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Bridges with Multiple Cable-Stayed Spans Michel Virlogeux, Civil Eng. Consulting Engineer and Designer, Bonnelles, France

Summary

This paper is devoted to a new field of application of cable-stayed bridges: bridges with multiple cable-stayed spans. It begins with a short historical review and a special reference to Riccardo Morandis bridges It then describes the very few bridges that have been built recently with multiple cable-stayed spans and the designs that have been proposed in the last thirty years. It ends with the pre- sentation of three recent major projects, at least one of which will be built. These three projects show the extreme efficiency of this concept for crossing wide rivers and sea channels.

Historical Review

The first cable-stayed bridges were erected at the beginning of the 19th century. but disasters occurred with the collapse of the bridges over the Tweed and Saale rivers. Designers at the time ignored the real flow of forces, did not consider wind effects. even through an evaluation of static forces produced by wind pressure on the structure. The French scientist Henri Navier even proved that suspension bridges are far more efficient than cable-stayed bridges These acci- dents and this scientific demonstra- tions halted the development of cable- stayed bridges for almost a century, and cable stays were only used in some suspension bridges close to pylons in order to stiffen the structure: the most famous example being the Brooklyn Bridge, USA.

In France in the first years of the 20th century, Albert Gisclard erected several bridges with a specific cable system, intermediate between suspension and cable staying, giving much more importance to the cable stays. His ideas were occasionally reproduced.

However, it was in Spain in 1925 that Eduardo Torroja built the first real cable-stayed bridge in concrete, the Tempul Aqueduct. Here, a cable stay simply replaces a classical support that could not have been built due to the site configuration.

The real development of cable-stayed bridges came with the ideas and publi- cations of Franz Dischinger in the 1930s and 1940s Surprisingly, the first application was in France in 1952 when

Albert Caquot erected the cable- stayed bridge over the Donzbre Canal in reinforced concrete. This bridge, very often forgotten in the history of cable-stayed bridges, preceded by some years the famous Stromsund Bridge erected in Sweden under Dischingers influence. A fantastic development of cable-stayed bridges fol- lowed, fxst in Germany and later all over the world. But just when the design of modern cable-stayed bridges was being developed. with flexible towers and a continuous deck, Riccardo Morandi ori- ented his own ideas in a very different direction. His towers were extremely rigid, in the shape of a portal frame longitudinally (an inverted V), with inclined struts to support the deck at a distance on each side. Each tower suspended a double cantilever - with a rigid connection to the tower - and drop-in spans produced the link between adjacent cantilevers.

This principle was applied for the first time for the erection of the Lake Maracaibo Bridge in Venezuela (Fig$. 1-3). which was built between 1957 and 1962 [l]. The central part of it is made of six towers and five main spans each 235 rn long. The erection of this bridge was a major technical achievement at the time, and can be compared to the construction of the bridges he- tween Honshu and Shikoku in Japan, or of the Storebelt and Oeresund Bridges in Northern Europe. For this reason, the Lake Maracaibo Bridge deserves to be part of the series of the most famous bridges over the world, with the Golden Gate Bridge, the bridge over the Firth of Forth, the

Brooklyn Bridge and the Garabit Viaduct.

Furthermore. the Lake Mardcaibo Bridge has some common points with the bridge over the Firth of Forth. Both were technical deadlocks new structural concepts which were immediately surpassed by more efficient ones: classical cable-stayed bridges with flexible towers and continuous decks. condemned Morandis concept in the same way that classical suspension bridges condemned the sophisticated truss structures inspired by Fowler and Bakers Bridge. But, like the bridge over the Firth of Forth, the Lake Maracaibo Bridge is admired by architects who understand the evident flow of forces and who are sensitive to the impression of strength that em- anates from the mass and shapes of the structure.

Nevertheless, Riccardo Morandi built several bridges according to the same principles:

- the Polcevera viaduct near Genoa, Italy, built between 1960 and 1964, with three towers and two main cable-stayed spans each 280 m long - (Fig. 4j

- two smaller bridges in Italy, i.e. the bridge over the Tevere at Mogliana built between 1963 and 1%7, and the Carpineto Viaduct built between 1971 and 1974, with one and two towers, respectively

- the Wadi Kuf Bridge in Libya, built between 1965 and 1971, with two pylons and a main span of 281 m, which was for seven years the longest concrete cable-stayed span in the world.

Only one bridge has been built by another engineer following these principles, namely the Chaco Corrientes Bridge over the Rio Parana in Ar- gentina, designed by Jean Courbon. This bridge was completed in 1973 with two pylons and a central span of 245 m (Fig. 5).

Before concentrating on our theme, we may evoke some major aspects of the evolution of modern cable-stayed bridges.

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Fig. 1. Longrrudinal V I ~ W S ofthe Luke Maracarho bridge

Fig. 2: Erechon ofthe Luke Maracaibo bridge

I Fig. 3: The complered Lake Maracaibo bridge

Fig. 4: The Polcevera viaduct

A major step came with the notion of multiple cable stays suspending the deck at close intervals. developed by Helmut Homberg for the erection of the Friedrich Ebert Bridge in Bonn, Germany, in 1967. A further step was the concept of cable-stayed bridges with flexible decks, invented by Ulrich Finsterwalder and Fritz Leonhardt and developed by Rene Walther for the erection of the Diepoldsau Bridge. Switzerland, in 1985 and by Jorg Schlaich with the Evripos Bridge. Greece. completed in 1993, a project in which the author took part as consul- tant for the Greek administration.

Rapid progress has been made in span length in recent years. and cable- stayed bridges now compete with suspension bridges for spans between 700 and 1200. or even 1500 m. The erection of the Normandie Bridge, France, was a major step in this field. The author developed the design at the Service d'etudes techniques des routes et autoroutes (SETRA) in asso- ciation with several design offices and laboratories (Sofresid, Sogelerg, Seee. Quadric, Onera and CSTB). taking inspiration from the lectures of Fritz Leonhardt - who stated long ago that it is possible to erect cable-stayed bridges with spans up to 1500 m - and from English suspension bridges for their streamlining. The execution design was developed for the concrete parts of the bridge by the GIE du Pont de Normandie (including seven major contractors: Campenon Bernard, Bouygues, Sogea, GTM. Dumez, Quil- lery and Spie Batignolles) and for the steel part of the central span by Mon- berg and Thorsen with the participation of COW1 Consult. Bilfinger Berg- er and Freyssinet were subcontractors for the foundations and for the prestressing and cable staying, respectively.

The Normandie Bridge is no longer the longest cable-stayed span in the world. Since May 1999, the world record belongs to the Tatara Bridge. Japan. a very elegant structure. In the author's opinion, this is the most elegant of all Japanese bridges showing - if it were necessary - that cable-stayed solutions can be both extremely efficient and elegant.

The design of long-span cable-stayed bridges is dominated by the resistance to turbulent wind dynamic effects. and by aerodynamic stability. Streamlined box girders, inspired by the English suspension bridges and the Normandie Bridge, constitute the best technical

Fig. 5:'The Chuco Corrientes bridge ipltoro Freyssina)

solutions to these problems The author considers that they also have to be preferred for shorter spans, even though they are slightly more expensive. because they behave better than decks with I-girders. The latter have to be equipped with appendices. such as fairings and baffles. in order to reach an acceptable aerodynamic behaviour. which they do not have naturally through their shapes.

