Bridges with Multiple Cable-Stayed Spans

Michel VIRLOGEUX Michel Virlogeux, born 1946,Consulting Engineer and Designer worked as civil servant in Tunisia

President of fib (1970-1974) and then in France atBonnelles, France the SETRA. Head of the large

bridge division (1980-1994), hedesigned many bridges amongwhich the Normandie Bridge andthe Ré Island Bridge. NowConsulting engineer, he workedas consultant for the PortugueseAdministration for the Vasco deGama bridge.

Summary

This paper is devoted to a very important development of cable-stayed bridges, bridges withmultiple cable-stayed spans. Beginning with historical reference to pioneer bridges by RicardoMorandi, it evokes the very few bridges built with several cable-stayed spans and the projectswhich were proposed without success. It ends with the presentation of recent and importantprojects which evidence the possibilities of this new concept for wide river and sea crossings.

1. Historical background

As everyone knows, the first attempts to erect cable-stayed bridges in the beginning of the 19thcentury were unsuccessful with the collapse of the Tweed and Saale bridges; engineers ignoredat the time the real flow of forces and did not seriously consider wind effects even with asimplified and purely static approach. The famous French scientist Navier "demonstrated" thatcable-stayed bridges were unsafe and that suspension bridges were to be preferred. This stoppedthe development during a very long time, and cable-stays were only used in some suspensionbridges close to the pylons to stiffen the system; the best example is the Brooklyn Bridge, butmany others could be cited. In France, at the turn of the century, Gisclard increased the role ofcable-stays in his personal composite design associating suspension and cable-staying. The firstvery pure cable-stayed bridge has been built in Spain by Eduardo Torroja in 1925, in concrete, acable just replacing a pier which could not be installed due to the site.

But the real and scientific development of cable-stayed bridges came with the ideas and thepapers by Franz Dischinger in the late thirties and beginning forties. Surprisingly, the firstapplication was in France by Albert Caquot, in 1952 and in reinforced concrete, for the bridgeover the Donzère Canal, some years before the well-known Stromsund bridge in Sweden.Everyone knows the fantastic development of cable-stayed bridges which followed, in Germanyin a first step and in the whole world later.

But in the same time as the concept of modern cable-stayed bridges was being developed, with "flexible"pylons and a continuous deck - and later with multiple cable-stays following Helmut Homberg, totalsuspension initiated by Fritz Leonhardt and very flexible decks developed by René Walther and JorgSchlaich - Ricardo Morandi developed his own concept in a different direction, with extremely rigidpylons (inverted V shape longitudinally, with an additional V to support the deck), rigidly connected to adeck section cantilevering on both sides, and with simply supported spans to close bays between thedifferent cantilevers tied to their pylons. The first application of this concept was the Maracaibo Bridge,designed by Morandi and completed in 1962, with six pylons and five main cable-stayed spans 235 metres

long (figure 1). The same principle was used by Morandi, but with two pylons only, for the Wadi KufBridge in Libya (main span 282 metres in 1971), and for the Polcevera Creek viaduct near Genoa in Italy,with three pylons and two main cable-stayed spans (208 metres in 1964). It has been reproduced onlyonce by another designer for the Chaco Corrientes Bridge in Argentina with two pylons (245 metres in1973).

Figure 1 - Structural concept of the Maracaibo Bridge

2. The specific problem of multiple cable-stayed spans

As we shall see, the concept of Morandi's bridges is perfectly adapted to the specific problem ofbridges with multiple cable-stayed spans. Though evident, these problems must be evoked.

