view dimensions of a block and its bearing block

The table below gives the orders of magnitude of the critical values given by this calculation according to the strength of the concrete and the type of verification to be carried out:

Type of combinations at the Ultimate Limit State fclimFundamental combination only including permanent actions 0.61 to 0.65 fcjFundamental combination with variable actions 0.72 to 0.75 fcjAccidental combinations 0.94 to 0.98 fcj

The maximum stress that must not be exceeded is therefore:

fcmax = Min (fclim ; fcf)

Supposing that there are two blocks of dimensions a × b per support row, we have:

maxc

b

fR

ba2S =××=

a and b are determined by examining the plan view of the pier head unit, allowing for the dimensions of the permanent bearings and of all of the fittings on the pier heads.

Hooping identical to that used on the permanent bearings is calculated and added to the lower face of the segment on pier and underneath the temporary blocks (cf. Article A.8.4, Appendix E.8 of the BAEL 91).

Appendix A of the standard NF EN 1337.3 (classification T 47.820-2) may also be referred to, which considers uniformly loaded B0 surfaces.


The same principle is applied, but with an accidental combination. Therefore:

γb 1.15 for type B combinations

θ 0.85 for loads with a short duration of application



Firstly, we verify that the cantilever does lift up with the number of tendons determined previously. For this, Ra and Rb are calculated as if the cantilever was not lifting up:

ia FeM

2NR +−=

ib FeM

2NR ++=

If Ra is positive, there is no lifting up and the surface area of the blocks S is calculated by the formula:

maxc

b

fRba2S =××=

If Ra is negative, we solve the equations to , but this time Fg = Fi + ΔTg, < Fu1 (this time Fi is known).

This gives:

⎟⎟⎠

⎞⎜⎜⎝

⎛+×+××= M

e2K

NKFKeR 3

4i1

b

with:

( )221 eddK −+=

( ) ( eded2edK 32 −×−×+= )

213 eK2K −×=

( ) 22

4 deKed2K×

×−=

We determine the surface area of the blocks S using the same formula described previous paragraph.

The dimensions of the blocks determined in this way must be increased by 5 to 10 centimeters for the coating of the hoops.

5.5.3 - Calculat ion of the pier shafts and foundations

The static equilibrium combinations calculated previously for the equilibrium of the cantilever and the verification of the anchoring elements are directly used to verify the pier and its foundation at the strength ultimate limit state, without modifying the coefficients of these combinations.

The vertical reinforcement bars of the pier shaft must be verified at the ultimate limit states for bending and compression under the action of N and M. Type A combinations are considered to be fundamental combinations, whilst those of type B are accidental combinations (γb =l,15, γs =l,00).

The designer’s attention is drawn to the fact that this verification is only carried out at the ULS. It is thus important to limit the cracking of piers in temporary construction situations, i.e. with the equivalent of type A combinations at SLS. To account for this phenomenon, we can either perform an additional calculation at SLS by transposing type A combinations, or limit the working stress ratio of the reinforcement bars to the ULS under this same type of combinations, e.g. to 400 MPa.

However, the piers must also be verified at the SLS and ULS for all other situations in the construction and service phases.



5.6 - Verifications of other stabilization methods Without being exhaustive, this paragraph gives some information about the verification of cantilevers that are stabilized by temporary pilings or stays used outside the piers. The details of the verifications are the same as those given in the preceding paragraphs to which the reader can refer.

5.6.1 - Verif ications of stabil i ty due to temporary pi l ings

In the case of a single piling, the verification rules are similar to those described previously.

Therefore, we start by studying the imbalance on the side of the piling (the side where the first of a pair of segments is cast or assembled). Type A and B combinations are studied by verifying the same criteria as for a cantilever secured exclusively by vertical stitching tendons situated in the pier. The blocks must not lift up under type A combinations. Under type B combinations, the tension increase in the stitching tendons and the angle of rotation of the cantilever are limited to a value to be determined in the Special Technical Clauses (to approximately one degree).

The stability of the piling must then be verified. For short and massive pilings, a deviated bending and compression calculation suffices, while taking account of an additional eccentricity of the blocks in both directions or of a fault in the angle of the piling shaft. Further details about the values to be used in the calculations can be found in the BAEL 91 or BPEL 91. For very slender pilings, it is essential to perform a calculation to the second geometrical and mechanical order in order to prevent the buckling of this support. It is vital to connect the piling to at least the pier head and to connect very tall pilings to the shaft at one or more intermediate levels.

Next, we shall study the case of an imbalance on the opposite side to the piling during the assembly or casting of the second of the pair of segments. Here, the type A combination is only studied, because the form traveler or the prefabricated segment on the piling side has been made safe and is no longer likely to fall. The fact that there is no detachment from the support on the piling means that the stitching tendons placed in line with the piling can now be dimensioned.

The same type of calculation is used in the case of two pilings placed symmetrically in relation to the pier. However, detachment from one of the pilings is authorized under type A and B combinations. The cantilever then rests on one or two rows of blocks (type A or B combination) and on the piling situated on the side of the imbalance.

For prefabricated structures, the collapse of the form traveler is replaced by the collapse of the segment being moved in the aforementioned verifications.

5.6.2 - Verif ications of stabil i ty due to cable staying

The cable stays must be arranged in the most symmetrical arrangement possible in order to minimize the disturbance to the geometry of the cantilever during construction.

For this calculation, it is necessary to make the following simplifying assumptions (Fig. 5.32):

• As a simplification, the stitching cables are situated in line with the temporary blocks; e is the center distance between the two rows of cables; the cross section of one row of cables is s; the length of the cables is 1 and their modulus is E; the force exerted by a row of cables is Fi

• The pier, of height h and constant inertia I, is considered to be embedded on its foundation



• Each row of cable stays has a cross section of s’; the cable stays are all identical, of modulus E^ and length 1’ ; the initial force of a row of cable stays is noted as Fi’ (or Fg’ and Fd’ taking account of the variations in tension due to the tilting of the cantilever)

• The cantilever is considered to be undeformable in terms of longitudinal flexion (this hypothesis remains valid if the cable stays are not attached too far from the pier).

Furthermore, it must be remembered that the stabilizing cable stays contribute additional flexion forces that must be taken up by the cantilever tendons.

Fig. 5.32 – Forces applied to the cantilever without detachment from the support

In the absence of cable stays and supposing that the cantilever does not lift off, the support reactions on the rows of blocks A and B are as follows:

iA FeM

2NR +−=

iB FeM

2NR ++=

In general, if the reaction RA is positive, the cantilever does not need to be stayed. As this situation is of little relevance to this paragraph, we shall instead assume that cable stays are required.

In order to calculate the cross-section of the cable stays, we differentiate between situations with type A and type B combinations. As with cantilevers stitched by two rows of cables, there are two stages to the calculation:

• Firstly, the cross sections of the cable stays are dimensioned by limiting their increasing of the tension and the rotation of the cantilever under all combinations (types A and B) and by making sure that the blocks in row A are not decompressed under type A combinations

• Once the cross section of the cable stays has been determined, the support blocks are dimensioned by verifying the compression on row B for type A and B combinations.

The calculation described hereafter does not follow this scheme but the underlying principles are clearly shown.



5 .6 .2 .1 – Temporary cons truct ion s i tua t ion (A combinat ions )

The cantilever must not lift off. The staying must therefore compensate for the rising reaction force of block A under the action of M and N

0'FFeM

2NR iiA ≥++−=

'FFeM

2NR iiB +++=

In general, the cable stays are made to work at 30% of their maximum capacity. In fact, the tension increases are larger than those of the tendons. Furthermore, this low initial tension means that they can be used as temporary cable stays on other cantilevers on the structure. Finally, when stressed in this way, they only undergo very small delayed losses.

As the cantilever does not lift off from its support blocks, the stitching tendons are not subjected to any tension increase. On the other hand, due to the flexibility of the pier under rotation, the cable stays are subjected to variations in tension and the cantilever rotates to a certain extent.

It is thus necessary to verify that there is no movement from the blocks and that there is an acceptable amount of variation in the tension of the cable stays and in rotation of the cantilever.

Given that:

k is the flexibility of the pier under rotation: pIE

hk = ( pMk=θ )

with hp : height of pier

Ip : its inertia

E : modulus of the pier concrete

θ : angle of rotation of the cantilever

Mp : moment applied to the pier head unit

K’ is the flexibility of the cable stays: 'sE

'l'Ks

=

with Es : modulus of the cable stays

ΔTg’ and ΔTd’ are the variations in tension of the cable stays under the effect of the rotation of the cantilever. Their tensions are equivalent to:

Fg’=Fi’+ΔTg’ and Fd’=Fi’+ΔTd’

As the cantilever is undeformable, we have:



'e'l

2'e'l

2tg dg Δ−=

Δ=θ≈θ (Δl'g et Δl'd are the variations in length of the cable stays)

Given that:

'e'T

'K2'e

'T'K2tg dg Δ

−=Δ

=θ≈θ

pMk=θ and therefore: 'K2

k'eM'T pg =Δ and 'K2

k'eM'T pd −=Δ

The moment Mp is expressed by:

'e'TM2'e'T

2'e'TMM gdgp Δ−=Δ+Δ−=

We can therefore determine the tension in the cable stays and the rotation of the cantilever:

2ig'ek'K2

'ekM'F'F+

+= and 2id'ek'K2

'ekM'F'F+

−=

M'ek'K2

k'K22+

≈θ

By expressing the equilibrium on block B, we obtain the support reactions:

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−++=

2

2

iiA'ek'K2

'ek1eM

2N'FFR

AiiB RN'FFR −++=

However, this calculation is only valid if a block A remains compressed. Thus, it is necessary to verify that:

e2N'FF

'ek'K2'ek1M ii2

2⎟⎠⎞

⎜⎝⎛ ++≤⎟

⎟⎠

⎞⎜⎜⎝

⎛

+−


The calculation is similar, but the detachment of the cantilever from block A is permitted while limiting the rotation of the cantilever.

Fig. 5.33 – Forces applied to the cantilever in the event of its detachment from the support on side A



The additional terms ΔTg1’ and ΔTdl’ due to the rocking of the bridge deck on block B are added to the expression of the tensions in the cable stays (Fig. 5.33):

Fg’ = Fi’ + ΔTg‘ + ΔTg1’ et Fd’ = Fi’ + ΔTd’ + ΔTdl’

On the other hand, the tendons in row A are overstressed. Their tension can be expressed as:

Fg = Fi + ΔTg

If we note K as the stiffness of the tendons (sE

lKs

= )

as the cantilever is undeformable, the variations in the lengths of the tendons and cable stays are proportional:

'Ke2

)'ee(KT'T g1g+

Δ=Δ et 'Ke2

)'ee(KT'T g1d−

Δ=Δ

Finally, we must add the effect of the overstressing of the tendons in row A under moment M. Therefore, we have:

2eT

2'e'F

2'e'FMM gdgp Δ++−=

or by replacement in the expression of ΔTg’ :

( )'K4'eekT

'K4'ek'F'F

'K2'ekM

'K2'ekM'T g

2

gdpg Δ−−+==Δ

which can be introduced into Fg‘ :

( ) ⎟⎠

⎞⎜⎝

⎛ +−Δ−++=+

e'eeK2'eekT'F'ekM'ek2F'K4'ek'K4'F gd

2i

2g

The sum of Fg’ and Fd’ gives:

'K

KT'F2'F'F gidg Δ+=+

and the equilibrium of the moments on block B

02eNeT

2e'e'F

2e'e'FM ggd =−Δ−

+−

−+

The resolution of equations , and gives Fd’, Fg’ and ΔTg.

By expressing the equilibrium on block B, we obtain the support reaction RB: B

RB = FB d’ + Fg’ + 2Fi +N + ΔTg

The rotation of the cantilever is the sum of the flexion rotations of the shaft and of the rocking around the support B:

( )eKT

'e'K'F'F2 gdg Δ+−≈θ



6 - Construction technology This chapter covers the technology required for the construction of prestressed concrete bridges using the cantilever method. The first part deals with cast-in-situ structures and pays particular attention to the design of temporary structures (form work for segments on piers, form travelers etc.) and cantilever stabilization systems. The second part is dedicated to structures made from prefabricated segments. Therefore, this includes a detailed description of the prefabrication plant and the equipment used for the transportation and assembly of segments (launch beam, crane, low-bed semi-trailer, etc.).

6.1 - Construction using cast-in-situ segments When fewer than 350 to 400 segments need to be constructed, the bridge deck is cast in-situ. This applies to the vast majority of bridges.

Every year, numerous bridges are built using this method in France and abroad. Some of the largest structures built in recent years include the bridge over the River Rhine to the south of Strasbourg, the Viaur viaduct at Tanus for the RN88 main road, the second Genevilliers viaduct over the River Seine for the A15 highway and the viaduct over the River Loire at Cheviré. Notable examples outside of France include the Norwegian bridges of Stolma and Rafsundet, the Brisbane Bridge in Australia and the Hamana bridge in Japan, all of which are notable for their great span.


Segments on piers are always built using special formwork which is specially designed for this part of the bridge deck and assembled on a work platform attached to the tops of the piers (Fig 6.1).

The external formwork consists of fixed metal shuttering. The internal formwork is either built from traditional wooden shuttering or carried out using an articulated metal tool. On certain structures with only one or two piers, the length and thus the cost of the external shuttering for the SOP are reduced by using the external formwork of the form travelers to encase the lateral sections of these segments.

Fig. 6.1 – Construction of segments on piers

The working platform, fixed to metal inserts embedded on the top of the pier head unit, is externally rectangular in shape (Fig. 6.2). It has cut-outs in the middle for direct access to the underside of the segment on pier and the top of the stability blocks and bearings.

Segments on piers are usually built in two phases: the first phase includes the lower slab, the gussets gusset and the base of the webs; the second phase features the rest of the transverse section and the crossbeam on pier. The



completion time for a segment on pier is 6 to 10 weeks for a traditional structure but may stretch to 15 weeks for structures which are very wide and/or with a very lon span .

Fig. 6.2 – Work platform for segment on pier formwork

6.1.2 - Standard segments

6 .1 .2 .1 – Background in format ion about form trave lers

Standard segments are built using highly complex formwork equipment called form travelers (Fig. 6.3). Depending on the situation, this equipment is either built specifically for the site or existing equipment is adapted to suit the site.

Like many other formwork tools, form travelers include three major elements, each of which performs a particular function:

• A metal structure: used for attaching the form traveler and the future segment to the most recently constructed segment

• Metal shuttering panels: used for giving the concrete the required shape

• Gangways and work platforms: for access and to allow employees to work in all areas of the segment being built.

Fig. 6.3 – General view of a form traveler

Although a large variety of form travelers are available, they are usually broken down into three families according to the position of their supporting beams or their main beams in the metal framework. These categories are:

• Form travelers with supporting beams situated above the upper slab



• Form travelers with supporting beams situated along the webs of the box girder

• Form travelers with supporting beams situated below the lower slab.

In France, the second type of form travelers, with supporting beams situated along the webs, is by far the most commonly used, especially because the absence of any beams at the base of the segment to be constructed makes it possible to insert a reinforcing cage that has been entirely prefabricated at ground level (Fig 6.4).

Fig. 6.4 – Upper clearance of a “below-slab” form traveler

Frequently used after World War II, the first type of form travelers is no longer widely used in France. However, they are regularly used in other countries (Fig. 6.5).

Fig. 6.5 – Upper clearance of an “above-slab” form traveler

The third type of form travelers is only used in very specific cases.

The second and third types of form travelers are often called “below-slab” models, as opposed to the first type of “above-slab” form travelers.

In the rest of this chapter, we have decided to concentrate exclusively on the second type of form travelers, i.e. those with supporting beams situated along the webs. This family of form travelers can be split into two sub-groups: those with an upper beam of the same width as the box girder, which are ideal for segments of a standard height and width, and form travelers with a smaller cross beam and launch or transfer beams, which are commonly used for very tall or wide segments.



6 .1 .2 .2 – S impl i f i ed descr ip t ion o f form trave lers wi th fu l l upper beams

In recent years, these form travelers have been used in the construction of numerous bridge decks and notably those of the second Pont Salomon viaduct [DEW 01], the Digoin viaduct [DIEU 00], the Tanus bridge [SER 98], etc.

Described schematically, their metal framework consists of three large sub-structures (Fig. 6.6):

Fig. 6.6 – Principle of the framework for a form traveler with lateral beams

• A large U-shaped structure situated under the bridge deck, supporting the formwork for the underside of the cantilevers and the external faces of the webs, along with the formwork for the lower slab; this structure consists of two large longitudinal lattice girders, called supporting beams, and one vertical “front” beam, which is also a lattice girder. This girder is situated at the end of the form traveler on the segment n + 1 side, with segment n being the segment to be cast. In certain cases, horizontal bracing is added to these two elements and situated under the lower slab

• An upper crossbeam, sometimes referred to as a transverse transfer beam, positioned on the upper slab of segment n-1, at its free end (Figure 6.6 shows the specific example of a C-shaped upper beam)

• Sliding beams, supporting the formwork for the internal surfaces of segment n and situated under the central part of the upper slab.

6 .1 .2 .3 – Operat ion o f form trave lers wi th fu l l upper beam

The design of the different elements described above takes account of two very different situations: the movement of the equipment on the one hand, and the reinforcement, cabling and concreting on the other.

In the static phase, the connections between the three sub-structures are as follows:

• The upper beam rests upon the upper slab of segment n-1

• The U-shaped structure is fixed to the upper beam via rods across the upper slab that has already been constructed; these rods are highly prestressed in order to reduce the deflection of the U-shape under the weight of the concrete

• The sliding beams are supported on the front beam on the side of segment n+1 and attached to the upper slab via transverse hangers on the side of segment n-1.



In the movement phase (Fig. 6.7), the support conditions for these elements evolve in the following way:

• The upper beam still rests on the concrete

• The U-shaped structure is suspended on the upper beam, either via rods situated on either side of the box girder, and thus without crossing the upper slab which has already been constructed, or via brackets extending out from the upper beam under the cantilevers (in which case, this is called a C-shaped upper beam). Other methods are also used. As the centre of gravity of the U shape is situated well in front of the suspension plane, it has a tendency to tip on the crown side, but this movement is stopped by wheels fixed to the rear of the supporting beams and blocked by the cantilevers that have already been constructed (Fig. 6.8)

• The sliding beams are cantilevered.

Fig. 6.7 – Static schema of the form traveler during translatory movement

Fig. 6.8 – Supporting beams rested on C-shaped upper beam ends

The movement of the upper beam and the U-shaped structure is carried out using long-stroke horizontal jacks situated on the upper slab and pushing against the upper beam (Fig. 6.9). Depending on the situation, the sliding beams are moved by tackle (Fig. 6.10) or by a second set of long-stroke jacks (Fig. 6.11).



Fig. 6.9 – Upper beam with long-stroke jack (at bottom of photo)

Fig. 6.10 – Manually-operated sliding beam

Fig. 6.11 – Sliding beam operated by a long-stroke jack



6 .1 .2 .4 – Construct ion sequence for a s tandard segment

Using the form travelers described above, the major stages in the construction of a standard segment are as follows:

1 Installation and stressing of cantilever tendons for segment n - 1

2 Dismantling of rods attaching U-shaped structure to the concrete of segment n - 2; the U-structure is now fully suspended from the upper beam

3 Sliding of the upper beam and thus of the U-structure suspended from it

4 Installation of rods attaching the U-structure to the concrete of segment n - 1

5 Adjustment of the external formwork and formwork of lower slab

6 Installation of lower reinforcement cage of segment N, with its ducts and anchorages

7 Dismantling of rods attaching the sliding beams and sliding of the latter

8 Sliding and adjustment of the internal formwork

9 Installation of rods fixing the sliding beams to the concrete of segment n - 1

10 Installation of the upper reinforcement cage of segment n with its ducts and anchorages

11 Casting of segment n

Standard segments of conventional dimensions and shapes are almost always cast in a single phase, with a construction cycle of between 48 and 72 hours per pair.

6 .1 .2 .5 – Form trave lers wi th t rans fer beams or launch beams

For a large segment, the suspension of the lower part of the form traveler from the ends of the upper beam requires very large and thus very costly upper beams. For the construction of very wide bridge decks, it is thus increasingly common to use form travelers that are designed to move on a “transfer frame”, which is positioned transversally, very close to the webs.

Very simply, these form travelers consist of:

• An upper beam without cantilevers, supported at right angles to the webs (Fig. 6.12)

• Longitudinal upper transfer beams, only used in the movement phase (Fig. 6.13)

• A main metal framework, which is virtually identical that used for the aforementioned type of form travelers, with two large support beams and one front beam, usually in the form of lattice girders

• Sliding beams situated under the central section of the upper slab, as for the first type of form travelers

• Lower transfer beams, or sliding beams, situated along the two support beams.



Fig. 6.12 – Upper beam without cantilever

Fig. 6.13 – Upper transfer beam

In the static phase (Fig. 6.14), the support and operating conditions for the form traveler are virtually identical to those for the first type of form travelers. The main difference concerns the presence of lower transfer beams, which in this phase are fixed to the two support beams.

Fig. 6.14 – Form traveler in static phase

The differences are greater in the movement phase (Fig. 6.15). Indeed, in this phase, it is necessary to:

• Place the two upper transfer beams on the segment that has just been constructed

• Release the lower transfer beams and suspend them from the two upper transfer beams in order to form a frame capable of accommodating the main framework of the form traveler

• Release the main framework (both support beams and the front beam), lower it onto the frame consisting of the four transfer beams and slide it into its new position, normally via long-stroke jacks

• Fix the main framework to the concrete and the upper beam

• Move the central section of the formwork forward

• Re-attach the lower transfer beams to the support beams, separate them from the upper transfer beams and remove the latter.



Fig. 6.15 – Form traveler in movement

The form travelers used for the Pays de Tulle viaduct on the A89 highway are good examples of this type of form traveler [LAC 02].

6 .1 .2 .6 – Other comments regard ing form trave lers

Other t ypes o f form t rave le r s

As mentioned at the beginning of paragraph 6.1.2.1. of this guide, there are many different types of form travelers and the preceding presentation is far from exhaustive. Special form travelers are commonly built for the construction of bridge decks with struts, lateral shell elements or even hybrid structures (e.g. the bridge over the Bras de la Plaine, the Vecchio bridge, the Corniche bridge in Dole, etc.) [CHU02], [PAU 00].

Modi f i ca t ion o f form t rave le r s for reuse

Considering the very high manufacturing costs for a pair of form travelers, efforts are often made on new projects to reuse equipment that was designed for a previous site.

Unfortunately, as the decks of large bridges have no standardized elements, significant modifications often have to be made to the form travelers in order to reuse them for the construction of a new bridge deck. Considering the risks involved, the engineering design and implementation of these modifications must be handled with the same care as for the original design and manufacturing phases.

Weight o f form t rave l e r s

The weight of form travelers that are custom-made for a specific project is normally quite close to half of the weight of the heaviest standard segment. However, this ratio is sometimes exceeded, especially when a form traveler that was originally designed for a wider bridge deck is reused on a narrower project.

6.1.3 - Deviator segments

The vast majority of deviator segments on composite prestressed concrete bridges are constructed in two phases: the standard section is built using the form traveler used for the standard segments; the lower beam and the deviator beams are built using wooden formwork with the concrete introduced through apertures left in the upper slabs directly above the beams (Fig. 6.16). With this method, the reinforcement bars awaiting insertion into the beams must be bent and then unbent - requiring the use of ADX steel - in order to allow the inner core of the form traveler to slide freely. However, it is increasingly common to use mechanical couplers at the junction between the webs and the deviator beams, making these operations unnecessary. It is now also possible to use special high bond strength reinforcing steels which are capable of withstanding a bending-unbending cycle without any loss of strength.



Fig. 6.16 – Second phase in the construction of a deviator beams

There are several structures in which the deviator beams were built in a single phase. In some of these structures, a special metal core was built specifically for these segments.

6.1.4 - Segments buil t by over-canti levering

In terms of their construction, segments built by over-cantilevering are similar to standard segments. Therefore, they are built using form travelers designed for these segments.

6.1.5 - Closing segments

Closing segments are normally constructed in a single phase, using one of the form travelers used for the construction of the standard segments. If it is possible to remove the central core once the final segment is in place, the internal parts of the closing segments are encased using the original core, as is the case for the standard segments. If this is not the case, which is by far the most common situation, it is necessary to design and use a special inner core, which can be broken down into small, easily transportable sections.

It should be noted that the most common practice is to use standard form travelers for the construction of the closing segments. However, this does not happen systematically, and on certain projects, contractors prefer to build special equipment for these segments, which allows them to remove their form travelers as quickly as possible.

During the construction of the closing segment , the formwork equipment is positioned on simple supports at both ends of the cantilevers because it would not be strong enough to withstand the thermal effects that might develop in the continuously-rendered span. If the formwork equipment is specially built, these support conditions pose no problems, but if one of the standard form travelers is reused, special precautions must be taken because the majority of these tools are designed to operate in an overhanging position.

On certain sites, it is important for the aforementioned formwork equipment to be equipped with a system designed to prevent certain parasitic movements of the cantilevers - especially their rotation around the axis of the piers due to the effect of wind. Normally, this system consists of longitudinal beams fixed to the overhangs of the last standard segment in each cantilever.

The time of the casting of a closing segment must be chosen with care. It is important to prevent the development of significant thermal effects between the setting of the concrete – the moment at which the span becomes continuous – and the stressing of the first continuity tendons. Therefore, casting in the late evening is recommended during very sunny periods.

Two to three days are required to complete a closing segment, depending on the project.



6.1.6 - End sections

In the majority of cases, the longitudinal profile of the natural terrain around the abutments makes it necessary to construct the end sections on horizontal centering resting on the abutment crosshead and on one or more temporary metal pilings (Fig. 6.17). The formwork for the bridge deck is then erected on this centering and the casting is carried out in sections of 3 to 4 m.

Fig. 6.17 – Construction on centering of the end section of an end span

However, it is possible to construct the end sections of the bridge deck on centuring towers, if the natural terrain lends itself to this solution. This is the most economical technique.

End zones may also be built directly using the same form travelers used to construct the standard segments. In order to limit the imbalance of the cantilever, a temporary piling is placed under the last standard segment on the abutment side and then caulked after the cantilever tendons associated with this segment have been stressed. This piling also helps to reduce flexion at the end of the bridge deck (Fig. 6.18) [DEM 02].

Fig. 6.18 – Construction using form traveler and temporary piling on the end section of an end span

6.1.7 - Stabil ization of canti levers

The following section contains technical information concerning the stabilization of cantilevers. This supplements Chapter 5 of this guide.

6 .1 .7 .1 – S t i t ch ing pres tress ing

Stitching prestressing is normally carried out by tendons. In the lower section, according to the piers, these tendons may be anchored on the underside of the crosshead, by forming a loop in the shaft or on the foundation bulkheads. In the upper section, they must be anchored to anchor plates housed in the upper slab of the SOP. If this solution is impossible due to the density of reinforcements in these parts, the anchorages are housed in



prefabricated concrete blocks positioned on top of the SOP and removed after the stress has been released from the stitching tendons. A resin or mortar is inserted between these blocks and the SOP in order to guarantee the correct transmission of forces between these elements.

Some contractors also use bars to provide the temporary prestressing. However, this solution is not to be recommended because any error in the positioning of the prestressing ducts could result in parasitic flexions in the bars or could even make it impossible to insert the bars.

6 .1 .7 .2 – Concre te b locks

If the pier head unit is big enough to accommodate the bearings, blocks, stitching tendons and jacks simultaneously, the most economical stabilization system consists of temporary prestressing and hooped concrete blocks placed directly on the pier head (Fig. 6.19).

Fig. 6.19 – Concrete stabilizing blocks

During construction, the cantilevers rest on the concrete blocks and the bearings are in place but not in contact with the SOP.

After the closing segment is in place, the structure can be placed on the permanent bearings. This consists of:

1. Raising the bridge deck using jacks

2. Caulking the gap above the bearings

3. Bringing the structure down onto the hardened caulking.

Once these operations have been carried out, the blocks are no longer in contact with the SOP and may be removed by a crane or other equipment (Fig. 6.21). In this way, the support reaction of the bridge deck is gradually transferred from the stabilizing blocks onto the permanent bearings.

6 .1 .7 .3 – Concre te b locks on sand boxes

If the pier head units are too small to accommodate jacks and blocks side by side, the cantilevers are constructed on concrete blocks placed on sand boxes consisting of a removable metal shell filled with graded sand (Fig. 6.20). Once the closing segment is in place, the gap between the underside of the SOP and the top of the bearings is caulked as before; finally, the sand is blown out of the boxes (Fig. 6.21). Thus, vertical forces are progressively and without jack transferred from stabilizing blocs to permanent bearings.



Fig. 6.20 – Concrete stabilizing box placed on a sand box

Fig. 6.21 – Detail of an open sand box

A large variety of sand boxes are available. On the simplest projects, they are rectangular and four boxes are used per pier. On more complex projects, the sand boxes are proper cylindrical pot bearings and up to a dozen may be used per pier. Whatever their type, these boxes must be dimensioned and designed to be undeformable. If not, this could lead to an uneven distribution of the support reactions between the sand boxes, thus resulting in structural and/or geometric disorders.

It should also be noted that the geometry of the cantilevers has to be perfect with this system, because as a sand box can only be emptied, it cannot be used to raise the bridge in case of problem.

6 .1 .7 .4 - Jacks

Although this technique is rarely used, it is also possible to construct a cantilever entirely on jacks. This technique has the benefit of using the same system to perform both jacking and blocking functions, so that smaller pier heads can be used. For this to be possible, the jacks are immobilized during the construction of the cantilevers. They must therefore be equipped with lock nuts.

6 .1 .7 .5 – Other methods

When the structure is positioned quite low above the natural ground and if the pier head unit is too small to accommodate blocks, e.g. because it is an “exact” match for an older design, it is possible to stabilize the cantilevers using temporary pilings placed either side of the piers (Fig. 6.22). At the bottom, these pilings, which are usually metal tubes filled with concrete, are attached on top of the foundation bulkhead; at the top, they are attached underneath the lower slab of the segments on piers or of the first standard segments.



Fig. 6.22 – Stabilization of a cantilever by tubular metal pilings

For the second Saint-André de Cubzac viaduct, and still because of excessively small pier head units, composite systems with blocks and cable stays were used tostabilize the cantilevers [JAE00].

In the interests of thoroughness, we should also mention the second Gennevilliers viaduct over the River Seine for the A15 highway, which was equipped with self-leveling pot bearings injected with silicone rubber [CHA 94].

6.1.8 – Prefabricated butt blocks

In order to allow for the rapid stressing of cantilever tendons, contractors sometimes prefabricate the concrete which surrounds the anchor plates for these tendons.

As the cantilever tendons on older structures were often anchored quite low down, as their alignment was designed to reduce shear force, these elements were situated in the webs of the box girder and were rectangular in shape.

Today, rectangular blocks are still used when several tendons need to be anchored in close proximity to each other. However, for single tendons, more and more contractors are using prefabricated cylindrical blocks whose only reinforcements are helical hoops with jointed coils which also form the external formwork of the prefabricated block (Fig. 6.23 and 6.24).

Fig. 6.23 – Cylindrical butt blocks



Fig. 6.24 – Cylindrical butt block in position in the form traveler

6.1.8 - Inf luence of form travelers on the dimensioning of bridge decks

It is imperative for the weight of the form travelers to be considered in the calculations for longitudinal flexion, as this increases the forces on the structure, particularly during the construction of the cantilevers.

The form travelers may also influence the positioning of the cantilever tendons and continuity tendons, as their operation relies on prestressing bars which cross the slabs close to the webs where the internal prestressing tendons are situated. During the design stage for pretressed concrete bridges built by the cantilever method using reused form travelers, it is not possible to choose the position of these bars. This must be accounted for in the design of the cantilever tendons.

It is also important to consider the forces caused by the form travelers when analyzing tranverse flexion. These forces usually lead to the localized strengthening of the reinforcements in the upper slab and in the top part of the webs (Fig. 6.25).

Réaction de l'appui support de lapoutre supérieure

Précontrainte des suspentesdes poutres latérales

Fig. 6.25 – Example of localized forces exerted by the form traveler on the box girder in the construction phase

In conclusion, it is essential for the organization and methods department and the engineering firm to work very closely together during the construction surveys for a structure built by the cantilever method.

6.2 - Construction by prefabricated segments It is generally considered that it is more economical to prefabricate a bridge deck than build it in-situ when the number of segments to be constructed exceeds 350 to 400 units.



However, specific difficulties may raise or lower this threshold. Thus, a very short contractual completion time or difficult climatic conditions may increase the appeal of prefabrication. On the other hand, a lack of space close to the site or difficult access conditions may mean that there is no alternative to the in-situ construction of reasonably long structures.

French bridges built recently using this technique include the Ile de Ré bridge, the Saint-André viaduct for the A43 highway in Maurienne, the Rogerville viaduct on the A29 [JAC 98], the second A20 viaduct over the River Dordogne at Saint-André de Cubzac [JAE 00], and finally, the Avignon viaducts for the TGV Méditerranée high-speed rail line.

6.2.1 - The segment prefabrication plant

The prefabrication plant is set up on a site of approximately 2 hectares in area. This is usually located next to the site, but it may also be situated several kilometers away. It can be broken down into two major areas: the first is used for the construction of the segments and the second is reserved for their storage (Fig. 6.26).

Fig. 6.26 – General view of the units of a prefabrication plant

Prefabrication units have been preferred for the construction of segments for the past ten years or so. Thanks to significant improvements in geometrical accuracy, this method has definitively taken over from the costlier long bench method with an ogee mold (Fig. 6.27) which also requires more space.

Fig. 6.27 – Prefabrication using an ogee mold

A prefabrication unit is a construction area the length of two to three standard segments, in which the assembly of formwork and the casting of segments take place (Fig. 6.29 and 6.30). The lateral formwork consists of two metal sides; longitudinally, this function is carried out by a metal plate on the crown side and a by segment n-1 on the pier side, which results in a perfect joint between the different elements (Fig. 6.28). A well designed unit produces one standard segment per day or one segment on pier every two days. In order to maintain such high rates of production, the units are equipped with concrete distribution booms supplied by pipework or conveyors connected to a concrete plant on site. They also take delivery of complete reinforcing cages, which are manufactured on jigs by specialist workshops and are equipped with all inserts (ducts, anchor plates, anchor rails).



Fig. 6.28 – Breakdown of a prefabrication unit

Fig. 6.29 – Prefabrication units

Fig. 6.30 – Detail of a prefabrication unit (from left to right: the matched mold

segment, external formwork, internal formwork)



Depending on the number of segments to be constructed, there may be between three and several dozen units in total. Some of these units specialize in segments on piers and abutments while the others are reserved for standard segments.

Segments on piers are always split into two in order to avoid the need for oversize transportation and hoisting equipment. The half-segments on piers are manufactured side by side in specialized units; after separation, they are transported to the units specializing in standard segments for use as matched molds for the first standard segments of each cantilever. According to the project, the deviator segments are either built in specialized units or in the standard segment units, with the beams being constructed in the second phase outside of the unit in order to avoid having to modify the construction cycle for the standard segments. Specialized units are reserved for the construction of hinged segments, if these are included in the design of the bridge deck.

Considering the errors that they have to compensate forr, the closing segments are cast-in-situ rather than prefabricated. They are also reduced to several tens of centimeters in length.

The segments are stored on the prefabrication site for a period of one to three months. The concrete is thus extremely strong when the segments are assembled; therefore, the prefabricated anchor blocks described previously (see 6.1.8) can be dispensed with. In general, the segments are stored on just one level. If necessary, and after verification of the segments, they may also be stored on two or even three levels. The segments are first transported by large traveling gantry, initially from the prefabrication units to their storage area and then onto a mode of transport (barge, low-bed semi-trailer, etc.).

6.2.2 - Transportation of prefabricated segments

6 .2 .2 .1 – Transporta t ion by low-bed semi - tra i l er

Tyre-mounted low-bed semi-trailers are the most widely used form of transport for segments (Fig. 6.31). Depending on the sites and the chosen assembly mode, the semi-trailer is either driven onto the portion of bridge deck that has already been constructed or onto a track marked out on the ground in line with the structure to be built. Loaded is usually carried out by a gantry crane at the prefabrication site and unloading is performed by the assembly equipment (see 6.2.3 above).

Fig. 6.31 – Semi-trailer used for transporting segments

6 .2 .2 .2 – Transpor ta t ion by barge

The segments can also be transported by barge if the structure crosses a navigable waterway or one that can be made navigable, e.g. by dredging [JAE 00].