Cable vibrations have affected several major bridges in the last ten years. Despite better understanding of the phenomena that produce such vibrations, one cannot consider the problem solved, as some points are still contro- versial. Some cable vibrations might be produced by limited movements of a deck that is not well streamlined movements which induce a parametric excitation of cable stays. Rain, in some cases. might accelerate the phenome- non to an alarming scale.

On the other hand, it is known how to master cable vibrations by different types of countermeasures. To eliminate rain-and-wind induced vibrations. ducts can be shaped to channel rainwa- ter down the cables (as used on the Hi- gashi Kobe Bridge, Japan). A better solution consists of destroying the coherence of excitations by installing thin helical filets on the ducts, which do not increase the drag forces very much (as used on the Normandie Bridge), or by creating a series of dim- ples in the ducts, with a random distribution (as used on the Tatara Bridge). Another approach. adapted to almost all types of cable vibrations, consists of increasing the damping in cable stays by the installation of dampers of different types at the lower anchorage to the deck, or at both anchorages. To eliminate parametric excitation, the best solution generally is to attach all the cable stays in a plane with aiguilles (cross cables) to change the natural frequencies of cables in their plane (vertical vibrations) and to make them very different from the natural fre-

quencies of the structure itself. It is es- sential that these aiguilles have a high internal damping, in addition to a high fatigue resistance, in order to contribute to the global damping and to avoid a transfer of energy to other types of vibrations. In summary, aiguilles are more adapted to long or very long spans.

Much progress has been made in the design of cable stays themselves, passing from lock-coil cables to parallel wires under the influence of BBR and Fritz Leonhardt, and more recently to cables made of parallel prestressing strands Tbe last step in this direction was the development in 1988 of parallel auto-protected strands by Freyssinet. Modem cable stays made of parallel strands provide very good protection against corrosion, high strength, and high fatigue resistance. However, if all details and the need of dominating cable vibrations are considered, then we have to speak of cable-staying systems rather than of cable stays. Existing specifications about cable stays, which were not based on a very scientific approach, have to be updated to adapt them to real goals and needs The use of rod bars to constitute cable stays has not been evoked, as they are considered not adapted to such a use, due to their lower ductility, their sensi- tivity to bending stresses, and their lower fatigue resistance. The need for more modem specifications is enhanced by a new development of cable-stayed bridges con- ceived by Jacques Mathivat, namely extradosed bridges, which became very popular in Japan. Some engineers use the same specifications for extradosed cables as for prestressing tendons since they are much more favourable than those for cable stays Even though an intermediate stress level has been adopted in Japan for extradosed cables, it will become necessary to develop a kind of continu-

um in the applications of prestressing strands, from internal tendons to cable stays, passing through external tendons and extradosed cables, and per- haps ending with suspension cables made of parallel prestressing strands.

Specific Problems of Bridges with Multiple Cable-Stayed spans

In a classical three-span cable-stayed bridge, loading the main span produces a downward deflection and, due to a tension increase in the corresponding cable stays, a deflection of both pylons towards the loaded span (Fig. 6). The cable stays that suspend the side spans suffer only limited tension variations, and side spans deflect upwards in the global deformation due to their reduced rigidity. Only back stays, which are anchored close to the abutments, are subjected to high tension variations since their lower anchorages are almost fixed and cannot give way in the same manner as other ones in side spans These hack stays control the pylon deflection towards the loaded span, balancing practically all the horizontal component of the tension variations in the cable stays of the main span. The disymmetry in the distribution of tension variations in the rear cables - high tension variation in back stays and very low tension variation in all other cable stays in the side spans - produces high bending moments in pylons In order to reduce them, it is necessary to concentrate anchorages in the pylon heads in bridges that have such a configuration. The reduction of the distances between the attachments of rear cable stays reduces the bending moments produced by the concentration of tension variations in the back stays. When a side span is loaded, it deflects logically downwards with a tension increase in all cable stays that suspend

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. . a) Static oinfiguurstion

h) Effect on a span loiiding with a simple line of bearings on the piem to support [he system of deck and pyloo~ no participation c i I lhc piers and pylons turning almost freely

E ) Effect of a span loadin& with &ding pien taking pan in the limitation of deflections

Fig. 9: Structural bvhuvionr of a bridge with mulfiple cable-stayed spans when pylons are rigidly connected to the conrinrrous deck. which is supported on independent piers through irnique lines of bearings, compured to the strucrural behaviour of a bridge with towers

This study begins with a bridge having towers. with a design very similar to those of the classical three-span bridges discussed before.

When a span is loaded, it deflects downwards, tension is increased in the cable stays which suspend it, and due to this tension increase the adjacent towers deflect towards the loaded span. This deflection lifts the adjacent spans which move upwards, and Uue to this movement in the adjacent spans the other tower in each of them deflects slightly in the opposite direction (Fig. 8). This global deflection is only controlled by the rigidity of deck and towers. There is no back-staying effect to limit deflections and deformations and to improve the efficiency of the cable-staying system.

If one of the adjacent spans is loaded, it now deflects downwards and the spans and towers deflect in the opposite direction than in the previous loading case. This means that each structural member is subjected to in- tense bending moments. in one direction and the other, resulting in high stress variations.

An even worse situation appears with a structure made of a continuous deck to which the pylons are rigidly connected. and which is simply supported by the piers with a single line of bearings When a span is loaded it deflects downwards, but this time the adjacent pylons turn almost freely because there is almost no tension variation in the cable stays that suspend the loaded span (Fig. Y). Only the deck rigidity can balance the load effects. while the

cable-staying system has a very limited influence on the control of deflections and bending moments. Cable stays are only efficient to balance permanent loads self-weight and equipment.

These two examples demonstrate the basic problem of bridges with multiple cable-stayed spans: how to control efficiently, economically and elegantly deflections and bending moments produced by live loads? But they also show that there is a major interest iq taking advantage of the pier rigidity. The best solution is to design rather rigid towers with the deck passing inside, or to produce a rigid connection through the deck between the pier and the pylon. A rigid connection between the deck and the towers increases the structural efficiency, by the transfer of part of the flexural effects to the towers. However, this raises a new problem: the structural system has to adapt to the deck length variations produced by temperature, concrete creep and shrinkage, as well as the structural shortening produced by prestressing forces installed after closing the spans

R i m d o Morandis Solution

l%e structural system developed by Riccardo Morandi perfectly deals with the above problems. Towers are extremely rigid, having the shape of an inverted V longitudinally, and can balance alone the effects of asymmetrical live loads The installation of inclined struts, which support the deck on each side of the tower, is only needed when

the cable stays are concentrated into a single strut at the cantilever ends. With a uniformly distributed cable-staying system, as developed in modern cable- stayed bridges, these inclined struts are not needed. And the drop-in spans between the cantilevers allow for free length variations in the deck.

The drawbacks of this structural system are its high cost (induced by the structural complexity and the multipli- cation of the construction equipment for different erection techniques), the large volume of concrete needed for the different structural members, and the large number of expansion joints which limit the user comfort and re- quire frequent and costly mainte- nance.