2.1 In a classical cable-stayed bridge with three spans, loading the main span produces itsdownwards deflection and due to the tension variation in cable-stays the pylons bend towards the loadedspan; the cable-stays which suspend side-spans receive a tension variation to balance horizontal forces inthe pylons but due to the limited rigidity of the deck it deflects upwards and tension variations areconcentrated in the backstays, anchored at the abutment and which have anchorages fixed vertically due

Figure 2 - Structural behaviour of a classical three-span cable-stayed bridge

to their position (figure 2). This unequal distribution of tension variations in the cable-stays whichsuspend the side-spans produces important bending forces in the pylons: the backstays, anchored on top,balance alone the tension variations in the cable-stays suspending the main span. This is why it isnecessary to concentrate cable anchorages when the cable-stayed bridge has this classical configuration:the reduction of the distances between anchorages in the pylons reduces the bending moments.When a side-span is loaded, it deflects downwards, and due to the tension variation in the correspondingcable-stays, the adjacent pylon deflects towards the loaded span; thus the tension decreases in thebackstays and in the same time the main span deflects upwards.The backstays have a very specific role to stabilize the pylons, and receive the largest tension variations inthe bridge.We have the same situation with cable-stayed bridges continuously extended by access spans on bothsides, where the group of cable-stays anchored close to the first pier on each side acts as backstays; andwith cable-stayed bridges having two spans, one shorter with the backstays anchored at the correspondingabutment.

2.2 As demonstrated in many occasions, for example for the Seyssel Bridge (Travaux, October, 1988),the design of classical cable-stayed bridges can be improved by the installation of intermediate supports inthe side-spans: when the main span is loaded, all cable-stays anchored in the side-spans act as backstayssince they are tied to an almost fixed deck at their lower anchorage; the deflection of pylons towards theloaded span is thus reduced and the efficiency of cable-staying increased; even the downwards deflectionsof the main span is reduced by the greater rigidity of the system. And when side-spans are loaded, theload directly passes in the intermediate supports and there is practically no effect in pylons and main span.The same of course applies to a cable-stayed bridge with two spans, when intermediate piers are installedin the shorter one.

2.3 If we consider now a bridge with multiple cable-stayed spans, the situation is very different.When one span is loaded, it deflects downwards; the corresponding cable-stays receive an increasedtension; the adjacent pylons deflect towards the loaded span and the adjacent spans upwards without anyother restraint than their own rigidity. There is no more any backstaying effect (figure 3). Deflections canbe only limited by the rigidity of pylons or deck, or of pylons and deck.

Figure 3 – Structural behaviour of a bridge with multiple cable-stayed spans

The situation appears even more critical with the effects obtained when loading one of the adjacent spans:the span which was deflecting downwards with the load now deflects upwards with large bendingmoments, and the adjacent pylons deflect in the opposite directions.

2.4 The design must produce the necessary rigidity. One of the possible solutions consists in rigidlyconnecting the pier below the pylon, the deck and the pylon, so that the pier rigidity takes part in therestriction of deflections. But this immediately produces a new problem: the structural system must adaptto the length variations in the deck due to the elastic shortening produced by prestressing forces installedafter span closure, to temperature variations and also to concrete creep and shrinkage.

3. The Morandi's concept

3.1 Clearly the concept developed by Ricardo Morandi perfectly answers the different questions: thepylons are extremely rigid and can directly balance the effects of live loads on either sides; and with thesimply supported spans between the cantilevers supported by the pylons, length variations can freelydevelop. The single drawback of this solution is its high cost and weight; this is why - though it must beconsidered as the pioneer one for multiple cable-stayed spans - it has not been reproduced.