6.2.3 - Assembly of prefabricated segments

6 .2 .3 -1 – Assembly us ing a launch beam

Background informat ion

Launch beams are the most widely used method for assembling prefabricated beams in successive cantilever segments. This self-propelled handling device is supported by the bridge deck and piers and therefore is free from almost all of the constraints relating to the crossing (Fig. 6.32). The initial cost of a launch beam is very high, but as it is usually designed to be used on several consecutive sites, it can be paid off over a long period.

In recent years, numerous bridges have been built using this method. In France, the most notable examples include the Sylvans and Glacières viaducts on the A40 highway [BOU 90], the Ile de Ré Bridge, the Boulonnais and the Rogerville viaducts on the A29 highway [JAC 98] and the Saint-André bridge on the Maurienne highway (A43). Examples in other countries include the access viaducts for the second Severn crossing in England [COM 96], the access viaducts to the Prince Edward Island viaduct in Canada [COM 98] and numerous urban bridges in Thailand and Hong Kong.

Fig. 6.32 – Standard launch beams

Structure of standard launch beams

Standard launch beams can be broken down into around ten elements, all of which are made of metal (Fig. 6.33 and 6.34):

• Two triangular-section lattice girders of between 3 and 5 m tall and 100 to 250 m in length according to the beams, made from sections assembled using prestressing bars

• Two front and rear lattice towers, acting as main supports

• Two front and rear legs, acting as secondary supports

• Two bridge cranes traveling on the lattice girders and used to manoeuvre the segments.



Fig. 6.33 – Cross-section of a standard launch beam

Fig. 6.34 – Main constituent elements of a launch beam

The lattice towers and legs can be moved longitudinally along the lattice girders using to a system of capstans. The lattice towers can also slide inside their supporting cross beams. This transverse movement is required for the construction of curved sections, for example. The bridge cranes are equipped with spreaders which are used to position the segments as closely as possible to their final position, both longitudinally and transversally and for any type of geometry.

A standard launch beam weighs between 300 and 600 tonnes. The completion time for its construction is approximately one year and it costs between 1.5 and 3 million euros.



Sequence o f opera t ions for the assembly o f segments

During the assembly of the segments on piers on support Pn, the launch beam rests on its two lattice towers and the front leg. Once both half-SOPs have been assembled, adjusted and stitched, the rear leg is removed and the front lattice tower slides in place on top of the SOP on pile Pn. The beam can then be moved forward so that the rear lattice tower is positioned at the end of the cantilever centred on Pn-1. The front leg is then placed at the end of the lattice tower on the Pn+1 side, so that it does not obstruct the assembly of the standard segments. This operation can now begin (Fig. 6.35).

Fig. 6.35 – Different stages in the sequence of operations for a launch beam

During the construction of a cantilever, the two symmetrical segments S and S' are normally assembled one after the other. On some sites, a “symmetrical” assembly method has been used. This method, which consists of synchronizing the release of the two S and S' segments by both carriages, reduces the stresses imposed on the supports by eliminating non-accidental imbalances.

When the bridge deck consists of two parallel bridge decks, it is very common for the adjacent cantilevers of the two decks Fa and Fb to be constructed simultaneously. To this end, the two lattice towers are placed on the transverse rails straddling the central gap, which allows the launch beam to cross over from one bridge deck to the other and thus to assemble cantilever Fa immediately after cantilever Fb. This method is also used when the bridge deck consists of two box girders joined in the middle and when each box girder is built and assembled on-site before the longitudinal grouting of these box girders is carried out. In general, this technique improves the speed of the assembly and prestressing of the segments. In the case of box girders joined side by side, this also significantly reduces the differential creep between the two box girders.

Spec ia l launch beams

Without going into too much detail, it is worth mentioning certain launch beams that have been specially designed or used by French companies in France or abroad.



A cable-stayed launch beam was used on the construction of the Ile de Ré Bridge. This solution helped to keep the lattice girders to a reasonable height despite the length of the spans to be crossed (110 m). This also played an important role in helping to reduce wind effects (Fig. 6.36).

Fig. 6.36 – The cable-stayed launch beam used on the Ile de Ré viaduct

The launch beam used for the construction of the H3 highway viaduct on the island of Oahu in the Hawaiian archipelago in the United States, featured two independent upper beams, each of which was positioned on a separate bridge deck. These beams were connected by a bridge crane.

This arrangement made it possible to assemble the segments on two parallel bridge decks of different levels and separated by a very wide central gap.

6 .2 .3 .2 – Assembly by crane

If the piers are not too tall and it is possible to use heavy equipment at the foot of the bridge deck, prefabricated segments can be assembled using cranes, which significantly reduces the initial investment costs.

If the structure crosses an expanse of water, the assembly is carried out using a 200T to 500T lattice boom crane mounted on a barge (Fig. 6.37). If the structure crosses land, the assembly is carried out using a tracked crane with a lattice boom of the same capacity (Fig. 6.38). Given the order of assembly of the segments, the crane constantly moves from one end of the cantilever to the other.

Fig. 6.37 –Assembly using a river crane Fig. 6.38 – Assembly using a land-based crane



Whatever type of crane is used, a spreader is positioned between the hook of the crane and the segments. If the transverse slope and longitudinal profile are minimal, the segment can be guided by joining frames and the spreader can therefore be very simple. If the transverse slope or longitudinal profile is very pronounced, it is better to offer up the segments in a position close to their final position, which requires much more complex spreaders with transverse and/or longitudinal adjustments.

Several structures have been built using this technique in recent years. The most notable examples are the Arcins viaduct over the River Garonne in Bordeaux [ABE 94], the second viaduct for the A10 highway over the River Dordogne at Saint-André de Cubzac [JAE 00] and the "central" and “Expo" viaducts of the bridge over the River Tage in Lisbon.

6 .2 .3 .3 – Other as sembly methods

In addition to the launch beam and the crane, other methods exist for the assembly of prefabricated segments.

When each segment can be positioned on the ground in line with its final position, it is possible to “winch” segments or parts of segments up to the bridge deck using lightweight metal girders. This method has been used on at least four sites in France: on the Falaises viaduct on the A20 highway, on the Ottmarsheim bridge, where it was used to raise whole segments and on the Sermenaz and Arrêt-Darré viaducts ([SER 90], Fig. 6.39), where it was used to raise sections of segments.

Fig. 6.39 – Winch assembly principle (on the site of the Arrêt-Darré viaduct)

As the structure for the West Kowloon Expressway project, in Hong Kong, occupied a totally virgin site, the segments were assembled using a gantry crane operating on both sides of the bridge deck (Fig. 6.40). The same system was used for the Khurays Road viaducts in Riyad and, closer to home, on the A10 highway bridge over the River Loire at Tours.



Fig. 6.40 – Assembly using a gantry crane

6.2.4 - Temporary lashing

In order to release the assembly equipment as quickly as possible, the segments being assembled can be lashed in place before the cantilever prestressing is brought into operation. This lashing generally consists of Ø36 mm bars anchored in blocks at the top and bottom of the webs, in the web uprights or in the slabs (Fig 6.41). It is dismantled after the stressing of the permanent tendons and the hardening of the epoxy adhesive. A normal stress of approximately 0.2 MPa must be exerted by these bars, which guarantees the correct distribution of the adhesive and helps it to set, while preventing any decompression at the end of the segments.

Fig. 6.41 – Anchor block for a lashing bar Fig. 6.42 – Construction of a closing segment with strip formwork

6.2.5 - Mid-span closures

The mid-span closures between cantilevers are constructed in the traditional manner, by casting an in-situ joint of approximately 20 centimeters in length. For such short joints, contractors often use strip formwork (Fig. 6.42).

6.2.6 - Sections on the abutment side of end spans

As for in-situ casting, the extremities of end spans on the abutment side are usually built on falsework. In the case of prefabricated segments, the corresponding segments are positioned and assembled on falsework. In order to allow the movement necessary for perfect joints at the crowns, blocks or jacks are placed between the bottom of the segments and the top of the falsework.



6.2.7 - Bonding of the segments

Before assembly, an epoxy adhesive is spread on the pier-side face of the segment being assembled. This adhesive is spread by hand just before assembly to a thickness of approximately 1 mm.

6.2.8 - Stabil ization of canti levers

As mentioned in the part of this chapter devoted to cast-in-situ segments, the choice of a stabilization system for cantilevers is highly dependent on the size of the pier head units. Under these conditions, the stabilization techniques for bridges made from prefabricated systems are the same as those described in section 6.1.6 above. However, as it is difficult to correct the geometry of the cantilevers once the segments are joined, the cantilevers are often built on supports featuring jacks equipped with lock nuts. If conventional blocks are used, caulking must be applied between the top of the blocks and the bottom of the segments on piers in order to correct any construction defects or errors in the assembly of these parts.

To be exhaustive, it is worth mentioning that cantilevers are sometimes stabilized by the launch beam itself. This technique was used for the construction of the Baldwin viaduct in the USA [FUZ 94], and for the B3 South viaduct to the north-east of Paris.

6.2.9 - Speed of construction

The instantaneous construction rate on a site using prefabricated segments varies significantly. At the start of the project, no more than 3 m per day are completed. However, under normal operating conditions the speed of construction reaches 12 m or 4 segments per day. The average speed is therefore 6 m per day.

6.2.10 - Inf luence of methods on the dimensioning of structures

Assembly using a crane or gantry crane creates very few longitudinal forces on the bridge deck, as the loads applied to the cantilevers are limited to the weight of any work platforms that might be used. If the segments are assembled using a launch beam or winch, greater forces develop in the bridge deck due to the weight of this equipment and the segments being handled and must therefore be allowed for in the design.

For localized flexion, it is important to verify that the reinforcing of the segments is capable of taking up any transverse moments that develop during the storage and handling of the segments, regardless of the assembly method used. If the assembly uses a launch beam and/or requires the use of a low-bed semi-trailer, it is also necessary to consider the localized forces created by this equipment when dimensioning the non-prestressed reinforcements of the segments.

As for construction using cast-in-situ segments, it is important to perform a thorough analysis of the positioning of the handling hangers and the internal cables in order to prevent any interference between these elements.

In conclusion, as for the construction of bridge decks using cast-in-situ segments, the design and construction of bridge decks made from prefabricated segments using the cantilever method requires a very close collaboration between the engineers of the engineering and design department and those of the organization and methods department.



7 - On site Monitoring This chapter covers the monitoring operations and particular precautions that need to be implemented during the project. It places particular emphasis on topics relating to the construction of bridges by the cantilever method. In the process, it extends its scope to the monitoring that must be performed and the particular precautions that must be taken during the construction of all types of large engineering structures.

7.1 - Background information On-site monitoring mainly relates to quality, quantities and the monitoring of deadlines. This chapter only covers qualitative monitoring.

Monitoring prior to construction is primarily designed to evaluate the methods which are likely to be used by the contractor and which will go some way towards defining some of the specifications of the contract.

Some of these monitoring operations will not be covered in this chapter, including the certification of companies, the monitoring of plans and design calculations, the inspection of the SOPAQ (Schéma organisationnel du plan d’assurance qualité - Quality Assurance Plan Organizational Scheme), and the Quality Assurance Plan itself.

However, other monitoring operations performed prior to construction will be developed in the following sub-chapters, including the inspection and approval of materials, the monitoring of the materials used and process controls.

Inspections carried out during construction are designed to verify the correct application of the technical specifications and compliance with the rules of good practice. Different aspects of these inspections will be described in the following sub-chapters.

Post-construction inspections are designed to ascertain whether the initial objectives have been achieved. If both of the previous types of inspections have been carried out, post-construction inspections will be a formality. Therefore, they will receive only minimal coverage in this chapter.

7.2 - Inspection of geometry The quality and accuracy of the topographic surveying that is carried out before, during and after construction, depends to a considerable extent on the care that is taken over the development of the geometric framework.

Technical Document 4 entitled “Instruction technique sur la surveillance et l’entretien des ouvrages d’art : topométrie" (Technical instructions for the monitoring and maintenance of civil engineering structures: topographic surveying) is currently being prepared by Sétra. In Appendix 3, it provides a number of definitions which help to specify the vocabulary to be used for clarifying the exchanges in this field.

The concepts of measuring points, reference points, frames of reference and networks are thus defined and are clearly explained in the following section.

Measur ing po in t

A measuring point is a point to which coordinates are attributed in order to monitor relative or absolute movements.

Three categories of measuring points can be defined:



• A visible point on the structure: rivet head, hole, paint mark, punch mark

• A point given by a part that has been fixed or welded to the structure: target, leveling stud

• A specific point in relation to a part that has been fixed or welded to the structure and designed to accommodate accessories positioned by forced centring.

Reference po in t

A reference point is the association of a system of orthonormal axes and a point representing the origin of the system of axes and whose movements are to be measured.

As a general rule, the orthonormal reference point is defined by:

• The Ox axis following the tangent to the longitudinal axis of the bridge deck.

• The Oy axis following the normal to the longitudinal axis of the bridge deck,

• The Oz ascending vertical axis.

Frame o f re fe rence

A frame of reference is a system of orthonormal axes (Ox, Oy, Oz) associated with a point of origin O, which is used to identify the position from any point in space.

This conventional system, which is the working reference point established by the surveyor at the start of the topographical operations, is used to calculate the position of the measuring points.

Network

A network is an arrangement of points determined by a set of planimetric and/or altimetric measurements. These points are usually marked out on the site.

Two types of networks may be used in the topographical monitoring of civil engineering structures: absolute reference networks or relative measurement networks.

Topometric operations consist of determining the positions of certain points whose movements will be monitored, in relation to a previously defined network.

7.2.1 - Inspection of pier geometry

Obtaining the correct bridge deck geometry involves considering any data that might have a bearing on the geometry of the piers and using reverse deflections to negate any drift that these data are likely to produce.

7 .2 .1 .1 – Account ing fo r ver t i ca l s e t t l ement

The following effects must be carefully evaluated:

• The settlement of foundations under the action of the selfweight of the pier and the cantilever

• The elastic shortening of the pier due to the same actions



• The effect of shrinkage and creep due to the weight of the cantilever.

The bridge deck is normally supported by bridge bearings which operate between concrete support blocks. An inaccurate estimation of the vertical settlement of the pier may be compensated for by adjusting the thickness of these elements. However, this is a difficult operation requiring careful preparation.

In the case of relatively small structures, it might be possible to consider the settlement of the foundations only.

This approach guarantees a successful closure of the span. While the aforementioned effects may be small for small bridges, they increase in proportion to the height of the piers and the length of the spans. Piers of a hundred or so meters tall, span lengths of approximately 180 m and a bridge deck of 20 m wide may result in downward loads of approximately 20,000 tonnes and a vertical shortening of around 4 centimeters including creep.

7 .2 .1 .2 – Account ing for o ther phenomena

In the case of a rectilinear bridge deck, the construction tolerances inherent to any structure may lead to shifting in the horizontal plane between cantilevers.

However, it is important to remember that a thermal gradient may act upon a pier shaft and cause a horizontal shift of the pier head unit capable of affecting the measurements of movement during the construction of the cantilevers.

In the case of curved bridge decks, it is necessary to examine the effect of the torsional moment applied to the segment on pier by the cantilever under construction. This effect increases in proportion to the height and/or flexibility of the pier.

Indeed, when a curved cantilever is built, the torsional moment applied to the segment on pier causes flexion in the pier shaft which can alter the position of the pier head unit. Therefore, rather than building a perfectly straight pier, it is necessary to anticipate this movement by building in a pre-deformation in the opposite direction. The construction of the cantilever will have the following effects:

• The pre-deformation will be accentuated for the first segments, because the weight of these segments remains offset in relation to the plane containing the pile axis and tangent to the curve of the horizontal alignment of the bridge deck

• The construction of the following segments will gradually straighten out the pier until it becomes vertical, provided that the estimate was correct.

The accuracy of the result is dependent on the awareness of the rheology of the concrete used. The concrete must have consistent characteristics and the conditions of application must be the same throughout all stages in the construction of the pier shaft.

Creep tests should therefore be performed on the chosen formula of concrete in order to obtain an accurate estimate of the deformations in the structure.

7 .2 .1 .3 – Measur ing po in t s to moni tor geometry

Several types of measuring points can be positioned on the structure in order to help the surveyor monitor the geometry. Each point has a specific function



Rive t s

A rivet is a measuring device with a rounded head. It is used to monitor the leveling of a horizontal plane. This inexpensive tool must be made from a hard-wearing, undeformable material designed to resist the effects of weather and impacts on the site. A sufficient number of rivets must be used in order to monitor the elastic curve accurately.

Medal l ions

A medallion is a piece of rustproof metal which is fixed to the structure. It features a rounded upper support surface. The horizontal plane tangent to the top of the sphere supports the sight.

Medallions are used to monitor the levelling of a vertical plane and cost approximately the same as the rivets. As for the rivets, exploitable data are only obtained if a sufficient number of medallions is used. This is particularly important if a bi-directional phenomenon is being monitored.

Targe t s

Self-adhesive targets are discs marked with concentric circles which are attached to bonded metal elements or directly onto the concrete itself, depending on the type of model used. They are used for monitoring verticality in particular.

Targets can be used to measure both angles of orientation of a viewing axis from a known reference marker. If repeated from three markers, this operation provides a good estimate of the position of the target point.

A retroflective target gives a third component in space: namely the distance from the observation point to the measuring point. In certain cases, this component can increase the accuracy of the calculations, provided that this distance is no more than approximately 100 meters. Therefore, it is important to make sure that the type of theodolite used is compatible with the constant of the target in question, as this may vary from one model to another.

The limitations of targets concern the mediocre accuracy of the measurements and the fact that their bonding fails after a few years. Furthermore, on uneven sites, it can be difficult to position three markers with clear visibility between each one.

Pr i sms

Prisms are a little more expensive and are positioned on a bonded base in the form of a corner plate that allows the angle of the prism to be adjusted. A prism gives a direct measurement by defining the sighting angle and the distance to the measuring point from a single known reference marker to which it is permanently directed.

The prism must be sited and angled in such a way as to reduce the damaging effects of dust, bad weather and birds.

This type of measuring point has numerous advantages:

• Greater accuracy for a measuring point which is difficult to access

• Saves time for the surveyor

• Single measurement reduces the risk of error.



As with targets, it is important to check that the modele of theodolite used is compatible with the constant of the prism in question, as this may vary from model to model.

7.2.2 - Monitoring the geometry of the bridge deck

A cantilever consists of several segments, which are manufactured, assembled and stressed at different ages, using a material whose characteristics and composition may vary over time. It is important to predict the exact extent of the deformation of the cantilever element in order to determine an adequate reverse deflection which will be implemented in the prefabrication unit if the segments are prefabricated or in the form travelers if the segments are cast in-situ.

When the structure is isostatic, the deformation of the cantilever is due to:

• The weight of the concrete beam

• The weight of the form traveler or the assembly equipment

• The cantilever prestressing (Fig. 7.1).

The effects of concrete creep and the delayed prestressing losses are added to the instantaneous deformation.

After the closure of the different cantilevers, when the structure becomes continuous and hyperstatic, the bridge deck continues to deform due to the following effects:

• The interior and/or exterior continuity prestressing

• The removal of the form traveler or the assembly equipment

• The removal of the temporary piers and the temporary cantilever stabilizing systems

• The erection of superstructures.



Fig. 7.1 – Concreting curve for a single cantilever Fig. 7.2 – Concreting curve for a standard bridge built by the

cantilever method

Following this, the deformations due to concrete creep and delayed prestressing losses continue to develop.

It is therefore necessary to build in a reverse deflection in order to compensate for these different types of deformations (Fig. 7.2).

The calculation of this reverse deflection must account for the probable values of the different applied loads:

• The density of the concrete must be realistic for the calculation of selfweight

• The coefficients of friction for the cantilever tendons in a straight line and on curves will only increase very slightly

• The weight of the form traveler and the site equipment situated at the end of the cantilever will be evaluated as accurately as possible.

The modulus of elasticity for concrete varies according to the age of the load and the duration of this load. Therefore, it is always difficult to predict and control the deformations resulting from the construction of a cantilever with accuracy. This difficult problem obviously supposes that the actual position of the segment on pier in space is accurately known and is as close as possible to the theoretical position.

For a more detailed consideration of geometric monitoring, it is important to distinguish between cast-in-situ segments and prefabricated segments. Indeed, a different frame of reference applies to each of these methods of construction.

For segments which are cast in-situ using a form traveler, the frame of reference is absolute and relates to the pier, which is also globally referenced. The construction of a new segment makes it necessary to adjust the form traveler considering its position in space in relation to the overall geometry of the cantilever.



For segments which are cast in a prefabrication unit, the frame of reference relates exclusively to the preceding segment. When a new segment is constructed, it is necessary to adjust the prefabrication unit in relation to the end of the segment that is postioned as a matched mold.

7 .2 .2 .1 – Br idge decks cas t in - s i tu us ing form trave lers

Moni tor ing o f l eve l l ing

The monitoring of the levelling of segments under construction is based on a document drawn up by the engineering firm called the "construction pyramid". This indicates the theoretical dimensions to be obtained for each stage in the progression of the cantilever and for each segment joint. These dimensions incorporate all of the forces that apply to the cantilever under construction.

This pyramid is used to determine the dimensions for the adjustment of four key points on each segment joint: both cantilevered ends and both ends of the lower slab, i.e. points P1to P4 shown on Figure 7.3.

P5 P6

P1

P2 P3

P4

Fig. 7.3 – Key points for levelling adjustment

Two additional points will be chosen on site in areas which seem to be the least affected by secondary deformation, i.e. close to the webs, namely points P5 and P6 in Figure 7.3, which will be the first measurement reference to be determined on site. The other points will be verified in accordance with this reference.

The only effect not to be considered in the engineering firm’s calculation is the deformation of the form travelers. This phenomenon must include the form traveler’s suspension bars. The construction of the first segment will incorporate a deformation assumption which will then be adjusted in accordance with the measurements taken after casting. This deformation assumption may include the deflection of the form traveler’s main girders if they were load tested during the acceptance inspection.

Adjus tment o f the form t rave l er

The adjustment of the form traveler is carried out by localization using localized reference points in relation to the segment on pier, which is repositioned globally.

When the form traveler has been moved forward in order to build segment Vn, and before the final tightening of its lashing onto segment Vn-1, the alignment of the formwork equipment and horizontal adjustment of the form traveler are verified by theodolite.

The form traveler is now considered to be properly adjusted in relation to segment Vn-1 and the following operations are carried out:

• Inspection and adjustment of the leveling and horizontal alignment of points P5 and P6

• Inspection of the levelling of the cantilevers and adjustment of points P1 and P4 if required



• Adjustment and monitoring of the leveling of points P2 and P3 defining the height of segment V

• Inspection of the spacing of points P2 and P3, i.e.of the width of the bottom slab.

Once the form traveler has been adjusted, all of the reinforcements for the segments can be installed.

Two corner irons are bolted onto the mask. These are marked with a punch and are integral with the concrete of the upper slab close to points P5 and P6. The upper face of these corner irons is horizontal and is situated 20 mm underneath the extrados for protection. This upper face is kept clear of the concrete during casting.

Finally, an additional levelling inspection is carried out at the level of the mask.

The internal formwork of the form traveler is adjusted:

• At the back, by placing it against the concrete of the previous segment

• At the front, by altimetric adjustment in relation to the external formwork at the level of the supporting beams (points P7 and P8).

Moni tor ing the geomet ry

Once the casting of the segment Vn has been carried out, it is necessary to carry out a general inspection of the levelling of the cantilever. This operation begins as early as possible the following morning. This is the best time of day to avoid the manifestation of parasitic forces due to temperature. A cantilever that is subjected to a temperature gradient behaves like a highly sensitive bimetallic strip. The operation must be completed as quickly as possible.

The corner iron is unbolted so that the mask can be removed. The corner iron becomes the measuring point for monitoring the deformations of the cantilever.

The levelling measurement is carried out from segment Vn, which has just been concreted to the SOP, and is repeated at each joint of the segment. The values measured are recorded on the monitoring documents and are compared with the values given by the construction pyramid.

By analyzing the deviations that are observed (which is always a difficult operation), corrections can be made to the adjustment of the form traveler for the construction of segment Vn+1.

The levelling measurements are completed before the form traveler is moved forward and before the prestressing is tightened. Particular attention must be paid if heavy equipment such as a mobile crane is present on the cantilever that has already been constructed, in order to ensure that the measurements are taken under identical load conditions. Additional measurements can be performed in other phases if necessary.

It is important to pay great attention to the consistency of the measurements taken on site and the information given by the construction pyramid. Any correction of the measurements must be performed after examining the assumptions and the data used to create the construction pyramid. If differences go uncorrected on the first cantilever, the risk of error becomes greater the closer we get to the closing segment with the cantilever already constructed

The simultaneous monitoring of the geometry of the support is essential to ensure that the surveyor is always capable of relating the pyramid to the absolute dimensions of the objective to be achieved.



Finally, it should be mentioned that for the construction of cast-in-situ segments using form travelers, the sequence of operations always starts on the same side of the cantilever in general. There is no point in accounting for this dissymmetry in the calculations if the form travelers are always adjusted on the basis of the measurements made in the morning. On site, however, this sequence of operations could be modified by reversing the order of casting if the levelling measurements reveal a systematic discrepancy between the two sides of the cantilever.

7 .2 .2 .2 – Br idge decks cons i s t ing o f pre fabr ica ted segments

During the setting up and commissioning of the prefabrication units in the prefabrication workshop or plant, a number of precautions must be taken to facilitate the work of the surveyor and increase its reliability.

This means verifying:

• That the longitudinal axes of the units follow the same alignment, which is called the prefabrication axis

• That the points which are used to measure the alignment and to mark out the prefabrication axis are adequately spaced and perfectly visible from the units

• That the theodolite support frame is not exposed to hot sunshine, which reduces the size of the alignment corrections

• That the support for the theodolite and the level are correctly in line with the prefabrication axis and that these appliances are placed slightly above the upper level of the concrete of the segments

• That the reference point used for measuring the levelling is separate from the mask. This point could consist of a measuring point on the structural steelwork of the unit or a graduated rule permanently attached to a concrete post.

Adjus tment o f the match-cas t s egment

This is a complex topographical problem, as it involves constructing the independent segments on the ground in such a way that they can be assembled in space in accordance with the established geometric data (Fig 7.4).



Fig. 7.4 – Adjustment of the match-cast segment

A prefabrication unit is described in Paragraph 6.2.1 and Figure 6.28 of this guide. Three parts of this unit can be considered from the perspective of adjustments and monitoring:

• An initial mobile part: the core or internal formwork of the segment, which leans against the mask on the one hand and the matched mold on the other; it requires no adjustment

• A fixed part, the mold or the unit itself, consiting of the mold base, the sides, wings and the mask; in theory, this is fixed and its assembly requires great precision

• A second mobile part: the matched mold, consisting of the previous cast segment, placed on jacks used to adjust the angle and position according to the geometric data.

The choice of adjustment points is thus of paramount importance. Their positions are identified by corner plates bearing a punch mark or, better still, with a hemispherical indentation into which a ball bearing can roll. The recommended configuration for these corner plates is shown in Figure 7.5:

• The adjustment points for levelling are situated in the areas least affected by deformations

• The adjustment points for alignment follow the segment’s true axis.

The measuring points may also consist of small plates capable of housing a mini-prism.



Fig. 7.5 – Adjustment points for a prefabricated segment

It is essential to position the points in such a way as to avoid any possibility of them being moved at elevation when the casting is completed and to set them back slightly from the joint in order to protect them.

An additional precaution is taken for structures with a curved longitudinal profile or a variable transverse slope: the distance from the measuring points to the joint and the axis of the segment shall be identical from one segment to another.

Topograph ica l inspec t ion in s tandard cons t ruc t ion cyc le s

The construction of a standard segment Vn requires three topographical inspections to be carried out on segment Vn-1:

• Mapping of the levelling points and the prefabrication axis on Vn-1 in the prefabrication unit

• Adjustment of Vn-1 in the match cast position

• Mapping of Vn-1 in the match cast position after casting of Vn.

Two precautions must be taken during these operations:

• The surveyor must take the measurements before the removal of any of the formwork, as any impacts could compromise the accuracy of the measurements taken

• It is advisable to check both alignment measuring points systematically before and after each operation, as slight deformations may affect the base of the theodolite (due to strong sunshine or instability).

The final inspection concerns the recording of measurements of length.

Adjus tment o f the segment on p ie r

The segment on pier is particularly difficult to adjust. Accuracy is of the utmost importance because the accuracy of the geometry of the cantilever to be built depends upon this adjustment.

In order to obtain a precise adjustment in space, it is possible to use angled blocks, wedges, bolts, etc. to make fine adjustments to the position of the segment.

During the manufacture of the segment in the prefabrication unit, it is also important to provide secondary alignment measuring points which mark out the entire width of the transverse axis of the segment (Fig. 7.6).



Fig. 7.7 – Adjustment of the segment on pier at ground level Fig. 7.6 – Alignment markers on the segment on pier

These measuring points are used to make adjustments at ground level through the observation of both axes of the segment (Fig. 7.7).

Method for moni tor ing changes in geomet ry

Base curves, namely the alignment curve and the two levelling curves i.e the longitudinal profiles given by the position of the rivets, are used to monitor and control changes in geometry.

The effects of the weight and bevahior of the concrete, prestressing and superstructures are anticipated and compensated for via reverse deflections calculated by the engineering office. Although it is essential to incorporate these reverse deflections, their calculation is only approximate and uncertainties remain with regard to the accuracy of the geometry.

In order to track the changes in the actual geometry of the cantilever, simultaneous digital and visual inspections are carried out in the form of graphs, base curves and the monitoring of lengths. These inspections obviously incorporate the adjustment dimensions that result from the measurement of the existing segments and are applied to the next segments to be manufactured.

The monitoring may reveal a systematic lateral drift if the stressing of the cantilever tendons always starts from the same web. To counteract this, the order in which the cantilever tendons are stressed can be alternated.

Excep t iona l correc t i ve ac t ions

It is possible that a mistake in the prefabrication might be overlooked on the prefabrication site, thus leading to a fault in the geometry of the cantilever during the assembly process.

In the event of a major fault, the solution might be to disconnect one or more segments and carefully place wedges in the joints with the segments securely lashed together. The remaining spaces between the joints must be caulked before the segments are prestressed, taking care not to create obstructions in the sheaths that pass through the modified joints.

This illustrates the importance of ensuring the accuracy of the geometry for prefabricated segments.



7 .2 .2 .3 – Comments concern ing both t echniques

Compar i son o f de format ions

For the construction of both cast-in-situ and prefabricated segments, it is necessary to analyze each phase in the construction of the cantilever and to determine the deformation curve for each cantilever element, phase-by-phase.

An example of a five-segment cantilever is shown in Figure 7.8 hereafter.

The line 1-2-3-4-5 represents the envelope of the different deformations, or the trajectory followed in space by the end of the cantilever at each phase of construction.

By modifying the angular positions of the segments in small angles of α1, α2, etc., the cantilever may be constructed in such a way that once completed, it has a satisfactory longitudinal profile, as shown in Figure 7.9 for the example in question. In each section, the modified profile will effectively compensate for the future deformation.

Fig. 7.8 – Deformations phase-by-phase

Fig. 7.9 – Correction of the profile to compensate deformations

It is interesting to compare the relative importance of the deformations and reverse deflections affecting prefabricated and cast-in-situ segments. Figure 7.10 below shows these relative values for a structure designed according to these two methods.



Fig. 7.10 – Comparison of deformations for prefabrication and casting in-situ

The design assumptions given in this figure show that in the majority of cases, the difference between the methods will be greater if a cycle of less than one week is used for the in-situ casting of the segment and if the prefabricated segments are stored for more than two weeks.

Whatever the circumstances, the deformations affecting a cast-in-situ cantilever will normally be two to three times greater than for an equivalent prefabricated cantilever.

Inspec t ing the geomet ry o f the compe ted can t i l ever

Once completed, the geometry of the cantilever must be inspected; this inspection must be carried out as early as possible in the morning. This involves plotting curves corresponding to all of the measuring points in order to obtain a geometrical representation of the area obtained.

The advantage for a cast-in situ cantilever is that corrections are made after each casting. Corrections are therefore less likely to be needed when the cantilever is completed.

If the entire cantilever is incorrectly aligned, it is possible to improve its geometry to a certain extent by using hydraulic jacks to alter the position of the segment on pier after the stitching tendons have been slackened off, if the cantilever is simply supported on the pier. This may require the modification of the adjustment pyramid for the adjacent cantilever if it has not yet been constructed. If the errors are significant, the general longitudinal profile will have to be rectified.

If the cantilever is embedded on its pier, the misalignment can only be compensated for over the length of the closing segment. The lashing of the last cantilever segment to the opposite cantilever, or the loading of the higher cantilever may partly rectify this misalignment. However, such a manoeuvre is ill-advised, as it has the disadvantage of modifying the stress state that was designed for the structure.

If the curves corresponding to all of the measuring points reveal localized irregularities, the following actions may be considered once the whole structure is completed and continuous:

• It may be possible to plane off the humps, provided that a sufficient thickness of concrete remains over the reinforcements



• If hollows exist, they must first be outlined by a trench of at least 10 mm; they can then be filled with resin. After the application of the waterproofing, a first layer of asphalt will be applied and then planed in order to modify the profile, supposing that the profile has been accurately determined in advance and allows for thermal effects, for example. A second layer will then be applied. The disadvantage of such a process is that it limits the thickness of any new layers of asphalt that will be added to the pavement at a later date

• An extra layer of asphalt may be sufficient to level out the irregularities, but this technique also limits the thickness of any new layers of asphalt that will be added to the pavement at a later date.

7.2.3 – Monitoring the geometry of the f inished structure

7 .2 .3 .1 – The compromise between commiss ion ing and inf in i t e t ime

For 15 to 25 years after the bridge is commissioned, creep continues to affect the structure. After this time, the evolution of delayed deformation is normally no longer significant. Therefore, in the first part of the life span of the structure, deformations continue to affect the bridge deck. For the majority of structures, this is illustrated by a lowering of the reference axis, the extent of which varies according to the sections in question.

The theoretical reference axis during construction must therefore be specified.

If the theoretical longitudinal profile were to be obtained at the start of the bridge’s service life, this would lead to a gradual decrease in user comfort over the years, corresponding to the development of creep within the structure.

On the other hand, a policy of aiming to achieve the theoretical profile in the long term would result in a structure that might be uncomfortable at the start of its service life, but this would improve with age.

Therefore, a compromise can be sought: the target profile is considered to be midway between the profile when the bridge is commissioned and the long-term profile. The comfort of the structure can be optimized by adjusting the thickness of the surfacing. This may be adapted throughout the decades in which the structure is in use.

It is essential that the chosen profile and the profile that is actually obtained are clearly defined in an appropriately referenced document. Both of these elements must form part of the as-built file and shall be included in the zero-point file for the structure.

7 .2 .3 .2 – Moni tor ing the de format ion o f s t ructures subjected to load ing t e s t s

For non-standard structures, these tests shall involve the systematic testing of all of the characteristic sections of the structure, i.e. at least the sections on supports and the sections of greatest flexion on the span.

If the structure consists of a large number of almost identical spans, the testing of bearing sections can be limited to just a few spans. However, it is important to carry out a load test on the middle of each span.

Although load tests involve no more than a simple observation, a number of special precautions must be taken.

Carry ing ou t the measurements

When test trucks are used, it is important to start by loading the supports. The corresponding topographical measurements are recorded for information purposes. A zero-point measurement is then taken which is used to accurately determine the height differences between the supports and the middle of spans.



For box girder bridge decks, it may be beneficial to perform precise levelling measurements from inside the box girder as this provides good measuring conditions and there is no interference from the trucks.

Before performing the measurements under load, it is necessary to wait for the structure to stabilize. This period can be estimated at 10 minutes after the trucks have been positioned. In any event, the measurements cannot be taken until the trucks’ engines have stopped.

The measurements are taken from points marked by studs or rivets with rounded heads which have been carefully positioned and provide a single point of contact with the base of the levelling rod. Laser sightings may also be performed.

Analyz ing the re su l t s

The precise analysis of the results requires an adequate knowledge of the unladen thermal behavior of the structure is established, which also allows the thermal effects to be dissociated from the combined effects of the test loads.

The deflection values obtained during the tests are considered to be satisfactory when the measurements taken coincide with the authorized range for the values calculated (1.1 times the probable values / 0.8 times the probable values), allowing for the uncertainty of the measurement. This range, which conforms to the value recommended by the "Guide des épreuves des ouvrages routiers" (Guide to Testing for Road Structures) currently being prepared by Sétra, corresponds to a design-based approach that is more accurate than the current methods.