As stated above, the Lake Maracaibo Bridge is one of the major bridges built during the 20th century, and its design was adapted perfectly to the technical needs of this project and to the erection techniques and ideas of the time. We may think that this fantastic achievement had such an influence on Riccardo Morandi that it has been very difficult for him to develop new concepts, even when he had to build cable-stayed bridges with three spans, for which his system was unnecessarily complicated. Only in his last years could he design more classical cahle- stayed bridges. more efficient and more in agreement with the international trends.

Several designers were inspired by Riccardo Morandi to develop bridges with multiple cable-stayed spans, but none of them has been erected.

In 1967, Ulrich Finsterwalder proposed for the Great Belt crossing, Denmark, a series of spans 350 m long. The deck was extremely slender, being just a slab in reinforced and prestressed concrete, and was connected rigidly to the very rigid towers, with an expansion joint at mid-span. The piers were divided into two shafts longitudinally to allow for length variations in the deck. Therefore, it was not necessary to have an expansion joint in each span (Fig. 10).

In 1966-1968, Fritz Leonhardt proposed a project to cross the River Ganges at Allahabad in India, with a series of main spans, each 159 m long; the bridge was about 4 km long. The towers were again extremely rigid. with pylons having the shape of invert-

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Fig. 10: Finsterwalder~ project for the Great Belt bridge (1967)

-- Fig. 11: Leonhardtkproject for a bridge over the river Ganges (1968)

ed V longitudinally. and piers divided into two shafts, one below each of the two pylon legs (Fig. If). Drop-in spans were installed in each bay between cable-stayed cantilevers, to allow free length variations in the very slender deck. More recently, the contractor Grands Travaux de Marseille (GTM) developed three projects, the first two of which had no more success than those of Finsterwalder and Leonhardt. The first one, developed with SOF- RESID and Jean-Claude Foucriat, was part of a project to cross the English Channel, between England and France, at the beginning of the 1980s A long bridge was proposed on each side of the Channel, giving access to an offshore structure in which a helical ramp lead the traffic to an immersed tunnel that crossed the central part of the Channel. Each of the two bridges was made of a series of cable-stayed cantilevers; the deck was a rectangular orthotropic box-girder, totally suspended by cable stays to a steel pylon having the shape of an inverted V, longitudinally and tranversally The cantilevers were prefabricated and installed by a strong floating crane on top of corre-

sponding piers and connected to them. Adjacent cantilevers were joined by short drop-in spans, 60 m long, to constitute a series of bays. 500 m long (Fig.

This project. directly inspired from Morandi's designs. was a forerunner of the Rion-Antirion project. and one of the first attempts to develop heavy prefabrication. This technique later received many attractive applications, specially under the inlluence of Ballast Nedam, for example the Bahrein Coastway, the Great Belt West Bridge. the Second Severn Crossing in the UK, the Confederation Bridge in Canada which gives access to Prince Edward Island. and the Oeresund Bridge. The second project, directly inspired from the previous one but with much shorter spans was developed in coop- eration with Campenon Bernard for the R6 Island Bridge competition in 1986. As in the previous project. the bridge was made of complete cantilevers. totally in prestressed concrete. The slender deck was suspended and rigidly connected to a rigid pylon having the shape of an inverted V, longitudinally and tranversely, and was installed on the corresponding piers by a

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Fig. 12: CTM and SOFRESIDkprojecl for a Channel bridge

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only 140 m, the cantilevers were joined

span. The deck cross section. designed by Jean Muller. had the shape of a thin slab stiffened by multiple floor beams, with the sidewalks at a lower level to produce flexural inertia. The author reused this principle with some

1 directly via an expansion joint at mid- I I

I amendments and improvements for 14n.im the Burgundy Bridge at Chalon-sur- r 1 SaBne. France.

GTM came back to the ideas of Ric- cardo Morandi and to its Channel Dro- . ~ - ject to develop the preliminary design of the Rion-Antirion Bridge, Greece, in the late 1980s. Jean Paul Teyssandier and Yves Maury's team designed four large cable-stayed cantilevers, each supported on a large off-shore caisson which at the same time serves as a foundation and a pier. Drop-in spans, SO m long, are installed between cantilever ends to complete the spans (Fig. 14). Each cantilever is made of a pylon with four converging legs -with the shape of an inverted V longitudinally and transversally - and a composite deck rigidly connected to the pylon and suspended to the pylon by cable stays. Each of the three main spans, 560 m long, is thus made of two main cantilevers 255 m long, and a drop-in span. Side spans are made of one cantilever. also 255 m long, and of a drop-in span SO m long to reach the abutment (an approach viaduct).

There is only one difference from Morandi's design: cantilevers (with their pylons) are not connected rigidly to the piers below. Instead. to limit seismic forces, cantilevers rest on piers through a series of sliding bearings, with a system of horizontal dampers to limit longitudinal and transverse displacements during earthquakes It will be explained below how this preli-

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minary design has been improved to eliminate drawbacks produced by the

Fig. 1.7: Prulrcr for the Re rslund bridge by Cumpenon Bernard and GTM (1986)

large number of joint$ bending forces 311s rn I 560 rn 560 rn 560 m 5 induced by the concentration of loads I T r T Y and cable-stays at the cantilever ends, I I I I I I large movements in drop-in spans, and complications due to the installation in a restricted area of a large series of big dampers that needed to be specifically designed and fabricated. I

560 m

1 Different Types of Solutions

even if some appear inelegant, aesthet- Fig. I4: Preliminury projen forrhr Riori-Airtirim bridge, by GTMurid 1ngerop (1988)

a) Intermediate support every second span

c) Long cables from a pylon head 10 an adjacent pylon 01 the deck lcvcl

d) Cable-slays mming from both adjiilcent pylons to support the central part of each span

Fig. 15: Some more or less acceptable solirtions to stiffm a cable-sta.yed bridge wirh malriplc spans

Fig. 16: The Kojima-Sakaide suspension bridges, with their intermediate support (phrxrt tfsm

Fig. 17: The suspension bridge over the river Garonne at le Mas dAgenais 1pIvm Frryrsmbil

ically or from a structural point of view (Fig. 15). Problems related to deck length variations will be ignored here in order to concentrate on the reduction of bending forces induced by live loads. The design of pylons - an axial pylon or lateral pylons (one on each side of the deck) -will not be considered here since this choice is much more related to length variations than to the balance of live loads.

The first solution consists of introducing an intermediate support in every second span. This is the solution classi- cally adopted for suspension bridges when two or three major suspended spans are to be erected. Some examples are famous, such as the two Oak- land Bay suspension bridges. USA, the two suspension bridges on the Kojima- Sakaide route of the Honshu-Shikoku project, Japan (Fig 16), and the three suspension bridges that cross the Ku- rushima Straights on the Onomichi- lmabari route, Japan.

It is not always possible to install such intermediate supports and the author considers this solution the most inelegant for the design of bridges with multiple cable-stayed spans. Fortu- nately, nobody dared to do it so far.