3.2 But it inspired many designs, though none of them received an application.- We can mention the project proposed in 1967 by Ulrich Finsterwalder for the Great Belt Bridge, withsolid and rigid pylons suspending a series of spans 350 metres long, with a very flexible deck andexpansion joints at mid-span in each bay ([5] p. 38; [7] pp. 17-20-33; [9] p. 142).- And also the project for a bridge across the river Ganges in India, designed by Fritz Leonhardt withten pylons and nine central spans 159 metres long. Pylons were also solid and rigid, allowing for alimitation in the number of expansion joints, only in some spans ([4] pp. 28-42-45; [7] pp. 33-34).More recently, the Grands Travaux de Marseille - GTM- developed two important projects which had nomore success than the previous ones for the Great Belt and the River Ganges.- The first one is part of the GTM Channel Project prepared in the early eighties, which comprised abridge on each side of the Channel to give access to a central immersed tunnel. Each of these bridges wasmade of a series of complete cable-stayed cantilevers - composite deck rigidly connected to the concretepylon, and cable-stays -, totally prefabricated and installed with the help of heavy floating cranes on thecorresponding piers; the cantilevers were joined by drop-in spans to constitute a series of typical spans520 metres long. This project was in the same time a prefiguration of the Rion-Antirion conceptualdesign, and one of the first attempts to develop heavy prefabrication techniques which received largeapplications later with the Storebelt Western Bridge, the Second Severn Crossing and the ConfederationBridge in Canada.- The second one, very much inspired from the Channel project, has been jointly proposed by GTMand Campenon-Bernard for the Ré Island Bridge in 1986. The same concept was used of complete cable-stayed cantilevers - totally in prestressed concrete this time -, prefabricated and installed on the piers. Butwith spans limited to 140 metres, the cantilevers were only joined by expansion joints at mid-span in eachbay. The cross-section of the deck, proposed by Jean Muller and inspired from a previous idea by PierreXercavins, consisted in a flat slab stiffened by multiple floor-beams and with side walks at a lower levelto produce the desired rigidity; we developed and applied this concept for the Burgundy Bridge at Chalon-sur-Saône (Travaux, October, 1991 and July-August, 1992).- GTM came back to these principles and very close to Morandi's ideas with the conceptual design ofthe Rion- Antirion bridge, developed in the late eighties by Jean-Paul Teyssandier, François Lempérièreand Yves Maury's team. The bridge is made of four cable-stayed cantilevers, each resting on a largefoundation caisson which constitutes a pier in the same time, and of simple spans between the cantilevers.Each cantilever consists in a four-legged pylon, rigidly connected to the composite deck, and of twocantilever arms, 255 metres long from the pier axis. Each central span, 560 metres long, is made of twocantilever arms - coming from the two adjacent pylons - and of a simple span 50 metres long. Each side-span is made of one cable-stayed cantilever hanging from the corresponding pylon, also 255 metres long,

Figure 4 – The peliminary design of the Rion-Antirion Bridge

and of a single span 50 metres long to join the cantilever with the end support (figure 4). The soledifference with Morandi's design is that the cantilever - with its pylon - is not rigidly connected to the pierbelow; to reduce seismic forces, the cantilever is installed on sliding bearings with a system of largedampers in both directions - longitudinal and transverse - to limit seismic movements. We shall see laterhow this initial concept has been amended and improved for a much better design.

4. Typical solutions

4.1 Some other solutions than the Morandi's concept can be considered, though many of them are notextremely elegant (figure 5).

4.2 One consists in introducing an intermediate support at mid-span in every second span. Of coursethis is not always possible, and this is certainly the weakest way to introduce the necessary rigidity.Fortunately, nobody dared doing it.

4.3 The second solution is inspired from suspension bridges, which are even less adapted to the conceptof multiple spans than cable-stayed bridges. To prevent pylons from bending towards the loaded spans,they are connected from head to head by horizontal cables, headcables ("câbles de tête" in French).Several French bridges built in the first half of the century have several suspended spans with such head-cables ; we can cite the bridges at Châteauneuf-sur-Loire, Langeais …The same could be done for cable-stayed bridges, though this solution is probably not so efficient as forsuspension bridges since the structural rigidity of cable-stays is greater ; the additional effects of head-cables may be more limited. In addition this does not look so elegant, with the introduction of a new linein the structure, reducing the architectural simplicity. A unique project referred to this technique, thewinning design of the Poole Harbour competition, but construction is not yet decided.

4.4 A third solution consists in introducing, in addition to the classical cable-stays distributed to carrythe deck loads, diagonal cable-stays which are only installed to stiffen the pylons; a typical diagonal cableis anchored on top of a pylon and at the deck level in one of the two adjacent pylons. Once again, thissolution introduces a new line in the structure, reducing the architectural simplicity. It has been adoptedby Jorg Schlaich for the design of the Ting Kau Bridge in Hong Kong. Since it has only three pylons andtwo central cable-stayed spans, only the central pylon had to be stabilized by diagonal cables of this type.