The design assumptions must not be too conservative. Instead, they should be as realistic as possible as physical quantities will be measured. In particular, it is important to account for:

• Deformation due to shear force in the beams

• The contribution of the superstructures to the rigidity of the structure

• The law of the actual behavior of the materials derived from the testing of test samples

• The rigidity of the supports, mainly with regard to rotation

• The skew of the structures

• The curvature of structures

• The cracking of parts operating as reinforced concrete and the reduction of torsional inertia due to the cracking

• The effective width of the slab on supports

• The probable prestressing value (using the results of the measurements of transmission factors) for partially prestressed structures

• The actual geometry of the structure, if on-site incidents have led to modifications.

If the deflection values are unsatisfactory, the results must be examined with a critical eye in order to find an explanation for the anomalies: non-linearity of the behavior, abnormal changes in the deflections measured for a



non-standard section, etc. A new calculation must establish a range of theoretical values to be monitored on the structure, based on realistic high and low assumptions made for the significant physical values.

In all cases, after performing a global analysis, the engineering office draws up a summary report. The Owner decides whether or not the deflections are satisfactory according to the Construction Manager’s recommendations.

7.3 - Inspection of temporary structures It is increasingly common for temporary structures to be listed in the first category under the terms of Article 41 of fascicule 65A of french CCTG. This does not include scaffolding, working platforms and protective structures.

Article 42 of this fascicule defines the role of the Chargé des Ouvrages Provisoires (Head of Temporary Structures – COP).

It is important to emphasize that the COP cannot, under any circumstances, replace an external inspection agency approved by the French Ministère du Travail (Ministry of Labour), either at the design stage or during construction on site. This important point should be clearly explained in the STC (Special Technical Clauses).

7.3.1 - Inspection of form travelers

The different phases in the inspection of a form traveler, from its design through to its use, are sequenced in the following way:

• External inspection of the design calculations for the dimensioning of the form traveler focusing particularly on the load-bearing elements.

• External inspection of the supporting beams using load testing to examine their elastic behavior and evaluate their remanent deformations, to examine the welds after loading and to measure and monitor the deflections.

These inspections are carried out by an organization approved by the Ministry of Labor such as french APAVE, VERITAS, SOCOTEC, etc.

• External inspection by the Construction Manager who verifies that all documents guaranteeing the traceability of the different inspections are available in accordance with the company’s Quality system

• Manufacturer’s inspection of the equipment in order to verify the conformity of the different manufacturing stages

• External inspection of the conformity of the assembly of the form traveler on the segment on pier, carried out by an approved organization upon completion of the assembly and before casting.

It should be emphasized that an inspection by an approved organization involves much more than a simple visual inspection of the apparent condition of the equipment. This inspection must produce a general report, confirming that all of the inspections required for the approval of the equipment have been performed and guaranteeing that the construction is consistent with the design. It must be rounded off by a definitive acceptance report attesting to the conformity of the equipment i.e. its fitness for use.



• Inspection by the COP of the conformity of the assembly of the equipment on the segment on pier, performed upon completion of the assembly and before casting

• Inspection by the COP of the validity of the procedure used to move the form traveler forward. This procedure will also be internally monitored on a systematic basis every time the equipment is moved forward.

Before the first time the form traveler is properly used, it is essential to define the maximum number of times the high-tensile steel bars forming the hangers can be used. This number shall be determined prior to the start of work on site (see paragraph 7.5).

Finally, although this concerns the use to which the equipment is put rather than the form traveler itself, it is important to mention that the contractor shall perform an internal inspection of the adjustment of the equipment after it has been moved forward and before the reinforcements are installed.

7.3.2 - Trial assembly of a form traveler

This does not refer to an assembly carried out by the manufacturer of the equipment in the factory, but to a “test” assembly that is normally carried out on site, in order to test the supporting beams, which are the main structural components.

These beams are assembled on a flat surface, in opposition with the insertion of jacks. The resulting deflections in these elements are verified under loads which increase progressively until the nominal load corresponding to the forces encountered when the equipment is in service is reached.

7.3.3 - Centering

Chapter IV of fascicule 65A of the french CCTG covers temporary structures, with centering specifically described in Article 45.

7 .3 .3 .1 – Tes t ing o f bear ing capac i ty o f the so i l

The testing of the bearing capacity of the soil for centering must be covered in the company’s QAP.

It is essential to verify the soil that will support the centering. To this end, it is possible to perform a static plate load test defined by the standard NF P 94-117-1 of April 2000. This involves determining a value for the modulus of the soil by subjecting it to the action of a plate whose diameter and stiffness are normalized according to a standardized procedure, and then by measuring how far it sinks down.

Plate load testing provides a model, but the design verifications for centering are expressed in the form of pressure exerted on the soil. For typical cases concerning 1 m x 1 m sole plates, with compaction limited to 3 mm and for soils with no underlying soft layers, the inspection of bearing capacity may be performed while assuming that the value of the modulus at the plate Ev2 is 350 times greater than the permissible soil pressure.

In the case of vertical types of centering, it is important to be particularly attentive to the risk of differential compaction due to the presence of a large number of supports and to the effects of successive compactions on the geometry and stresses.

7 .3 .3 .2 – Inspec t ion o f equ ipment

The inspection of the equipment used in the centering must be covered in the company’s QAP.



It is important to highlight the dangers that could be caused by any laxity with regard to the inspection of the equipment in use. Any makeshift repairs could soon lead to a catastrophe. Therefore, the COP must certify that all of the elements used in the centering are fully functional.

When inspecting the centering, two factors must be considered: the wear of the equipment and the extent of any corrosion.

The wear of the equipment relates to its use on other sites. Fascicule 65A (Article 4 of Appendix B, in addition to Article 44) uses a coefficient α in order to reduce the bearing capacity of the equipment. The value of this coefficient can be as low as 0.75 for equipment with more than 10 consecutive uses.

In the same way, the corrosion of the equipment due to its different uses and periods of storage is determined in the calculations using a reduction factor β equal to:

Corrosion condition β Absence of corrosion 1 Slight corrosion (presence of oxide modifying the color of the element)

0.95

Notable corrosion (small, thin particles of oxide) 0.85 Major corrosion: the element cannot be used

The two coefficients α and β are accumulated.

7 .3 .3 .3 – Inspec t ion o f the erec t ion

The inspection of the centering erection must be covered in the coontractor’s QAP.

The inspections must target the areas of greatest risk in the centering structures. Therefore, the following areas and inspections must be covered:

At the base of the centering:

• Verify that the manufacturer’s recommended runout ranges for the jacks are not exceeded

• Check that drainage has been installed on the platform in order to channel the runoff

• Make sure that improvised extensions and wedges are not used.

In the intermediate section:

• Inspect the bracing on towers, posts and girders

• Verify the convergence of the joints in the centering structure

• Makes sure that the horizontal forces are correctly taken up.

At the top of the centering:

• Follow the same precautions as at the base



• Verify that the structural beams or girders are correctly centred in the forks

• Make sure that any risk of accidental relative movement is avoided above the metal-to-metal contacts.

At the level of the planking:

• Check that the load transmission areas have been stiffened

• Verify that there is no irregular and/or complex stacking

• Check the reliability of the support conditions

• Verify the existence of lateral limit stops if there is a danger of slippage

• Make sure that bracing is fitted in all directions.

7 .3 .3 .4 – Inspec t ion o f de format ions

It is important to inspect any deformations of the centering throughout the entire casting phase and to monitor the compaction of the supporting soils. A simple way to monitor this compaction consists of attaching vertical bars under the centering which meet a fixed independent marker at ground level.

The monitoring of deflections is designed to:

• Verify whether the final target profile will be obtained

• Detect any anomalies that might be indicative of an imminent accident.

7.4 - Inspection of concrete Article 76 in fascicule 65A of the french CCTG defines all of the elements involved in the inspection of the manufacture and application of concrete.

7.4.1 - Inspection of the components

Article 23 of fascicule 65A describes the inspection procedures for the constituents. The following additional points should also be noted.

7 .4 .1 .1 – Inspect ion o f the mix ing water

The mixing water must conform to the standard P 18-303 of August 1999 which prescribes appearance tests, chemical tests and defines the testing methods, the frequency of these tests and how to evaluate the conformity of the water being tested.

Drinking water usually conforms to the standard. However, under specific climatic conditions, particularly in tropical regions, drinking water may not conform to the requirements of the standard.

The use of seawater is strictly prohibited.



7 .4 .1 .2 – Moni tor ing o f cement

The acceptance inspection involving the rapid identification test defined by the standard P 15-466 of August 1983 is used by the contractor to verify the conformity of the cement at every delivery. Precautionary samples are thus taken.

External monitoring tests in the framework of the standard P 15-300 of December 1981 enable to contractor to confirm this conformity. For example, these tests may involve the following operations:

• Measurement of specific surface

• Determination of strength after 2 days

• Measurement of anhydride sulfurique SO3 content, or Na20 equivalent, or shrinkage test for cements exposed to the action of deicing salts

• Measurement of hydration heat, tricalcium aluminate C3A content, or shrinkage test if these characteristics are significant, etc.

External inspection tests are carried out by the Construction Checker and its laboratory.

7 .4 .1 .3 – Inspec t ion o f aggregates and addi t ives

Internal inspections must be carried out at two levels: by the producer and by the contractor. Their main elements are:

• For sands: Sand equivalent, particle size, fineness, hygrometry

• For chippings and pebbles: particle size and cleanliness

• For aggregates: sulfate, sulfide and chloride content

• For additives: expiry date, characteristics specified by the standards.

The contractor’s external inspection consists of an acceptance inspection and possibly spot checks corresponding to tests laid down in the standard P 18-540 of October 1997. Inspections of storage conditions for the aggregates and additives may be added to these.

7 .4 .1 .4 – Moni tor ing the a lka l i reac t iv i ty po tent ia l o f the aggregates

Monitoring the alkali reactivity potential of aggregates is a complex task which is covered in detail in the “Recommandations pour la prévention des désordres dus à l’alcali-réaction" (Recommendations for the Prevention of Problems Relating to Alkali Reactivity” published by the LCPC (Central Public Works Research Laboratory) and in the appended document "Guide pour l’élaboration du dossier carrière" (Guide to the Creation of the Quarry File).

Furthermore, Sétra’s "Guide pour la rédaction des pièces écrites des marchés" (Guide to the Drafting of Written Documents for Contracts) concerning the "Prevention of Problems Relating to Alkali Reactivity" lists the clauses to be inserted into the written documents for the DCE (Document de consultation des entreprises) [Contactor Tender Document] and the contracts.



Considering these two documents, major structures are usually placed in category C. As a consequence, only NR (non-reactive) or PRP (potentially reactive to pessium effect) aggregates shall be used in their construction.

7 .4 .1 .5 – Et tr ing i te format ion in concre te

Presen ta t ion

The deterioration of concrete due to sulfates has been known about since the beginning of the 20th century. It may have internal or external origins.

If it has external origins, it is caused by industrial emissions, the presence of sea water or the action of constituents of the soil in contact with the concrete (this applies to gypsum, for example). This is a known effect and the recommendations of the standard NFP 18-011 of June 1992 help to control it via the choice of cements and the concrete formulas.

If the problem has internal origins, it bring sulfates in the cement into play. These consituents are required for slowing down the setting of the concrete. As the problem appeared relatively recently, less is known about it. Indeed, its existence was only reported in 1986, concerning problems in prefabricated parts which look similar to those caused by alkali reactivity, but which are, in fact, a different type of pathology.

This sulfate reaction of endogenous origin, which modifies the hydration reactions of concrete, has been observed in many countries, although France has only recently started to pay serious attention to it. It is true that it remains a limited phenomenon, as it only concerns around 10 structures in France at present. However, as certain application conditions and certain current trends appear to be favorable to its appearance, it wouild appear to be important to summarize the current levels of knowledge about this problem ([DIV 98] and [DIV 00]).

Parameters

While the alkali reactivity of concrete is governed by the three main parameters of moisture, alkali content and reactive silica content, ettringite formation in concrete seems to be a more complex phenomenon.

Moisture is essential to the process. Parts of the structure which are subjected to alternate wetting and drying, such as those exposed to differences in water level, are all the more vulnerable.

Temperature increases are equally important. Different authors suggest different upper limits, and their recommendations relate more to a precautionary approach than to objective studies. However, this temperasture range does depend on the type of cement used. A low sulfate and alkali content allows for a higher temperature limit.

The composition of the cement is important in terms of the contents of three of its constituents: tricalcium aluminate, sulfates and alkalis.

The type of aggregates must finally be mentioned. Indeed, with a limestone aggregate, the cement mixture has better adhesive properties, which seems to prevent interstitial dissolution.

It is noticed that there is a greater number of parameters than for alkali reactivity. This indicates that it is a more complex, though less frequent phenomenon.

Prob lems , ana lyses and precau t ions

The problems observed have three underlying causes:



• Construction systematically carried out during the summer, a period in which the temperature of the concrete is higher

• Use of cements that are too rich in high-risk components

• Use of highly exothermic cements.

This demonstrates the importance of choosing the correct type of cement. Indeed, the clinkers in modern cements are ground increasingly finely, rendering the mixture particularly volatile and subject to large increases in temperature.

This risk seems to increase for the construction of bigger parts; in this case, particular care should be taken to choose less exothermic cements.

There are certain statutory texts which cover this problem at least partially:

• Standard ENV 13 670-1 of September 1999 (construction of concrete structures). Paragraphe 8.5 "Cure et protection des bétons coulés" (Curing and Protection of Cast Concrete) limits the temperature in large parts to 65°C

• The European pre-standard Pr EN 13 369 of 1999, which requires testing and recommends very low temperature limits.

In this respect, France is far behind many other industrialized nations. Based on the current state of knowledge, it would seem to be advisable to check the moisture levels of the environment; in a dry environment, the risks are obviously very small, but in a wet environment every precaution should be taken to ensure that the temperature of the concrete does not exceed 65 to 70° C and to opt for cement with a low alkali content. Indeed it would not be reasonable to allow concrete temperatures to reach 80 or 90° C as this could risk reducing the life span of our structures.

7 .4 .1 .6 – Su i tab i l i ty t e s t and contro l t e s t

The suitability test is used to verify the likelihood that the nominal formula of the concrete and its implementation conditons satisfy the requirements of the contract in terms of its strength and the application conditions. It is particularly useful for verifying the concrete resistance to frost and the effects of deicing salts, where necessary. Article 77.1 of fascicule 65A provides information about the nature of this test.

The control test is used to verify the conformity of a batch of concrete. The control procedure is detailed in Article 77.2 of fascicule 65A.

7.4.2 - Information tests

7 .4 .2 .1 – The main in format ion te s t

The aim of the information test is to verify that, under actual hardening conditions, especially with regard to ambient temperatures, the strength achieved at an early age j, corresponding to a very precise phase of construction, is above a predetermined value fcj .

This value fcj is establishjed after analysis in order to make sure that the strength of the concrete us compatible with the construction procedures set out in the QAP, particularly in the casting program or prestressing program.



For example, these tests shall concern:

• Removal of formwork from pier shafts

• Removal of formwork from pier crossheads

• Removal of formwork from lateral overhangs on the bridge deck cross section

• Removal of formwork equipment from inside the box girder

• Removal of falsework from parts of the structure built on centering

• Stressing of certain tendons (generally cantilever tendons): in this case, the tensile strength value ftj is just as important as fcj

• A temporary or permanent loading operation.

The information test may also have other aims, e.g. to verify that the compactness of the concrete, a genuine guarantee of durability, conforms to the expected values.

7 .4 .2 .2 – Addi t iona l in format ion te s t s

Additional tests are normally carried out as of the 7th day in order to make sure that the required level of strength at is likely to be obtained at 28 days.

A third type of information test may be performed in order to obtain information about characteristics that are not specified in the contract such as the modulus of elasticity, tensile strength (if this was not evaluated in the main information test), long-term strength, creep effects, etc. In this case, these tests could be considered to be control tests.

7 .4 .2 .3 – Condi t ions o f execut ion

The test samples used fore the information tests shall be obtained and conserved in accordance with the provisions of the standard P18-405, and of articles 1.5 and 6.3 of the P18-504 documentation booklet.

The concrete shall be cured in accordance with the recommendations of Article 74.6 of fascicule 65A.

7.4.3 - Maturometry

7 .4 .3 .1 – The pr inc ip le o f maturometry

Maturometry is based on the existence of a relationship between the quantity of heat released by concrete when setting and its mechanical properties.

If the same type of concrete is subjected to different thermal conditions but releases the same amount of heat since the start of the manufacturing process, it will have the same mechanical strength.

In physical terms, this is shown by the fact that the hydration levels of the concrete will be identical.



Arrhenius’ Law is used to express the changes in the strength of concrete according to a temporal parameter: the concept of equivalent age, which is independent of temperature. The concrete is characterized in an instrinsic manner using a “reference curve”.

7 .4 .3 .2 – Pract i ca l eva lua t ion o f s t rengths

The reference curve is established by measuring the strength of standardized test samples stored at 20°C on precise dates. The thermal monitoring of the concrete in these test samples is used to calculate an equivalent age of this concrete at the desired reference temperature on each of the test dates at which the strength is tested until breaking.

The apparent activation energy of the concrete must be known for this last operation. This depends on the type of cement used and is adjusted according to the temperature.

In addition, thermistors linked to a central readout station are implanted in the concrete of the most recently cast part of the structure and the temperature is recorded at regular intervals.

To exploit the data from these measurements, it is necessary to:

• Transform the actual age of the concrete into an equivalent age (time required for the concrete to develop the same degree of hydration under isothermic conditions at 20° C)

• Read off the strength value corresponding to this equivalent age on the reference curve for the concrete.

This evaluation can be performed directly by the maturometer, which shows the level of strength obtained in the concrete at the different positions where the thermistors have been implanted.

7 .4 .3 .3 – Advantages o f maturometry

In practice, the temperature histories of the test samples used for the information tests are very different to those of the concrete that forms part of the structure. Therefore, there is a risk that the strength measurements obtained for these samples may not be representative of the actual situation.

Furthermore, the validity of the laboratory compression test is affected by the method used to remove the samples from their container.

This illustrates the advantages of maturometry, because this process is not affected by different temperature histories and only uses the total quantity of heat. It also shows the advantage to measure the maximum temperature obtained in the middle of the concrete.

The significant reduction in the number of test samples required is also an advantage of this process, although it is essential to use a sufficient number of samples to guarantee the validity of the measurements. For every five findings by maturometry, one test sample shall be verified using a conventional information test.

7 .4 .3 .4 – Requirements for the use o f maturometry

The method requires the use of an activation energy value that corresponds to the type of cement, to any additives used (e.g. extra fillers), and to the external ambient temperature. This activation energy will then be confirmed or adjusted by referring to the strength/equivalent age curves obtained from the analysis of test samples.



These tests are performed on samples stored at different temperatures, e.g. externally, in the laboratory, in an isothermic box kept in the laboratory, etc.

Calibration may be quite a lengthy process; it will therefore be necessary to allow a sufficient period of time for this process starting from when the concrete formula has been specified (3 to 4 months may be required). It should also be noted that the maturometer must be recalibrated at regular intervals (see manufacturer’s instructions).

As far as the measurements themselves are concerned, the first choice to be made is to determine the critical areas of the structure in which the evolution of strength is representative of the operation to be tested.

If the aim is to determine the age at which the concrete is strong enough to resist the removal of formwork, instruments will be placed in the area in which the last mix of concrete was added. It is also necessary to position thermocouples so that information can be obtained for parts of the bridge deck box girder, for example.

Remote temperature sensing elements are used to evaluate the mass effect in the webs, which helps the maturing process, and measure heat losses in the upper slab close to the edges. These can be positioned according to the plan shown in Figure 7.11 below, for example.

Fig. 7.11– Maturometry: an example of a layout for temperature sensing elements

7.4.4 - Inspecting the application of concrete

7 .4 .4 .1 - Appl i ca t ion

For the construction of cast-in-situ segments, the planned sequence of operations generally starts at the same side of the cantilever. This sequence of operations can be modified by reversing the order of casting if the levelling measurements reveal a systematic discrepancy between the two sides of the balanced cantilever.

The inspection of the application of concrete must focus on the following points:

• Cleanliness of the bottom of the formwork

• Availability and condition of the equipment required

• The release of pressure from the jacks used to adjust the matched mold for segments prefabricated in the prefabrication unit

• The conformity of the composition of the concrete shown by the information given on the delivery slip. It is essential that the delivery slip shows the following information: the differences between the theoretical weight and the actual weight of the constituents expressed as a percentage, and the water content of the aggregates so that the total quantity of water can be recalculated



• The slump test and the estimate of entrained air. The slump test is difficult to perform when the concrete is in liquid form: the wattmetric readings of the output of the mixer motor are therefore an important source of information and these readings must be attached to the delivery slips. The presence of this information will be verified during the acceptance inspections

• Compliance with the casting plan for the application of the concrete (fascicule 65A, Article 75.3): maximum time from the end of the manufacturing process to the completion of casting, casting phases, height of drop, vibration, floating of the upper face of the lower slab for which formwork was not used

• At the end of casting: surface condition, possible use of thermal protection devices, cleaning of starter bars, and treatment of construction joint surfaces

• Check that any thermal devices are operating correctly.

Fig. 7.12 – Precautions to take for the casting of segments

It is particularly important to comply with the casting plan. Figure 7.12 above shows the main precautions to be taken.

An addtional precaution to be taken for the casting of very tall segments is to use tubes which are designed to reduce the height from which the concrete is supplied, therefore minimizing the risk of segregation. These tubes can be shortened as the operation progresses.

For high-quality casting, the vibration of the concrete must be carefully controlled in order to eliminate segregation and voids. The main precautions to be taken are summarized in Figure 7.13 below. It is particularly important to make sure that vibration is not carried out in the immediate vicinity of prestressing ducts. As a precaution, guide channels can be used in conjunction with the vibrating needle. These consist of expanded metal mesh cylinders which are securely attached to the reinforcements.



Fig. 7.13 – Precautions for the vibration of concrete

The final inspections for the application of concrete consist of:

• Verifying that the required levels of strength have been obtained before authorizing the removal of formwork

• Performing a general inspection of the segment, either at the extremity of the cantilever or in the reception area for a prefabricated segment.

After the inspection of a prefabricated segment in the reception area, a specific identification number is painted onto the concrete of the web inside the box girder on the side of the mask.

Special conditions apply to the manufacture and application of concrete if the temperature recorded on the site falls below 5°C or rises above 25°C. In this case, special provisions must be made to produce concrete at a temperature of approximately 15 to 20°C. Upper and lower limits of 5°C and 40°C must not be exceeded during the manufacturing process.

These provisions are described in detail in "Procédés généraux de construction - tome 1" (General Construction Procedures-Information Document 1) by J. Mathivat and C. Boiteau, and "Le béton hydraulique - mise en œuvre" (Hydraulic Concrete – Application) by J.M. Geoffray [GEO 96].

The recommendations of Article 74.3 of fascicule 65A must be followed for the treatment of construction joints.

7 .4 .4 .2 – The t e s t segment

It is always essential to construct a test segment. This may be reduced to a half-test segment for economic reasons.

This element must be manufactured under actual site conditions in order to give an accurate picture of the problems encountered in the casting of segments.

This element must be truly representative of the difficulties that are likely to be encountered on site. Therefore the test piece will be artificially subjected to the full range of potential problems. Therefore, this segment will normally be at least two meters long in order to include a prestress anchor block.



The following points will be verified in particular:

• Conformity of the facings (color, appearance, etc.)

• Casting methodology (application, vibration, drying)

• The setting behavior of the fresh concrete in lower slabs without upper formwork

• The practicality of the implementation of internal ducts, transverse single-strand tendons and reinforcing bars, particularly in problematical areas

• It will also be verified that the physical references for the adjustment of the alignment of prestress tendons are accurate, unambiguous and fully understood by everyone working on site.

Differences and changes in temperature over time may also be recorded. Samples may also be extracted for subsequent testing.

A specific procedure must be developed for the construction of the test segment.

7.4.5 - The application of high-performance concrete

A certain number of specific precautions must be taken with regard to the manufacture and application of high-performance concrete.

The concrete plant must be capable of handling silica fume, and staff must be properly trained.

When transported in the truck mixer, the concrete behaves like a fluid, with the associated risks of spillage. Vigilance is therefore required.

In view of the fluidity of HPC, the consistency of the fresh concrete must be inspected on site by measuring its spread on a flow table in accordance with the P 18-432 and NF EN 12350-5 standards. Slump test measurements are neither appropriate nor accurate for fluid concrete.

The application of the concrete requires completely leak-tight formwork, as the slightest loss of laitance could result in segregation. The floating and levelling of the surfaces must be carried out by teams of workers aware of the viscous and self-adhering behavior of this type of concrete.

In the case of a structure with variable inertia, the angle of the lower slab on segments close to the piers could be steep enough to cause the concrete to slide down the slope. Formwork must then be erected on the extrados of the slab. It may also be beneficial to use concrete of different consistencies for the webs and slabs. Full-scale testing is required to verify this.

The curing of HPC must also be more meticulous and more intense than for ordinary concrete. HPC is more sensitive to the effects of drying, because as the water contained within the concrete has been used up in the hydration process, there is practically no more free water. While this constraint improves the durability of the concrete, it also increases the risk of cracking in areas where shrinkage could be obstructed. Therefore, it is important pay attention to the proportion and design of the non-prestressed reinforcements, using small diameters and reduced center distances between the bars. This is particularly important for the construction of cast-in-situ segments using the cantilever method.



7.5 - Inspection of formwork The inspection of the formwork on the form traveler or in the prefabrication unit covers the following points:

• Numbers and indices of the plans used (which must be approved plans)

• Cleanliness of the work area and flushing out of the formwork bases before installation of reinforcements

• Systematic verification that any laitance deposits on construction joint surfaces have been purged and cleaned prior to the closure of the formwork

• Stability of centering, stem clamps and of the rigidity of the equipment

• Condition of the equipment: structural condition, flatness of panels, absence of distortion at the edges which form joints, leak-tightness of different seams and foam strips, cleanliness, elimination of traces of laitance and oxidation, and oiling of outer skin

• Tolerances of panels for unevenness and the conformity of the dimensions in relation to plans

• Hydraulic jacks positioned under the segment acting as a matched mold - straightness, squareness of application of load and performance of lock-nuts

• Conformity of inserts and fixings in relation to the plans: positioning, dimensions, type and number.

For the construction of cast-in-situ segments, it is very important to scrupulously observe the procedures governing the movement of formwork tools and systematically inspect the supporting and attaching elements.

The rigorousness of the inspection procedures reduces the likelihood of accidents.

In particular, systematic visual inspections of the hangers are carried out in order to check for straightness and the absence of impact marks or welding spots.

Checks shall also be performed to ensure that bolts are easy to tighten and that they act squarely on the plates. If there are any doubts, the hanger is be scrapped – or better still, cut into one metre long pieces and replaced.

Furthermore, the hangers will be reused no more than 30 to 40 times and they will be automatically replaced when this limit is reached. The number of uses could be painted on the hanger after each operation in order to monitor their use. Needless to say, the hangers must be new at the start of construction on site.

7.6 - Inspecting the reinforcements The following list describes the main inspections to be performed concerning the reinforcements for a segment prior to casting:

• Inspection of the numbers and indices of the plans used

• Acceptance inspection of the reinforcement bars: existence of the approval certificate, condition of the bars (straightness, rust, dirt,), compliance with reinforcement bar list, welds

• Verification of conformity to the reinforcement plan: diameter, length and bending



• Inspection of implementation: position, coating and setting, solidity of binding of blocks which must be clean and made from concrete, absence of contact between these bindings and the near wall, length of overlapping between the reinforcement bars and the starter bars

• Inspection of stability, rigidity and strength of the entire reinforcement cage with a view to casting. The bar chairs should not be used to improve the rigidity of excessively flexible cages. It is better to use frames to make stiffening trusses.

It is important to pay particular attention to the hooped reinforcements required due to the application of concentrated forces. The accuracy of the positioning of the hoops on the prestress anchorages must be carefully inspected. The centering on the trumplate must conform to its theoretical positioning, with the minimum deviation allowed from this position. The scale of the plans used for these areas must be large enough to allow for the precise management of the positions and sizes of the reinforcements. Three-dimensional modeling may be used for certain critical areas. The test segment (see 7.4.4.2) will provide important information about the feasibility of these arrangements.

For parts whose formwork has one or two lines of symmetry but whose reinforcements are asymmetrical, it is important to verify that the reinforcement cage is not inverted.

The inserts designed for the structural element in question will also be inspected.

7.7 - Inspection of prestressing Prestressing is carried out under the supervision of a specially qualified manager called the CMP (Chargé de la Mise en Précontrainte - Prestressing Manager), whose expertise is recognized by the Construction Manager and approved by the distributor of the prestressing process used. Article 95.1 of fascicule 65A describes the CMP’s role.

7.7.1 - Inspection of materials

7 .7 .1 .1 - Procurement

The delivery conditions for the prestress reinforcements conform to Article 5 of fascicule 4, Titre II. The renewal of the protection is carried out in compliance with the stipulations of Article 66.2 of the supplement to fascicule 65A.

The delivery of all of the components of the anchorages must be protected according to the provisions of Article 92.1.2 of fascicule 65A and Article 71.2 of its supplement. These conditions must also comply with the provisions of Article 3-5 of Circular no. 86-64 of September 4 1986 concerning the delivery conditions for parts and the checks to be performed.

7 .7 .1 .2 - S torage

Storage procedures are defined in Article 92.1.3 of fascicule 65A and Article 76.2 of its supplement, and also in Articles 4.1 to 4.3 of Circular 94-34 of April 19 1994). The storage conditions for prestressing elements must be rigorously inspected and particular attention should be paid to the following points:

• The hard steel, factory-oiled prestressing cable reels must be stored in enclosed and well-ventilated premises. They shall be placed on battens or pallets in order to keep the rims off the floor



• Prior to use, the parts can be stored temporarily under a shelter with a removable roof or under ventilated tarpaulins, making sure there is no contact between the tarpaulin and metal. Wood with a high tannin content must not be interposed between the reels, as this could affect the oiling

• Anchorages must be stored under a ventilated shelter and their crates or packaging are placed on battens or platted to avoid contact with the ground. Key bolts are kept in their original packaging until use

• Ducts are stored in bundles under ventilated tarpaulins. They are also placed on battens or pallets to avoid contact with the ground.

7.7.2 - Inspection of implementation

The accuracy of the installation of the prestress components is dependent on the methods used on site. It is unrealistic to demand accuracy greater than 5 mm. The calculations and construction provisions must take account of this.

7 .7 .2 .1 – Geometry o f duc t s

The inspection of the installation of the ducts is a complex matter. Indeed, problems regularly arise on site due to inadequate positioning.

This applies to the internal continuity tendons which may move during casting if they are incorrectly attached. It may also result in the spalling of the lower slab due to delamination under the parasitic radial tendon forces that are thus generated (Fig. 7.14 and 7.15).

Fig. 7.14 – Risks related to inaccurate duct geometry Fig. 7.15 – Spalling of the lower slab/Angled view from below

These problems must be borne in mind when designing the reinforcement plans, with regard to the systems used to fix the internal continuity tendons in place and during the construction and implementation of these systems. A spacing of approximately 0.75 m must be allowed between the ducts supports.

These systems are designed to align the ducts perfectly in accordance with the prestressing plans. Rigid sections of ducts can be specified around joints with a view to maintaining the continuity of this alignment.

The same precautions must be taken for the cantilever tendons close to the facing on the upper slab.



Problems due to the incorrect geometrical positioning of the ducts are also observed on the external tendons. These problems normally concern two phenomena: the localized spalling of the concrete due to parasitic forces resulting from badly positioned deviators, or an excessively high number of breakages of single-strand tendons when the structure is stressed and if parasitic angular cracks have developed close to the anchorages.

Fig. 7.16 – Spalling of a deviator when the structure is stressed

Fig. 7.17 – The deviator after cleaning

To prevent these problems, it is first of all important to make sure that an efficient procedure exists for adjusting the angle of the deviator tubes. As many basic errors are still committed on sites – e.g. inverting the deviators – it is important to carry out general inspections and to take a regular overview.

It is also important to make sure that the beams situated at the base of the deviator beams are correctly reinforced, including their edges, because the large-diameter bars which are commonly used require large bending radii. Figures 7.16 and 7.17 show the problems caused by an incorrect reinforcement of one of these edges on a deviator beam. These problems could have been minimized by the addition of small-diameter non-prestressed reinforcement bars positioned close to the facings.

Finally, deviator tubes should be designed in such a way that the pressure exerted by the tendon on the concrete is directed into the body of the structure and stops before the facings in the coating areas. Accordingly, the concrete formwork tubes must be bell-mouthed so that the curvature of the tendon effectively starts around 10 cm from the facings (Fig. 7.18). The reader is advised to consult the Sétra document entitled "Précontrainte extérieure" (External Prestressing), published in February 1990.

The geometrical accuracy of the ducts is very important. Therefore, in the contract documents, it is necessary to designate a person in charge of monitoring the geometry of the prestress ducts before and after casting.

Fig. 7.18 – Cross-section of a deviator tube

7 .7 .2 .2 – Ins ta l la t ion o f the pres tress ing components

The following inspections must be performed during the installation of the prestressing elements:

• Verification that the sleeves of the thin metal ducts are correctly tightened: the prefabricated lengths of ducts with sleeve extensions are designed to provide a satisfactory fit at the level of the facing



• Verification that the alignment of the ducts and their attachments conforms to the plan (Fig. 7.19)

• Verification that the ducts are in good condition and that there are no significant distorsions or out-of-roundness

• Adjustment of the duct supports in relation to formwork if necessary

• Inspection of the attachment of all ducts to the non-prestressed reinforcements

• Accurate inspections of the alignment of the ducts, particularly in the areas of deviation close to the anchor block attachments (Fig. 7.20).

In general, this inspection must be carried out according to unambiguous physical references which are fully understood by everyone working on the site. It is assumed that the plans show dimensions relating to existing physical objects or lines marked out on site.

In areas of large deviations (emergence of tendon from anchor block, deviation area close to an anchorage, etc.), in which it is better to use rigid tubes rather than thin steel ducts, it is possible to mark out the outline of the curvature of the duct by making a light saw mark on the end sections of tube. This tip can also be applied to the deviator tubes for the external prestressing ducts.

Fig. 7.19 – Conflict between non-prestressed reinforcements and ducts

Fig. 7.20 – Verification of a duct alignment in space



When completed, the installation of the ducts and the anchorages must be verified by a competent surveyor who must check the following points:

• That stiffening devices are used to ensure a continuous alignment of the ducts around the joints, without sudden changes of angle. These stiffening solutions may be used for the ducts throughout the entire length of the segment to be cast; the angles at which the ducts emerge from the joint sections are inspected for compliance with the values shown on the plans

• Use of coupling sleeves and the adhesive sealing of the sleeving joints

• Fixing of the trumplate to the formwork: verification of orientation, rigidity of the fixing and angle of the injection hole

• Fitting of the duct in the end of the trumplate via a coupling sleeve

• Absence of sudden changes of angle, i.e. verification of the coaxiality of the different elements and of the adhesive sealing

• Distribution of vents and the positioning of the vent outlets in the facings.

For the external prestressing, it is necessary to use temporary supports for the ducts in order to make sure that the tendon is in the correct position before it is stressed (Fig. 7.21). The number and spacing of the supports will depend on the number and strength of the prestressing units. A spacing of 4 to 5 m is typically used.

Should transverse prestressing be required, it is particularly important, given the thinness of the parts, to verify the accuracy of the duct alignment and the presence of a support system designed to maintain this alignment (Fig. 7.22). Furthermore, as tranverse reinforcement made from small-diameter bars is likely to be significantly t distorted during casting, it is advisable to stiffen the reinforcement cages in order to make sure that the ducts remain in the correct position.

Fig. 7.21 – Support system for HDPE ducts for external tendons

If the prestressing passes through the webs, the type and frequency of the tendon supports should be carefully inspected in view of the forces exerted during casting; this also applies to the ducts left empty in reserve (Fig. 7.23).



Fig. 7.22 – Inspection of supports for transverse prestressing

Fig. 7.23 – Supports for prestress ducts in the webs

It is also important to make sure that “removable” elements can actually be removed, especially when double ducting is used on the deviators.