The second solution is also inspired ffim suspension bridges. To prevent pylons from bending towards the loaded spans, their heads are connected by head cables. Several suspension bridges with multiple spans built in France during the 19th century and the first half of the 20th century have head cables, for example the Sully-sur-Loire Bridge (which collapsed on a very cold day in January 1985) and the Chateauneuf-sur-Loire. Langeais and Mas d'Agenais Bridges (Fig. 17). The solution might be adopted for cable-stayed bridges with multiple spans, but it is probably less efficient than for suspension bridges since cable-stayed bridges are more rigid. and the addi- tional rigidity provided by head cables would be more limited. In addition, the system looks less elegant than for suspension bridges, because of the in- troduction of a new line that clashes with the inclination of cable stays but is too similar, thus destroying the structural simplicity of classical cable- stayed bridges and producing some confusion. Only one project took inspiration from this concept. namely the one that won the design competition for the Poole Harbour Bridge in the UK, whose erection has not yet been decided upon.

A third solution is to introduce, in addition to the classical cable stays distributed along each span from the pylon to mid-span, long stabilisation cables that are anchored on one side at a pylon head, and on the other side at an adjacent pylon at the deck level. These stabilisation cables also introduce a new line in the structure, thus rupturing the harmo- nious distribution of classical cable stays

This solution was adopted by Jorg Schlaich and Rudolf Bergermann for the Ting Kau Bridge in Hong Kong (Figs 18 and 19). As this bridge has only three towers. only the central one had to be stabilised this way. The composite twin decks rest on cantilevers laterally extending from the axial towers through classical bearings. so that length variations can develop freely.

One might think that this solutioncould be improved by distributing classical cable stays from each pylon, the last ones being anchored beyond mid-span so that the central part of the span is suspended from both pylons by crossing cable stays. This can be efficient only if the deck is extremely rigid, because the weight of this central section of the span has to be divided between the cable stays that suspend it from both pylons.

In fact, this type of solution was ini- tiated by Fritz Leonhardt and Jorg Schlaich in 1971 when designing the Patna bridge over the river Ganges (Fig. 20). From the lessons of the Allah- abad project, they decided to shorten every second span by 20% (the span lengths becoming equal to L and 0.80 L alternatively), and to install crossing stabilization cables in these shorter spans Length variations could develop in expansion joints in the main spans. that is every second span: but the expansion joints were designed to trans- mit bending moments in addition to shear forces, as we shall see later. The main spans were about 200 metres long and the total hridge length was about 4 kilometres.

Jorg Schlaich. who worked for the Al- lahabad and Patna projects. reused the concept for the Prince Edward Island link competition around 1990, with in addition an extensive use of heavy prefabrication (Fig. 21). The spans were alternatively 220 and 180 metres long. with stabilization cables crossing in the shorter spans: short drop-in spans. only 20 metres long. were installed in the longer spans to free length variations. The project was to prefabricate 380 metres long units,

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I ll jIl i Fig. 18: Schematic b'iews of the Ting Kau bridge

I I I I -. Fix 20 The Patna bridge cromng Ihe river Ganges ( I 971)

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Fig. 21: The cable-sfnyed option proposed by Chlnich und Bergermann for the bridge to the Prince Edward Island

Fig. 22: Longifudinul view of the Mucuu bridge

Fig. 23: The Macau bridge during erection

Fig. 24: The Macau bridge ufier completion

consisting of a short span with its two pylons cable-stays and stabilization cables, and with the two long cantilevers which will be later part of the adjacent longer spans; the closing between adjacent units, after their installation OR piers, was produced by the drop-in spans.

This list may be completed with the Macau Bridge, designed by Jose Luis Cancio Martins. with the collaboration of Jorg Schlaich. which was inspired by this concept. It has two main spans 112 m long; but with two towers and a short span between the two long ones, it behaves like two independent cable- stayed bridges and thus cannot constitute a real bridge with multiple cable- stayed spans (Fig~s 22-24). It was completed in 1994.

Distribution of Rigidity between the Structural Members

The best solution, and the most elegant, is to distribute rigidity between the different structural members (the deck, piers, and pylons) in order to hal- ance bending effects produced by asymmetric live loads and to limit deflections From one extreme to the other, several solutions might be compared (Fig. 25): - A deck with high enough rigidity to

resist bending moments induced by live loads This solution is only ap- plicable for cable-stayed bridges with small or medium spans.

- Pylons with high bending rigidity. for example having the shape of an inverted V longitudinally. with a transfer of bending forces in the piers below to limit the rotation at the deck level. Under these conditions it is possible to have a very slender and flexible deck.

- Distribute rigidity between all the structural members deck and towers.

As stated above. the structural design must allow for length variations produced in the deck by the installation of continuity prestressing tendons in the spans after they have been closed, concrete creep and shrinkage which develop after closing the spans, and temperature variations. All practical solutions will therefore be analysed one at a time.

The first solution is to give the deck a high flexural inertia, large enough to

balance bending moments produced by asymmetrical live loads (Fig 26). Pylons have a flexural inertia similar to those of classical cable-stayed bridges and are rigidly connected to the deck. The structure composed of the pylons and deck is supported by the piers below through a single line of bearings on each pier. If loads are rather limited, these bearings can be classical neoprene 4earings, but more generally they have to be pot bearings. On the two or three central supports. depending on the flexibility of the piers and foundations and on the span length, they can be fixed bearings, but sliding bearings are needed on the extreme piers to allow free length variations.

This solution is adapted to axial and lateral suspension, but only for small or medium span lengths. The deck flexural rigidity alone cannot balance asymmetrical live loads in bridges with long or very long spans.

Three bridges have been built according to these principles, but due to their limited span lengths they have received almost no attention despite their great importance in terms of technical evolution.

The first one is the Kwang Fu Bridge in Taiwan, designed by T.Y. Lin and completed in 1978 (Fig. 27). It has three pylons and two main spans 134 m long. The deck is made of prefabricated and prestressed concrete girders. with very classical shapes, installed on temporary supports and joined by longitudinal closures, cross beams and a cast-in-situ upper slab. Extreme pylons, on the extreme piers, are sta- biked by back stays in a classical way, even though the side spans are slightly longer than usual. Only the central pylon is subjected to important rotation- al movements produced by asymmetrical live loads. which are controlled by the deck flexural inertia. Pylons and cable stays are in vertical planes, one on each side of the structure (lateral suspension),

The second example is the Colindres Bridge. Spain, completed in 1993. It also has three pylons and two main cable-stayed spans 125 m long. As in Tai- wan, the extreme pylons are stabilised by back stays and only the central pylon is subjected to important movements produced by asymmetrical live loads, which are controlled by the deck flexural inertia. Pylons and cable stays are axial.

h) Intermediate mlutims with rigidity distributed between piers deck and pylons

cI Rigid pylons and flexible deck. with a trhnrmi~~ion of momcm between pylons and pien

Fig. 2.5: Distrihulihn ofrigidirv hetwem deck and towers, from very rigid decks wirh "classical" rowers, 1 0 slender decks and rigid mw'ers

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The third and the most elegant example is the Arena Viaduct, Spain, designed by Juan Jose Arenas, which was completed in 1993 (Figs. 28-30). This is a real cable-stayed bridge with multiple spans since it has six pylons and five main spans 105 m long. The

relatively small spans limit flexural problems, and the deck flexural inertia easily balances the effects of asymmetrical live loads The bridge elegance is increased by the S-shape of the road alignment.