The composite deck is supported on the piers by classical bearings so that length variations can easilydevelop.Almost the same idea consists in installing cable-stays from each pylon beyond the mid-span section ofthe two adjacent spans; the central part of each bay is thus suspended from both adjacent pylons. But thiscan be efficient only if the deck has a rather large rigidity.

4.5 Fritz Leonhardt proposed a last solution many years ago ; it consists in amending the distribution ofspans with a longer and a shorter one for each group of two. With a ratio of about 0.90 to 1.10 or 0.85 to1.15, the shorter span stiffens the longer one. But this system also has serious drawbacks ; the differencesin span lengths and in the distribution of stays, is not so elegant, and in addition the distribution ofpermanent loads is not well balanced, calling for serious amendments.The Macau Bridge - designed by José Luis Cancio Martins with two central cable-stayed spans 112metres long - can be related to this concept ; with two pylons and a very short span between the two mainspans, it works like two successive and independent cable-stayed bridges and cannot be considered as areal reference for bridges with multiple cable-stayed spans. It has been completed in 1994 ([11] p. 52;[12]).

Figure 5 – A series of more or less acceptable solutions for multiple cable-stayed spans

5. Distribution of rigidities

5.1 Finally, the best solution appears to be the research of an adapted distribution of rigidities betweendeck, piers and pylons to resist bending forces and limit deflections (figure 6). From one extreme to theother, several solutions can be considered :

- on the one hand, we can have a very rigid deck and flexible pylons on condition that spans are not toolong. Then the deck can be simply supported on the piers with pylons rigidly connected to the deck forsimplicity.- Rigidity can be distributed between piers, deck and pylons with a careful attention to the deck lengthvariations.- And on the other hand, we can have a very flexible deck on condition to have rigid pylons, either bytheir shape (an inverted V, longitudinally) or their dimensions. Of course, bending moments must passfrom pylons to piers, either through two lines of bearings to adapt to length variations or with a rigidconnection between pylon and pier on condition that the design of piers adapts to the deck lengthvariations.

Figure 6 – Distribution of rigidity between piers, deck and pylons

5.2 As already mentioned, length variations are produced in the deck by the elastic shortening inducedby prestressing forces installed in the structure after the span closure, by temperature variations and byconcrete shrinkage and creep. The design must be such that they can develop almost freely. Threesolutions can be proposed (figure 7).- The first one consists in installing between piers and deck special bearings, sliding except on one, two orthree central piers - the number depending on the piers flexibility - where fixed bearings can beintroduced. There may be only one line of bearings on each pier if the deck is extremely rigid as alreadyshown (paragraph 5. 1) but there must be two lines of bearings to take advantage of the piers rigidity.This solution is not so simple due to two different problems: if the bridge is very long, the displacementsproduced by length variations produce load eccentricity (the deck and pylons move on the piers andreceive excentered reactions) ; and due to the heavy loads on the supports, friction on sliding bearings canproduce important bending forces in high piers.- The second solution is more efficient and more elegant. It consists in producing a rigid connectionbetween the deck - which may be rather flexible - and piers made of two flexible parallel shafts. Suchpiers are extremely rigid as regards rotations, but rather flexible as regards length variations in the deck.This concept of twin flexible shafts was developed by Jacques Mathivat in the early sixties.

Figure 7 – Solutions to allow for length variations with rigid piers

- The last solution consists in introducing an expansion joint in some - few - spans. But to avoid anincrease in vertical deflections, the continuity of bending moments can be restored by introducing a steelcontinuity beam in the deck (figure 8) ; as done for example by Jean Muller for the Rogerville viaduct, arather classical prestressed concrete box-girder bridge. But this is possible only with a box-girder deck ofrather large dimensions, just to leave the necessary place.

Figure 8 – A continuity beam to transfer bending moments through a joint

5.3 Though some of these ideas already appeared in one or two early projects, such as twin flexibleshafts, no real application was made of this global concept.

5.4 We can only mention that after the first competition for the Storebelt crossing another project wasproposed in Denmark for the Samso Belt, in 1972, this time with a continuous deck ; the project had fourspans 264 - 624 - 624 and 264 metres long ([5] pp. 313-314). The lateral pylons were stabilized bybackstays but the central one had to receive a very large rigidity. Of course - and as for almost all the otherbridges which will be evoked in this paragraph - the situation is extremely favourable with only fourspans.