Finally, before casting, it is highly advisable to verify that the ductsducts have not been blocked by any foreign objects: bottles, cans, tools, etc. This inspection can be carried out by flushing a ball through the sheath with compressed air.

7 .7 .2 .3 – Vi sua l inspec t ion o f s t rands

It is essential to reject strands showing signs of pitting due to oxidation, scratches, nicks or other defects likely to affect their mechanical strength.

A corrosion table specifying up to five levels of corrosion, of which only the fifth level was unacceptable, was once used by certain contractors. We consider this table to be far too lax and believe that corroded reinforcements should never be accepted.

7 .7 .2 .4 - Threading

Strand-by-strand threading is the most commonly-used threading method for bridges constructed by the cantilever method. During this operation, it is particularly important to make sure that:

• The strands have been sufficiently well oiled in order to reduce the friction forces in the later phases

• The distance between the pay-off reel and the cable pusher is kept to a minimum and that, over this distance, the strand is well protected by a tube or duct

• The cable reel has been placed in the static pay-off reel in such a way that the lay of the coil being unwound lies in the same direction as lay of the stranding, so that the strand tends to pull itself tight while is unwinding

• Each tendon is made up of strands from the same supplier

• The additional length required for the stressing has been allowed for before the strand is cut to length

• The strand has not been marked by the rollers on the cable pusher; this particularly applies to the last strands to be threaded, when the pressure of the rollers tends to increase

• A thick wooden shield is securely fitted over the strand outlet in order to protect staff

• Particular attention is paid to the threading of the last two strands of the tendon, as these are always the most difficult to thread through the duct (for long tendons, i.e. over 50 m in length, speed of threading is preferred to force in order to prevent the jamming of the last strands on the approach to the outlet)

• After the threading of every strand of an external prestressing tendon and the positioning of the anchorages, it is important to verify that the entire tendon can move inside the duct. This helps to position one strand in relation to another and also helps to check that there are no blockages.

7.7.3 - Inspection of stressing

7 .7 .3 .1 – Inspec t ions pr ior to s t res s ing

Lubrication, oxidation and cleanliness play a vital role in the correct installation of a traditional strand-jaws anchorage.



The anchorage must be properly lubricated if it is to work correctly and the lubrication conditions must be specified in the internal procedures recommended by specialist distribution companies. The exact type of lubricant to be used must also be specified.

Oxidation must not be considered to be acceptable in the mechanical assembly of the anchorage.

Finally, cleanliness is essential and a there must be no laitance whatsoever.

These three parameters are vital for the correct operation of the conical wedging of the strand-jaws in the anchorage.

In addition to the fact that successful stressing depends on the quality of casting in the anchorage area, it is also important to verify the following points when fitting the anchor head on the tendon:

• That the strands are clean

• That they are disentangled if necessary, so that there are no brakages due to crossed strands near the anchorage

• That the conical holes in the anchor head are clean and have no rust that cannot be wiped off.

It is also important to check that the jack is aligned concentrically on the anchor head and coaxially in relation to the tendon.

7 .7 .3 .2 – Inspec t ion p lan

An inspection plan must be drawn up prior to the start of the stressing operations. It specifies the types of inspections, the frequency of the inspections and identifies the tendons to be inspected.

These inspections may be systematic in terms of:

• Measuring the extension and pressure in stages

• Monitoring the position of tendons during threading in order to detect any possibility of crossed ducts.

They may also take the form of spot checks, e.g. when measuring transmission factors, which at first are systematically verified for each family of tendons at the start of stressing operations, and then are checked at random.

Before the jacks are threaded, it is advisable to cut all of the strands to the same length; this shows up any problems with the jaws and reveals any broken strands. The marking of the strands at the back of the jack is another, albeit less effective, solution.

Finally, before the start of operations, it is necessary to verify that engineering office has allowed for the additional lengths of cable which are gripped by the jacks in their calculations of the extension of the tendons.

7 .7 .3 .3 – Precaut ions dur ing s tress ing

During stressing, the following points require special attention:



• Verify that the internal friction on the jacks and their anchorages has been correctly accounted for in the interpretation of the pressure readings on the manometer

• Do not forget to correct the pressure reading in accordance with the calibration chart for the pump manometer: the pressure is used as the reference measurement and not the extension, which is indicative

• Check that the correction for the compaction of the jaws has been properly allowed for in the measurement of the extension on the piston of the jack.

7 .7 .3 .4 – Coef f i c i ents o f f r i c t ion

Coefficients of friction are monitored by measuring the transmission factor. The principle behind this measurement is described in detail in Article 95.4.2 of fascicule 65A and Appendix I of its supplement.

Before carrying out this measurement, it is essential to make sure that the jacks have been properly tared (using a calibration chart). It is also important to verify the calibration chart for the manometers on the pumps (test date).

7 .7 .3 .5 – Precaut ions to be ta ken wi th regard to concre te

During the construction of a cantilever with cast-in-situ segments, it is essential to verify that the value fcmin which is mentioned on the french CIP (Commission Interministérielle de la Précontrainte-Interministry Prestressing Committee] accreditation and in the construction design calculations has been achieved by the concrete before stressing is carried out. The use of a sclerometer to perform this verification is strictly prohibited.

The cantilever tendons are sometimes only stressed after the form traveler has been moved forward. This operation, which is designed to shorten the segment construction cycle, means that the last segment to be cast behaves as reinforced concrete with regard to the loads exerted by the form traveler. Normally, this poses no problems in terms of general flexion, but particular vigilance is required with regard to the localized stresses applied to the new concrete. This operation must be described in a detailed construction procedure and the engineering office must apply specific design calculations to it.

7.7.4 - Inspection of injection

7 .7 .4 .1 - In jec t ion

The injection of prestressing ducts and anchorages is intended to:

• Completely fill the void left in a duct

• Passivate of the steels due to the action of the products used

• Protect steels against corrosive external agents.

The combination of these three fundamental actions produces a permanent barrier against corrosion and guarantees the longevity of the prestressing.

7 .7 .4 .2 – Cement grout

Two types of grouts are identified:



• Traditional grout, which is fluid after manufacture

• Thixotropic grout: a traditional grout to which a thixotropifying agent is added at the end of the manufacturing process.

The main characteristic of this second type of grout is its capacity to change from a gel when stationary to a liquid when shaken. This has two advantages: the injection conditions remain the same as for a traditional grout, and the front wall of the grout remains almost perpendicular to the duct and does not collapse as it passes through high points. However, this property depends on the shearing threshold of the grout for a given slope and on the steepness of the slope for a given grout.

Numerous tests must be performed on the grout. These are specified by European standards and are referenced in Article 92.3 of fascicule 65A. They involve:

• Measuring fluidity, which determines the flow

• Measuring exudation, which defines the stability of the grout

• Measuring the variation in volume, which characterizes the filling volume

• Measuring compressive strength.

Testing using a transparent inclined tube, using the method described in Appendix 3.1 of Circular no. 99-54 of August 20 1999, is essential in view of the representativeness of this test and the unsuitability of the other tests with regard to the characterization of the in-situ stability of grout.

However, grouts may be used without preliminary testing if they have been given a favorable technical evaluation report or a favorable provisional report by the CIP, except when testing is specifically requested by the Construction Checker, provided that the components of the grout, the equipment used for their injection and the temperature conditions for their application comply with the the conditions described in the technical evaluation report. If just one of the conditions is not respected, it is essential to perform a new inclined tube test on site.

7 .7 .4 .3 – Spec i f i c inspec t ions and precaut ions dur ing the in jec t ion o f cement grout

Precaut ion to be taken dur ing the in jec t ion s tudy

Injection tests have shown that the appearance of pockets of air due to the collapse of the front wall of the grout as it passes through high points can be prevented by optimizing the speed of advancement of the grout in accordance with the alignments and the prestressing units used.

Therefore, it is important to use an appropriate speed of injection, generally: Horizontal or undulating tendons with ducts of Φ < 100 mm

8 to 14 m per min

Horizontal or undulating tendons with ducts of Φ > 100 mm

16 to 20 m per min

Vertical or steeply angled tendons 3 to 8 m per min

Furthermore, the phasing of the injection must be adapted to suit the alignment of the tendon in question. This analysis must be carried out upstream of the process in order to make sure that the position of the vents is consistent with this phasing.



Precau t ions to be taken dur ing cons t ruc t ion

Bleeder valves and vents are identified by marking or labeling according to the vent plan which must be supplied by the contractor. During the construction of the bridge, these vents must be closed in order to prevent water from seeping into the ducts. The bleeder valves are kept open.

Precau t ions taken when prepar ing for the in jec t ion

Mixers and storage tanks must be protected from water penetration and prevented from drying out due to direct sunshine.

An air compressor and a pressurized water inlet must be operational on the structure and kept ready in case of problems during the injection process.

Pre- in jec t ion inspec t ions

Before any injection takes place, it is compulsory to test the leak-tightness of the ducts in order to identify any potential anomalies. This test can be carried out using compressed air or by creating a partial vacuum. This also helps to check that the numbering of the ducts matches that of the vents. If the test shows the existence of any connections between the ducts, the tendons concerned will be injected simultaneously.

Preparations for the injection must also take account of the weather forecast. The rheology of the grout must be adapted to the ambient temperature and humidity.

Finally, it is important to remember to check the equipment and make sure that the necessary materials are supplied in sufficient quantities.

Inspec t ions dur ing in jec t ion

During pressurized injection, the monitoring of the injection pressure is of paramount importance to the success of the operation. The fundamental value to be considered is that the pressure in the duct must not exceed 1.5 MPa.

It is also necessary to perform systematic tests of the bleeding of the anchor caps and vents at the high points.

Fluidity and exudation tests are performed according to the recommendations of Article 95.5.l.B of fascicule 65A.

Pos t - in j ec t ion inspec t ions

After the injection, the different levels will be inspected in order to make sure that the ducts are properly filled. This involves:

• Visual inspections of the ducts

• A statistical inspection by removing the caps

• An acoustic sounding inspection

• A gammagraphic inspection, if allowed by the thickness of the concrete (e < 0.50 m).



7 .7 .4 .4 – In jec t ion o f ex terna l pres tress ing

Circular no. 2001-16 of February 28 2001 relative to the “Conception de la précontrainte extérieure au béton” (The design of prestressing external concrete) describes the possible solutions used for the design of external prestressing and mentions the risks involved in its removal. In practice, this leads to the use of protected and sheathed single strands in a general duct injected with cement grout or ungalvanized strands in a general duct injected with a flexible product, usually petroleum wax.

7 .7 .4 .5 – F lex ib le products

Wax

Wax is a malleable, crystallized solid material which is preferred to grease due to the absence of syneresis, which improves its stability over time.

As wax must be injected at temperatures higher than its melting point, between 90 and 120° C, certain important precautions must be taken.

Firstly, it is of paramount importance to consider the thermal exchanges with the adjacent materials and the ambient temperature during the injection process. During cooling, the wax contracts significantly, to the order of 5 to 10 %, and this can lead to the creation of voids. Therefore, it is important to take special precautions such as re-injecting the high points. However, in the case of the external prestressing, a large proportion of the shrinkage of the wax is compensated for by the cooling of the HDPE duct, which was heated by the passage of the hot wax.

It is absolutely essential to prevent any leakage of wax during the injections. If this happens, staff could be burned and the surrounding concrete could be impregnated with wax, with disastrous consequences. To reduce this risk to a minimum, it is important to only use materials which are resistant to high temperatures and to make sure that the ducts and anchorages are perfectly leakproof by carrying out rigorous inpections and tests (As the risks can never be entirely eliminated, it is important to ensure that everyone present is protected against the risk of burning by the wax).

Grease

Because of its syneresis, it is prohibited to use grease for the protection of prestressing units that are not self-shielded.

For self-shielded units such as those which are often used in transverse prestressing, the protection of anchorages using grease must be carried out on site. The greatest care must be taken to ensure there are no leaks.

7.8 - Other important points

7.8.1 - Adhesive and its applicat ion (prefabricated segments)

7 .8 .1 .1 - Charac ter i s t i c s

The adhesive used for prefabricated segments consists of epoxy resins mixed with a hardener. Its main properties are:

• Density of approximately 1.50

• Compressive strength of between 15 and 25 MPa



• A low modulus of elasticity of between 1,500 and 2,500 MPa.

Adhesives bearing the "NF-Produits spéciaux destinés aux constructions en béton hydraulique" (French Standard – Special products intended for hydraulic concrete structures) label in the structural adhesives category, or products bearing an equivalent European label are highly recommended.

7 .8 .1 .2 – Adhes ives and the ir ro le

The term “adhesive” is not strictly accurate. In fact, results from the laboratory testing of concrete-to-concrete bonding, structural demolitions and analyses of structural behavior show that under normal conditons on construction sites, the joints are not actually bonded because tensile strength is not created in the joint.

Nevertheless, adhesive plays an important role by:

• Filling the openings between joints caused by the differential shrinkage of different parts of the section of the box-girder; these openings may reach 0.3 mm in size

• Partially correcting imperfections in joints because the adhesive has a similar compressive strength to the concrete

• Lubricating the surfaces when the parts are brought together, minimizing the damage caused by the inevitable minor impacts during handling operations

• Helping to center the match casted surfaces

• Sealing prestress ducts.

7 .8 .1 .3 – Tes t ing o f s e t t ing t ime

Before the segments are assembled and bonded, it is necessary to test the time taken for the adhesive to set, i.e. the time between the start of the mixing of the components and the moment when the mixture no longer adheres on contact. The following precautions must be taken when performing this test:

• The components of the test sample must be similar in quantity to the mixture that will be used on site in practice

• Care must be taken to avoid trapping air when mixing the components of the glue

• The temperature and humidity conditions for the test must be representative of the actual conditions and conform to the specifications.

7 .8 .1 .4 – Appl i ca t ion precaut ions

The following precautions should be taken when applying the adhesive:

• Ensure that if it rains, protective measures such as the sheeting of the bonding area and the creation of an run-off barrier near the joint are implemented in order to prevent contact with rainwater run-off before and after the bonding of the segments and until they are securely lashed together

• Verify that a sufficient amount of adhesive is applied to the joints of both segments to form a seam of excess adhesive on the edges of the joints



• Verify that this seam has not been ground down after polymerization, except on the bridge deck extrados, in order to facilitate the surfacing required for the application of the waterproofing layer.

It should be noted that the formation of a seam of adhesive as mentioned below simplifies inspections in the short and long term by guaranteeing that the joint has not been been altered after the clamping of the parts.

7 .8 .1 .5 – Repa ir o f bonding de fec t s

A major bonding defect can only be repaired by an injection of resin according to a specific procedure adapted to each case.

Resurfacing with cement mortar may make it harder to evaluate the type and extent of any defects. This evaluation must imperatively be carried out before any repairs are made.

Minor defects such as impact damage to the concrete on the edge of a joint are better left exposed. If resurfacing is necessary, a recess should first be created around the damaged area and an epoxy resin-based mortar should be used for the repair.

7.8.2 - Segment facing

The inspection of the general appearance of a segment concerns three criteria: shape, corresponding to the different geometrical dimensions of the segment - texture, which is given by the formwork skin - and color, which is governed by the concrete.

These three criteria are interrelated.

For example, color is quite difficult evaluate in isolation because it depends on how the surface reacts to the light. In fact, the type of surface finish can attenuate differences in the color of the concrete. Color therefore relates to texture. The color obtained also depends on the number of times the formwork is reused – which turn depends on the resources allocated to the project.

Three factors play an important role in determining the color of the segment facings on structures built by the cantilever method: the quality of the concrete, the formwork and vibration.

7 .8 .2 .1 – Concre te qua l i ty

The final appearance of the segment facings should be considered when choosing the concrete formula because the color depends on the rheology of the concrete. The amount of water used, the proportions of additives and the temperature are the three key, interdependent factors which must be controlled. The additives and their effects on the water and temperature are particularly important.

It is now known that changing the formula of the concrete to suit the season plays a key role in producing a high-quality facing. Concrete for the construction of bridges built by the cantilever method is now manufactured during several seasons. A reference formula for spring and autumn has to be changed to allow for higher temperatures and lower rainfall in summer and is changed again in winter to account for the reversals of these same parameters. It is particularly important to account for the variation in the water content of the components. Only a detailed rheological study will satisfy this requirement.

Maturometry, which generalizes the evolution of the hydration parameters for concrete, helps to improve the management of the quality of concrete. It is also a valuable indicator for the removal of formwork, as it can be



used to determine how long the formwork needs to remain on the part and this is one of the key factors in determining the homogeneity of the facing.

This factor is particularly important for the prefabrication of segments in prefabrication units. The daily cycle which leads to the removal of formwork in the morning, is actually quite hard to reconcile with the stoppage of work at the weekend.

7 .8 .2 .2 – Formwork and formwork sk ins

Today, the most widely used formwork is made of steel or bakelite plywood (film-faced plywood, which is less expensive, may cause problems depending on the type of aggregates used). These materials are used primarily for economic reasons and their characteristics are not ideal for the creation of high-quality facings.

A double formwork skin is better suited to this task. This consists of a thickness of no more than 10 mm of ordinary plywood fixed to the standard formwork. In this case, the formation of bug holes can be prevented by making sure that the wood fibres are aligned in the same direction as the pouring of the concrete.

The drawback to this technique relates to the time required for the assembly and the dismantling of the formwork skin each time it is replaced, rather than the costs of the materials. Indeed, beveled vertical slats of unfinished wood have already been used for this purpose.

Formwork skins, made from composite materials which can be reused at least three hundred times, are a new arrival on the market. These materials are very expensive, however, and are not suitable for all shapes.

Another important contribution of the formwork skin to the creation of a high-quality facing is to dampen the vibrations transmitted to the formwork during the vibration of the concrete, thanks to the column of air between the formwork skin and the formwork itself.

7 .8 .2 .3 - V ibrat ion

A large number of defects are caused by incorrect vibration. Two pitfalls must be avoided:

• Over-vibration - meaning that part of a component has been vibrated for too long. On a constant cycle, which is the most common situation, this means that another part of the component has not been vibrated for long enough

• Post-vibration - involving the creation of secondary vibrations caused by the hard spots of the reinforcements or formwork structures.

The importance of the type of formwork skin is illustrated by the fact different materials have different capacities to absorb vibrations.

Flat vibration, e.g. of a slab, often creates intermittent vibrations in the reinforcements which act as secondary vibrators when the concrete is tightly compacted.

To make sure that the upper section of a layer of freshly-poured concrete is sufficiently vibrated, it is necessary to vibrate it for one to two minutes after air bubbles have ceased to emerge from the concrete.

Finally, it is important to follow a vibration plan corresponding to the shape of the component. This plan is drawn up by a specialist or with specialist help (see paragraph 7.4.4 concerning the inspection of application).



Differences in the appearance of the facing can be reduced by the use of white cement or light-colored cement. Clinker has a distinctive color and additives can be used to attenuate its impact. Therefore CHF-CEM III/A and B, and CPJ-CEM Il/A and B cements produce light-colored facings.

The test segment is used to experiment with all of the aforementioned factors and eventually arrive at a comprehensive solution for the production of high-quality facing. However, it is also necessary to anticipate changes in the quality of the formwork skin. For example, if the skin is made from painted sheet metal, this paint will gradually disappear, thus changing the final appearance.

As fascicule 65A does not address all of the issues relating to facings, the Construction Manager may also refer to the Projet National Qualibé (National Concrete Quality Project) report for additional information.



8 - Pathologies and repairs This chapter begins with a quick reminder of the changes in the regulations applicable to structures built by the cantilever method. It then goes on to describe the main pathologies affecting these structures and the corresponding repair techniques.

8.1 - History of the regulations This paragraph mentions certain key events in the evolution of French regulations and the technical texts relating to prestressed concrete bridges built by the cantilever method.

8.1.1 - 1946-1952: the f irst prestressed bridges

In this era, there were no French regulations concerning prestressed concrete.

8.1.2 - 1953-1964: the f irst regulations for prestressed concrete

The first French regulations applicable to prestressed concrete appeared on October 1 1953, (Circular no. 141 issued by the Ministère des Travaux Publics, des Transports et du Tourisme [Minsistry of Public Works, Transport and Tourism] - a Provisional Instruction concerning the use of prestressed concrete). Essentially, it recommended the use of fully compressed concrete (with minimum compression on one axis equal to at least 8% of the maximum compression), but it hinted at the use of partially prestressed structures.

This instruction recommended the inclusion of certain clauses in the Cahiers des prescriptions spéciales (Special Conditions) [CPS]) relating to the composition of concrete (minimum cement batching of 400 kg/m3) and the quality of prestressing reinforcements. It also made the use of strong sealed metal ducts compulsory for prestressing by post-tensioning.

8.1.3 - 1965-1975: constantly changing regulations

This was a time of enormous changes and constantly changing regulations.

In 1965, Circular no.44 of August 12 1965, relating to the instruction provisoire (Provisional Instruction) for the use of prestressed concrete (called “IPl”), replaced the 1953 Provisional Instruction. Complete prestressing remained, but there was no lower compression limit (σmin ≥ 0). Cylinder strength at 28 days replaced cube strength at 90 days. It should be noted that this circular was written primarly for bridges with prefabricated girders. It incorporated the advances made since 1953, especially regarding the calculation of losses of tension (e.g. formulae for relaxation losses).

1966 saw the publication of the Provisional Directive for the construction of prestressed concrete bridges. This was intended to prevent accidents during the construction of bridges or on structures in use. It made changes to the “construction” section of the IPl and insisted on:

• The need for a waterproofing layer

• The use of APC (Artificial Portland Cement) 325 or CFA (Cement – Fly Ash) 400 cement, batched at 400 kg/m2 for the manufacture of concrete, in order to reduce the risks of corrosion (the use of PCS [Portland Slag Cement] cement had to be approved by the LCPC)



• The almost total prohibition of admixtures after the collapse of a beam on the Guerville viaduct. This accident was caused when an incorrect dose of an admixture prevented the concrete from hardening properly; as a result, the bottom flange of the girder was crushed during prestressing

• Precautions for the storage of prestressing reinforcements on site, in order to reduce the risks of stress corrosion

• Inspections during stressing operations in order to reduce prestress losses

• The care to be taken over the injection of ducts and the need to allow a maximum period of 8 days between the stressing and injection operations, again with a view to reducing the risks of stress corrosion (only APC 325 cement was allowed for the injection grout and sealing mortar).

1971 saw the introduction of the Directives Communes relatives au Calcul des Constructions (DC71) [Common Guidelines relating to Structural Design], which was the first document to cover the concept of limit states. These guidelines were intended to be used as the basis for the creation of new design rules for metal, reinforced concrete and prestressed concrete structures.

In the same year, the 1960 load regulation was replaced by Titre II of fascicule 61 of the Cahier des Prescriptions Communes (CPC) [Common Conditions]. This regulation significantly reduced the intensity of the distributed loads A (l) for bridges of moderate length (between 15 and 80 m) and introduced degressivity factors according to the number of loaded lanes and the category of structure.

The Provisional Directive for the injection of ducts on prestressed concrete structures appeared on March 28 1973. This highly informative document covered the requirements for grouts (traditional and special), the characteristics of study and suitability tests, the manufacturing conditions for grouts, the execution and inspection of injected materials, accidents, etc. This directive led to real improvements in the quality of the protection applied to prestress tendons.

In December 1972, Sétra published the first version of its Technical Bulletin on bridges built by the cantilever method, called “BT7”. This document covered the history, engineering, design and construction of these structures. Appendix I of this document featured a design example incorporating changes due to creep and thermal gradients. Appendix II included a collection of 55 monographs on structures built between 1960 and 1972 in France and abroad.

In 1973, Circular no. 73-153 of August 13 1973 introduced Provisional Instruction no. 2 (called “IP2”) relating to the use of prestressed concrete. This consisted of a design rule based on “limit states” methods. The IP2 introduced the use of:

• The characteristic strength of concrete instead of the nominal strength

• Types or classes of prestressing (from type I: no decompression of concrete, to type III: limitation of the opening of cracks)

• Characteristic values of actions due to prestressing (P1 and P2)

• Specific rules relating to end or support areas and to concentrated forces during post and pre-tensioning

• Rules to account for delayed deformations in concrete due to shrinkage, creep, etc.



During this period, private and public engineering firms were not ready to face up to the practical difficulties relating to the application of this new regulation (complete overhaul of design programs, difficulty of applying the range of characteristic values of the prestressing when there was a redistribution of efforts due to delayed obstructed deformations, etc.). Therefore, the IPl, which remained valid, continued to be used except for the pre-tensioning, the distribution of concentrated forces and for the precise calculation of delayed deformation effects.

Circular no. 74-60 of April 23 1974 made changes to the following articles of the IP1 in accordance with the new Titre II in fascicule 4 of the CPC of March 5 1971, and March 26 1973:

• Article 10, relating to the calculation of relaxation losses in the prestressing reinforcements, established relaxation at 3,000 hours

• Article 12 reduced the initial tension of the tendons

• The values of the coefficients of friction f and φ specified in the IP1 were used in the certificates of approval, except for structures with numerous joints for which they were determined by the CPS (Special Conditions).

The Direction des Routes et de la Circulation Routière (Department of Roads and Traffic) published a circular on April 2 1975, after analyzing and determining the causes of cracking observed on a number of bridges built by the cantilever method. This document was designed to supplement the IPl with regard to the following points:

• Redistribution of forces due to delayed deformation

• Distribution of prestressing loads (concentrated forces) and the accumulation of shearing stresses with or without transverse or vertical prestressing (stressed stirrups)

• Traction forces exerted by tendons anchored in the slab of a box girder

• Thermal gradients (5°C under rare combinations and 10°C under practically permanent combinations in the sense of the BPEL 91, while taking account of the instantaneous deformation modulus of the concrete)

• radial tendon forces in curved slabs

• The continuity of reinforcements close to joints, etc.

By introducing rules to allow for creep and the thermal gradient, this circular brought an end to the era of second-generation bridges (see Chapter 1) and paved the way for a new generation of much better dimensioned bridges.

8.1.4 - 1975-1982

This period saw the publication of new regulations which, on the one hand, incorporated the concept of quality and on the other, abandoned the "allowable stresses" calculation in favor of "limit-states" calculations.

1979 saw the publication of four important circulars:

• Circular no. 79-23 of March 9 1979, which included the instruction of January 15 1979 relating to the inspection of concrete quality (conditions for the execution and interpretation of study, suitability and inspection tests which were not included in fascicule 65 of August 13 1969, and described in Circular no. 69-92, or in a usable form within Appendix B of the IP2)



• Circular no. 79-78 of August 16 1979 relating to the implementation of prestressing units, which established:

– The values of the coefficients of friction f and φ (according to the radius of curvature, the number of joints crossed and the type of tendons: smooth wires or strands)

– The moduli of elasticity of the wires (200,000 MPa) and strands (190,000 MPa) – The measuring conditions for the transmission factors – The choice of ducts (ducts and tubes), in addition to the diameters, radii of curvature and the

continuity of the ducts – The limit of the initial stress to be 0.7 Frg for reinforcements with a small radius of curvature

(stressed stirrups) – The strength of the concrete close to the anchorages and the minimum distances to the facings

of the anchor plates – The conditions of execution for the tensioning – The need and the implementation conditions for temporary protection and sealing

• Circular no. 79-121 of December 14 1979 concerning the reprint of the IPl, which incorporated the modifications made by Circulars 74-60 of April 23 1974 and 77-67 of April 25 1977

• Circular no. 79-25 of March 13 1979 relating to the new Directives Communes pour le Calcul des Constructions (D.C.C.C.79) [Common Guidelines for Structural Design]. These guidelines served as the basis for the creation of BAEL and BPEL rules and the design rules for foundations.

A supplement to Technical Bulletin No.7 also appeared in April 1979, introducing the requirements of the Circular of April 2 1975 and its implications concerning the quantities of materials, new design programs, the stability of cantilevers under construction, design examples, construction advice (prefabricated segments, measurement of transmission factors, form travelers, stressed stirrups, segregation of concrete, workability, protection of anchorages, etc.).

8.1.5 - 1983 to the present day

This period was marked by the generalization of "limit states" design rules. The introduction of Quality Assurance and the development of French and European standardization led to significant changes in the rules relating to the construction of structures.

The development of “external prestressing” had a major impact on the development of prestressing procedures, and much less of an influence on the development of prestressing reinforcements.

Significant changes were made to the design of large prestressed concrete structures, but construction techniques remained very similar.

It should also be noted that the effects of Circular 82-50 of May 24 1982 began to felt. This involved the notions of quality of use, the organization of quality, internal and external inspections and independent inspections, etc.

All of these notions concerning quality were applied to each of the texts relating to the construction of structures.

In 1983, the regulations relating to the design of prestressed concrete bridges were revolutionized by the appearance of fascicule 62 Titre l Section 11 of the french CCTG (General Technical Clauses, technical design and calculation rules for prestressed concrete structures according to the limit states method, called the “BPEL



83”). It should be noted that the BPEL 83, the IPl and the IP2 were all applicable until December 31 1985 according to certain procedures established by decree.

The BPEL 83 rules introduced:

• External prestressing

• The notion of verification categories for structures (Class I authorizes no traction and is mainly used for prefabricated bridges; Class II, in which the tensile stresses are limited, is used for major bridges and large standard bridges or those situated in harsh environments; Class III, covering “partial prestressing”, was applied to prestressed concrete bridges built by the cantilever method, certain types of standard bridges in reasonably benign environments (2nd and 3rd category road bridges) and for bridge slabs with transverse prestressing

• A characteristic thermal gradient value of 12° C for verifications at service limit state

• Characteristic strength as the specified strength for concrete

• The possibility of performing verifications with the probable prestressing Pm, instead of range calculations using P1 and P2 (characteristic values).

In 1984, Sétra published two information notes:

• The first covered the anchoring strength of external prestress tendons in the event of overtension in order to prevent the blockage of wedges by the cement grout

• The second dealt with the use of single and multi-strand couplers, the precautions to be taken with keyed anchoring and problems relating to the use of “super” strands.

In February 1990, the CTOA (Centre des techniques d’ouvrages d’art - Center for Engineering Structure Techniques), a division of Sétra, published a guide entitled "Précontrainte extérieure" (External Prestressing). It gave additional information on subjects covered by the BPEL 83, with a particular emphasis on external prestressing technology.

The BPEL 83 rules were replaced by the BPEL 91 rules at the start of 1992. The major modifications introduced by this new version included:

• Extending the rules to concrete with characteristic strength of between 40 and 60 MPa

• Improving SLS verifications for the different classes I, II and III

• Introducing a "θ" coefficient into the formula giving the value of the compression limit stress of concrete at ULS, as a function of the duration of applied of loads

• Reduction of the 1983 shear limit stress which was considered to be too forgiving

• Reduction of the working stress ratio for stressed stirrups

• For coastal structures: increasing the depth of coating on non-prestressed reinforcements without individual protection from 4 to 5 cm



• Appendix 3, which assigned numerical values to the coefficients of friction f and φ for tendons inside the concrete, sheathed and protected strands and tendons outside the concrete.

It should be noted that the BAEL 83 rules were simultaneously replaced by the BAEL 91 rules.

At the end of the 1990s, the BPEL 83 was modified again, becoming the BPEL 91, revised in 1999. An additional appendix (Appendix 14) was included in this new version, relating to concrete with a characteristic strength of between 40 and 60 MPa.

The end of the 1990s was also marked by the appearance of two circulars relating to prestressing using post-tensioning techniques:

• The first, dated August 20 1999, prohibited the washing of sheathed tendons with water, established a number of new requirements for HDPE tubes and promoted the injection of external tendons with wax

• The second was published on February 28 2001 and imposed new requirements concerning the injection of external prestress tendons (see paragraph 7.7.4.4).

8.2 - Pathologies specific to the cantilever construction technique As for most other types of bridges, specific types of problems have affected the first prestressed concrete structures built by the cantilever method.

The purpose of this section is to briefly outline the principal specific disorders that have been identified for these structures and to describe the lessons that have been learnt with regard to the design of modern structures built by the cantilever method. In the interests of relevance, we shall only cover problems with structural origins, as problems caused by other factors (materials, use, maintenance, etc.) are not exclusive to the cantilever construction method.

For more detailed information about problems affecting prestressed concrete structures, the reader is invited to refer to Sub-Section 32.2 of the second part of the Instruction technique pour la surveillance et l’entretien des ouvrages d’art (Technical Instruction for the Monitoring and Maintenance of Civil Engineering Structures), published in 1979 and modified in 1995.

8.2.1 - Reminder concerning cracking on prestressed structures

The appearance of significant deformations and/or cracks on prestressed concrete structures may be evidence of structural disorders.

Not all of the cracks found on prestressed concrete structures are signs of defective behavior.

When analyzing the problems on a structure, it is important to consider all of the characteristics of the cracks observed.

8 .2 .1 .1 – Open ing and widening o f cracks over t ime

The opening and widening of cracks if they are active are obviously the first elements to consider. However, this information is insufficient in itself to evaluate the condition of the structure.



Prestressed concrete structures built by the cantilever method are often only prestressed longitudinally. They therefore behave like reinforced concrete in the transverse direction. As a result, fine longitudinal cracks may develop and in most cases, these are evidence of normal transverse flexion behavior in reinforced concrete.

This applies to the fine cracks that can be observed in the upper slabs. It also applies to the fine cracks found in the deviators on structures with external prestressing.

As a guide, it shall be considered that the opening of the cracks on elements behaving like reinforced concrete must not exceed:

– 0.1 mm in the case of systematic cracking (multiple, evenly-distributed cracks), for the average width of all of these cracks

– 0.2 mm for the average width of an individual crack – 0.3 mm in localized cases for the width of an individual crack.

These openings are values under dead loads and were established in the framework of studies relating to the penetration of corrosive agents into the concrete. For structures or parts of structures situated in relatively non-corrosive environments, these values could therefore be increased.

8 .2 .1 .2 – Des ign assumpt ions and the in f luence o f regu la t ions

Structures built according to the Instruction Provisoire n° 1 (Provisional Instruction no. 1) or the BPEL in Class I were designed to be totally prestressed, as, in theory, no traction is allowed with regard to flexion when the bridge is in service. As a result, minimal longitudinal reinforcement is used and this would be incapable of compensating for any unforeseen tensile forces. On this type of structure, transverse cracks are usually evidence of abnormal longitudinal flexion behavior. In particular, cracks crossed by prestress tendons are problematic because of the risk of fatigue in the prestressing reinforcements.

On the other hand, tensile forces are allowed at the design level for structures dimensioned according to Classes II or III of the BPEL. Efforts are made to keep the opening and widening of any cracks to acceptable levels in order to:

– Prevent the risk of fatigue in the tendons crossing areas likely to be tensioned – Limit the penetration of corrosive agents through the gaps caused by excessively wide cracks.

With this in mind, stresses or stress variations within the concrete and reinforcements are minimized and non-prestressed longitudinal reinforcement bars are added to control the cracking.

These structures were built more recently and benefit from the lessons learnt on older structures. Fine transverse cracks, which are closed when the structure is not loaded, are usually evidence of normal behaviour in prestressed concrete, in accordance with the regulations. Excessive cracking (open cracks when the structure is not loaded, etc.) is obviously a sign of abnormal behavior.

8.2.2 - Stabi l i ty of canti levers

8 .2 .2 .1 – Prob lems observed and the ir causes

Problems arose during the construction the cantilevers on some of the first structures built using the cantilever method and a spectacular accident occurred on the site of the Viosne viaduct on November 13 1970, when the first cantilever tipped over, fortunately without any serious consequences (Fig. 8.1).



Fig. 8.1 – Tipping of the first cantilever of the viaduct over the Viosne

Accidents have also been caused by the collapse of prefabricated segments and form travelers, e.g. on the bridges of Calix, in 1975 and Bellegarde in 1982.

8 .2 .2 .2 – Impact on des ign

Design rules governing the stability of cantilevers under construction were established and published in the supplement to Technical Bulletin (BT) no. 7, published by Sétra in 1979. These rules, which are included in this guide along with several additions, have now been successfully used for over twenty years. No cantilevers have collapsed since their publication, despite the collapse of several form travelers.

8.2.3 - Cracks due to insuff icient longitudinal strength


The majority of structures built using the cantilever method prior to 1975 have suffered from transverse cracking or the opening of joints in the lower slab, towards the middle of the central spans or in so-called “low bending moment” zones (Fig. 8.2).

Fig. 8.2 – Flexion cracks

These cracks are evidence of insufficient resistance to longitudinal flexion. This type of cracking is particularly serious given that the cracks or open joints are often crossed by continuity tendons inside the concrete, thus exposing these reinforcements to the risk of fatigue.