27.h 1

Fig. 28: Schematic views of the Arena viadm

To improve the system piers and pylons must contribute to the global rigidity. The simplest solution is to maintain the previous design, i.e. a bridge with a relatively rigid deck and pylons above the deck that are rigidly connected to it. However, the deck and pylons structure is supported on the piers through two lines of hearings (Fig. 31). Once more these bearings can be classical neoprene bearings, but more generally and specially for large loads, they might be pot bearings, fixed on the two or three central piers and sliding on the other ones. However, this solution does not solve completely the problem of length variations At first, if vertical loads are very high (e.g. for long-span bridges). high horizontal forces develop on pier heads due to friction on the sliding bearings (it is necessary to count at least 2 or 3% for the friction coefficient). If the piers are tall or very tall, this can be prohibitive. Another problem, which can be mastered more easily, is the importance of the relative movements of the deck (and pylons) on the piers. It is necessary to consider these movements in the design since the reactions from the sliding bearings - fixed on the piers - move by tens of centimetres below the deck. The cross beams in the deck above the supports and their reinforcement have to be designed accordingly. In addition, though this is of limited practical importance, it is impossible to predict the relative movements of the deck on the supports; because they are controlled only by friction on the sliding bearings they cannot be evaluated directly since sliding movements are non-linear and non-reversible. These movements can be only evaluated after selecting a value for the friction coefficient and a complete time history of loads and

Fig. 29-30: Two views of the Arenu viaduct (phoms krrvwneii

length variations (temperature, concrete creep and shrinkage. etc.). If the relative movements can be very large (about 0.5 m for a very long bridge), great care must also be given to the shapes of piers and deck to avoid evidencing the off-centering. These rea- sons explain why the author disregard- ed this solution when he designed the Millau Viaduct, France, which is pre- sentea below. even though two lines of sliding bearings on rather strong piers could have appeared as a possible design.

An extremely interesting alternative exists to the solution with two lines of bearings on the piers: piers are made of two parallel shafts at a relatively small distance from each other longitudinally. As shown by Jacques Mathi- vat at the beginning of the 196Os, for the erection of the Choisy-le-Roi and Courbevoie Bridges in France, a pier made of two parallel slender shafts

controls flexural rotations very well and produces an almost rigid connection of deck to piers. However, it also makes the longitudinal movements of the deck almost free if the shafts are individually flexible.

It is thus possible to design cable- stayed bridges with multiple spans having a relatively flexible deck, rigidly connected to rigid pylons above and to piers made of two parallel and flexible shafts below (Fig. 32). The bridge length is, however, limited by longitudinal movements which cao be accepted by the extreme piers, as they are generally shorter and thus more rigid.

This solution was identified very quickly and Fistemalders project for the Great Belt Bridge had piers made of twin shafts with a rigid pylon above, as did Leonhardts project for the Ganges Bridge (see above). However, in both cases there were expansion

Fig. 31: Pylons rigidly connected ro fhe deck, resting on piers below fhrough two lines of bearings

Fig. 32: Towers wirh a rigid higherparf above the deck (pylon) and a lowerpan divided info twin shaffs, and rigid connecrions with fhe deck

joints to allow for longitudinal movements in some spans

The solution was adopted in another project in Denmark, namely in 1912 for crossing the Samsobelt, but with a continuous deck. The bridge had three pylons and four spans 264, 624, 624 and 264 m long. Extreme pylons were stabilised by classical back stays and only the central pylon had to be highly rigid. Piers made of twin flexible shafts made free the bridge length variations, the importance of which was relatively modest at the extreme pylons with a dilatation length of only 624 m. Unfor- tunately, this project had no more success than the other two evoked above.

In a completely different approach, the deck can be cut with an expansion joint, but the classical articulation in a mid-span cross section, which produces excess flexibility in the structure, is rejected. The principle consists of producing a continuity of bending moments through the joint or joints - in the mid-span cross section of one or several spans -by introducing a drawer beam inside the deck (Fig. 33). This drawer beam, which has to be in steel to limit its size and weight, is supported up and down on two lines of hearings in each of the two cantilevers that it joins It is fixed in one of the two cantilevers and slides inside the other one. Jean Muller developed a system of this type for the Rogerville Viaduct, France, a classical box-girder bridge in prestressed concrete, where the pier architecture - structurally illlogical - made such a design necessary. A similar concept was adopted by T.Y. Lin International for the new Benicia- Martinez Bridges now under construction in the USA, which are also classical box-girder bridges in prestressed concrete made from precast segments. Such a solution is only feasible when the deck, preferably a box-girder, has dimensions large enough to house the drawer beam, and has been designed from the start considering the corresponding constraints

Another solution is to completely sep- arate the deck from the pylons. The pylons are then directly extending piers to constitute towers (Fig. 34). This solution is extremely practical when the towers are made of two columns, one on each side of the deck. It can also be foreseen with axial pylons that pass through the deck. in a hole wide enough to allow for possible relative movements. The deck is supported on the towers through bearings

-fixed or sliding, depending on the po- sition of the tower in the bridge - installed on a cross beam when the tower is a portal frame, or directly on the pier if the axial pylon extending the pier passes through the deck.

In such designs, length variations are - are completely separated. On the not limited by the towers rigidity. and other hand. the load transferred from the two main problems - bending the deck to the pier (the part of the forces produced by asymmetrical live tower below) is rather low since it is loads and length variations in the deck limited to self-weights and loads corre-

sponding only to the part of the deck close to the tower. The largest part of the loads is transferred to the tower

Fixed bcanngs

All bearings are sliding except on one line

fig. 33: Rigid rowers rigidly connected ro the deck with expansion joints i i i sumc .span.$ equipped with n drawer beam to transfer hending mnnicnr.~ thrargh the jriiiir

Fig, 34: Deck independent from rigid towen

938.91 57.m 79.86 311.44 2W.46 -. 83.84 ,mp.

I I I

I I I X IMJ u 2.740 Fig. 35: Longifudind view and cross-section ofrhe Mrzcda bridge

heads by cable stays and from there passes directly through the towers to the foundations without any interfer- ence with the deck. Friction on sliding bearings is thus limited and cannot generate high bending forces in towers.

For this reason this is an extremely efficient solution which was adopted for the Mezcala Bridge in Mexico. completed in 1993. with three towers and two main spans 312 m long (Figs. 35-37). Due to site conditions, the extreme pylons which are stabilised by classical back stays, are shorter than the central one. The composite deck passes freely through the two legs of each tower and is simply supported on the pier, which constitutes the lower part of each tower. This and the Ting Kau Bridge are the only examples to date of cable-stayed bridges with multiple long spans. The single drawback of this solution is its lack of elegance, with the two columns of the towers framing the structure and giving it a rather stocky appearance. The upper cross beam between the two columns does not improve it, nor the wide pier below the deck with its lateral extensions to drive the columns on each side of the structure. This is the reason for the choice of axial pylons and cable stays when the author designed the Millau Viaduct.