5.5 Since this time some medium-span cable-stayed bridges have been built, almost unnoticed, withseveral cable-stayed spans.

The first one is the Kwang Fu bridge in Taiwan, designed by T.Y Lin and completed in 1978 ([11] p. 10).It has three pylons and two central cable-stayed spans, 134 metres long ; pylons have classical shapes anda limited rigidity ; the effects of traffic loads are balanced by bending forces in pylons and deck - whichhas a rather large flexural rigidity as compared to the span - and also by the side-spans with cables actingas backstays due to the high deck rigidity. These backstays control the deflection in the lateral pylons,only the central pylon being really flexible. Such a design has been reproduced in Spain for the ColindresBridge completed in 1993 with three pylons again and two central spans 125 metres long ([11] p. 49). Butthe most important application has been for the construction of the Mezcala Bridge in Mexico, still withthree pylons and two main spans 312 metres long, completed in 1993 ([11] p. 44). Due to some specificsite conditions controlling the distribution of spans, the central pylon is taller than the lateral ones, as inthe Ting Kau Bridge.We must insist on the favourable situation of these bridges with only three pylons and two central cable-stayed spans. This is only an intermediate step between classical cable-stayed bridges with two pylons anda central span and the real multispan cable-stayed bridges. The single application of really multiple cable-stayed spans is the Arena viaduct in Spain, designed by Juan José Arenas and completed in 1993, with sixpylons and five central spans, 105 metres long ([11] p. 48). But the reduced span length limits the rigidityproblems in this bridge and prevents learning much from its design: the classical rigidity of deck andpylons is perfectly adapted to the forces in such spans.We must add that in all these bridges - Kwang Fu, Colindres, Mezcala and Arena - the deck is supportedon the piers with classical bearings to adapt to length variations.

6. Geneva and Millau

6.1 Two very large projects developed in the nineties produced a gigantic step forward, for the Millauviaduct over the River Tarn valley, and to cross the Lake of Geneva. We developed the concept for theMillau viaduct in 1990-1991 but the design remained preliminary until 1993, due to the many obstaclesmet by the project. Jean- François Klein and Pierre Moia took inspiration from it to design a bridge acrossthe Lake of Geneva in a project competition which they won ; they developed in 1993-1994 an excellentproject with a completely detailed design. Being in the jury of this competition, we have taken inspirationfrom their project for the later development of the design of the Millau viaduct so that these projectshelped each other as it happens frequently.

Figure 9 – The bridge designed to cross the Lake of Geneva

6.2 The Pont de la Rade in Geneva has four pylons and three central spans 350 metres long. It has aslightly curved alignment for the bridge elegance (R = 900 metres). The deck is extremely wide, 33.46metres. Its design is specially elegant, balancing rigidity between a relatively slender deck (an elegantstreamlined box-girder, 3.50 metres deep) and rather rigid piers and pylons (figure 9). Length variations,produced by temperature, shrinkage and creep are permitted by the relatively limited distance between thecentral point and the extreme pylon but also by soil conditions. Unfortunately a general votation isnecessary in Switzerland to build very large structures and the Geneva population voted against theproject for financial reasons.

6.3 The Millau viaduct is even more ambitious; almost 2.5 kilometres long, it comprises seven pylonsand six central spans 342 metres long with two piers about 240 metres tall. The development of theproject has been extremely complex, with an initial design by the SETRA and two design competitions, arather informal one in 1993 and a more formal one in 1995-1996. Five teams of engineers and architectswere constituted for this second competition, from the result of the first one and each in charge ofdeveloping a different type of solution. The cable-stayed solution with multiple spans, developed from ourconceptual design by SOGELERG - Europe Etudes Gecti - SERF and the British architect Sir NormanFoster, was selected in July, 1996 and we developed the project with this team between the end of 1996and September, 1998.