These cracks have several causes which are often cumulative and include:

• The failure to account for the redistribution of forces due to the delayed obstructed deformation of materials in the calculations. For simplicity’s sake, these forces are often put down to "redistribution by creep" (in general, this error leads to the normal stress in the lower axis at the crown being overestimated by 2 to 3 MPa)

• The failure to account for the thermal gradient in the calculations (in general, this omission also leads to an overestimation of the normal stress in the lower horizontal plane at the crown of approximately 2 MPa for a thermal gradient of 6° C)

• The overestimation of the prestress effect, due to over-optimistic coefficients of friction or underestimations of relaxation losses

• Parasitic forces locked into the structure when the closing segment is assembled due to adjustments made on site (realignment of cantilevers, correction of reverse deflections, unforeseen site loads, incorrectly controlled weight of the form traveler etc.).

8 .2 .3 .2 – Impact s on des ign

The Circular of April 2 1975 and the supplement to the BT7 of April 1979 defined the design rules to be adopted in response to redistributed forces due to the delayed obstructed deformation of materials and in response to the thermal gradient. For structures dimensioned according to the IPl, this resulted in a significant reduction in the recommended slenderness ratio at the crown, from l/50th to 1/40th, i.e. the bridge deck became considerable thicker in this area.

With regard to the coefficients of losses by friction, the values adopted by the BPEL were more conservative than those in the previous regulations. The BPEL paid particular attention to the case of tendons crossing numerous joints, as happens on bridges built by the cantilever method. In addition, empty ducts allow for additional prestressing to be used if the actual friction is greater than the friction values allowed for in the design. Finally, the design allows for the use of additional prestressing (anchorages, deviator tubes, etc.) in order to facilitate any future structural repairs or reinforcements (see the recommendations in Chapter 3 of this guide).

8.2.4 - Cracks and problems due to excessive radial tendon forces


Two types of disorders may point to the existence of excessive radial tendon forces: longitudinal cracking in the lower slab in the crown area and localized cracking, delamination or spalling of the concrete.

Longitudinal cracking in the lower slab is caused by downward thrusts in continuity tendons inside the concrete in structures of variable depth and most commonly affects the central span (Fig. 8.3 and 8.4).



Fig. 8.3 – Cracking due to downward thrust at the web-slab junction

Fig. 8.4 – Cracks caused by downward thrust

These problems affected first-generation structures because a large number of low-strength continuity tendons were spread across the entire width of the lower slab, mainly in the central span. Also, many of these early structures were built without gussets at the junction between the web and lower slab.

Localized cracks, delamination and the spalling of concrete are caused by the errors in the positioning of the ducts such as the festooning of ducts between two joints, badly-positioned tendons, sudden changes in angle close to the joints etc. These problems create radial tendon forces.

8 .2 .4 .2 – Impacts on the des ign

Gussets are now systematically used at the junction of the webs and the lower slab of box girders. Furthermore, the practice of spreading the tendons across the full width of the lower slab has now been abandoned, especially for bridge decks of variable depth. Tendons are now usually placed in the gussets or very close to them, which is made easier by the fact that fewer internal continuity tendons are needed for mixed prestressing.

To combat problems caused by incorrectly positioned ducts, the Instruction Technique pour la Surveillance et l’Entretien des Ouvrages d’Art (Technical Instruction for the Monitoring and Maintenance of Civil Engineering Structures) recommends using a reinforcement plan that is designed to take up any parasitic radial tendon forces due to angular fractures in proximity to the joints.



Fig. 8.5 – Suggested reinforcement plan designed to compensate

for accidental radial tendon forces close to joints

8.2.5 - Other pathologies

For information, we shall also mention two other important pathologies found on prestressed concrete bridges built by the cantilever method:

• Badly fitting joints in the case of prefabricated segments

• Deflections of cantilever arms close to joints.

Bridges built by the cantilever method are, of course, not immune to the more general problems affecting prestressed concrete structures (distribution of concentrated prestressing forces, injection defects, corrosion of tendons, etc.). It should be noted that the positioning of cantilever tendons inside poorly protected channels on the extrados - a technique specific to bridges built by the cantilever method - proved to be particularly damaging in terms of the corrosion of tendons and was quickly abandoned.

To round off this section, it should be mentioned that external prestress tendons have failed on several occasions in recent years. This problem has affected tendons whose ducts were injected with a cement grout which had failed to set properly in certain areas due to the phenomenon of settling (fresh grout).

8.3 - Main repair techniques In France, the first significant repairs to prestressed concrete bridges built by the cantilever method were carried out at the beginning of the 1970s (Bussang bridge etc.). Since then, major structural repairs have been carried out on around sixty structures using a variety of techniques described below.

8.3.1 - Addit ion or replacement of prestressing

The most commonly used repair technique consists of adding extra prestressing or replacing the original prestressing. In the latter case, the original prestressing must be dismantled, which is a difficult process, especially for tendons situated inside the concrete. It should be noted that these techniques are also used for reinforcing operations.

Longi tud ina l p res t re s s ing

The tendon layout may be rectilinear or polygonal. In the latter case, it is angled by deviators added to the initial structure (Fig. 8.6).



Fig. 8.6 – Additional longitudinal prestressing Fig. 8.7 – Anchor block for additional longitudinal

prestressing

The additional anchor blocks may be situated beyond the abutment, as on the Corbeil bridge, in Essonne, or more conventionally, inside the box girder (Fig. 8.7 above).

Transverse pres t re ss ing

Transverse prestressing may be carried out on the lower slab (Fig. 8.8), the webs, or both (Fig. 8.9).

Further information on this subject is given by the following articles [RIC 93], [DEL 94], [BAR 94], [PER 94], [JEH 94], [DEL 98], [BAR 98], [POI 99], [TAV 00], [BOUT 1] and [GIA 01] listed in the bibliography in the appendix to this guide.

8.3.2 - Other techniques

Other techniques are also used. For information, these include adjusting the height of the supports and adding extra material, glued steel plate sheet or FRP (cf. article [POI 92]).

8.3.3 - Repair design

There is little information concerning repair design for prestressed concrete civil engineering structures. However, the following documents provide useful information for anyone interested in the repair of prestressed concrete bridges:

• Maintenance et réparation des ponts (Bridge Maintenance and Repair) [Presses de l’ENPC – 1997]

• French standard NF P 95-104 - Réparation et renforcement des ouvrages en béton et en maçonnerie - Spécifications relatives à la technique de précontrainte additionnelle (Standard NFP 95-104 – Repair and Reinforcement of Concrete and Masonry Structures – Specifications Relating to the Additional Prestressing Technique)

• Ponts en béton précontraint par post-tension (Post-tensioned Prestressed Concrete Bridges) [HA, Sétra, TRL, LCPC]

• Annales de l’ITBTP n° 501 de février 1992 : Journées réparation et renforcement des structures de bâtiments et d’ouvrages d’art (Annals of the ITBTP no. 501 of February 1992: Information Days for the Repair and Reinforcement of Buildings and Civil Engineering Structures).



Fig. 8.8 – Additional transverse prestressing of the lower

slab

Fig. 8.9 – Additional vertical prestressing of a web and

transverse prestressing of the lower slab



9 - Provisions to facilitate maintenance This chapter describes the provisions to be made at the design stage with a view to facilitating the maintenance of bridges incorporating box-girder bridge decks. These provisions are intended for prestressed concrete bridges built by the cantilever method, but they are also applicable to concrete structures with box-girder bridge decks built by other methods (on falsework, by incremental launching and by temporary cable-staying).

9.1 - General principles In general, the bridge’s design and construction should incorporate measures to facilitate the inspection and maintenance of all parts of the structure, including the interior of hollow sections, without requiring heavy equipment.

With these provisions in place, it must be possible to perform bridge management and maintenance operations in accordance with labour legislation and particularly with regard to french Law no. 93-14-18 of December 31 1993, which introduced the Dossier d’Intervention Ultérieur sur Ouvrage (DIUO) [Post-Construction Works File].

Finally, these access arrangements must not make the structure vulnerable to acts of vandalism.

9.2 - Bridge deck

9.2.1 - Prestressing

9 .2 .1 .1 – Replaceab i l i ty o f ex terna l pres tress ing

Mixed prestressing has been used on the vast majority of large bridges built in recent years. This means that a certain number of tendons are situated outside the concrete. To benefit fully from this technique, it must be possible to replace these tendons without having to demolish any part of the structure.

The requirements concerning the tendons and their layout are set out in the Sétra guide entitled "Précontrainte extérieure" (External Prestressing), published in 1979. It should be noted that a large number of the provisions specified in this guide are included in Chapter 7 of the supplement to fascicule 65A of the french CCTG and that, notwithstanding any contrary provisions in the STC, these provisions are compulsory.

The provisions concerning the injection of these tendons are defined by the french circular of February 2001 relating to the injection of prestress tendons situated outside the concrete. It should be remembered that this circular only authorizes the use of non-adhesive products (factory-applied grease and wax), unless special equipment capable of absorbing the energy of the tendon during its removal is used.

9 .2 .1 .2 – Prov i s ions for the implementat ion o f addi t iona l pres tress ing

At a given moment in the life of a bridge, it may be decided to strengthen the prestressing. This may be due to a pathology affecting the structure or to a change in its functional design. For a box-girder structure, it is important to allow this possibility by building in the means to add additional external tendons if they are required. This includes leaving room to pass formwork tubes housing an extra pair of tendons through cross beams and deviators, and placing extra trumplates in the cross beams. It is also necessary to allow the forces added by this extra pair of tendons when dimensioning the reinforcements for the deviators and cross beams. The original type of tendons is used for the extra tendons and they are aligned according to the same rules. They



are then stressed according to the same procedures used for replacement external tendons. (Further information on this point can be found in Article 64 of the supplement to fascicule 65A of the CCTG and its comments).

9.2.2 - Access inside the box girder

9 .2 .2 .1 – Min imal depth o f br idge deck

To allow for easy movement inside the box girder (Fig. 91), it is important to design bridge decks of sufficient depth. For bridge decks of a constant depth, the problems caused by an insufficient depth could affect the entire structure; therefore, it is recommended to fix the minimum total external depth at 2.20 m. For bridge decks of variable depth, the access problems are occasional and only concern areas in the middle of the spans or close to the abutments, so a minimum depth of 2 m can be accepted. It is important to note that these depths are given for bridge decks without transverse ribs. For bridge decks with transverse ribs, it is necessary to add the internal height of the ribs (usually 0.75 m to 1 meter) to the minimum depth.

Fig. 9.1 – Example of a very small box girder

9 .2 .2 .2 – Normal movement

In the majority of structures, there is sufficient room – at least 0.75 m – between the external tendons nearest to the middle of the box girder to walk comfortably on the concrete surface of the lower slab. When this is not the case, either because the lower slab is very narrow or because there are too many external tendons, it is possible to install a gridded steel walkway over the tendons. This passageway may be cramped in the middle of the spans due to tendons rising up close to the piers. (N.B. If the box girder is too narrow for normal maintenance, it is possible to use completely internal prestressing, which is not as bulky as mixed prestressing).

Fig. 9.2 – Passageway clearances



9 .2 .2 .3 – Cross ing o f cross beams and dev ia tors

Cross beams on modern box girder bridges always have access shafts to allow access for construction workers and, when the bridge is in service, maintenance staff. For easy and, above all, risk-free movement through this passageway, it is important to ensure that the height clearances in the shafts correspond to the values shown in Figure 9.2.

Furthermore, if these deviators and crossbeams have low beams which hinder the movement of staff and equipment – a common situation – it is advisable to install metal or concrete stairways or concrete ramps on either side of these elements (Fig. 9.3). Important: if the vertical height exceeds 1.50 m, these elements must be equipped with guard rails.

9 .2 .2 .4 – Access to p ier head un i t s

An access shaft must be made in line with each pier in order to allow access from the bridge deck to the piers and vice-versa. For obvious reasons, this shaft must be positioned in line with the inspection pits in the pier head units (see 9.3.2.1 below). In order to prevent this shaft from adversely affecting the mechanical behavior of the slab or lower part of the cross beam, it should be circular in shape and 80 cm to 1 m in diameter. For safety reasons, it is essential to keep this shaft closed under normal conditions, using a metal grid which cannot be removed and closes automatically. An effective system consists of placing a square metal grid inside a square rebate built into the top of round access hole.

Fig. 9.3 – Ramp for crossing the lower beam of a deviator

9 .2 .2 .5 – E lec tr i ca l sys tem

All large prestressed concrete bridges must have an electrical system that is used to light the inside of the bridge deck and to supply power for any tools required during maintenance operations (flood lights, power drills, etc.).

The lighting in the box girder must be powerful enough to allow staff to move around in complete safety (Fig. 9.4). For this purpose, bracket lights with spherical light bulbs or, more commonly, neon tubes or fluorescent strip lights are used. These lights are positioned centrally underneath the upper slab with a longitudinal center-to-center spacing of no more than fifteen meters and the high-risk areas around the cross beams and deviators must be adequately lit. If the total length of the structure does not exceed 400 to 500 m, all of the bracket lights can be operated simultaneously using 2 two-way switches situated at both ends of the bridge deck. For bridges of over 500 m in length, it is recommended to organize the lighting system into sections of 300 to 400 m. In this case, in addition to the two switches on the abutments, two-way switches must also be fitted at the ends of each section N, in order to control the lighting for sections N and N+1. In the interests of economy, it is also possible



to fit a timer to the lighting system, but this must be set to stay on for a long time (at least 10 hours) in order to avoid plunging workers into darkness when they are still inside the box girder.

Fig. 9.4 – Internal lighting in a box girder

Electricity is supplied by power sockets, which are usually positioned one meter above the lower slab, directly below the light fittings. To allow for the use of power tools inside the box girder, a 220- volt system with a frequency of 50 Hertz must be installed. In certain systems, these sockets are accompanied by safety sockets supplying 24-volt current. In all cases, the power socket circuit in the box girder must be totally independent from the lighting circuit, so that a problem with a tool does not suddenly extinguish the internal lighting.

The electrical system must comply with the general standards in force for low-voltage electrical systems (i.e. the NF C 15-100 standard on the publication date of this guide). After installation, it must be approved by an accredited organization.

There must be no risk of damaging the non-prestressed reinforcements or the prestress tendons during the installation of the system.

Fig. 9.5 – Access hatch for cabling

9.2.3 - Miscellaneous

9 .2 .3 .1 – Access hatches for equ ipment

As explained in the Sétra “Précontrainte Extérieure” (External Prestressing) guide, it is necessary to examine different ways of routing extra or replacement tendons through the bridge deck, and for transporting the equipment needed for their installation. If it turns out to be impossible to route the tendons via the abutments, another solution would involve making a 1 m x 0.80 m hole in the lower slab, directly in line with a road lane if possible. Under normal conditions, this hole would be closed using a galvanized steel hatch (Fig. 9.5 and 9-6). For further information about this point, the reader is recommended to refer to section 5.45 in the guide mentioned above. These hatches may also be used to supply any other equipment, of course.



In the past, certain box-girder structures featured access hatches in the central part of the upper slab. As these hatches cause maintenance and durability problems, this technique must be completely prohibited.

9 .2 .3 .2 - Dra inage o f the lower s lab

Water frequently penetrates into the box girder due to leaks in the structure or during maintenance operations. In order to allow this water to drain away quickly, it is essential to leave holes of 10 to 15 cm in diameter in the lower slab, equipped with a beveled tube extending through the intrados to form a drip groove. The longitudinal positioning of theses holes must take account of the longitudinal profile of the top of the lower slab, which is very different to the longitudinal profile of the road for a bridge deck of variable depth. It is also important to consider the position of the cross beams and deviators, which form a barrier preventing the drainage of water. Care must betaken to ensure that this configuration does cause water to run down the facing of the piers. Transversally, it is also important to account for the transverse slope of the top of the lower slab and of the tendons which might be installed there.

Fig. 9.6 – Piercing of a lower slab required by the lack of

an access hatch

9 .2 .3 .3 – F ix ing ra i l s for fu ture ne tworks

In order to facilitate the installation of networks inside the box-girder at some future date, it is common practice to install anchor rails or couplings on the underside of the upper slab. Usually made from galvanized or stainless steel, these fittings form the upper anchorages for the bars to which pipework, or a metal frame supporting the networks, can be attached.

Fittings situated close to the tendon anchorages on piers may also be used for jack hoists, subject to their nominal load being greater than 20 kN.

The principal characteristics of these rails and bushes (position, orientation, length, nominal load, cross section, etc.) must be determined according to a precise set of specifications for the networks they are designed to support. This guarantees their suitability for their future tasks.

9 .2 .3 .4 – Ident i f i ca t ion and or i enta t ion

It is advisable to number the segments using indelible paint and a stencil according to the construction plans. This type of identification prevents the use of different numbering systems in inspection reports carried out over the years. On certain very large structures, it might also be useful to label cross beams on piers with the number of their corresponding pier as this could facilitate the identification of certain works.

9.3 - Piers



9.3.1 - Space between the underside of the bridge deck and the top of piers

In order to facilitate monitoring and maintenance operations, it is recommended to leave a minimum space of 0.50 m between the top of the piers and the underside of the bridge deck.

9.3.2 - Design of the pier head units

9 .3 .2 .1 – Access and inspec t ion p i t s

If the height of the piers exceeds 8 to 10 m, it is recommended to build a pit into the pier head units. This pit, resembling a bathtub in shape, allows work to be carried out "comfortably" in the pier head area, in spite of the limited space between the top of the pier and the underside of the bridge deck (Fig. 9.7 and 9.8). These pits are usually 0.80 to 1 m deep and one meter wide; their length depends on the center distance between the bearings. A ∅ 100 mm drain hole is built into the pit for the drainage of any water that might enter, especially during construction.

9 .3 .2 .2 – Pos i t ion o f the jack ing po int s for the br idge deck

A bridge deck often has to be jacked up after commissioning in order to change the bearings, reset the slide plates or make adjustments due to the subsidence of a pier or a geometrical defect. To prevent problems or damage to the structure during jacking, it is necessary to determine the position of the jacking points at the design stage.

The size and location of these jacking points depends on the amount of space available on the pier head unit. It is also important to position the jacking point as close to the axis of the nearest web as possible. In general, two jacking points are provided for each bearing. However, if the pier head unit is too short to accommodate two jacking points per bearing, it is possible to allow two points between both bearings, i.e. one point per bearing. These points will also be be situated as close to the webs as possible. Once these jacking points have been determined, the next stage is to design and install the reinforcements or prestressing required to take up the forces generated in the piers and bridge deck under these support conditions. It is also necessary to mark the jacking points on the plans and identify their positions on the top of the pier. Support blocks (Fig. 9.9) are usually used for this operation, although durable markers (studs, etc.) may be used if the geometry of the structure prevents the use of blocks.

9.3.3 - Inspection of hollow piers

9 .3 .3 .1 - Inspec t ion

Hollow piers are usually equipped with a system of safety ladders and landings throughout their full height (Fig. 9.10) for use during internal monitoring and inspection operations. This system is allows for the regular examination of the inside of piers with a level of accuracy that satisfies the requirements of scheduled inspections. For more detailed inspections, it is possible to use binoculars or additional ladders if stairs are fitted.



Fig. 9.7 – Access to bridge deck from piers and vice-versa

Fig. 9.8 – Inspection pit on pier head unit

Fig. 9.9 – Block marking the location of a jacking point

The dimensions of the system (height and depth of steps, frequency of landings) are determined according to the standards in force relating to stairs in buildings. NF E 85-010 "Échelles métalliques fixes avec ou sans crinolines" (Fixed Metal Stairs With or Without Safety Bows) was the applicable standard on the publication date of this guide.

Considering the financial investment required for this type of equipment, precautions must be taken to guarantee its longevity. Stairs or ladders must be made from hot galvanized steel thick enough to ensure that minor corrosion does not affect the strength of these elements. Landings can be made from galvanized steel or the same concrete that was used to construct the pier shafts.

In recent years, some Owners have decided to restrict the fittings inside hollow piers on large bridges to a single metal gridded platform situated just underneath the crosshead and couplings to which harnesses can be attached (Fig. 9.12). This creates a working platform from which inspectors equipped with climbing gear can operate. This system reduces the initial investment costs and guarantees that inspections will be carried using the latest totally compliant equipment. However, an inspection of the piers under these conditions requires more equipment and more time, which also increases the cost of the operation, of course.



Fig. 9.11 – Access door to a pier or an abutment with

five-point safety lock Fig. 9.10 – Safety ladders and landings inside a pier

Fig. 9.12 – Minimal fittings inside a pier

9 .3 .3 .2 - Access

Whatever the context, it is necessary to allow access to hollow piers from the bridge deck. For this, a shaft is usually created at the bottom of the inspection pit described in Paragraph 9.3.2.1. As before, this hole must normally be closed using a metal grid or plate. It must also be offet in relation to the shaft built into the cross beam on pier, to make sure that if someone falls from the bridge deck, they will not fall further than the bottom of this pit.

In the majority of cases, a second access point is also provided via a metal door at the base of the pier. Considering the risks of vandalism, it is necessary to use the same type of doors as those recommended for the abutments (see 9.4.2 and Fig. 9.11). It is also possible to situate these doors three or four meters above ground level, requiring a ladder for access. These doors are rarely aesthetically pleasing and it is important to make sure that the architecture of the pier is as complimentary as possible.

If it is impossible to provide doors at the base of the piers (e.g. piers on the sea bed, risk of vandalism too great, insufficient strength, etc.), it is necessary to create a reasonably large shaft leading from piers to the bridge deck. Indeed, this passageway must be big enough to be used for transporting and removing maintenance equipment. In the event of an accident during a maintenance operation, any victims will also have to be evacuated via this single passageway.

9 .3 .3 .3 - L ight ing

Hollow piers must be equipped with a lighting system similar in design to the system used for the bridge deck.



9.4 - Abutments

9.4.1 - Access to abutments

Access points to the abutments must be designed and built with care. In general, access is gained from the supported road, via the return walls of the abutments. However, it is also possible to enter abutments from another road below the structure if parking spaces are provided. These access points must be created with care (concrete surfacing, concrete or wooden stairs, guard rails if necessary, etc.). However, they must also be as unobtrusive as possible in order to avoid attracting unwanted attention.

9.4.2 - Restrict ing access in the abutments

On large bridges built in recent years, the front face of an abutment is usually closed off by a concealing wall, which is entered through a metal door. This system is highly recommended, as it denies access to unauthorized persons and therefore prevents malicious damage to the bridge bearings, external continuity prestressing and the guttering under the joints. This solution is also aesthetically pleasing, given that these walls hide the inside of the abutments which are never very attractive. It is also important to fit high-quality locks on the doors. Five-point safety locks bearing the "A2P trois étoiles" label awarded by the french APSAD (Assemblée Plénière des Sociétés d’Assurances Dommage - Plenary Assembly of Damage Insurance Companies) are particularly suitable for this task (see Fig. 9.11 on previous page).

In addition to this important provision, as little room as possible should be left between the concealing wall and the outer edges of the box girder. No more than 15 cm should be allowed for this gap, including between the underside of the bridge deck and the top of the central part of the concealing wall.

9.4.3 - Electrical system

Although covering a much smaller area than a bridge deck, an abutment must have the same type of electrical system (lighting and power sockets). It is important to fit a light switch next to the door mentioned in 9.4.2 above.

9.4.4 - Depth of abutments

Typ ica l example o f abu tment s w i th cab le pu l l ing chamber

One of the essential requirements for changing the external prestressing is the ability to gain access to the anchorages to stress the new tendons. As mentioned in section 5.42 of the "Précontrainte extérieure" (External Prestressing) guide published by Sétra, the design of an abutment must incorporate a cable pulling chamber if the external tendons are attached to stressed anchorages on the cross beam directly above the abutment. In order to determine the effective length L of this chamber, i.e. the distance between the internal face of the abutment wall and the end of the bridge deck, not including the corbel, it is necessary to consider the phase of the replacement process which requires the most room. For external tendons injected with a flexible product (wax or grease), this key phase in the design of this chamber is when the new tendons are in their ducts and the tensioning jack is positioned at the end of the strands prior to “swallowing” them up (Fig. 9.13). In this phase, the space required corresponds to the length of the jack Lv plus the length of the strands connected to the jack prior to stressing Lt.



Fig. 9.13 – Key design phase for determining the minimum length of the cable pulling chamber

The following table gives the lengths Lv, Lt and (Lv+Lt) for the 19T15S, 27T15S and 37T15S types of tendons used in certain French prestressing systems.

Unit 19T15S 27T15S 37T15S Supplier System Lv Lt Lv + Lt Lv Lt Lv + Lt Lv Lt Lv + Lt Freyssinet C with jack

Cl 000F 1.28 1.11 2.39 1.29 1.12 2.41 1.25 1.08 2.33

SEEE FUT 1.07 1.25 2.33 1.18 1.40 2.58 1.20 1.40 2.60 Spie

Précontrainte SB 1.14 1.20 2.34 1.16 1.25 2.41 1.18 1.38 2.56

At the design stage, it can therefore be considered that the effective length L of the chambers must be at least 2.40 m for 19T15S cabling and 2.60 m for 27T15S or 37T15S cabling.

Spec i f i c examples o f abu tment s w i thou t cab le pul l ing chambers

In certain very specific cases, cable pulling chambers may not be built into abutments. In this case, the additional length described above is no longer required. However, the distance between the end of the bridge deck and the abutment wall must not be reduced too much. A minimum distance of 0.80 m to 1 m is essential for inspecting and correctly maintaining these parts of the structure.

9.4.5 - Collect ion of water under the expansion joint

Expansiont joints are fitted at the ends of almost all large modern bridges, and are therefore situated directly above the abutments. Despite the care and attention devoted to their design and fitting, these joints are never totally watertight. Therefore, it is necessary to collect any water that percolates through them in order to protect the abutment crossheads, bridge bearings and the external prestressing anchorages situated at the ends of the structure.

The best systems are shown in Figures 9.14 to 9.l6, consisting of a metal gutter positioned under the joint. Supported by galvanized steel brackets, this gutter must be positioned centrally under the expansion joint, which requires a corbel of 30 to 40 cm on the side of the bridge deck. In order to prevent splashes, it is necessary to channel the water using vertical neoprene splash guards enclosing the space between the joint and the gutter. These splash guards, which are usually different to those supplied with the joint, must be weighted for maximum resistance to the draft of air created by passing trucks. To facilitate the cleaning of the gutter, it is recommended to fit a water tap on the abutment, provided that the structure can be connected to the drinking water network at reasonable cost. The pipes must then be protected from freezing.



Fig. 9.14 – Collection of water under pavement joints

Fig. 9.15 – Gutter under joint (the distance to the slab allows for easy cleaning)

Fig. 9.16 – Gutter attachment

9.4.6 - Space between the underside of the bridge deck and the top of the crossheads

As for the piers, it is advisable to leave a minimum gap of 0.50 m between the top of the abutment crossheads and the underside of the bridge deck in order to facilitate maintenance operations.

9.4.7 - Bridge deck jacking points

Like piers, abutments must have jacking points for the bridge deck. These are determined according to the procedures described in paragraph 9.3.2.2 above.



10 - Recommendations for the creation of a Contractor Tender Document This section contains a number of recommendations and instructions for the creation of a Contractor Tender Document for a prestressed concrete bridge built by the cantilever method, and particularly with regard to the drafting of the written documents required. Given that it is impossible cover all of these aspects, these recommendations focus above all on items which are strongly influenced by this particular construction method and on the associated bridge deck structures.

10.1 - Nature of the tender enquiry In France, the vast majority of bridges built by the cantilever method are constructed in the framework of a restricted invitation to tender, i.e. with a preliminary shortlisting of applicants.

In most cases, the contract is not divided into tranches or packages. Very large projects, however, may sometimes be broken down into tranches in order to stagger the financing of the works, although this system is not be recommended because the tranches can rarely be considered in isolation.

10.2 - Creation of a Contractor Tender Document Apart from in very specific situations, Contractor Tender Documents consist of three sub-groups or schedules.

Sub-group 0 is reserved for the tender regulations (règlement de la consultation [RC]).

Sub-group I contains the documents that make up the contract. It contains the frameworks for the tender document, the price schedule, cost estimate, draft the Special Administrative Clauses (Cahier des Clauses Administratives et Particulières [CCAP]), the Special Technical Clauses (STC), and occasionally, price breakdowns and breakdown frameworks. It also includes a series of documents appended to the STC, including:

• Site plan

• Plan view

• Longitudinal cross-section

• Transverse cross-sections of bridge deck

• Detailed plan of cross beams and deviators

• Detailed plan of bridge deck superstructures

• Pier formwork plans

• Abutment formwork plans

• Contractual part of the geotechnical survey, i.e. usually consisting of the borehole logs.



In certain cases, sub-group I also contains specific studies which have a direct influence on the design of the structure: hydraulic studies, wind-effect study, etc. In other cases, certain architectural studies may also be included in sub-group I in order to make the information relating exclusively to these studies contractually binding (reference to a matrix for the bottom shuttering matrix, aggregates, etc.). Finally, if the structure has to be built over or close to a traffic-bearing road, railway or waterway, sub-group I must also contain a document listing the road, rail or water-related constraints facing the contractor during the works.

Sub-group II is made up of documents intended for information purposes only. For structures built by the cantilever method, this sub-group usually includes the following items:

• Plan of the areas capable of accommodating the site installations

• Plan of possible access routes to the site

• Longitudinal cabling plan

• Transverse cabling plan (for structures featuring transverse prestressing)

• Plan of the bridge deck showing a breakdown of segments

• Scheme of construction operations

• Plan of the cantilever stabilization system

• Preliminary quantity survey

• Architectural study

• The non-contractual part of the geotechnical survey: usually the pre-design for the foundations produced by the laboratory in charge of this survey.

In addition, sub-group II sometimes contains initial plans for the bridge deck reinforcements, along with design calculations or miscellaneous studies containing information for contractors.

In recent years, sub-group II of certain Contractor Tender Documents has also included reports concerning the formulation of concrete, including the results of specific studies carried out upstream by the Construction Manager (HPC, alkali reactivity, frost and salt-resistant formulas, etc.)

10.3 - Tender regulations

10.3.1 - Supplements to the Special Technical Clauses / Technical proposals

Technical proposals are detailed precisions that contractors are obliged to include in their bid in addition to their proposed basic solution. Article 2.3 b of the Tender regulations specifies the structural elements for which technical proposals must be submitted. With regard to the bridge deck of a structure built using the cantilever method, the following points must be covered in these proposals:

• Origin of the components, the composition and the application of the concrete

• Bridge bearings



• Prestressing processes

• Procedure for the waterproofing layer

• Expansion joints.

10 .3 .2 – Technica l var iant s

The Owner may authorize contractors to offer variants with a view to encouraging competition. Contrary to the technical proposals, these variants, if they are accepted, may require alterations to be made to the price schedule, cost estimate and of course the Special Technical Clauses and the attached plans.

The permissible technical variants are listed in Article 2.3 of the Tender Regulations. The most common variations include:

• The breakdown into segments

• Types of prestressing units used

• Internal form of bridge deck gussets

• Scheme of construction operations

• Cantilever stabilization system.

More flexible variants are sometimes permitted. These may include:

• The replacement of concrete webs with lightweight metal webs (for long span bridges)

• Substitution of the cantilever construction technique by the incremental launching method, with or without pilings depending on the situation (for moderately long bridges of a constant depth)

• A change of construction technique for the foundations of one or more supports.

10.4 - Tender document

10.4.1 - Period of val idity for bids

The evaluation phase for the bids for a structure to be built by the cantilever method is often longer than for a basic structure. Therefore, the first article of the tender document should specify a reasonably long period of validity for the bids (a minimum of 180 days), or even longer if contractors are likely to propose major variants.

10.4.2 - Preparation period

As we have already mentioned, construction surveys for structures built by the cantilever method are long and complex. Sufficient time must also be allowed for Construction Managers to evaluate these surveys. For certain structures, work on site may sometimes advance at a faster rate than the construction surveys can be carried out. In order to prevent the interruption of work due to delays in the availability of construction plans that have been approved by the Contruction Manager, it is essential to allow a sufficiently long preparation period in which the engineering firms can reach a stage that is well ahead of the work carried out on site. The period required varies



from structure to structure, but the amount of time required is inversely proportional to the time allowed for the construction of the piers.

10.5 - Special Administrative Clauses

10.5.1 - General contract documents

For a structure built by the cantilever method, the list of general documents to be included in the contract includes at least the following documents:

• Fascicule 61 Titre II of the french Cahier des Prescriptions Communes (Common Conditions) [CPC]) : "Programme de charges et épreuves des ponts-routes" (Program of Loads and Tests for Road Bridges)

• Fascicule 61 Titre IV Section II of the french General Technical Clauses (GTC): “Actions de la neige sur les constructions” (Effects of Snow on Structures) (DTU P 06-006 of September 1996)

• Fascicule 62 Titre I - Section I of the french GTC: "Règles techniques de conception et de calcul des ouvrages et constructions en béton armé suivant la méthode des états limites" (Technical Rules for the Engineering and Design of Reinforced Concrete Structures According to the Limit State Method) [BAEL 91 revised in 1999]

• Fascicule 62 Titre I - Section II of the french GTC: "Règles techniques de conception et de calcul des ouvrages et constructions en béton précontraint suivant la méthode des états limites" (Technical Rules for the Engineering and Design of Reinforced Concrete Structures According to the Limit State Method) [BPEL 91 revised in 1999]

• Fascicule 65-A of the french GTC and its supplement: "Exécution des ouvrages de génie civil en béton armé ou précontraint" (Construction of Reinforced and Prestressed Concrete Civil Engineering Structures) in their updates published in August 2000

• Fascicule 62 Titre V of the french GTC: "Règles techniques de conception et de calcul des fondations des ouvrages de génie civil" (Technical Rules for the Engineering and Design of Civil Engineering Structures)

• Fascicule 68 of the french GTC: "Exécution des travaux de fondation des ouvrages de génie civil” (Construction of the Foundations for Civil Engineering Structures).

For structures supporting oversize loads, it is also necessary to mention:

• French Circular no. R/EG3 of July 20 1983 entitled "Transports exceptionnels, définition des convois types et règles pour la vérification des ouvrages d’art" (Exceptionally Large Trucks: Definition of Standard Loads and Rules for the Verification of Civil Engineering Structures), published by the Direction des Routes (Highways Department), for structures supporting these types of vehicles.

In earthquake zones, it is also necessary to add the following specific documents:

• The AFPS 92 guide for the seismic protection of bridges, edited by the Association Française du Génie Parasismique (AFPS) [French Seismic Engineering Association], published by the École Nationale des Ponts et Chaussées (National School of Civil Engineering)



• The officially approved standard NF P 06-013, more commonly known as the "Règles de construction parasismique - règles applicables aux bâtiments - PS92" (Antiseismic Construction Rules – Rules Applicable to Buildings – PS92), with regard to the foundations

• Order no. 91-461 of May 14 1991 relating to the prevention of seismic risks and to the Decree of September 15 1995 relating to the classification and rules for antiseismic constructions applicable to bridges in the “normal risk” category.

10.5.2 - Preparation period

Article 8.1 of the Special Administrative Clauses (Cahier des Clauses Administratives particulières [SAC]) specifies the length of the preparation period and indicates whether or not this is included in the contract period. Further details concerning this point are given in article 10.4.2 of this chapter.

10.5.3 - Examination period for construction surveys

As conflicts between the Contractor and Construction Manager often arise over compliance with acceptance deadlines, it is recommended that Article 8.2 of the Special Administrative Clauses should contain a text which clearly mentions:

• The documents considered by the Construction Manager to form an indivisible whole

• The deadlines that the Construction Manager agrees to observe, in the framework of the first and subsequent evaluations of the documents.

Although it could probably be improved, the following text could serve as an example for this text:

Delays for the examination and approval of construction documents

The contractor must submit the construction surveys for each part of the structure to the Construction Manager for approval in the form of homogeneous groups of documents (e.g. formwork plans, reinforcement plans and design calculations for the section concerned), accompanied by the corresponding construction procedures.

The Construction Manager shall notify the contractor of his findings in writing and within a maximum period of forty-five (45) working days for the first examination of the "longitudinal flexion of the bridge deck" and “transverse flexion of the bridge deck" groups and twenty-five (25) working days for the first inspection of the other groups of documents. These deadlines are reduced to fifteen (15) and five (5) working days for the subsequent examinations of these groups of documents.

It should be noted that in the event of the staggered arrival of documents within the same group, these periods start on the arrival date of the last document.