The Ting Kau Bridge follows these lines with free length variations and axial pylons for greater elegance. The deck is made of two parallel composite structures, each comprising two steel I-girders and a reinforced concrete top slab, connected by a series of steel cross beams that are extended in the twin decks as floor beams. me axial pylons are installed in the open space between the twin decks, suspending them through four planes of cable stays. The twin decks are simply supported on transverse corbels extending from the pylons, so that length variations are free. only limited by friction, and loads transferred to the corbels are rather low. Nevertheless. the pylon strength is increased by a transverse cable-staying system.

Figs, 36.77: Two views of the Mezcnla bridge f p h o m Frcysrinrrond A. Chovvin)

This last family of solutions leads directly to a new concept of total suspension. This concept was developed by Fritz Leonhardt for classical cable- stayed bridges with the erection of the Pasco-Kennewick Bridge in the USA in 1978, and reproduced in 1986 by Pe- ter Taylor for the Alex Frazer Bridge near Vancouver. Canada. The concept adapts perfectly to cable-stayed bridges with multiple spans in that it permits complete free longitudinal movements of the deck - limited only by the stress variations in cable stays produced by the movements - without any direct in- terference with the rigidity of towers. Length variations due to temperature, concrete creep and shrinkage are thus completely free (Fig. 38).

This efficient solution was proposed by the contractor Bouygues for the Re Is- land Bridge competition in 1986. Pierre Richard had the idea of forming the bridge, about 2.8 km long. from a series of cable-stayed spans 210 m long. The deck was continuous from one end to the other. totally suspended from the towers through which it passes (Fig. 39). Unfortunately, just after the successful erection of the Bubiyan Bridge in Kuwait and when the erection of the Syllans and Glacikres Viaducts was beginning in the French Alps, Pierre Richard designed a three- dimensional truss for the deck in prestressed concrete, the high cost of which killed the solution. Bending forces produced by asymmetrical live loads were balanced easily by the high flexural inertia of the deck so that the towers were rather slender. More rigid towers not very much more expensive, could have allowed for a slender deck with a much lower cost than the proposed one, the total suspension making the length variations completely free. As shown below,

inspiration was taken from this project for the development of the design of the Rion-Antirion Bridge.

Simplified Evaluation of Forces

At a meeting in Tokyo, Jean Schmitt gave us a very simple way to evaluate some forces in bridges with multiple spans Considering that the deck is so flexible, we can neglect bending moments in it when analysing the global equilibrium of loads. We could extend his approach, supposing that longitudinal deformations in the deck are very small, when compared to horizontal deflections produced by bending moments in pylons or toweq even if they are very rigid.

For simplicity, we suppose that the deck is horizontal, but it would be easy to introduce a correction when it has some inclination.

A uniform load on a cantilever arm is directly balanced by the vertical component of cable tensions (Fig. 40); considering the global load on the cantilever arm. it is balanced by the tension in the average cable-stay with

T = - 4L 2 s i n a

where L is the span length and a the inclination of the average cable-stay. The pylon or tower thus receives a horizontal force given by:

Finally:

F = - 4L2 8h

where h is the vertical distance cov- ered by the average cable-stay between deck and pylon or tower.

As an approximation, and with an un- known hyperstatic effect given by the value of the normal force in the mid- span cross-section: the compressive force in the deck due to this load varies from zero, in the mid-span cross section. to qL%h near to the pylon or tower.

When analysing the effect of permanent loads in a cable-stayed bridge with multiple spans, due to symmetry, pylons or towers are only subjected to compressive forces The normal force in pylons or towers due to the deck weight is equal to p L where p is the deck linear weight (including equipment); horizontal forces due to the weight of cantilevers on both sides of each pylon or tower are balanced. Normal forces in the deck vary in a first approximation from zero at mid- spans to pL2/8h at the pylons or towers: only construction effects (including prestressing forces if any), temperature variations, concrete creep and shrinkage can alter this distribution of compressive forces. depending on the type of connections between deck and pylons or towers. The situation is completely different for live loads The case of a uniform load on a complete span, on a deck which is totally suspended from the towers, or resting on all towers through neoprene or sliding bearings is shown on Fig. 41. Towers on both sides of the loaded span receive a horizontal force equal to qL2/8h: since no other (important) force can come from the deck due to the type of connection, these towers receive a bending moment which varies linearly and is equal to:

qL2(H + h ) 8h

M ( 0 ) =

at the tower basis, where H i s the tower height below the deck.

Fig. 38: Rigid towers independent from a completely suspended deck

I 210.IxxI

1

%1uI J

Fig. 39: Schemaric views of rhe Bmrygues' solution for rlir Re islund bridge

And since the deck can receive no (important) horizontal force from the towers. through the hearings. the normal force produced hy live loads at the towers is equal to zero: an hyperstatic effect develops i n the loaded span. and the normal force is a tension in the mid-span cross-section of the loaded span, given by:

leading to the effective distrihution of normal forces in the deck produced hy these live loads.

If the deck is rigidly connecled 11) classical towers. or connected to classical towers by fixed hearings, the situation is completely different: a frame erfect develops in the loaded span and the adjacent towers (F;g. 42). Supposing for simplicity that they have the same height helow the deck. the horizontal displacement at the deck level is equal to zero for symmetry iind due to thc fact that the longitudinal deformation in the deck is very small as compared to the horizontal displacernents o f towers. The horizontal force in the tower produced by the load. qL'ltUi. is "halan- ced" by a rcaction R at the deck level with: *

and thus :

The distrihution o f normal lorccs i n the loaded span directly derives from this result.

I t is clear that thc distrihution o f hending forces i n the towers is much more favourable than with a totally suspended deck (or a deck on ncoprene or sliding hearings): at the tower basis. the bending momcnt is given hy:

But, practically. when the deck is rigidly connected to towers their lower part is organised so as to free length variations in the deck. for example hy div-

rx L

J

Fig. 40: Evidencing loads and forces in a loaded span Fig. 41: Live loads on a complete span, with a deck completely SIU- pended to towers

Fig. 42: Live loads on a complete span, with a deck rigidly connected Fig. 43: Live //,ads on a contplere span. with a deck rigidly connected to rigid towers to towers divided into twin shafis below

iding them into two parallel shafts (Fig. 43): below the deck, toyers do not resist to horizontal forces but only

andthus:

R, = N 2 &

El

H ,

to bending moments; we can then as- j(Y-4 - sume in a simplified approach that the 0 (9) shear force is equal to zero in towers below the deck. Thus we have: The tower supporting the loaded cantilever arm receives from the deck a horizontal force R, as indicated in formulae 10 and 11, below.

(10) I &

The bending moment is constant in the 811 El 0 El lower part of the tower$ and the distribution in the deck of normal forces

8, (7) qL' H * dr R = - 4'

8h u = - j(h + y - .)( y - .)- - R, j ( ~ , - .r) - From this re,,ation, R, is obtained:

dx produced by live loads is the same as for permanent loads. The analysis is more sophisticated R, = -

( H , - x) ~ when only half a span is loaded. The simpler case this time corresponds to 0 El a deck rigidly connected to classical towers (at least partly), or connected to classical towers through fixed bearings (Fig. 44). Neglecting longitudinal deformations in the deck, it moves horizontally as a whole on a distance u.

deck (or through fixed bearings) -ex-

loaded cantilever arm - receive from the deck a horizontal force, Rj, given

U

2 dr 8h 11,

The equilibrium of the deck gives the equation:

- + I: R, = R, 8h

and finally :

qL2

dx All towers rigidly connected to the H,

cept the one which suspends the qL' = - 8

From this result and formulae 7 and 9 it is easy to evaluate bending forces in all towers, and also the distribution of normal forces in the deck, compressive on one side of the loaded cantilever (on the displacement side), and tensile on the other side.