Figure 10 – The Millau viaduct (prestressed concrete solution)

Two alternatives are proposed, the deck being either in prestressed concrete or in steel with almost thesame design adapted to the specific conditions of multiple cable-stayed spans and to the extreme windforces due to the high position of the bridge in the valley. The rigidity is distributed between the deck,piers and pylons. The deck is a trapezoidal box-girder with a rather narrow bottom flange so that it isalmost triangular; it is about 4.50 metres deep. The pylons, 90 metres tall, have the shape of inverted Vfor a very high rigidity. The design of piers is more complex since the taller ones have to resist importantforces due to wind and to second order effects ; and the extreme ones - about 90 metres high - must adaptto very important length variations due to the bridge size (about ± 0.80 metres). As soon as in 1992-1993,

with Emmanuel Bouchon we decided to have these extreme piers made of two parallel, flexible shaftswith a unique line of fixed bearings on top of each to increase their flexibility.The architect later preferred to have the same design for all the piers; this led to the final design of solidpiers which divide into twin shafts in the upper part, 90 metres high (figure 10).This very elegant bridge will be built - if decisions taken are applied - in the years to come with aconcession.

Figure 11 - The four pylons of the Rion-Antirion Bridge

7. Total suspension

7.1 A last idea must be evoked to complete this overview : the total suspension concept. It has beeninitiated with the Pasco Kennewick bridge and soon after for the Alex Frazer Bridge in Canada. It mustbe clear that it adapts very well to the concept of multiple cable-stayed spans since it allows for freelength variations without any interference with the rigidity of piers and pylons.This concept has been proposed by Bouygues and Pierre Richard for the Ré Island Bridge in 1986. Theyproposed a cable-stayed bridge with a continuous deck, almost 2800 metres long and with a series ofcentral spans 210 metres long. Unfortunately, just after the successful construction of the Bubiyan Bridgeand at a time when the Syllans and Glacières viaducts were to be built, Pierre Richard preferred for thedeck an expensive three-dimensional prestressed concrete truss the cost of which eliminated the solution.The deck was totally suspended from the pylons to adapt to longitudinal length variations - concrete creepand shrinkage, elastic shortening produced by prestressing tendons installed after span closure and effectsof temperature - in complete opposition with the solution proposed for Millau and Geneva. Traffic loadswere perfectly balanced by the large flexural inertia of the three dimensional truss which constituted thedeck, and very classical, almost slender pylons could be designed in this situation.

7.2 This is why, when Jacques Combault asked for our opinion on the design of the Rion-AntirionBridge, we suggested to have a continuous deck, totally suspended from the four pylons. The concept hasbeen immediately adopted and developed with many advantages as compared to the initial design :continuity, a regular distribution of cable-stays in the spans to perfectly balance loads... Rigidity this time

comes from the pylons, made of four legs with an inverted V-shape in both directions ; the compositedeck is rather flexible. The final project, now being detailed by GTM and Ingerop, has a continuous deckwith five spans, 286 - 3 x 560 and 286 metres long; and pylons are rigidly connected to the piers, a muchmore comfortable situation than installing a cantilever on sliding bearings and dampers (figure 11).

Figure 12 – The final design of the Rion-Antirion Bridge

8. Conclusion

As evidenced by this survey, cable-stayed bridges with multiple spans might develop rapidly in thecoming years, specially if the Millau viaduct and the Rion-Antirion bridge are erected as expected,evidencing the enormous capacities of this new structural type.

Literature

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New York. 1976.[5] Gimsing N.J. Cable-supported bridges. Concept and design. John Wiley and Sons.

Chichester. 1983.[6] Wittfoht H. Bridges. BetonVerlag. Düsseldorf. 1984.[7] Walther R. and als. Ponts haubanés. Presses polytechniques romandes. 1985.[8] Leonhardt F. Ponts. Puentes. Presses polytechniques romandes. 1986.[91 Troitsky M.S. Cable-stayed bridges (second edition). BSP Professional Books. Oxford. 1988.[10] Ricardo Morandi. Innovazione, tecnologia, proggetto. Gangemi. Roma. 1991.[11] Freyssinet. Cable-stayed bridges. 1994.[121 The new Macau-Taija Bridge. The friendship bridge. Port and Bridge office. 1994.