10.5.4 - Operating constraints in the public domain

Many bridges are built immediately next to or even above other traffic-bearing routes. Under these conditions and for safety reasons, it is necessary to wait until the traffic on these arteries has been interrupted before carrying out certain operations.

As traffic can normally only be interrupted at certain times of the day, work on site may be disrupted. It is important to mention these constraints clearly in articles 8.4 and 8.5 of the SAC, either by describing the constraints directly in these articles, or by referring the reader to another of the documents included in the Contractor Tender Document.



10.5.5 - Duration of hold points

Article 91 of the SAC outlines the main hold points on the site as well as the time necessary for the Construction Manager to cancel these hold points. The following table gives a non-exhaustive list of the hold points likely to apply to the bridge deck of a structure built by the cantilever method in addition to the average delay before they can be lifted.

Hold points Time required Casting and formwork removal Acceptance of the quality control element Authorization for the casting of a part of the structure Authorization to move form travelers forward Authorization to remove falsework from a section of bridge deck

1 day 1 day 1 day 1 day

Prestressing Authorization for tensioning of prestressing Acceptance of tensioning before reinforcements are cut Authorization for the injection of prestressing ducts

1 day 1 day 1 day

Bridge bearings Acceptance of bearing blocks Acceptance at moment of delivery Acceptance of the fitting of bridge bearings (adjustment and positioning)

1 day 1 day 1 day

Fittings Acceptance of waterproofing substrate Acceptance of waterproofing; authorization to apply surfacing materials Acceptance of a quality control element for the prefabricated concrete cornice Acceptance of the adjustment of cornices before sealing Acceptance of pavement joints before fixing or sealing Acceptance of retaining systems before sealing

1 day 1 day 1 day 1 day 1 day 1 day

Testing Authorization to perform loading tests 1 day

10.6 - Special Technical Clauses

10.6.1 - Preamble

There now follows a list of points that must be clearly specified in the Special Technical Clauses (STC) for the Contractor Tender Document.

These points may be broken down into two categories. The first concerns elements of additional information to that provided in the GTC and by the applicable standards, either because these documents are incomplete, or because none of them cover the field in question. The second category concerns the options proposed by these texts.

In line with the standard STC included in the CAPT-DCE-OA software published by Sétra, none of these points repeats the requirements laid down in the GTC and the applicable standards, because they are already binding for the contractor.As these points concern conventional types of box girders built by the cantilever method, additional information may be required for more sophisticated box girder designs.

10.6.2 - Construction survey program for the structure

As we have already mentioned, great care should be taken with regard to the quality and execution of the surveys. With this in mind, it is advisable to include an article entitled “Programme des études d’exécution” (Construction Survey Program) in the Special Technical Clauses. This can be worded in the following manner:

Construction Survey Program

The Contractor must submit a construction survey program which includes a list and a provisional schedule of the documents to be drawn up.



The list enumerates the documents that must be submitted for the construction of both temporary and permanent structures. It shall be drawn up in accordance with the framework of surveys specified in the contract.

The provisional schedule includes the deadlines for the submission of documents and the fixed or tentative deadlines for approval by the Construction Manager, in accordance with the minimum deadlines established by Article 8.2 of the SAC. It presented in the form of a bar chart clearly showing the critical tasks and the time allowed.

10.6.3 - Construction surveys for the structure

10 .6 .3 -1 -Act ions

The STC must state all of the actions to be considered in the verifying calculations for the structure.

Many of these actions are defined in fascicule 61 Titre II of the french CPC and in the BPEL 91 revised in 1999. These actions, which are normally listed and described in the STC are:

• Selfweight of the bridge deck (specify the unit mass of the concrete)

• Weight of the fittings added to the bridge deck

• Prestress forces

• Concrete shrinkage and creep (specify the area in which the structure is situated)

• General thermal effects (gradient and uniform variation)

• Thermal effects (uniform variation) to be considered for the expansion joints

• Predicted overloads from road vehicles and pedestrians on the structure, including fatigue trucks, if used

• Impacts on restraint systems.

These actions must be accompanied by certain actions which are specific to box girder bridge decks and the method of construction. These must be specified in the STC and relate toconcern:

• Selfweight of temporary structures (form travelers, launch beam, etc.)

• Site overloads defined in Chapters 3 and 5 of this guide, only to be used for calculations in the construction phase before the closure of a cantilever

• Specific site actions (e.g. an unbalanced segment, collapse of one of the form travelers, forces transmitted by launch beam supports, etc.), also described in Chapter 5 of this guide.

Depending on the situation, it may also be necessary to mention certain additional actions such as:

• Impacts on cetain supports

• Thrust due to water or ice

• Wind and/or ice to be considered for certain very exposed sites



• Seismic effects

• Etc.

10 .6 .3 .2 – Combined ac t ions

The STC usually mentions the different combined actions that have to be considered. The combinations to be used for the in-service verification of the structure are specified in the BPEL 91 revised in 1999. Combinations to be used for verifying the structure with regard to the risks of cantilever instability are given in Chapter 5 of this guide. It should be noted that they differ from those mentioned in the Directives Communes (Common Guidelines) of 1979.

10 .6 .3 .3 –Ver i f i ca t ion o f the br idge deck

The STC must specify:

• The verification categories, as described in Article 1.3 of the BPEL 91 revised in 1999, used to verify the longitudinal flexion of the bridge deck and the transverse flexion of the upper slab on structures with transverse prestressing (see Paragraph 3.3.2)

• The cracking categories, as described in Article A 4.5.3 of the BAEL 91 revised in 1999, for the verification of reinforced concrete parts (transverse flexion, deviators, cross beams, etc.)

• The thermal gradient and the thermal expansions to be adopted in the construction phase (see Paragraph 3.3.3.2).

As differences of opinion exist between Construction Managers, the STC must specify whether Article 6.1.2.3 of the BPEL 91 revised in 1999 is applicable in the strict sense, or whether different permissible stresses must be adopted. (For example, Paragraph 3.3.3 of this guide recommends the application of the comment in Article 6.1.2.3 in construction situations).

The STC must also state whether it is compulsory to perform a range calculation for prestress effects. If not, the STC must specify the values of k and k’ to be adopted for the application of Article 4.10 of the BPEL 91 revised in 1999. These values are directly related to the requirements formulated by the Construction Manager with regard to empty ducts and the measurement of transmission factors (see our recommendations in 3.2.3).

As the BPEL 91 revised in 1999 does not include any rules for the accumulation of non-prestressed reinforcement bars designed to compensate for transverse flexion on the one hand, and the tangent general flexion and distribution forces on the other, it is essential to include a rule of this type in the STC (see Chapter 4 of this guide). It would also be advisable to add a rule governing how to allow for different construction phases in the calculation of stresses at the ULS (see our proposals in paragraph 3.3.5).

In accordance with Paragraph 3.2.5, it is important to note that an as-built calculation must be performed after the completion of the construction work. This calculation takes account of the actual phasing of the work carried out on a bridge built by the cantilever method, with the actual dates of casting and any incidents that occurred on site (e.g. a broken strand that was not replaced). It may also consider the estimated coefficients of friction given by measurements taken on site.

Finally, depending on the structure in question, the following requirements may also be specified in the STC:

• Allow for the curvature of the structure on the horizontal plane in the calculations of longitudinal flexion



• Perform a finite elements calculation for a section of the bridge deck

• Perform a finite elements calculation for a specific part of the structure (segment on pier, segment on abutment, ribs, etc.)

• Perform a second-order calculation for one or more piers if they are very slender (in this case, the STC must specify the design assumptions for the horizontal forces in the pier heads)

• Etc.

Chapter 3 of this guide gives a lot of valuable advice on choosing the coefficients and rules mentioned in this paragraph.

10.6.4 - Bridge deck formwork

10 .6 .4 .1 - Formwork

The STC must specify the category of facing to be used for the inner and outer surfaces of the box girder. This category must conform to the definitions provided in Article 52 of Fascicule 65A of the french CCTG.

10 .6 .4 .2 – Smal l contro l s labs or t e s t s egment

The STC must specify whether the contractor must manufacture a test segment for the suitability tests or whether small control slabs or elements will suffice. In all cases, the STC must clearly mention:

• The dimensions of these elements

• The ducts and non-prestressed reinforcement bars that they must contain.

• Whether continuity cable anchor blocks must be fitted.

Furthermore, the STC must clearly define the acceptance conditions for these tests: inspection of facings, core sampling in the sheath areas, measurement of flatness of facings, etc.

10 .6 .4 .3 – Remova l o f formwork

It is advisable to establish a minimum strength requirement for the concrete at the moment the formwork is removed. This must not be less than 15 MPa.

10.6.5 - Prestressing

10 .6 .5 .1 – Cant i l ever tendons

The STC must precisely state the number and type of strands to be used for the cantilever tendons, along with their strength and relaxation categories. It must also mention the type of duct and, of course, the type of injection product to be used.

10 .6 .5 .2 - Cont inui ty t endons

The characteristics mentioned in the STC for the continuity tendons must be the same as those specified for the cantilever tendons. The Owner’s requirements for the permanent protection to be used on the anchorages (e.g.



conventional sealing, metal caps, etc.) must also be specified. Certain Construction Managers demand rigid ducts for the ducts at the level of the anchor blocks, guaranteeing a consistent alignment without any concentration of radial tendon forces.

10 .6 .5 .3 – Transverse tendons

If the project calls for the installation of transverse tendons in the upper slab or ribs, the STC must clearly state the applicable requirements, which are identical to those for the continuity tendons.

10 .6 .5 .4 – Externa l t endons

The characteristics mentioned in the STC for the external tendons must be the same as those specified for the cantilever tendons. The type of deviator tubes and corrosion inhibitors to be used in the structural deviators, in addition to the types of anti-vibration systems to be adopted, if any, must also be specified. Finally, the Owner’s requirements with regard to additional prestressing, and more specifically, to the capacity of this prestressing, must also be specified.

10.6.6 - Special f i t t ings in the box girder

As these fittings are not always clearly marked on the plans included in the Contractor Tender Document, the STC must clearly describe the maintenance fittings that the Owner has requested for the structure. These fittings include:

• The electrical system for the box girder, including the internal lighting

• Stairways or ramps for passing the cross beams and deviators

• Closing devices (doors, grids, plates, etc.) for the access points to the bridge deck (manholes in cross beams on abutments, manholes in the lower slab, on piers or close to abutments)

• Anchor rails fixed to the upper slab or webs, which may be used for the immediate or subsequent installation of networks in the box girder

• Handling rails fitted in the upper slab, in line with any hatches that may be built into the lower slab

• Rails used in the deployment of tensioning jacks for the external prestress tendons

• Inspection equipment for hollow piers.

Chapter 9 of this guide contains numerous guidelines for the drafting of the corresponding clauses.

10.6.7 - Inspection of work

As mentioned in Chapter 7, the inspection of work carried out on a structure built by the cantilever method is an important and complex task which the Construction Manager must start to organize quite a long time in advance.

The Contractor Tender Document (SAC, STC) must clearly specify these inspections, which usually correspond to hold points for contractors.



In addition, it may not be possible for the Contract Manager and his or her laboratory to carry out certain inspections. If this is the case, it will be necessary to use the services of an external inspection company. These inspections must be clearly defined and paid for separately.

10.7 - Price schedule A standard price schedule which is perfectly suited to the construction of all standard structures is appended to fascicule 65A of the french CCTG.

In addition to the prices normally shown in this appendix, the price schedule for a prestressed concrete structure built by the cantilever method using cast-in-situ segments must also include prices for the following elements:

• Cantilever stabilization systems

• Form travelers

• Formwork tool for segments on piers

• Centering for end sections.

The price for the cantilever stabilization system is normally given as a “fixed price” or a “fixed price per pier”, covering the supply, installation, and eventual removal of the temporary stability blocks, the temporary prestressing and, if necessary, the temporary pilings or cable-stays. The price also covers any jacking operations required during construction, especially during the transfer onto permanent bearings.

The price for the form travelers usually includes the design, construction, transportation, adjustments, successive movements during construction and the final dismantling of form travelers used on site, in addition to cost of external inspections. This is either a fixed price or, for very large structures, a “per pair” price. In view of the large sums of money involved, this price is normally paid in instalments as the work advances on site.

The price of the formwork tool for the segment on pier is given as a fixed or “fixed per pier” price. This normally includes the design, construction, transportation, adjustments, successive movements during construction and the final dismantling of structures used for centering and encasing the segments on piers, in addition to the cost of external inspections.

The price for the centuring of end sections includes the design, assembly and removal of the centuring used for the sections of bridge deck not built by form travelers, plus the costs of external inspections. Payment is often on a fixed-price or fixed price per abutment basis, although a price per square meter may also be charged according to the area of bridge deck to be shored up.



A1 Determination example Example of the determination of a bridge deck built by the cantilever method This appendix presents an example of the calculation of the bridge deck for a structure built by the cantilever method. It also provides information about specific aspects of the design.

A1.0 – Purpose of this appendix Based on a concrete example, this appendix describes a simplified method for roughly calculating the formwork and prestressing for a bridge deck of a cast in-situ structure built by the cantilever method. Considering the complexity of the calculations to be performed, this method is not designed to determine the definitive formwork and cabling. Instead, it is used to provide the minimum amount of information (e.g. formwork, breakdown into segments, cantilever tendons) required for the preparation of a more sophisticated computerized design model.

Like the rest of this guide, this appendix has been drawn up in accordance with the BPEL 91 revised in 1999 and fascicule 61 Titre II of french CPC.

A1.1 - Reminders

A1.1.1 - Notation

Figure A1-1 describes the notation used. We take:

G to be the centre of gravity of the cross-section

v to be the distance from G to the upper axis

v’ to be the distance from G to the lower axis

h = v + v’ to be the total height of the section

eo to be the off-setting (off-centring?) of the mean tendon

d to be the minimum distance from the mean tendon to the upper axis in order to guarantee the adequate coating of the tendons

d’ to be the minimal distance from the mean tendon to the lower axis in order to guarantee the adequate coating of the tendons



Fig. – A1.1 – Notations

Furthermore, we take:

B to be the area of the section

I to be its moment of inertia in relation to a horizontal axis passing through G

'BvvI

=ρ to be the geometric output of the cross-section

c = ρv to be the ordinate (in relation to G) of the highest point of the central core

c’= ρv’ to be the ordinate of the lowest point of the central core

Mg to be the moments due to the selfweight

Mq `to be the moments due to the fittings

Ms1 and Ms2 to be the maximum and minimum extreme moments respectively (counted algebraically) due to the imposed loads

Ml and M2 to be the maximum and minimum extreme moments respectively applied to a cross section

M = M1 - M2

F to be the prestress force (effective traction).

Finally, we use the same indices for shear forces (T) as for the moments.

A1.1.2 – Reminders about prestressing

A1.1 .2 .1 – L imi t s t res ses

In Class II of the BPEL, the limit stresses are:

- in compression: ccjc fkf −= 6.0σ with k = 0.02 for such a structure



- in traction: ( )ctjt fkf −−=−σ

Given that the hyperstatic forces due to prestressing are ignored, in each section we should have:

below Mmini = M2 tvI

MePBP σσ ≥

++= 20

sup (1)

cvI

MePBP σσ ≤

+−= '20

inf (2)

below Mmaxi = M1 cvI

MePBP σσ ≤

++= 10

sup (3)

tvI

MePBP σσ ≥

+−= '10

inf (4)

This can be expressed as:

PvI

PMce

PvI

PMc tt σσ

'¨' 1

02 +−≤≤−−−

A1 .1 .2 .2 – Sub-cr i t i ca l s ec t ions

These are sections in which we are not restricted by the coating requirements for the tendons; P can therefore be chosen so that:

PvI

PMc

PvI

PMc tt σσ

'¨' 12 +−=−−−

so

tBcc

MP σ−+

Δ=

' and

PvI

PMc

PvI

PMce tt σσ

−−−=+−= 210 '

'with ( ) dvedv −≤≤−− 0''

In so far as we can choose the thicknesses of the two members, we can choose them in such a way that

σΔ==

vv 'ΔMII (with Δσ being the range of stress variation tc σσ + ).

Thus, under extreme loading cases, we may obtain the four limit stresses (Fig. A1.2a), but if an excessively

thick member is dictated (e.g. an upper member for which σΔ

>v

ΔMI normally applies) we will only be able to

obtain three limit stresses (Fig.A1.2b).

²

0

0

σb 0 - tσ ≤ σb - tσ - tσ

0 σb σb tσ -



Fig. A1.2 – Limit stress diagrams for a sub-critical section

A1.1 .2 .3 – Over-cr i t i ca l sec t ions

These are sections in which we are restricted by the coating requirements for the tendons. Based on compliance with the minimum stress, this gives:

tt BhMB

ccMP σ

ρσ −

Δ=−

+Δ

≥'

P must therefore be at least equal to the higher of the two values below (according to the structurally significant moment):

tvIdvc

M

σ+−+ ''

1 and tv

Idvc

M

σ'

'2

+−+−

As in the previous situation, the number of limit stresses that can be obtained depends whether or not it is possible to modify the thickness of the members. Let us consider the example of a section that is mainly subjected to negative moments (e.g. a section on an intermediate support); therefore M2 (the minimum algebraic value) is structurally significant. If we are able to modify the thickness of the upper structural member, it will be possible to obtain three limit stresses (Fig. A1.3a), with:

tvIdvc

MPσ

''

2

+−+−= and

σΔΔ

=M

vI (compliance with the change of stress σb, in the upper axis).

If, as is usually the case, the size of the upper member is imposed (excessively thick), we will only be able to obtain two limit stresses (Fig. A 1.3b) with:

tvIdvc

MPσ

''

2

+−+−=

0 0 ≤ σb - tσ σb - tσ

sous M1 sous M1 sous M2 sous M2

σ- tσ σb b0 0

(a) (b) Fig. A1.3 – Limit stress diagrams for an over-critical section ≥



10.7.1 - Focal point method for the design of a continuous beam

Using the notation adopted by M. Courbon, the focal point method consists of using the mechanical constants ai, bi and ci for each span to calculate the focal point ratios for the left, (φi) and right, (φ’i). Both groups of equations are given below:

ϕ1 ψ1 = 0 ϕ‘n = 0

2

2

ϕb = a2 + c1 - b1 ϕ1

1

1

' −

−

n

nbϕ

= cn-1 + an - bn ϕ‘n

1

1

+

+

i

ibϕ

= ai+1 + ci - bi ϕi i

ib'ϕ

= ci + ai+1 - bi+1 ϕ‘i+1

n

nbϕ

= an + cn-1 - bn-1 ϕn-1 1

1

'ϕb = c1 + a2 - b2 ϕ‘2

Having ascertained the the focal point ratios and the rotations ω’i and ω"i for the end of span i, which is considered to be independent and subjected to the loading case in question, we can calculate the bending moments on the supports Ai-1 and Ai when span Ai-1 Ai is loaded.

Mi-1 = )1

'1(

"''

−

+

iii

ii

i

bϕϕ

ωϕω

Mi = - )1

'1(

"'

−

+

iii

i

ii

bϕϕ

ϕω

ω

The moments on the other supports are determined by the following focal point ratios:

Mi-2 = -ϕi-1 Mi-1 Mi-3 = -ϕi-2 Mi-2 etc.

Mi+1 = -ϕ‘i+1 Mi Mi+2 = -ϕ‘i+2 Mi+1 etc.

A1.1.4 – Units of measurement

The following units of measurement are systematically used in this example (unless otherwise specified) :

- Length: meter (m)

- Mass: tonne (t)

- Force: MegaNewton (MN)

- Stress: MegaPascal (MPa), which is also equal to 1 N/mm² or 103 kN/m².

In addition, we shall adopt a value of g = 9.81 m/s2 for gravity acceleration.



A1.2 – Source data

A1.2.1 – Length and depth of bridge deck

Fig. A1.4 – Longitudinal section of the structure

The example involves the determination of a structure with three asymmetrical spans totaling 214.50 m between the centers of the end supports. There are two end spans of 53.375 m and 63.375 m and one central span of 97.75 m. The bridge deck is cast in-situ due to its moderate length (Fig.A1.4).

Given the need to comply with clearance dimensions, the height of the box girder varies parabolically between:

- On pier: h1 = 5.30 m , giving a slenderness ratio of approximately 1/18

- At the crown ho = 2.30 m, giving a slenderness ratio of approximately 1/43 (*).

The segments on piers are 8.00 m long and the closing segment for the central span is 2.00 m long.

(*) This is quite a low slenderness ratio but it is imposed due to the fact that this structure is designed to double the capacity of an existing bridge.

A1.2.2 – Functional cross section

The supported platform is illustrated in Figure A1.5. However, only one side of the traffic lanes is shown, as the complete structure consists of two bridges fastened together.

Fig. A1.5 – Cross-section of the structure

According to fascicule 61 Titre II of french CCTG, the distributed overload A is given as:

Usable width = 10.15 m first category bridge

Loadable width = 10.15 - (2 x 0.50) = 9.15 m

Number of loadable lanes = entire section (9.15/3) = 3 lanes



a1 = 0.9 as the bridge features three lanes

Width of lane = 9.15 / 3 = 3.05 m

a2 = 3.5/3.05 = 1.15

Considering the third comment in Article 4.21, the linear loads according to the length of loaded section is given by:

≤ 200 m s = 9.15 A2( ) = 9.15 x 0.90 x 1.15 A( ) = 9.45 A( )

with A( ) = 12

36000230+

+l

(A(l) in kg/m² and l in m - units used in fascicule 61 Titre II).

A1.2.3 – Weight of f i t t ings

The probable linear weight of the fittings is taken to be q = 47.4 kN/m.

A1.2.4 – Characteristics of materials

The characteristics of the materials used are as follows:

- For the concrete: compressive strength fc28 = 35 MPa, for a permissible in-service compression stress = 0.6 x 35 = 21 MPa

- For the cantilever and continuity tendons, we use 12T15S prestress units, giving an effective mean in-service force estimated at 1.95 MN; the overall diameter of the ducts is 80 mm

-For the external tendons, we use 19T15S prestress units, giving an effective mean in-service force estimated at 3.1 MN; the overall diameter of the ducts is 100 mm.

A1.2.5 – Cross sections of the bridge deck



Fig. A1.6 – Cross sections of the bridge deck

As the total width of the slab is equal to 10.95 m, including the longitudinal anchoring girders for the safety barriers, it is logical to design a box girder with two webs positioned according to the findings of a summary analysis of the transverse behavior. This analysis was also used to establish the thickness of the upper slab between the webs at 25 cm, whereas the thickness of the webs (36 cm) is determined by the casting conditions, allowing for the diameter of the ducts. Vertical webs were chosen for aesthetic reasons. The thickness of the cantilevers varies between 25 cm on the BN4 side and 30 cm on the web side. The mean thickness of the upper slab is therefore 27 cm. Figure Al.6 shows the cross-sections used as the basis for the first approximate calculations.

Finally, we know that there must be room to accommodate gussets in the slabs. Although we do not yet know the precise dimensions of the formwork for these elements, we must allow for them in our calculations. As an initial estimate, we shall use the dimensions given in Figure A1.7.



Fig. A1.7 – Detail of the gussets in the box girder

The transverse surface area represented by the gussets is:

²m4905.008.04.02

20.0x40.02

08.0x40.0240.0

460.0x20.1x2S

222

=⎥⎦

⎤⎢⎣

⎡++++

−= xπ

In the central spans, the total height of the box girder varies parabolically according to following the law:

h(x) = h0 + (h1 - h0) 22

⎟⎠⎞

⎜⎝⎛l

x

using the notation shown in Figure A1.8 below:

Fig. A1.8 – Variation in height of bridge deck in central span

In the end spans (Fig. A1.9), the total height varies parabolically at first (section closest to pier), and then it becomes constant and equal to h0, close to CO and C3.



Fig. A1.9 – Variation in height of bridge deck

We can schematize the sections according to Figure A1.10.

Fig. A1.10 – Calculation of the mechanical characteristics of the bridge deck

We then have to establish the thickness ε (x) of the lower slab; in fact, for this, we shall use a parabolic variation law similar to the one used for h(x), with ε0 and ε1 the thicknesses at the crown and on the pier:

ε(x) = ε0 + (ε1 - ε0) 22

⎟⎠⎞

⎜⎝⎛l

x

As an initial estimate, we shall use ε0 = 24 cm: a value which is imposed by the casting conditions, and ε1 = 45 cm: a value chosen in view of the span lengths and the slenderness ratios.

A1.2.6 – Characterist ics of the sections

A computerized calculation gives us the mechanical characteristics of the sections on pier and at the crown.

Section at the crown Section on pier h(x) 2.300 m 5.300 m ε(x) 0.240 m 0.450 m B 6.0965 m2 9.3129 m2

v 0.860 m 2.420 m v’ 1.440 m 2.880 m I 4.620 m4 41.532 m4

ρ 0.612 0.640

A1.2.7 – Sequence of construction operations

In the following calculations, we shall use the sequence of construction operations shown below: 1 Construction of cantilever on P1 2 Construction of the cast-on-falsework section near to C0 3 Closure of C0-Pl, stressing of continuity tendons for C0-Pl and transition to permanent bearings for P1 4 Construction of cantilever on P2 5 Construction of cast-on-falsework section near to C3



6 Closure of P2-C3; stressing of tendons for P2-C3 and transition to permanent bearings for P2 7 Closure of P1-P2 and stressing of continuity tendons for Pl-P2 8 Stressing of external tendons 9 Installation of fittings and commissioning

A1.3 – Cantilever prestressing design

A1.3.1 - Moment on pier during the casting of the f inal segments

The complete cantilever is shown in Figure A1.11 below. In order to simplify the calculations, we consider that the bridge deck is supported on the centerline of the pier. The moment resulting from this assumption is slightly higher than if the calculation were to be performed in line with the temporary stabilizing blocks.

Fig. A1.11 – Determination of the support moment during the casting of the final segments

The calculation of Mg is shown hereafter (with x defined in Figure A1.8):

4905.0875.48

21.024.003.5875.48

00.330.272.027.023.10)(B22

+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛++

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛++=

xxxx

Hence, with a unit mass of 2.5 t/m3, therefore a unit weight of 0.024525 MN/m3:

g (x) = 0.024525 B (x) = 0.149990 + 33.02.10-6 x2

- Tg(x) = = 0.149990 x + 11.01.10( ) ξξ dgx

∫0

-6 x3

- Mg(x) = = 0.074995 x( ) ξξ dTx

g∫−0

2 + 2.75.10-6 x4

For the section on pier, i.e. for x = 48.875 – 1.00 m (½ closing segment), this gives Mg = - 186.34 MNm.

At this moment Mg, it is necessary to add the moment due to the known site loads (Qc1) in addition to the moment due to random site loads (Qc2 and Qc3).

Qc1 Moment due to the weight of the form traveler, assumed to be equal to approximately 40 t, i.e. 0.40 MN, and exerted at 3.00 m / 2 + 1 m = 2.5 m from the crown:



MQc1 = Mform traveler = - 0.40 x 46.375 = - 18.55 MNm

Qc2 Moment due to a distributed load of 200 N/m² over a half-cantilever

Qc3 Moment due to a concentrated load of (50 + 5b) kN, with b being the width of the upper slab of the box girder:

MQc2 = - (200 x 10.95 x 47.875) x 0.000001 x (47.875 / 2) = - 2.51 MNm

MQc3 = - [(50 + (5 x 10.95) 1 x 0.001 x (47.875 – 3.00) = - 4.70 MNm

We can therefore consider that: Mg = - 186.34 – 18.55 – 2.51 – 4.70 = - 212.10 MNm. The shape of the moment curve in cantilever Mg is shown in Figure A1.12 below.

Fig. A1.12 – Bending moment in the cantilever under selfweight + form traveler

A1.3.2 – Calculat ion of canti lever cabling

Background: Cantilever tendons: 12T15S

Effective force: 1.95 MN

Sheath diameter: 81 mm

Concrete: B35

We consider the bridge deck to be cast in-situ with certain precautions taken (presence of empty ducts, measurement of transmission factors). The strength of the concrete in the segments on piers at the moment of the casting of final pair of segments is taken to be fcj = 35 MPa. The allowable stress in the upper axis is therefore:

σt = 0.7 ftj - k fcj with k = 0.02

σt = 0.7 x (0.6 + 0.06 x fcj) – 0.02 x fcj = 0.7 x (0.6 + 0.06 x 35) – 0.02 x 35 = 1.19 MPa

The force N developed by the cantilever tendons in the section on pier must satisfy the following condition:



bIveN

IvM

BN σ≥++ 0

with B = 9.3129 m2, I = 41.532 m4 ,v = 2.420 m and M = -212.10 MNm

e0 = 2.258 m position of the mean tendon supposing its distribution over two beds

e0 = v - 2 φg with φg = 0.081 m

MN74.46

532.4142.2x258.2

3129.91

532.4142.2x10.21219.1

Ive

B1

IvM

N0

=+

+−=

+

−−≥

bσ

2495.174.46ntendons ≈≥ tendons

to which we add two tendons in order to prestress the final pair of segments.

We therefore have 13 pairs of 12T15S tendons, allowing us to divide the cantilever into 2 x 13 standard segments of 3.375 m in length (see Figure A1.13 below).

Fig. A1.13 – Breakdown of cantilevers into segments

The shape of the moment curve in the cantilever under selfweight and prestressing is given in Figure A1.14 below.

Fig. A1.14 – Bending moment in the cantilevers

A1.3.3 - Verif ication during the casting of the P1-P2 closing segment

At this stage in the design, it is advisable to make sure that the cantilever tendons are strong enough to take up the weight of the bridge deck and form traveler during the construction of the central closing segment. To this end, two vertical forces are applied in a downward direction at each end of the cantilevers (figure A1.15). These



forces represent the effect of the weight of the form traveler and the concrete for the closing segment when still wet. These forces are exerted on two independent and isostatic structures because, at this stage, the two halves of the bridge have not yet been connected.

Fig. A1.15 – Effects of the weight of the form traveler and of the closing segment

In this new phase, the forces and stress in the upper horizontal plane along the centerline of the piers can be expressed as follows:

M = - 186.34 - (18.55/2) – 16.84 = - 212.45 MN.m

Ncantilever = 2 x 13 x 1.95 = 50.7 MN

Misocantilever = 50.7 x 2.258 = 114.48 MN.m

41.53242.2x)48.11445.212(

3129.97.50. +−

+=+=I

vMBN

sσ

MPai 19.1MPa26.0 b −=≥−= σσ ==> The dimensioning is therefore correct.

A1.4 – Prestressing design for the closing segment

A1.4.0 - Preamble

We have seen in A1.2.7 that the closing segments were constructed in the following order:

- Closure of C0-Pl and stressing of continuity tendons for C0-Pl

- Closure of P2-C3 and stressing of continuity tendons for P2-C3

- Closure of P1-P2 and stressing of continuity tendons for P1-P2.



The continuity tendons must be determined in reverse order. By starting at the final closing segment, the hyperstatic effect of the continuity tendons stressed during the previous closing operations is not an unknown.

Al.4.1 – Closing segment between PI and P2

The continuity tendons for the span P1-P2 must take up the selfweight of the closing segment, the forces resulting from the removal of the form traveler and the effects of the thermal gradient. In contrast to the other continuity tendons, they develop both isostatic and hyperstatic moments. Figure Al. 16 below represents the structure at the moment of the P1-P2 closure.

Fig. A1.16 – Detail of central closing segment

In order to determine the number of tendons necessary for the closing segment in the central span, we shall study each phase of the closure and determine its effect on the structure.

A1.4 .1 .1 - Ef fec t o f the se l fweight o f the c los ing segment and the form trave ler

As mentioned previously, the first stage of the closure can be simulated by applying two vertical forces in a downward direction at each end of the cantilevers (figure A1.15). In this phase, the bridge deck still consists of two independent isostatic structures. Therefore, this phase has no bearing on the calculation of the continuity tendons.

A1.4 .1 .2 – Ef fec t o f the remova l o f the form trave ler

This phase can be broken down into two parts. In the first part, two vertical forces are applied in an upward direction at each end of the cantilevers (Figure A1.17). These forces represent the effect of the removal of the form traveler and the concrete used for the closing segment (fresh concrete). In the second part, these forces will be replaced with a uniformly distributed load directed in a downward direction and representing the set concrete (Figure A1.18). In this phase, the structure is hyperstatic.

Fig. A1.17 – Diagram of moments due to the removal of the form traveler



Fig. A1.18 – Diagram of moments due to weight of closing segment

At the end of these two stages, the moment to be considered for the calculation of the continuity tendons for the span P1-P2 is:

MG = -7.75 + 3.40 = - 4.35 MN.m

A1.4 .1 .3 – Ef fec t o f the thermal gradient

Figure A1.19 below represents the bending moment due to a thermal gradient of 12° C.

Fig. A1.19 – Diagram of the moments due to a thermal gradient of 12°C

The value of the moment at the crown used for the calculation of the continuity tendons for P1-P2 is therefore:

Mtherm = 12.65 MN.m

A1.4 .1 .4 – I sos ta t i c moment o f cont inu i ty t endons for P1-P2

The isostatic moment is an unknown and is proportional to the prestressing that is used (Figure A1.20). The isostatic moment is calculated in the following way:

Miso = N . e0 with N = normal force due to the tendons in the section and e0 = offsetting of the mean tendon

In our example: N = 1.95 x ntendons and e0 at the crown = 1.318 m



Fig. A1.20 – Diagram of isostatic moments for continuity tendons

A1.4 .1 .5 – Hypers ta t i c moment for P1-P2 cont inu i ty t endons

As the structure is hyperstatic when the continuity tendons are stressed, a hyperstatic moment is set up in the central span which is of the opposite sign to the isostatic moment developed by the tendons. This hyperstatic moment is an unknown and depends on the intensity and the distribution of the prestressing in the span (alignment and length of tendons) and on the characteristics of the structure in question (whether or not there is variation of inertia). The diagram for this is shown in Figure Al.21 below.

Fig. A1.21 – Diagram of the moments due exclusively to the hyperstatic effect of the P1-P2 continuity tendons

At the pre-design stage, it is possible to use a simplification which consists of considering the span to be embedded on its supports (Figure Al.22). In this case, the hyperstatic moment can be evaluated in the following way:

span oflength diagrammoment isostatic of area Mhyper −=



Fig. A1.22 – Diagram of moments exclusively due to the hyperstatic effect of the continuity tendons according to a simplified

calculation

A1.4 .1 .6 – Ca lcu la t ion o f P1 -P2 cont inu i ty t endons



Sheath diameter: 81 mm

Concrete: B35

As before, we consider the bridge deck to be cast in-situ with certain precautions taken (presence of empty ducts, measurement of transmission factors). The strength of the concrete in the segments on piers at the moment of the removal of the form traveler used for the closing segment is taken to be fcj = 16 MPa. The allowable stress in the bottom axis is therefore:

bσ = 0.7 ftj – k fcj with k = 0.02

bσ = 0.7 x (0.6 + 0.06 x fcj) – 0.02 x fcj = 0.7 x (0.6 + 0.06 x 16) – 0.02 x 16 = 0.77 Mpa

The force N developed by the continuity tendons in line with the closing segment must satisfy the following condition:

bHyperThermG

IvM

IvM

IveN

IvM

BN σ−≥−−−−

'''' 0

with B = 6.0965 m2 I = 4.620 m4 v’= 1.440 m M = 13.57 MN.m

e0 = -1.318 m position of mean tendon e0 = - (v – 1.5 φg) with φg = 0.081 m

As we do not know the number of tendons required, we also do not know their position in the box girder or their isostatic moment diagram. Therefore, an iterative calculation is performed, starting with a single pair of tendons 22.25 m long, spanning six segments of 3.375 m and the closing segment of 2 m.



The distribution of the prestressing produces an isostatic moment which is distributed almost uniformly if a single pair of tendons is used (subject to the variation in e0 and the variation of inertia of the section). The hyperstatic moment is therefore:

ntendons = 2 fu = 1.95 MN

Fp = 3.90 MN

e0 = -1.318 m at the crown

L = 97.75 m

lc = 22.25 m

Miso = Fp x e0 = -5.14 MN.m at the crown

Mhyper = - (lc x Miso) / L = 1.17 MN.m

hence bbb MPa σσσ −≥⇒−= 71,0

We will therefore choose one pair of 12T15S tendons.

In the event of one pair of tendons being insufficient, it would be necessary to repeat the calculation with two pairs of tendons and recalculate the hyperstatic moment with the newly tendons arrangement.

A1.4.2 – Closing segment between C0 and P1

The continuity tendons for the span C0-Pl must take up the selfweight of the cast-on-falsework section. Figure Al.23 below shows the structure at the moment the span is closed.