If towers are very flexible helow the deck as regards horizontal forces, the shear force is equal to zero in the tower supporting the loaded cantilever. and again:

qL R=- Xh

is given as a first approximation; it is not possible to evaluate the horizontal displacement when considering towers very flexible.

The analysis is much more difficult when the deck is totally suspended from all towers, or supported on all towers through neoprene or sliding bearings (Fig. 45). When loading a cantilever arm, the tension increase in the cable-stays which support it produces a horizontal force in the deck, qLz/(uI, which induces a horizontal displacement of the deck, u. The vertical deformation of the deck corresponds to a downwards deflection in half can-, tilever arms, including the loaded one, and upwards deflections in other ones; the vertical deflection is very small at mid spans. For this reason the longer cables work as backstays, and they are the most efficient to limit the horizontal deck movement.

For this reason, even if far from cor- rect, it can be assumed that the deck remains horizontal and moves hori-

zontally as a whole on the distance u. It is also assumed that pylons are rigid and have horizontal deflections which are small as compared to u. The length variation in a typical cable-stay in a cantilever deflecting downwards is thus given by : ( I + dl) = (x, + u y + 11, where ,r8 is the horizontal distance he- tween the anchorage in the deck and the tower in which the cable is anchored. And thus: dl = u c o s a

where ai is the cable inclination to the horizontal. The tension variation is then given by:

dT= - d l = - cosa, u (71, (71, and the horizontal action on the deck by:

dR= - cos a ;~

The same result is obtained in a cantilever arm deflecting upwards, if the horizontal action is counted in the same direction. With n cable-stays in each cantilever, and N towers, the global reaction is given by :

(71;

R = 2 N It: - cosa, u (14) [,:, (71, I Since this reaction has to balance the horizontal effect of live loads, it can he concluded that:

This evaluation is-an underestim.ation due to the effective horizontal deflections of pylons, and to the vertical deflections of the deck which limit the tension increase in intermediate cahle- stays. But it can be considered as a first approximation. From it. bending forces can be evaluated in pylons, from a horizontal force at the cable anchorage level given by:

H = - 2 [ ~ ( ~ ) , c o s i a , ] u ,=, (16)

in typical pylons. and by:

H = - - - - 2 $ [,:,[?I, - cosa, ] u (17) in the pylon which supports the loaded cantilever arm.

The deck horizontal displacement can he overestimated by considering that intermediate cable-stays receive only very small tension variations due to the deck flexibility - and related vertical deflections -and by using formulae 14.15,16 and 17, where only the longer cable-stays are considered.

Finally, Jean Schmitt noted that when a cantilever is loaded in every span. always on the same side, horizontal f&es are to be balanced in each tower (Fig. 46). Only the shear force in the deck at mid-span can then balance the loads, with:

so that the deck has to receive some rigidity.

YL XI, -

*r 2. * - H,

Fig. 46: Live loads on a cantilever urm in

ed to tower.s euch span. with a deck completely suspend-

u deck complctcly suspended to cowers Fig. 45: Live loads on u cuntilever arm. with Fig. 44: Live louds oti acuntilever arm, with

a deck rigidly connected to towers

Major Projects

Ik/o projects developed in the early 1990s produced important progress in the design of cable-stayed bridges with multiple spans, namely the Millau Viaduct, which crosses the deep Tarn Valley, and a bridge over the lake in Geneva, Switzerland. The abthor prepared the conceptual design of the Millau viaduct in 1990-1991, and developed the preliminary design in 1992-1993 while still working at SETRA. However, despite the support of the local authorities, the project has progressed very slowly due to many difficulties induced by its importance and cost, and by some oppo- sition. Jean Franqois Klein and Pierre Moia took some inspiration from it to design a cable-stayed bridge across Lake Geneva. Their project was award- ed the design competition organised to by-pass the city of Geneva on the east- em side, with a crossing of the lake via a tunnel or bridge. They were in charge of developing a detailed design in 1993-1994. This excellent design inspired the Millau project from 1994 on, so that both projects helped each other.

63.50 160.50 350.03 350.03 350.*1 160.50 63.50

1 T I

Lake Geneva Bridge * The Geneva Lake Bridge is made of four pylons and three main cable- stayed spans 350 m long (Fig. 47). The alignment is slightly curved to increase the bridge elegance and more specially to improve the view that users would have of the structure when passing along it . Despite this curvature, the pylons and cable stays are axial. The deck is extremely wide, 33.46 m. with an extremely elegant cross section: a trapezoidal three-cell box-girder, almost triangular, extended on each side by wide overhanging slab elements. Rigid- ity is distributed efficiently between the piers, the pylons, and the relatively slender deck. Longitudinal deformations produced by concrete creep and shrinkage, some prestressing effects, and temperature variations are limited by the relatively short distance between the central section of the bridge and the extreme py- 10115 (475 m). They are allowed for by the relatively high flexibility of piers with regard to longitudinal movements and by the foundation conditions in the Rhone alluvial deposits.

Unfortunately for the bridge engineer- ingcommunity, a vote was necessary to

i '-+-'3

Fig 47: Schematic views of the Lake Geneva projecf

decide upon construction, and the Geneva population opposed in 1997 any project across the lake.

Millau V d u c t The Millau project is even more ambi- tious. It is about 2.5 km long. with the road passing 270 m above the River Tam. It has seven pylons and six main cable-stayed spans 342 m long, with two piers more than 230 m tall, the pylons rising 90 m above the deck. How- ever, as stated above, developing the project took a very long time and many problem had to be solved. The preliminary project was estab- lished by SETRA, with a major con- cern about longitudinal deformations (Fig. 48). The idea of an intermediate expansion joint was eliminated following the recommendations of R e d Walther, who was member of a panel of experts in charge of the project evaluation, as he had been for the Nor- mandie Bridge. Rent5 Walther would have accepted some cracks in the extreme piers, resulting from length variations, which would have relaxed bending forces in these members.

However, this was against the author's ideas, as he prefered having no tensile force in the main members under permanent and frequent loads The author thus preferred to divide the extreme piers into twin parallel shafts in order to produce high rigidity for bending moments and large flexibility with regard to longitudinal movements. Em- manuel Bouchon increased this longitudinal flexibility by installing one line of fixed bearings on top of each of the twin shafts, which was better than producing a rigid connection as on the other supports. Not convinced by this project and seekmg some competition between different ideas, the Road Director organised two competitions ' h e first one took place in 1993-1994 to select new ideas and concepts Design offices and architects were consulted sepa- rately, but very few new solutions emerged. A second competition was organised in 1995-1996 between five teams of design offices and architects, each team being in charge of developing a project corresponding to one of the five families of solutions selected after the first consultation. The compe-

tition was thus more between projects of Sogelerg, Europe Etudes Gecti, Serf than between teams. The jury in and the architect Sir Norman Foster charge of the choice in July 1996 se- (F1g. 4). This team which the author lected the solution with multiple cable- joined after leaving SETRA was then stayed spans developed by a team made in charge of developing a detailed pro-

+"

j Coupe A.A

14.50

Fig. 4%: Schematic views of the preliminary project for the Millau viaduct fIYY3)

ject between 1996 and 1998, initially to prepare a call for bids between contractors However, it was recently decided to award a concession for the erection of. the section of the motor- way of which the viaduct is the major part, the shapes of the prepared project being mandatory.