Fig. A1.23 – Detail of the structure during placement of the closing segment on the C0 side

A1.4 .2 .1 – Ca lcu la t ion o f support react ions , shear force and bending moment

As the cross-section of the bridge deck is 6.0965 m² close to the abutments (h = 2.30 m), the load due to the selfweight of the cast-on-falsework section is equal to Q = 6.0965 x 0.02453 = 0.14955 MN/m.

As the structure in question is isostatic, we can easily calculate the support reactions and the longitudinal bending moment using static equations (Fig.A1.24):



Fig. A1.24 – Determination of the forces on the C0 side due to the closure of the span

Support reactions:

⎢⎣

⎡==

∑∑

00

MF

⇒ RP1 = 0.04238 MN and RC0 = 0.78015 MN

Shear force diagram:

Fig. A1.25 – Diagram of shear forces due to closure on C0 side

Bending moment diagram:

For the 5.50 m long section between C0 and the closing segment, the bending moment is equal to:

2x.Qx.RM(x)

2

C0 −= so for x = 5.217 m ⇒ M = 2.03 MN.m

Fig. A1.26 – Bending moment on C0 side due to the closure of the span

A1.4 .2 .2 – Ca lcu la t ion o f cont inui ty t endons between C0 and P1





Duct diameter: 81 mm

Concrete: B35

As before, the bridge deck is considered to be cast in place with certain precautions taken (presence of empty ducts and measurement of transmission factor) and the strength of the concrete is taken to be the value obtained when the falsework is removed fcj = 16 MPa. The allowable stress in the lower axis is thus:

bσ = 0,7 ftj – k fcj with k = 0.02

= 0.7 x (0.6 + 0.06 x fcj) – 0.02 x fcj = 0.7 x (0.6 + 0.06 x 16) – 0.02 x 16 = 0.77 Mpa


bIveN

IvM

BN σ−≥−−

'' 0

with B = 6.0965 m2, I = 4.620 m4, v’ = 1.440 m, M = 2.03 MN.m

e0 = -1.318 m position of the mean tendon e0 = - (v – 1.5 φg) with φg = 0.081 m

MN19.0

620.4440.1x318.1

0965.61

620.4440.1x03.274.0

Iv'e

B1

Iv'M

N0

−=+

+−=

−

+−≥

bσ

In principle, no tendons are necessary. However, in order to prevent any cracking due to parasitic phenomena (obstructed shrinkage, etc.), we shall specify one pair of 12T15S tendons.

A1.4 .2 .3 - Ver i f i ca t ion o f s t res ses a f t er c losure o f P1-P2

The calculation that we have just performed is intended to determine the amount of continuity cabling needed to consolidate the structure after the removal of falsework from the cast-on falsework section. However, somewhat higher forces develop in this area after the closure of P1-P2. Indeed, as the structure is now hyperstatic, the bridge deck becomes sensitive to the effects of thermal gradients, to which is added the hyperstatic effect of the continuity tendons for P1-P2.

In this new phase, the forces and stress in the lower axis are:

Mg = 2.03 MN

NcontinuityC0P1 = 2 x 1.95 = 3.9 MN

McontinuityC0P1 = 3.9 x -1.318 = -5.l4 MN.m

McontinuityP1P2 = 1.17 MN.m x 5.50 / 53.375 = 0.121 MN.m

MΔt = 0.5 x 12.65 MN.m x 5.50 / 53.375 = 0.65 MN.m



( ) ⎟⎠⎞

⎜⎝⎛ ++=−=

4.621.44 x 0.65 0.12 5.14 - 2.03 -

097.69.3'.

IvM

BN

sσ

MPa0.2MPa09.0 b −=≥−= σσ i (with j = 28 days)

The continuity cabling is therefore adequate.

A1.4.3 – Closing segment between P2 and C3

The continuity tendons for the P2-C3 span must take up the selfweight of the cast-on-falsework section. Figure A1.27 below represents the structure at the step when the span is closed.

Fig. A1.27 – Determination of forces on C3 side due to the closure of the span

A1.4 .3 .1 – Calcu la t ion o f support react ions and bending moments

A calculation similar to the one performed for the C0-Pl closing segment gives the support reactions and the bending moment:

⎢⎣

⎡==

∑∑

00

MF

⇒ RP2 = 0.28374 MN et RC3 = 2.03456 MN

M = 13.57 MN.m

A1.4 .3 -2 – Calcu la t ion o f the cont inui ty t endons for the P2-C3 span


bIveN

IvM

BN σ−≥−−

'' 0

with B = 6.0965 m2, I = 4.620 m4, v’ = 1.440 m, M = 13.57 MN.m

e0 = -1.318 m position of the mean tendon e0 = - (v – 1.5 φg) with φg = 0.081 m

MN07.6

620.4440.1x318.1

0965.61

620.4440.1x57.1374.0

Iv'e

B1

Iv'M

N0

=+

+−=

−

+−≥

bσ



395.107.6ntendons ≈≥

Therefore, we will opt for two pairs of 12T15S tendons.

A1.4 .3 .3 – Ver i f i ca t ion o f s t res ses a f t er c losure o f P1-P2

As before, prior to the stressing of the external tendons, it is important to verify the suitability of the cabling after the closure of the span P1-P2 and the stressing of the continuity tendons for P1-P2. In this new phase, the forces and stressing in the lower horizontal plane are:

Mg= 3.57 MN

NcontinuityP2C3 = 4 x 1.95 = 7.8 MN

McontinuityP2C3 = 7.8 x – 1.318 = - 10.28 MN.m

McontinuityP1P2 = 1.17 MN.m x 15.50 / 63.375 = 0.286 MN.m

MΔt = 0.5 x 12.94 MN.m x 15.50 / 63.375 = 1.58 MN.m

The continuity cabling is therefore sufficient.

A1.5 – External prestressing design

A1.5.0 - Presentation of the design method

The external prestress tendons must take up the forces due to the fittings, traffic loads A(l), thermal gradient and creep. In order to calculate the number of tendons required, we shall proceed in stages:

- Determination of geometry of tendons

- Computerized calculation of the envelope of longitudinal moments due to A(l)

- Choice of critical sections to be dimensioned or verified

- Computerized calculation of effects of thermal gradient

- Calculation of creep effects

- Determination of prestressing.

A1.5.1 – Determination of forces

A1.5 .1 .1 - Preamble concern ing the geometry o f the ex terna l t endons be tween CO and C3

For an initial estimation, we can use certain rules to define the mean alignment of the external prestress tendons.



Longitudinally, we shall place the intermediate deviators for the central span one third of the way along the span, i.e. at 32.583 m from the centerline of the piers. We shall also place a deviator on the end spans, also at 32.583 m from the centerline of the piers (Fig. Al.28). Remember that the deviators on piers position the external prestress tendons as close as possible to the upper axis of the bridge deck (negative longitudinal bending moment, whereas the intermediate deviators position these same tendons close to the lower axis (positive longitudinal bending moment).

Fig. A1.28 – Longitudinal geometry of alignment for external tendons at end of segments

Transversally on the section on pier, we shall make the minimum distance from the mean tendon to the upper axis equal to the thickness of the upper slab, i.e. 0.25 m. For the section at the crown, the minimum distance from the mean tendon to the lower axis shall be equal to the thickness of the lower slab plus 0.15 m. This value allows a gap of 0.10 m to be left between the sheath of the prestressing tendon and the top of the lower slab (Fig.A1.29).

Fig. A1.29 – Transverse geometry of external tendons

A1.5 .1 .2 - Over load A( l )

A computerized calculation gives us the envelope of the longitudinal moments due to the imposed loads A(1) (Fig.A1.30).



Fig. A1.30 – Diagram of moments due to the imposed load A(1)

The characteristic values of the enveloped curve below are used to determine the dimensioning sections and the verification sections for the external prestressing (Fig.A1.31).

Fig. A1.31 – Position of the sections used to analyze the external prestressing

The following table summarizes the forces due to A(l) and the type of calculation to be performed in each section.

Moments Sections Min Max

Type of calculation

Closing segment C0-P1 - 4.75 MN.m 8.39 MN.m dimensioning Σ1

Σ2 - 19.23 MN.m 19.87 MN.m verification Pier P1 - 45.71 MN.m 11.41 MN.m verification Σ3

Σ4 Closing segment P1-P2 - 6.36 MN.m 21.62 MN.m dimensioning Pier P2 - 43.50 MN.m 6.40 MN.m verification Σ5

Σ6 - 15.50 MN.m 23.63 MN.m verification Closing segment P2-C3 - 9.42 MN.m 19.59 MN.m Σ7 dimensioning

A1.5 .1 .3 - F i t t ings

A computerized calculation is used to obtain the curve of the bending moment due to the fittings. (Remember that the linear weight of the fittings is equal to q = 47.4 kN/lm).



Fig. A1.32 – Diagram of the moments due to the weight of the fittings

The table on the left summarizes the forces due to the fittings in each section.

Sections Moments

Closing segment C0-P1 1.94 MN.m Σ1

Σ2 -0.98 MN.m Pier P1 -41.25 MN.m Σ3

Σ4 Closing segment P1-P2 12.97 MN.m Pier P2 -45.16 MN.m Σ5

Σ6 4.44 MN.m Closing segment P2-C3 Σ7 6.37 MN.m

A1.5 .1 .4 – Thermal grad ient

A computerized calculation is again used to obtain the curve of the bending moment due to the thermal gradient of 12° C.

Fig. A1.33 – Diagram of the moments due to a thermal gradient of 12° C

The table below summarizes the forces due to the thermal gradient in each section.

Sections Moments

Closing segment C0-P1 1.27 MN.m Σ1

Σ2 5.18 MN.m Pier P1 12.36 MN.m Σ3

Σ4 Closing segment P1-P2 12.65 MN.m Pier P2 12.94 MN.m Σ5

Σ6 5.23 MN.m Closing segment P2-C3 Σ7 3.16 MN.m



A1.5 .1 .5 - Creep

As an initial estimate, we reserve a margin of 2 MPa for the stress in the lower axis. This reserve is used to calculate a creep moment in the central span:

v'M

Iv'M I

bb σσ −=⇒−=

Thus, for the section Σ4: v’ = 1.44 m I = 4.62 m4 MN.m42.644.162.42M == xcreep

In the end spans, the moment corresponding to this compression reserve will be determined by a linear interpolation between M = 0 MN.m on the abutment and M = 6.42 MN.m on the pier.

A1.5.2 – Dimensioning of external prestressing

As the calculations are similar and repetitive, we shall only dimension the external tendons close to the closing segment sections.

A1.5 .2 .1 – Ca lcu la t ion in sec t ion Σ 4 ( c los ing segment be tween P1 and P2)

Value o f long i tud ina l moments

Moment MG1 (state after construction, see Figures Al.17 and A1.18) MG1 = - 4.35 MN.m

Fittings MG fittings = 12.97 MN.m

Creep Mcreep = 6.42 MN.m

Overload A(1) MA(1) min = -6.36 MN.m and M MA(1) max = 21.62 MN.m

Thermal gradient MΔt = 12.65 MN.m

Calcu la t ion o f M Q

MQ =1.2 MA(1) + 0.5 MΔt or MQ = MΔt with the values above gives:

MQ min = -7.63 MN.m MQ max = 32.27 MN.m

Calcu la t ion o f Mmin and Mmax

M min = MG min + MQ min = (MG1 + MG equip) + MQ min

= -4.35 + 12.97 – 7.63 = 0.99 MN.m

M max = MG max + MQ max = (MG1 + MG equip + MG creep) + MQ max

= -4.35 + 12.97 + 6.42 + 32.27 = 47.31 MN.m



Calcu la t ion o f i sos ta t i c and hypers ta t i c moments o f con t inu i t y t endons

fu = 1.95 MN effective force for one 12T15S tendon

e0 =-1.318 m for the continuity tendons

n = 2 number of 12T15S continuity tendons

Miso = N . e0 = fu . n . e0 = 1.95 x 2 x -1.318 = - 5.14 MN.m

Mhyper ( )[ ]

75.9700.2375.3614.5 +

=xx

= 1.17 MN.m

Mpeci =Miso +Mhyper =-5.14 + 1.17 =-3.97 MN.m

Calcu la t ion o f i sos ta t i c and hypers ta t i c moments o f ex te rna l t endons

Fig. A1.34 – Longitudinal geometry of external tendons in the central span

e01 = - (1.440 – 0.24 – 0.10 - (0.10 / 2)) = -1.05 m

e02 = 2.420-0.25 = 2.17 m

fu = 3.1 MN effective force for a 19T15S tendon

n = number of 19T15S external tendons

Me1 = n . fu . el = n . 3.1 . (-1.05) = -3.26.n MN.m

Me2 = n . fu . e2 = n . 3.1 . (+2.17) = 6.73.n MN.m



Fig. A1.35 – Diagram of isostatic moment of external tendons in central span

m958.21583.32x26.373.6

73.6=

+=x

2 x S1 = 6.73 . n . 21.958 = 147.712 . n Hyperstatic moment

2 x S2 = 3.26 . n . 10.625 = - 34.584 . n

S3 = 3.26 . n . 32.584 = - 106.061 . n

7.067.n n.072.075.97

n.067.7Mhyper −=−=

MPext = Miso + Mhyper = - 3.26 . n – 0.07 = -3.33 . n

Calculation of stress:

( )I

vMMI

vMB

PPIvM

BN extecl PPextecl

i'.'.'. max +

−−+

=−=σ

( ) ( ) ( )[ ]620.4

44.1xn.33.317.114.5620.4

44.1x31.470965.6

n.1.395.1x2 −++−−−

+=iσ σi = (1.546 .n) – 12.87

for n = 6 MPai 0.2MPa60.3 b −=−<−= σσ for n = 8

MPaMPa bi 0.250.0 −=−>−= σσ We will therefore opt for 4 pairs of 19T15S tendons.

A1.5 .2 .2 – Calcu la t ion in the Σ1 sec t ion ( c los ing segment between CO and P1)


Moment MG1 (state after construction - see figures A 1.17,18) MG1 = 0.58 MN.m

Fittings MGfittings = 1.94 MN.m

Creep Mcreep = 6.42 x 5.50 / 53.375 = 0.66 MN.m



Overload A(1) MA(1) min = -4.75 MN.m et M MA(1) max = 8.39 MN.m



MQ =1.2 MA(1) + 0.5 MΔt or MQ = MΔt, which gives the following with the values above:

MQ max = 10.70 MN.m and MQ min = -5.70 MN.m


M min = MG min + MQ min = (MG1+ MGfittings) + MQ min

= 0.58 + 1.94 – 5.70 =-3.18 MN.m

M max = MG max + MQ max = (MG1+ MGfittings + Mcreep) + MQ max

= 0.58 + 1.94+0.66 + 10.70 = 13.88 MN.m



e0 =-1.318 m for the continuity tendons


Miso = N . e0 = fu . n . e0 = 1.95 x 2 x -1.318 = - 5.14 MN.m

Mhyper = 0 for the end span tendons

Mhyper mMN.06.0375.5350.5576.0

375.5350.517.1 =−= for the continuity and exterior tendons of the span

P1-P2

Mpeci = Miso +Mhyper =-5.14 + 0.06 MN.m =-5.08 MN.m




Fig. A1.36 – Longitudinal geometry of external tendons in span CO-P1

e1 = - (1.440 – 0.24 – 0.10 - (0.10 / 2)) = -1.05 m

e2 = 2.420-0.25 = 2.17 m

fu = 3.1 MN effective force of one 19T15S tendon


Me1 = n .fu .e1 = n .3.1 .(-1.05) =-3.26.n MN.m

Me2 = n . fu . e2 = n . 3.1 . (+2.17) = 6.73.n MN.m

Fig. A1.37 – Isostatic moment diagram for external tendons in span C0-P1

m625.10583.32x73.626.3

26.3=

+=x

S1 = (6.73 .n. 21.958)/2 = 73.856 . n Hyperstatic moment on pier

S2 = (3.26.n .10.625)/2 = - 17.292 .n

S3 = (3.26. n .15.292) = - 49.755 . n n.081.0375.53

2.n.163.2Mhyper ==

S4 = (3.26 . n . 5.500) / 2 = - 8.951 .n



-2.163 .n

n.008.0375.53

.50.5081.0)( 1 =×

=ΣnM hyper

MPext = Miso + Mhyper = -3.255 . n + 0.008 . n = -3.25 . n

Calcu la t ion o f s t r e s s in Σ 1( )

IvMM

IvM

BPP

IvM

BN extecl PPextecl

i'.'.'. max +

−−+

=−=σ

( ) ( ) ( )[ ]620.4

44.1x.25.309.014.5620.4

44.1x88.130965.6

n.1.395.1x2 ni

−++−−−

+=σ

σi = (l.524.n)-5.26

for n = 2 σi =-2.20 MPa <-σt =-2.00 MPa

for n = 4 σi = 0.84 MPa >-σt =-2.00 MPa

We will therefore opt for two pairs of 19T15S tendons.

A1.5 .2 .3 – Ca lcu la t ion in sec t ion Σ 7 ( c los ing segment be tween P2 and C3)


Moment MG1 (state after construction - see Figures A1.17 and A1.18) MG1 = 1.11 MN.m

Fittings MGfittings = 6.37 MN.m

Creep Mcreep = 6.42 x 15.50 / 63.375 = 1.57 MN.m

Overload A(1) MA(1) min = -9.42 MN.m et M MA(1) max = 19.59 MN.m



MQ=1.2 MA(1) + 0.5 MΔt or MQ = MΔt which, using the values above, gives:

MQ max = 25.09 MN.m and MQ min =-11.30 MN.m


M min = MG min + MQ min = (MG1 + MGfittings) + MQ min

= 1.15 + 6.37 – 11.30 = -3.78 MN.m



M max = MG max + MQ max = (MG1 + MGfittings + Mcreep) + MQ max

= 1.15 + 6.37 + 1.57 + 25.09 = 34.18 MN.m



e0 = -1.318 m for the continuity tendons


Miso = N e0 = 1.95 x 4 x -1.318 = - 10.28 MN.m

Mhyper = 0 for the end span tendons

Mhyper MN.m145.0375.6350.15576.0

375.6350.1517.1 =−= for the continuity and exterior tendons of the span

P1-P2

Mpeci = Miso +Mhyper =-10.28 + 0.15 MN.m = -10.13 MN.m


Fig. A1.38 – Longitudinal geometry of external tendons in span P2-C3

e01 = - (1.440 – 0.24 – 0.10 - (0.10 / 2)) = -1.05 m

e02 = 2.420-0.25 = 2.17 m

fu = 3.1 MN effective force for a 19T15S tendon


Me1 = n . fu. e1 = n . 3.1 . (-1.05) = -3.26.n MN.m

Me2 = n . fu.e2 = n .3.1 . (+2.17) = 6.73.n MN.m



Fig. A1.39 – Isostatic moment diagram of the external tendons in span P2-C3

m625.10583.32x73.626.3

26.3=

+=x

S1 = (6.73 .n. 21.958) / 2 = 73.856 . n Hyperstatic moment on support:

S2 = (3.26.n .10.625) / 2 = - 17.292 .n

S3 = (3.26. n .15.292) = - 49.755 . n n.581.0375.63

2 .n .417.18Mhyper ==

S4 = (3.26 . n . 15.500) / 2 = - 25.226 . n

-18.417 . n

n.142.0375.63

.50.15.581.0)( 7 ==ΣnM hyper

MPext = Miso + Mhyper = - 3.26 . n + 0.142 . n = - 3.113 . n

Calcu la t ion o f s t r e s s ( )

IvMM

IvM

BPP

IvM

BN extecl PPextecl

i'.'.'. max +

−−+

=−=σ

( ) ( ) ( )[ ]620.4

44.1x.113.328.10620.4

44.1x18.340965.6

.1.395.1x4 nni

−+−−−

+=σ

σi = (l.480.n)-8.404

for n = 4 σi =-2.49 MPa <-σt = -2.00 MPa

for n = 6 σi = 0.47 MPa >-σt = -2.00 MPa

We shall thus opt for two pairs of 19T15S tendons.



A2 Monographs of cast-in-situ bridges



NAME OF STRUCTURE

Situation, Contractors, Construction

dates

REF. SCHEMATIC LONGITUDINAL SECTION

Beaumont sur Oise bridge Contractor: Dragages et Travaux Publics Feb. 1986 - Dec. 1987

A1

Revue Travaux Oct. 1988

The piers are supported by six Ø1.40 m piles anchored in the limestone bedrock. The right bank abutment is built directly on the ground. Due to the presence of a thick layer of peat, the left bank abutment is built on four Ø 1.10 m diameter piles.

Poncin viaduct (A40) Consortium: - DTP (Dragages et Travaux Publics) - CITRA May 1984 - Sept. 1986

A2

Revue Travaux Oct. 1988 Revue Générale des Routes et des Aérodromes Oct. 1989 June 1986

The supports are all built on the bedrock, either directly on superficial footings (CO, PI, P3, P4, P5, C6 - 13m x l4m x 3 m), or on deep foundations: P2: 12.5m diameter box girder built from diaphragm wall elements. P3 : Four 5 m x 3 m H-shaped rectangular foundation piles

Champ du Comte viaduct (RN 90) Consortium: - SOGEA

Revue Travaux Apr. 1989 Revue Générale des Routes et des Aérodromes Feb. 1990

- GTM-BTP Dec. 1986 - Jan. 1989

A3

Champ du Comte viaduct (1,040 m) Supports and foundations: double portal frame configuration “Puits marocains” (deep pile foundation shafts) 4 to 5.60 m in diameter and 6.00 to 22.00 m in depth

The “Les outils" Collection – Sétra page 265 septembre 2007


CROSS-SECTIONS OF BRIDGE DECK CONSTRUCTION METHOD and

weight of segments

HEIGHTS OF BRIDGE DECK Slenderness

ratios

QUANTITIES OF MATERIALS

USED

COMMENTS

- Thickness of webs in central span: 0.36 m – Thickness of webs in end span: 0.36 m on the first 3 segments then 0.50 m, 0.70 m and finally 1.00 m before reaching the solid section. Solid rectangular section inside the counterweighted abutment

Cast-in-situ segments. Length of standard segments 3.53 m: End spans built on falsework

- On support: h = 6.60 m s (slenderness) = 1/18 - At the crown: h = 3.00 m s = 1/40

For the bridge deck: - Surface area of bridge deck :1,950 m² - Concrete: 1,793 m3 including 585 m3 of lightweight concrete - Non-prestressed reinforcement bars: 225,860 kg (126 kg/m3) - Prestressing bars: 72,650 kg (41 kg/m3) (37 kg/m2) - Mean thickness of bridge deck: 0.92 m over entire structure, 0.77 m in the central span.

- Bridge deck prestressing: half using 9T15 tendons and 12T15 internal tendons & the other half using replaceable 19T15 tendons –End span fixed to a weighted abutment acting as a counterweight with a solid 9.00m long rectangular section at the end.

ON SUPPORTS P1 and P2 CONSTANT DEPTH AT PI-P2 CROWN Thickness of webs near P3, P4 and P5: 1.20 – 1.10 – 0.90 m respectively

Cast-in-situ segments of variable depth. Length of standard segments: 3.30 m (weight: 120 to 220 tonnes) Incremental launching of end sections (constant depth)

- On support PI or P2: h = 10.00 m s= 1/15.5 - At crown of main span: h = 4.00 m s = 1/39

For the bridge deck: - Formwork: 27,850m² - Concrete: 11,270m3 - Non-prestressed reinforcement bars: 1,266,900 kg (112 kg/ m3) - Longitudinal prestress bars: 516,400 kg (45.8 kg/ m3) - Transverse prestress bars: 77,450 kg

Internal prestressing: - cantilever: 2 x 27 19T15 tendons - continuity: 2x7 12T15 tendons –External prestressing: 2 x 10 19T15 tendons

Viaduct with 2 separate bridge decks

Cross-section of 1 box girder

Cast-in-situ segments On support: h = 5.80 m s = 1/17 At crown of main span: h = 2.90 m s = 1/34.5

Main quantities: - B30 concrete: 8,500 m3

- B45 concrete: 17,000 m3

- Non-prestressed reinforcement bars: 3,800,000 kg - Longitudinal prestress bars: 850,000 kg

Internal prestressing: -cantilever tendons: 2 x 13 12T15 2 x 1 19T15 tendons - continuity tendons: 2 x 5 12T15 External prestress tendons: 2 x 3 19T15 2 x 1 12T15 tendons



NAME OF STRUCTURE


dates


Nantua viaduct (A40) Consortium: -GTM - Campenon Bernard June 1983 - Nov. 1986

A4

Revue Travaux Jan. 1986 Revue Générale des Routes et des Aérodromes Oct. 1989 June 1986

The variabile quality of the terrain required a wide range of foundations: P7 and P9: Four Ø2.20 m “puits marocains” (deep pile foundation shafts) P8: one Ø 6 m deep pile foundation shaft PI, P2 and P3: Ø 10 m diaphragm walls P4, P5 et P6: superficial footings of approx. 10 m x 10 m x 2.5 m

Lalleyriat viaduct (A40)

A5

Revue Générale des Routes et des Aérodromes Nov. 198

The structure consists of two bridge decks of different lengths with a height difference of 5 to 7 m,: * North deck: 130 m, 3 spans * South deck: 194 m, 4 spans and different widths: * North deck: 8.75 m * South deck: 11.75 m Length of central span for both decks: 58 m The majority of the foundations consist of footings built on sound bedrock.

Tacon viaduct Contractor: CITRA France A6

Revue Générale des Routes et des Aérodromes Nov. 1989 Revue Travaux Jan. 1986

The structure consists of two independent bridge decks with a height difference of approximately 6 m. Deep pile foundation shafts (P5: four Ø 2.40 m shafts) or cast-in-situ piles (P2, P3, P4 & P6: four piles of Ø 1.20 m to Ø 1.50 m)




weight of segments


ratios

QUANTITIES OF

MATERIALS USED

COMMENTS

Cast-in-situ segments. Length of segments: 2.50 to 3.50 m (60 to 85 t).

- On support: h = 6.65 m s = 1/17 - Fixed support of ½ cantilever: h = 8.44 m - At the crown h = 3m s = 1/38

For the bridge deck: - Concrete: 9,800m3

- Non-prestressed reinforcement bars: 1,250,000 kg (126kg/m3)

Internal prestressing using 12T15 tendons

- Prestress bars: 430 000 kg (44 kg/m3)

The viaduct ends in a 124 m span supported in the tunnel. To build & balance this span, a counterweighted span of approx. 3,000 t was built on centuring. This consists of two mobile sliding counterweights, each with a capacity of 1,500 t.

Cast-in-situ segments (method dictated by site access problems). Internal prestressing with possibility of adding extra external prestressing.

Constant depth of 2.,80 m s = 1/21

At the crown

On support (for the spans of variable depth): - height of bridge deck = 6 m - Thickness of bridge deck = 0.55 m

Cast-in-situ segments. Each segment measures 3.50 m long. Internal prestressing (12T15 tendons) with possibility of adding extra external and internal prestressing.

- On support: h = 6 m s = 1/15 - At the crown and for segments of constant depth: h = 3m s = 1/30

For the bridge deck: - Concrete: 4,820 m3 - Non-prestressed reinforcement bars: 554,000 kg (115 kg/m3) - Prestress bars: 185,000 kg (38 kg/m3)



NAME OF STRUCTURE


dates


Cheviré bridge over the River Loire Consortium: Concrete package: Quillery et Vezin Metal package: Baudin - Châteauneuf et ACP Dec. 1987 – Oct. 1990

A7

Revue Travaux Apr. 1989

Presence of joints between N5 and N6 & between S5 and S6

Pont à Mousson viaduct over the Moselle Consortium: Pertuy-Bouygues 1982

A8

Revue Travaux Jan. 1985

The viaduct consists of two independent structures: - The main crossing of the River Moselle and its lateral canal; - The SNCF (French state rail network) railroad crossing. Cast-in-situ pile foundations: P2, P3, P7 : Four Ø 1.30 m piles P4, P5, P6: Six Ø 1.30 m piles P1 : Six Ø 0.80 m piles

Chinon bridge in Indre-et-Loire

Entreprise: GTM

Sept. 1984 A9

AFPC (French Construction Association) Study Day, 12 June 1986 Revue Travaux Jan. 1986

The piers are built on footings within a cofferdam. The abutments are built on four Ø 0.80 m piles.




weight of segments


ratios


USED

COMMENTS

Cast-in-situ segments. Length of standard segments: 2.70 m (111 t) Length of segments on piers: 8.70 m. Segments on piers are cast horizontally then tilted to the required angle before the construction of the cantilever begins.

- On support: h = 9.00 m at level of NI and SI - Standard spans (constant depth): h = 4.55 m s = 1/14 - At end of cantilever above the River Loire: H = 5.20m

For the concrete bridge deck: - B35 concrete: 27,500 m3

-Non-prestressed reinforcement bars: 3,850,000 kg (140 kg/ m3) -Prestress reinforcements (longitudinal and transverse): 1,216,000 kg (44 kg/ m3)

- The first 6 meters of the end spans were cast on falsework. The central metal span was hoisted onto its permanent bearings in one operation. - Prestressing: int: (cantilever & continuity) 19T15 ext.: 27T15 ½ section on span

The initial pre-design did not feature any external prestressing. A summary analysis of mixed cabling was included but the dimensions of the structure were not modified due to a lack of time

Segments of the 3 large cantilevers are cast in-situ. The rest of the structure is cast on falsework.

- On supports 4, 5 & 6: h = 4.50 m s = 1/17 - Beyond the length of the parabolically variable section (18 m) either side of these supports: h = 2.75 m s = 1/27.5

For the entire bridge deck (including the cast-on-falsework sections): - B35 concrete: 3,437 m3

- Non-prestressed reinforcement bars: 466,000 kg (136 kg/m3) - Prestress reinforcements: int.: 71,600 kg ext.: 63,000 kg (in total: 39 kg/m3) Comment: The structure supports oversize Class E loads.

Large spans: cantilever: 24 x 12T15 continuity: 6 x 12T15 external: 8 x 19T15 Given the complex 2-dimensional alignment of the tendons and the thinness of the deviators, strong radial tendon forces of the deviators close to piers have resulted in the latter being reinforced.

½ -section at crown ½- section on pier

With its oversized dimensions, this bridge was designed to support thirty-meter long EDF (Electricité de France –French electricity supply utility) convoys weighing 650 tonnes

Cast-in-situ segments. The end of the end spans is cast on falsework.

- On support: h = 4.50 m s= 1/15.5

For the bridge deck: - B35 concrete: 1,385 m3

- Non-prestressed reinforcements: 205,000 kg (150 kg/m3)

- At the crown: h = 2.80 m s = 1/25

- Prestress reinforcements: internal: 28,500 kg external: 21,500 kg (in total: 50 t or 36 kg/m3) Equivalent thickness: 75 cm

Mixed prestressing: - int. tendons: cantilever: 2 x 9 12T15 continuity: 2 x 4 12T15 - ext. tendons: 2 x7 12T15 Comment: external tendons are somewhat limited in power



NAME OF STRUCTURE


dates


Bridge over the Loch d’Auray Consortium: - Campenon Bernard - E.T.P.O. Nov. 1986 – Mar. 1989

Al0

La Technique Française du Béton Précontraint, 11th FIP (International Prestressing Federation) Congress, Hamburg 1990 Revue Travaux June 1991

Bourran viaduct at Rodez Contractor: DODIN Sud Aug. 1989 - June 1991

A11

La Technique Française du Béton Précontraint, 12th FIP (International Prestressing Federation) Congress, Washington 1994 Revue Travaux Oct. 1991 July 1992

Engineering geology: risk of landslides Deep pile foundation shafts: one Ø3 m or Ø4 m shaft for each pier sunk to depths of 11 to 15 m.

Bridge over the Saint-Denis river on Reunion Island Contractor: SBTPC Aug.1989 - Aug. 1991

A12

La Technique Française du Béton Précontraint, 12th FIP (International Prestressing Federation) Congress, Washington 1994 Revue Travaux July 1992

Abutment C0, situated directly above a rocky spur embedded in the sand, is supported by two Ø2 m deep pile foundation shafts, one of which is extended by micropiles. The three piers are built on superficial footings. The ground had to be injected under P1.




weight of segments


ratios


USED

COMMENTS

Directly above portal legs

The large span has 2 cantilevers (3 m segments) built using form travelers. Two temporary pilings supported the portal legs before placement of the final segment. The rest of the structure was built on falsework.

- On support: h = 5.20 m s = 1/16 - At the crown: h = 2.50 m s = 1/33.5

For the cantilever sections: Mixed prestressing: - Internal tendons Cantilever: 12T15 Continuity: 2 x 6 12T15 - External tendons (from portal leg to portal leg) 2 x 2 12T15 The ribs are transversally prestressed.

In addition to the usual tendons In the end spans, rectilinear external prestressing, extending from the abutment to portal leg, has been added in order to restore a normal force virtually equal to that created by the thrust of the portal legs in the large span.

Thickness of webs in segments on P1 and P4: 60 cm. Slightly asymmetrical box girder: the transverse slopes begin at the centerline of the pavement which is not aligned with the centerline of the box girder. To avoid any difference in the height of the webs, the entire box girder has been tilted transversally (gradient of 0.69 %).

Construction using “from below” type of form travelers. Length of standard segments: 3.70 m, segments on piers: 9 m. Both ends of the bridge deck were built on falsework (17.70m in span S1 and 6.00 m in span T5).

- On support: h = 6.00 m s= 1/16.5 - At the crown: h = 3.00 m s = 1/33

For the bridge deck: - Concrete: 3,000 m² - Non-prestressed reinforcement bars: 365,000 kg (122 kg/m3) - Longitudinal prestress bars: 119,190 kg (40 kg/m³) Large cantilevers: - Cantilever 2 X 16 12T15 - Continuity 2x3 12T15 - External tendons 2x4 19T15 - Mean thickness of concrete: 0.71 m

- Possibility of adding extra tendons. - Vertical prestressing of segment on P1 - Given the flexibility of the piers in rotation (2 bent pier shafts for P2 & P3), the winds effects were calculated very accurately, but in the end, no bracing was provided.

Construction using “from below” type of form travelers. Length of standard segments: 3.45 m (max. weight: 120 t), segments on piers: 7.80 m. Both ends of the bridge deck were built on falsework.

- On support: h = 4.50 m s = 1/17 - At the crown: h = 2.50 m s = 1/31

For the bridge deck: - Concrete: 3,100 m3 - Non-prestressed reinforcement bars: 437,100 kg (141 kg/m3) - Longitudinal prestress bars: 59 t 12T15 62 t 19T15 (in total 39 kg/m3) Prestressing of upper slab via sheathed & greased single strands: 20,000 kg (6.5 kg/m3)

- Prestressing: cantilever : 2 x 14 12T15 continuity : 2 x 2 12T15 external tendons : 2 x 6 19T15 - provisional bracing of curved pier shells to take up forces due to cyclonic winds - Highly problematical construction of foundations.



NAME OF STRUCTURE


dates


Piou and Rioulong viaducts Consortium: - Quillery - Chantiers Modernes - Borie SAE

A13

La Technique Française du Béton Précontraint, 12th FIP (International Prestressing Federation) Congress, Washington 1994 Foundations: via footings for PI, P2 and P5 (with stitched reinforcement of the footings of the very

tall pier P2), via 7 m shafts for P3 and P4 Rioulong viaduct: 5 spans (45, 72, 81,81, 63 m), 6 % slope

Limay viaduct in Yvelines Consortium: - Nord France TP - Holzmann 1992

A14

Revue Travaux Apr. 1993

Foundations via cast-in-situ piles: - Six Ø 1.40 m piles for P2, P3, P6, P7 - Four Ø 1.40 m piles for P4 and P5 - Four Ø 1.20 m piles for C8 - Eight Ø 0,80 m piles for C1

Viaur valley viaduct (RN 88) Consortium: - SPIE T.R - DODIN Sud - SOGEA Feb. 1995 - Dec. 1997

A15

La Technique Française du Béton Précontraint, 13th FIP (International Prestressing Federation) Congress, Amsterdam 1998

- P1 and P2 are erected on superficial foundations. Their footings were temporarily anchored to the rock via 10 stressed 12T15 ties designed to take up the wind effects during construction. - P3 and P4 are supported on footings anchored to the rock by four 3 m shafts excavated using explosives - The bridge deck is embedded on P3 and P4.




weight of segments


ratios


USED

COMMENTS

Half-section of a standard section Half-section of sections close to piers

Construction using “from below” type of form travelers. Length of segments: 3 m (6.8 m on pier), with a stagger in the construction of the cantilevers to allow the incorporation of metal struts.

Constant depth h = 5 m s = 1/18

Piou viaduct: - Concrete: 6,500 m3 -Non-prestressed reinforcement bars: 819,000 kg (126kg/m3) - Longitudinal prestress bars 228,000 kg (35 kg/m3) int. (cantilevers and crowns) super 19K15 ext.: 27K15 super transversal: 92,000 kg (14 kg/m3) 3C15 - equivalent thickness: 0.73 m

Incoprporation of bracing: - When casting segment n, 4 fixing sockets were sealed in the bottom flange of the web, using a false strut to give the required accuracy. - The real strut was attached to segment n + 1 by bolting on the lower part and casting on the upper part.

Construction using form travelers. Length of segments on piers: 9.60 m Length of standard segments: 3.90 m.

- On support: h = 5.30 m s = 1/17 - At the crown and in spans of constant depth: h = 2.70 m s = 1/33

For the bridge deck: - Concrete: 4,680 m² - Non-prestressed reinforcement bars: 769,000 kg (164 kg/m3) -Internal longitudinal prestress bars: 119,000 kg External: 103,000 kg (in total: 47 kg/m3)

Mixed prestressing: - Cantilever tendons: 20 (piers on the island) to 30 (piers in the river) 12T15S. Continuity: 14 (in the 90 m spans) to 2 (for spans on the island) 12T15S. - Ext. tendons: 12 (at mid-span) to 8 (on pier) 19T15S

Construction using form travelers. Length of standard segments: 2.76 m. The extremities of the end spans are built on falsework.

- On support: h= 12m s = 1/16 - At the crown and in the spans of constant depth. h = 4.50 m s = 1/42

Main quantities: - Concrete: 21,000 m3

- Non-prestressed reinforcement bars: 3,900 t - Prestressing: 650 t

- Mixed prestressing: Int.tendons 19T15 Ext. tendons 27T15 - Transverse prestressing via single strands - Movements of major spans due to wind effects during construction limited by the use of vertical prestress tendons.



NAME OF STRUCTURE


dates


Doubling of the Général Audibert bridge over the Loire, in Nantes Contractor: ETPO Jan. 1987 - Mar. 1989

A16

Revue Travaux April 1989

Two independent but connected bridge decks, made from prestressed concrete box girders of variable depth. Length: 163 m (3 spans: 51 m + 67 m + 45 m). Width: 17.40 m.

Bridge over the Truyère at Garabit Consortium: - GTM-BTP - Dumez July 1990 - Feb. 1993

A17

Revue Ouvrages d’art n° 16 Nov 1993

Portal bridge with a prestressed concrete box girder. Bridge deck embedded on the portal legs and on simple supports on the abutments. Length: 308 m (3 spans: 82 m + 144 m + 82 m). Width:21 m.

Auxonne and Maillys viaducts in the Côte d’Or Consortium of contractors: - Dodin Sud : - SOGEA : - Dodin Ouest Sept. 1991 – Nov. 1993

A18

Revue Travaux Jul./Aug.1994

Structure with two separate bridge decks. Usable width of each of the two decks: 11m. 8 spans: 52 m + 77 m + 136 m + 77 m + 3 x 55 m + 45 m.




weight of segments


ratios


USED

COMMENTS

SEGMENTS ON PIERS SEGMENTS AT CROWN UPSTREAM DOWNSTREAM

Cast-in-situ segments. Length of segments on piers: 9 m. Length of standard segments: 3.50 m. Closing segments: 2m. Weight of standard segments: 45 tonnes.

- On support: h = 3.80 m s = 1/18 - At the crown: h = 1.80 m s = 1/37

For the bridge deck: - Concrete: 2,150 m3

- Prestressing: 85,190 Kg - Non-prestressed reinforcement bars: 338,000 Kg Usable area of the structure: 2,840 m3

Prestress tendons inside concrete: 12T 13 20.50

The box girder features: - a 20.50 m upper slab which is transversally prestressed by 4T15 tendons at intervals of 0.60 m; - two webs angled at 30%, with vertical thickness of 0.60 m (1.20 m towards the portal legs); - a lower slab whose thickness varies between 1.20 m directly above the portal legs to 0.25 m at the crown.

Cast-in-situ segments.

- On the abutment supports: 10 m. - At the crown: 3 m. -At the level of the portal legs: 8 m.

- Concrete: 16,000 m3 - Non-prestressed reinforcement bars: 13,700 m3 - Prestressing: 362 t.

- Int. prestress tendons: cantilever (2 X 35 per cantilever) and continuity (2 X 7 on end span and 2 X 2 on central span): FUC 19-620 - Ext. prestress tendons: FUC 19-620, remobvable on end spans - Transverse prestressing of upper slab: FUC 4-620

Large span and 2 adjacent ½ spans: successive cast-in-situ cantilever segments built using 2 x 2 form travelers. Cast-on-falsework end spans

SECTION THROUGH P3-P4 CANTILEVER On support In span

For the segments built by the cantilever method - On support: h = 6.50 m s = 1/21 - At the crown: h = 3.20 m s = 1/42 For the sections built on falsework: h = constant = 3.20 ms= 1/17

For the bridge deck: - B40 concrete: 10,300 m³ - Int. prestressing: 260 tonnes. - Ext. prestressing: 325 tonnes. - Non-prestressed reinforcement bars: 1,520 tonnes.

- Cantilever tendons: 12 T 15.- Continuity tendons: 12T15. - Continuity tendons outside concrete: 19T 15.



NAME OF STRUCTURE


dates


Corniche bridge in Dole Consortium: - Campenon Bernard Régions - Roux SA Feb. 1993 - Apr. 1995

A19

Revue Ouvrages d’art Nov. 1994 Revue Générale des Routes et des Aérodromes Nov. 1995

Length: 496 m (48 m + 5 x 80 m + 48 m). Width: 14.50 m.

Rivoire viaduct in Isère Consortium: - Razel - Fougerolle-Ballot - Royans Travaux July 1995 - Nov. 1996

A20

Revue Travaux Jul./Aug.1997

Two independent structures. Two concentric bridge decks with radii at the left edge of 984.50 m and 1001.15 m: center distance of 24.10 m. Length: 247 m ( 64 m + 113 m + 70 m).

Revue Ouvrages d’art Dec. 1998

Vecchio bridge in Corsica Contractor: Razel

A21

VIVARIO VENACO

3-span prestressed concrete structure (42.25 m + 137.50 m + 42.25 m), 10 m wide.




weight of segments


ratios


USED

COMMENTS

Cast-in-situ segments. Length of standard segments: 3.20m. Length of segments on piers: 6.40 m.

- On support: h =5.50 m e = 1/14 - At the crown: h = 2.50 m s = 1/32

For the bridge deck: - B35 concrete: 4,100 m3 - Prestressing: 190 tonnes.

First bridge with corrugated webs to be built by the cantilever method in France.

Length of segments on piers: 8.50 m. Length of standard segments: 16 x 3.20 m on central span and 17 x 3.20 m on end span. Standard segments built using “from below” type of form travelers.

For the bridge deck: - B35 concrete: 4,000 m² - Formwork: 15,200m² -Reinforcements: 690t - Prestressing: 174 t

Construction of central span in half- cantilevers using successive 3.60 m long cantilever segments using form travelers into which the prefabricated webs were placed. These are of variable depth and angle, due to the variation in width of the lower slab.

- On support: h= 11 m s= 1/12 - At the crown: h = 3.50 m s = 1/39

Prestressing: - cantilever tendons in the upper slab; - continuity tendons outside the concrete stretching from abutment to abutment; - internal continuity tendons in central span; - prestressing bar in web panels.



NAME OF

STRUCTURE Situation,

Contractors, Construction

dates


Bridge over the Rhine in Strasbourg Consortium: - Bilfinger - Berger and Max Früh 2001 - 2002

A22

Revue Travaux n° 783 FebThe piers. 2002

Length: 457 m (121 m + 205 m + 131 m). Width: 14.75 m.

Bridge over the Seine at Gennevilliers Consortium: - SPIE Batignolles - GTM - Fougerolles 1990 - 1992

A23

Length: 568 m (110 m + 169 m + 96 m + 169 m + 114 m). Width: 18.06 m.




weight of segments


ratios


USED

COMMENTS

Cast-in-situ segments.

Standard segments vary in length from 3.50 to 5.00 m. Length of segments on piers: 9.50 m.

- On pier: h = 9.00 m s = 1/23 - At the crown: h = 4.50 m s = 1/45 - On abutment: h = 3.20 m Variation according to a parabolic curve for the central span and a cubic curve for the end spans.

For the bridge deck: - B65 concrete: 7,750 m3

- Non-stressed reinforcement bars: 913,000 kg (118 kg/m3) - Prestressing: 598,000 kg (77 kg/m3)

SECTION ON PIER PILE SECTION AT CROWN Cast-in-situ segments.

- On pier: h = 9.00 m

For the bridge deck: - Concrete: 13,900 m3 - Non-stressed reinforcement bars: 1,711,000 kg (124 kg/m3)

Length of standard segments: 3.30m for the 96 m span and 3.60 m for the other spans.

- At the crown: h = 3.50 m

- Prestressing: External 241 t Internal 728 t Temporary 22 t



A3 Bibliography This appendix firstly mentions all of the official french texts relating to the engineering and design of bridges built by the cantilever method. It then goes on to list a large number of documents and articles dedicated to this technique.

A3-1 – Official texts

French texts related to al l structures

- Fascicule 61 Titre II of the french CPC: "Programme de charges et épreuves des ponts-routes" (Loading and testing program for road bridges).

- Circular no. R/EG3 of July 20 1983 entitled "Transports exceptionnels, définition des convois types et règles pour la vérification des ouvrages d’art" (Oversize loads, definition of standard convoys and rules for the verification of civil engineering structures) published by the Direction des Routes (Highways Department), for structures supporting these types of vehicles

- Fascicule 6l Titre IV Section II of the french CCTG: "Actions de la neige sur les constructions" (Effects of snow on constructions) (DTU P 06-006 of September 1996)

- Fascicule 62 Titre I - Section I of the french CCTG: "Règles techniques de conception et de calcul des ouvrages et constructions en béton armé suivant la méthode des états limites" (Technical engineering and design rules for reinforced concrete structures and constructions according to the limit states method) [BAEL 91 revised in 1999)]

- Fascicule62 Titre I - Section II of the french CCTG: "Règles techniques de conception et de calcul des ouvrages et constructions en béton précontraint suivant la méthode des états limites" (Technical engineering and design rules for prestressed concrete structures and constructions according to the limit states method) (BPEL 91 revised in 1999)

- Fascicule 65-A of the french CCTG and its supplement: "Exécution des ouvrages de génie civil en béton armé ou précontraint" (Construction of reinforced or prestressed concrete civil engineering structures)

- Fascicule62 Titre V of the french CCTG: "Règles techniques de conception et de calcul des fondations des ouvrages de génie civil" (Technical engineering and design rules for the foundations of civil engineering structures)

- Fascicule 68 of the french CCTG: "Exécution des travaux de fondation des ouvrages de génie civil" (Construction of the foundations for civil engineering structures)

- Standard NFP 95-104: "Réparation et renforcement des ouvrages en béton et en maçonnerie; spécifications relatives à la technique de précontrainte additionnelle" (Repair and reinforcement of concrete and masonry structures; specifications relating to the additional prestressing technique)



Texts exc lus ive ly re la ted to s t ruc tures s i tuated in ear thquake zones

- Decree no. 91-461 of May 14 1991 relating to the prevention of earthquake risks and the Order of September 15 1995 relating to the classification and rules for antiseismic constructions applicable to bridges in the “normal risk” category

- Guide AFPS 92 for the seismic protection of bridges, edited by the Association Française du Génie Parasismique (French Seismic Engineering Association), published on the presses of the École Nationale des Ponts et Chaussées (National School of Civil Engineering)

- The french standard NE P 06-013, more commonly called the "Règles de construction parasismique – règles applicables aux bâtiments - PS92" (Seismic Construction Rules – Rules Applicable to Buildings – PS92), with regard to foundations.

A3-2 – Sétra, Sétra-LCPC, Sétra-SNCF Guides - Sétra Technical Bulletin no.7 "Ponts construits par encorbellements successifs"

- This Design Guide

- Sétra Technical Guide "Précontrainte Extérieure" (External Prestressing)

- Sétra Technical Guide "Appareils d’appui en caoutchouc fretté" (Laminated rubber pot bearings)

- Sétra Technical Guide "Appareils d’appui à pot de caoutchouc" (Rubber pot bearings)

- The guide to the ordering and management of studies for civil engineering bridges

- Fascicule 32.2 of the technical instruction for the monitoring and maintenance of civil engineering structures, published in 1979 and modified in 1995

- The document entitled "l’Image de la Qualité des Ouvrages d’Art (Iqoa); catalogue des principaux défauts, aide à leur classification - ponts à poutre caisson en béton précontraint" (Image of the quality of civil engineering structures [IQOA]; catalog of the major defects and support for their classification – prestressed concrete box girder bridges) published by Sétra in 1997.

A3-3 – Other publications Presse de l ’Éco le Na t iona le des Pont s e t Chaussées

- La conception des ponts (Bridge design) [J.A. Calgaro and A. Bernard-Gely]

- Analyse structurale des tabliers de ponts (Structural analysis of bridge decks) [J.A. Calgaro and M.Virlogeux]

- Maintenance et réparation des ponts (Bridge maintenance and repair)

Thomas Te l ford , London

- Ponts en béton précontraint par post tension (Post-tensioned prestressed concrete bridges) HA - TRL - LCPC – Sétra



La co l l ec t ion de l ’ I rex

- Projet National Qualité (National Quality Project) - Opération du Plan Génie Civil (Operation of the Civil Engineering Plan) – Documentation booklet "Parements en béton" (Concrete facings)

Édi t ions Eyro l l e s

- Procédés généraux de construction (General construction process ) – Vol.1 (J. Mathivat and C. Boiteau)

A3-4 - Articles in miscellaneous publications There now follows a list of articles relating to construction using the cantilever method, published between 1990 and mid - 2002 in the main French civil engineering journals and in certain foreign publications. Each of these articles is followed by a code indicating the topic(s) covered. The following table shows the meanings of these codes:

Research, calculations

Design & construction of a bridge with cast-in-situ segments

Design and construction of a bridge with prefabricated segments

Design and execution of a repair or reinforcement project

Materials

AFPC/AFGC publications for FIB (Fédération de l’Industrie du Béton-Concrete Industry Federation) congresses - [VIR 90.1] M. Virlogeux: La résistance à l’effort tranchant des ouvrages constitués de voussoirs préfabriqués, La technique française du béton précontraint (The resistance to shear force of structures made from prefabricated segments, The French Prestressed Concrete Technique), Hamburg (1990)

- [MOS 90] J. Mossot: Le viaduc du Champs du Comte, La technique française du béton précontraint (The Champs du Comte viaduct, The French Prestressed Concrete Technique), Hamburg (1990)

- [BOU 90] J. Boudot: Le viaduc de Sylans et des Glacières - Les structures triangulées en béton précontraint, La technique française du béton précontraint (The Sylans et Glacières viaducts – Triangulated structures made from prestressed concrete, The French Prestressed Concrete Technique), Hamburg (1990)

- [SER 90] C. Servant, R Gallet, Ph. Lecroq, R Barras: Le viaduc de l’Arrêt-Darré, La technique française du béton précontraint (The Arrêt-Darré viaduct, The French Prestressed Concrete Technique), Hamburg (1990)

- [VIR 90.2] M. Virlogeux, G. Lacoste, M. Legall, RY. Bot, J-R Runigo, J. Combault, M. Duviard, G. Suinot and P. Fraleu: Le pont sur le Loch d Auray, La technique française du béton précontraint (The bridge over the Loch d’Auray, The French Prestressed Concrete Technique), Hamburg (1990)



- [VIR 94] M. Virlogeux, E. Bouchon, J.C. Martin, J. Lefevre, Y. Maury, T. Guyot, M. Pottier, A. Heusse, P. Fraleu, J. Ryckaert, J. Mathivat and B. Lenoir : Pont de Cheviré, La technique française du béton précontraint (The Cheviré bridge, The French Prestressing Concrete Technique), Washington (1994)

- [FUZ 94] J-R Fuzier, C. Adib: Poutres de lancement: le pont de Baldwin, La technique française du béton précontraint (Launch beams: the Baldwin bridge, The French Prestressed Concrete Technique), Washington (1994)

- [BOU 94.1] E. Bouchon, D. Lecointre, M. Virlogeux, R. Gachiteguy, G. Viossanges, R. Gai, M. Boy, P. Ballester, M. Roudanes, P. Fraleu : Le viaduc de Bourran à Rodez, La technique française du béton précontraint (The Bourran Viaduct in Rodez, The French Prestressed Concrete Technique), Washington (1994)

- [BOU 94.2] E. Bouchon, E. Conti, D. de Matteis, E Pero, M. Virlogeux, R. Damour, A. Abastado, E Edon, M. Tassone, A. Demozay, P. Jacques, F. Veyres, C. Lavigne: Le pont de la rivière Saint-Denis à la Réunion (Océan Indien), La technique française du béton précontraint (The bridge over the Saint-Denis river on Reunion Island [Indian Ocean], The French Prestressed Concrete Technique), Washington (1994)

- [CHA 94] P. Chassagnette, J.J. Lagane: Doublement du pont sur la Seine à Gennevilliers, La technique française du béton précontraint (Doubling the width of the bridge over the River Seine at Gennevilliers, The French Prestressed Concrete Technique), Washington (1994)

- [CRO 94] A. Crocherie, G. Gillet, B. Canitrot, F. Edon, P. Kirschner, B. Fournier, F. Renaud, T. Thibaux, P. Doguet : Les viaducs du Piou et du Rioulong, La technique française du béton précontraint (The Piou and Rioulong viaducts, The French Prestressed Concrete Technique), Washington (1994)

- [CAN 94] B. Canitrot, G. Gillet, B. Bouvy, A. Palacci, B. Raspaud: Le pont de l’autoroute A75 sur la Truyère à Garabit, La technique française du béton précontraint (The A75 highway bridge over the Truyère at Garabit, The French Prestressed Concrete Technique), Washington (1994)

- [LEB 94] J-D Lebon, A. Leveille: Le pont de la Corniche à Dôle, La technique française du béton précontraint (The Corniche bridge at Dôle, The French Prestressed Concrete Technique), Washington (1994)

- [COM 94] J. Combault, J.P Teyssandier, N.D. Haste, P Richard, M.S. Fletcher, Y. Maury, J. Mac Farlane: Le second pont sur la Severn, La technique française du béton précontraint (The second Severn Bridge, The French Prestressed Concrete Technique), Washington (1994)

- [MUL 94] J. Muller, G. Causse: Le pont à voussoirs préfabriqués de l’autoroute H3 à Hawaï, La technique française du béton précontraint (The H3 highway bridge made from prefabricated segments in Hawaï, The French Prestressed Concrete Technique), Washington (1994)

- [GAS 94] C. Gasaignes, J. Boudot, O. Martin: Ponts à voussoirs préfabriqués en Asie - L’exemple du projet du KwunTong By-Pass, La technique française du béton précontraint (Bridges built from prefabricated segments in Asia – The example of the KwunTong By-Pass project, The French Prestressed Concrete Technique, Washington (1994)

- [ABE 94] H. Abel, G. Causse, C. Outteryck, D. de Matteis, H. Capdessus, J. Bouillot, B. Grezes, G. Perez, J. Combault, A. Leveille,Y. Faup, F. Zirk: Le pont d’Arcins sur la Garonne à Bordeaux, La technique française du béton précontraint (The Arcins bridge over the Garonne in Bordeaux, The French Prestressed Concrete Technique), Washington (1994)



- [BAR 94] P. Barras, D. Poineau: Réparation du pont de Blagnac - Études, projet et suivi des travaux, La technique française du béton précontraint (Repair of the Blagnac bridge – Studies, design and monitoring of works, The French Prestressed Concrete Technique), Washington (1994)

- [VIR 96] M.Virlogeux, J.M. Lacombe, A. Le Bourdonnec: Practical design of cantilever tendons in bridges built by the balanced cantilever method, FIP Symposium, London (1996)

- [SER 98] C. Servant (Serf), E. Bouchon (Sétra), R. Gachiteguy (Aveyron DDE [Departmental Public Works Directorate]), J.J. Lagane, P. Chassagnette, V. Preyssas (Spie-BatignoUes TP): Record de portée dans la vallée du Viaur, La technique française du béton précontraint (Span length record in the Viaur valley, The French Prestressed Concrete Technique), Amsterdam (1998)

- [COM 98] J. Combault (Dumez-GTM): Le pont de la Confédération (Ile du prince Edouard - Canada), La technique française du béton précontraint (The Confederation Bridge [Prince Edward Island - Canada], The French Prestressed Concrete Technique, Amsterdam (1998) /

- [JAC 98] P Jacquet, M. Duviard: Le viaduc de Rogerville, La technique française du béton précontraint (The Rogerville viaduct, The French Prestressed Concrete Technique), Amsterdam (1998)

- [MEU 98] P. Meurisse, X. Pham, K. Gharbi, J.P. Viallon: Une nouvelle génération de ponts mixtes: les viaducs du Boulonnais, La technique française du béton précontraint (A new generation of composite bridges: viaducts in the Boulogne area, The French Prestressed Concrete Technique), Amsterdam (1998)

- [BOUS 98.1] C. Bousquet, J.M. Cussac, A. Fauvelle, B. Radiguet : TGV Méditerranée - Lot 2H -Viaducs sur le Rhône, La technique française du béton précontraint (The TGV Méditerranée high-speed rail line – Package 2H – Viaducts over the Rhône, The French prestressed Concrete Technique), Amsterdam (1998)

- [BOUS 98.2] C. Bousquet, J.P. Jung, F. Valotaire: Le viaduc TGV de Vernegues, La technique française du béton précontraint (The Vernegues TGV high-speed rail line viaduct, The French Prestressed Concrete Technique), Amsterdam (1998)

- [DEWI 98] M. De Wissocq, L. Paulik, M. Placidi, J. Vassord: Pont du Vecchio, La technique française du béton précontraint (The Vecchio bridge, The French Prestressed Concrete Technique), Amsterdam (1998)

Revue travaux - [VIR 91.2] M. Virlogeux, G. Lacoste, P Fraleu, M. Legall, P.Y. Bot , J.P Runigo, J. Combault, M. Duviard, G. Suinot, M. Le Corre: Le pont sur le Loch d’Auray (The bridge over the Loch d’Auray) (June 1991)

- [JOU 91] A. Jouanno, G. Gillet, B. Bouvy, J.C. Foucriat, J. Goyet: Autoroute A75 dans le Cantal: Les études du pont sur la Truyère (Studies for the bridge over the Truyère) (October 1991)

- [BOU 91] E. Bouchon, D. Lecointre, M. Virlogeux, R. Gachiteguy, G. Viossanges, R. Gai, M. Boy, R Ballester, M. Roudanes, R Fraleu: Le viaduc de Bourran à Rodez (The Bourran viaduct at Rodez) (October 1991)

- [BOU 92] E. Bouchon, E. Conti, D. de Matteis, E Vacher, M. Virlogeux, R. Damour, A. Abastado, E. Edon, M.Tassone, M. Bustamante, A. Demozay, P.Jacques, E Veyres, C. Lavigne: Le pont de la rivière Saint-Denis à la Réunion (The bridge over the Saint-Denis river on Reunion Island) (July-August 1992)



- [RIC 93] C. Ricard, J.Jouves, B. Bouvy, Ph. Dhiver: Remise en état du pont de la RD220 sur le canal d’amenée de la chute de Bourg-lès-Valence (Renovation of the RD220 road bridge over the head race canal for the Bourg-lès-Valence waterfall) (November 1993)

- [HUM 93] E. Humbert, J. Hooghe, X. Durand, Y. Picard: Le viaduc de Limay, Yvelines (The Limay viaduct, Yvelines) (1993)

- [BER 95] A. Bernardo: Le pont du Rambler Channel à Hong Kong (The Rambler Channel bridge in Hong Kong) (April 1995)

- [CON 95] E. Conti, H. Oudin-Hograindleur: Passerelle tournée sur l’autoroute A4 à Noisy-le-Grand (Rotated footbridge on the A4 highway at Noisy-le-Grand) (April 1995)

- [RIC 96] D. Richard, G. Frantz, R Jacquet: Le viaduc de Rogerville (The Rogerville Viaduct) (April 1996)

- [COM 96] J. Combault, J. Hervet, V.Vesval: Le second franchissement de l’estuaire de la Severn (The second crossing of the Severn estuary) (April 1996)

- [BOI 96] A. Boisset, J. Combault, M. Lefebvre, D. Maire: Le pont de l’île du Prince-Edouard (The Prince Edward Island Bridge) (July and August 1996) /

- [MAG 97] H. Magnon-Pujo, B. Deberle: Le viaduc de la Rivoire (Isère). Une construction anticipée pour faciliter la circulation de chantier (The Rivoire viaduct [Isère] Anticipatory construction in order to facilitate the movement of site traffic). (July-August 1997)

- [DEL 98] G. Delfosse, P. Eaure, G. Perez: Confortement par précontrainte additionnelle du pont de la Seudre en Charente-Maritime (Reinforcement of the Seudre bridge in the Charente-Maritime by additional prestressing) (February 1998)

- [QUI 98] D. Quivy, Y. Deleporte, B.Vincent: A39 - Les viaducs sur le Doubs et la Loue (A39 Highway – viaducts over the Doubs and the Loue) (February 1998)

- [DOG 98] P. Doguet: Un grand ouvrage sur l’Agout - Le viaduc de Castres (A major structure over the Agout – the Castres viaduct) (February 1998)

- [MON 99] J.Y. Mondon: Le Hung Hom by-pass à Hong Kong (The Hung Hom by-pass in Hong Kong) (January 1999)

- [ROI 99] D. Poineau,J.M. Lacombe, G. Desgagne, C. Creppy, H. Marneffe, L. Duflot, R Ribolzi, B. Vandeputte, R. Zanker: La réparation du pont de Châlons-en-Champagne (The repair of the Châlons-en-Champagne bridge (April 1999)

- [PAU 00] L. Paulik: Le pont du Vecchio en Corse (The Vecchio Bridge in Corsica) (January 2000)

- [DIEU 00] R Dieuaide: Le viaduc de Digoin (The Digoin viaduct) (January 2000)

- [DEM 00] A. Demare, G.Tréffot: Le projet du second pont sur le Rhin au sud de Strasbourg (The design of the second bridge over the Rhine to the south of Strasbourg) (January 2000)



- [JAE 00] J.M. Jaeger, S. Nunez, JJ. Blanchi, D. Primault: A10 - Le viaduc de la Dordogne (A10 Highway – The Dordogne viaduct) (January 2000)

- [DEW 01] V. Dewilde, E. Dallot, E. Tavakoli, D. Guio, D. de Matteis: Passage à l’Euro(code) pour le second viaduc de Pont Salomon (Transition to the Eurocode for the second Pont Salomon viaduct) (January 2001)

- [DEM 01.1] A. Demare, G.Tréffot: Second pont sur le Rhin au sud de Strasbourg: Les travaux sont commencés (Second bridge over the Rhine to the south of Strasbourg: Work has begun) (May 2001)

- [GIA 01] D. Giacomelli, L. Marraci: Conception de la réhabilitation du pont de Saint-André-de-Cubzac (Design of the renovation of the Saint-André-de-Cubzac bridge) (November 2001)

- [POR 01] T. Portefaix, C. Roude, L. Rosset: Le viaduc sur la Medway (The Medway viaduct) (December 2001)

- [BOUT 01] L. Boutonnet: Kingston Bridge à Glasgow (The Kingston Bridge in Glasgow) (December 2001)

- [CAY 01] F. Cayron, P. Cote: Un nouveau viaduc ferroviaire dans les nouveaux territoires de Hong Kong (A new railroad viaduct in the New Territories of Hong Kong) (December 2001)

- [LAC 02] J.J. Lacaze, D. Giacomelli, M. Duviard, V. Vesval, P. Charlon, C. Sandre: A89 - Le viaduc du Pays de Tulle (A89 Highway – The Pays de Tulle viaduct) (January 2002)

- [CHU 02] J.R Chuniaud, T. Jamet, J.M.Tanis, F. Menuel, E. Barlet, R Chatelard, J.R Viailon: Le pont sur le Bras de la Plaine (Ile de la Réunion): un ouvrage d’exception dans un site grandiose (The bridge over the Bras de la Plaine [Reunion Island]: an exceptional structure in a magnificent setting) (January 2002)

- [DEM 02] A. Demare, G.Tréffot: Second pont sur le Rhin au Sud de Strasbourg: La grande travée au-dessus du fleuve est achevée (Second bridge over the Rhine to the south of Strasbourg: The large span above the river is finished) (February 2002)

Sétra Bulletin ouvrages d’art - [CON 91] E. Conti, E. Vacher: Le pont sur la rivière Saint-Denis à la Réunion (The bridge over the Saint-Denis river on Reunion Island) (July 1991)

- [ABE 91] H. Abel-Michel, C. Outteryck, B. Grèzes, G. Ferez: L’exécution du pont d’Arcins (The construction of the Arcins bridge) (July 1991)

- [LEC 92] D. Lecointre, D. Lefaucheur: Ferraillage passif des bossages (Non-prestressed reinforcement of anchor blocks) (January 1992)

- [VIO 93] P.Vion: L’exécution du pont de Villeneuve-sur-Lot (Construction of the Villeneuve-sur-Lot bridge) (July 1993)

- [COM 93] J. Combault, B. Flourens: Le pont de la corniche à Dole, de nouveaux plis dans le Jura (The Corniche bridge at Dole, new undulations in the Jura) (March 1993)

- [BAR 93] R Barras: La réparation du pont de Blagnac: études, projet et suivi des travaux (Repair of the Blagnac bridge: studies, design and monitoring of work) (November 1993)



- [GIL 93] G. Gillet, B. Canitrot,A. Palacci, D. Froissac, P. Gernigon, B. Bouvy,J. Goyet: Le pont sur la Truyère à Garabit (The bridge over the Truyère at Garabit) (November 1993)

- [PER 94] G. Ferez, B.Taimiot: Le renforcement du pont de Bergerac (The reinforcement of Bergerac bridge) (July 1994)

- [JEH 94] J.C.Jehan, J.L. Bernard: La démolition du pont de Beaucaire sur le Rhône (Demolition of the Beaucaire bridge over the Rhône) (July 1994)

- [BOU 94.3] E. Bouchon, J. Lefevre: Pont de Tanus, les effets du vent (Wind effects on the Tanus Bridge) (November 1994)

- [REl 94] J.M. Reinhard: Le Pont de la corniche à Dole (The Corniche Bridge at Dole) (November 1994)

- [DEL 94] G. Delfosse, G. Ferez: Renforcement par précontrainte extérieure (Reinforcement via external prestressing) (November 1994)

- [GIL 96] G. Gillet: Contournement de Marvejols: les viaducs du Piou, du Rioulong et de la Planchette (The Marvejols By-pass: the Piou, Rioulong and Planchette viaducts) (July 1996)

- [JAC 96] R Jacquet: Le viaduc de Rogerville sur l’autoroute A29 (The Rogerville viaduct on the A29 highway) (July 1996)

- [TAV 96] F.Tavakoli: Modélisation STl d’un pont construit par encorbellements successifs (STL modeling of a bridge built by the cantilever method) (November 1996)

- [GAC 98] R. Gachiteguy, G.Viossanges: Le viaduc du Viaur, des fléaux sous haute surveillance (The Viaur viaduct: cantilevers under close surveillance) (March 1998)

- [BAR 98] P. Barras: Réparation de l’ouvrage sur le quai Deschamps à Bordeaux (Structural repair on the Quai Deschamps in Bordeaux) (August 1998)

- [PAU 98] L. Paulik: Le pont sur le Vecchio (The bridge over the Vecchio) (December 1998)

- [DAL 00] F. Dallot, D. de Matteis, V. Dewilde, F.Tavakoli: Passage à l’Euro(code) pour le second viaduc de Pont Salomon (Transition to the Eurocode for the second Pont Salomon viaduct) (August 2000)

- [GOD 00] B. Godart, L. Divet: Une nouvelle réaction de gonflement interne des bétons: la réaction sulfatique (A new internal swelling reaction in concrete: ettringite formation) (May 2000)

- [TAV 00] F. Tavakoli: Renforcement du pont sur la Saône à Lyon (Reinforcement of the bridge over the Saône in Lyon) (December 2000)

- [DEM 01.2] A. Demare, G.Tréffot: Second pont sur le Rhin au Sud de Strasbourg: études de faisabilité des BHP (Second bridge over the Rhine to the south of Strasbourg: HPC feasibility studies) (March 2001)

- [DEM 01.3] A. Demare, G. Tréffot: Second pont sur le Rhin au Sud de Strasbourg: des piles et des fondations profondes dans le fleuve pour résister aux séismes et aux chocs de bateaux (Second bridge over the Rhine to the south of Strasbourg: piers and deep foundations in the river to resist earthquakes and impacts from boats) (June 2001)



- [LEF 02] D. Le Faucheur: Cumul des aciers de cisaillement et des aciers de flexion (Cumulation of shear and flexion reinforcements) (July 2002)

Bulletin des laboratoires des ponts et chaussées - [DIV 98] L. Divet, F Guerrier, G. Le Mestre: Risque de développement de réactions sulfatiques dans les pièces en béton de grande masse, le cas du pont d’Ondes (Risk of the development of ettringite formation in massive concrete parts, the example of the Ondes bridge) (January-February 1998)

- [DIV 00] L. Divet: État des connaissances sur les causes possibles des réactions sulfatiques internes au béton (Extent of the understanding of the possible causes of ettringite formation in concrete) (July-August 2000)

Annales de l’ITBTP - [VIR 81] M. Virlogeux: Analyse de quelques problèmes spécifiques du calcul des ponts construits par encorbellements successifs (Analysis of certain problems specific to the design of bridges built by the cantilever method) (February 1981)

- [POI 92] D. Poineau, J. Theillout, F. Cusin: Réparation et renforcement des structures de bâtiments et d’ouvrages d’art; application des techniques de tôles collées et de précontrainte additionnelle (Structural repair and reinforcement of buildings and civil engineering structures) (February 1992)

Techniques de l’ingénieur - [GEO 96] J.M. Geoffray: Le béton hydraulique - Mise en œuvre (Hydraulic concrete – Application) (May 1996)

PCI JOURNAL - [SCH 95] J. Schlaich, K. Schaefer, M. Jennewein: Temperature induced deformations in match cast segments (July-August 1995)

- [ROB 97] C.L. Roberts-Woolman, J.E. Brein, M.E. Kregle: Towards a consistent design for structural concrete (May-June 1997)

Revue l’Industria italiana del cemento (IIC) - [SMI 97] Dennis R.Smith, PhD: Attraversando la baia di Narragansett, Rhodes Island USA, la costruzione del ponte Jamestown - Verrazzano (mars 1997)

- [ITA 99] Ing. Salvatore Giuseppe Italiano: II ponte sul fiume Ticino nei pressi di Pavia (January 1999)

- [ROS 00] Marco Rosignoli: Ponti in C.A.P. ad anime reticolani (May 2000)

- [REN 00] Ing. Marco Renga: Il ponte di Chivaso sulla S.S. 458 di Casalborgone (Torino) (July-August 2000)




This guide provides a highly detailed description of the design andconstruction of prestressed concrete bridges built by the cantilevermethod.

Highly informative and lavishly illustrated, each of the ten chapterscovers one of the stages in the development of these types ofstructures: preliminary design, detailed design, calculations,preparation of the invitation to tender, construction, monitoring ofworks, maintenance, etc.

Thanks to its comprehensive coverage of the subject, this guide willbe of interest to anyone involved in the design and construction ofbridges built by the cantilever method (project managers, consultingengineers or technicians, construction managers, works inspectors andarchitects) in addition to teachers specialising in civil engineering.

This technical guide is intended for engineers and architects involvedin designing, calculating and verifying concrete bridges built by thecantilever method.

This document is awailable and can be downloaded on Sétra website: The Sétra belongsto the scientific and

http://www.setra.equipement.gouv.fr technical networkof the French Public

Work Ministry (RST) Cover - Photographers: XXXXXXA compléter par l 'auteur The Sétra authorization is required for reproduction of this document (all or even part) © 2007 Sétra - Reference: XXXX - ISRN: XXXX