Two alternatives had been developed: one in prestressed concrete, the other with an orthotropic box-girder deck (Fig. 50). Both solutions have almost the same shapes, adapted to the specific conditions of cable-stayed bridges with multiple spans and to the very strong winds 100 or 150 m above the plateau. The shapes that have to be respected were developed in close co- operation with the architect to efficiently distribute rigidity between the different structural members but with the greatest care for the bridge elegance and for the aesthetic coherence of the different elements, seeking ap- parent simplicity and expressing the real flow of forces.

The deck has a trapezoidal shape, being almost triangular with a narrow lower slab. The triangular shape that had been contemplated was eliminated because of its poor aerodynamic behaviour. Compared with the prelimi- narf design, the deck is more slender, about 4.50 m compared with 5.50 m. The pylons are YO m high and are in the bridge axis for elegance and structural purity. They have the shape of an inverted V longitudinally to produce the necessary rigidity and to appear light and transparent at the same time. The design of piers below had to adapt to contradictory requirements: the tallest ones have to resist very high wind forces, whereas the extreme ones have to he flexible with regard to longitudinal forces. For project homo- geneity. the architect preferred to give all the piers the same shape, with a wide box section in the lower part of the high piers and a division into twin shafts in the higher part, ahout Po m high. The candidates for the concession were selected in ZOO0 and are presently preparing their offers. If this bridge is erected, as expected, i t will have a major impact on the profession due to its technical interest and its architectural perfection.

Fig, 49: Artist impression of the selecred solution for the MiNuu viaduct lfmm Sir Nomto~ fimfcr, 1%)

amending the shape of the offshore structures that constitute the foundation caissons and the piers in order to reduce the mass of water accompany- ing the caissons during earthquakes He entrusted the author with an audit of the project, asking for proposals to improve it. Referring to Pierre Richards project for the Re Island Bridge. the author recommended a continuous deck totally suspended from the four pylons, rigidly connected to the piers below (Fig. 51). This solution was adopted immediately, the side soam being shortened sliehtlv so that - . . the last cahe stays almost reach the end supports In comparison with the initial project, this solution has many advantages. Fy-

J Ions are connected directly andrigidly

Fig. 50: Schemaric views of rhe derailedprojei ahernarive (1998)

Rion-Antirion Bridge

A last project deserves attention, espe- cially as it is the single one under construction today, namely the Rion-An- tirion Bridge that will cross the Patras Bay. The initial design presented pre- viously in this article raised many questions. At first it was questionable, as structural safety relies completely on a series of huge dampers, which do not yet exist; the possible tectonic displacements reach 2.00 m and seismic forces are very high. Further space necessary to house all this equipment appeared lacking. despite the large dimensions given to the pier heads.

.I for the Milluu viaducf, preslressed concrefe

The idea that cantilevers would move by at least 1.00 m during extreme earthquakes was not very comforting with the drop-in spans between them. The concentration of several cable slays at the cantilever ends, in order to balance the weight of the drop-in spans. produced undesirable bending moments, much higher than in classical cable-stayed bridges Further artificial problems are produced when cable stays are anchored at close intervals. Finally, vertical effects of extreme earthquakes would shake the drop-in spans like pancakes in their pans

When Jacques Combault took charge of the project supervision, he began by

to the piers below, and the relative movements between piers and cantilevers, which appeared so questionable, are thus eliminated. The deck is continuous with no expansion .joint, producing greater comfort. Safety no longer relies on dampers, but on the ductility of the structural members, mainly the pylon legs, on which it is easier to be confident. Some dampers are used only to limit transverse seismic movements. Since the drop-in spans have been eliminated, cable stays can be uniformly distributed, and bending moments drastically reduced, and no more pancake effect has to be feared.

The final project has been developed on these bases by GTM and Ingerop. The bridge has five spans, 286,3 X 560 and 286 m long. The four supports keep the aspect of the offshore structures, with a direct foundation on the sea bed extended by a pier having the shape of a large circular caisson. The pier crown widens this caisson to leave passage for the deck and to allow the installation of the four legs that constitute a pylon, joining at the pylon top to have the shape of an inverted V longitudinally and transversally. The deck is a composite structure with two steel I- girders as edge beams joined by multiple floor beams and a reinforced concrete slab. This solution was selected for its lower cost, despite the aerodynamic behaviour of this type of profile, which is not the best.

Conclusions

This extensive review presents a new field of application of cable-stayed bridges. The erection of the Eon-An-

WITTFOHT. H. Triumph der Spannweire. Be- I 3M . 2% It% SM, SM, I ZH6 I 2 0 tonVerlag, Diisseldorf. 1972. r I I 1 r

23.30 J Fig. 51: Schemntic views of thefinal design f o r the Rion-Antirion bridge ( IYY8)

tirion Bridge, and hopefully of the Mil- lau Viaduct, will show the considerable interest in this type of solution, espe- The bridge spmning Lake Marocwibo in cially in larger projects l i e the Fern- Venezuela. Bauverlag. Berlin. 1963. belt Bridge between Gemany and the BOAGA, G.; BONI. G. The concreie archirer- Copenhagen Island. cure uf Riccwdo Morondi. Alrc Tiranti.

References

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GlMSlNG N. L Cable supported hridge,v: Con- eepr and design. John Wilcy & Sans. Chichester, 1983.

WITTFOfC H. Bridges BetonVerlag. DUssel- dorf, 19R4.

WALTHER, R. el al. Ponfs houbonds. Presses Polytechniqucs Romandes, Lausanne. lY86.

LEONHARDT, E Ponrs, Puenres Presses Poly- techniques Romandes. Lausanne. 19x6.

TROITSKY. M. S . Cable-sfoyed bridges. 2nd edi- tion. BSP Professional Books. Oxford, 19x8.

MORANDI. R Innovozione, Technologia, Prog- germ Gangcmi, Roma, 1991.

FREYSSINET. Cob/e-.myed bridger. Veliry-Vil- lacoublay, 1994.

The new, Mocau-Toija Bridge: the friendship bridge. Port and Bridge Ofice. Macau, 1994.

HOLGATE. A. The work of Jijrg Schlnich and his ream. Axel Mendcs, Stuttgan and London. 1997.

VIRLOGEUX M. Pmfs d hauhuns d rravees mulripler Progrks dans la conception des ou- wages d'art en beton. Journers detudes SIN GPC en I'honneur du 6S'" anniversaire du Pro- fesseur Renaud Favre. SIA DO160 Zurich. 1999.

SCHLAICH, 1. Conccptua/ Oaign of Bridges: More Varieiy! Bridge Engineering Conference. S h r m El Sheikh. Z(U0.

SCHLAICH. J. Voriery in Bridgp Design. Trends in Bridge Design (Conference). Madrid. 2NM.

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