he number of cable stayed bridgeswith concrete or steel has increased

dramatically during the last decade. Ref. Ipresents a survey of some 200 cablestayed bridges that have been designed orbuilt throughout the world.

Although most of these bridges aremade of steel, many of them could havebeen designed with prestressed concrete.In fact, by using this material, the design,structural detailing and constructionmethod can be simplified, thus producinga bridge that is economically and aesthet-ically superior.

Unfortunately, there are many bridgeengineers today that do not fully under-

stand the basic principles of cable staybridge design and construction. The pur-pose of this article is to present the lateststate of the art on cable stayed bridgeswhile elaborating upon the fundamentalsand possibilities pertaining to such struc-tures. The text will cover highway, pedes-trian and railroad bridges using pre-stressed concrete.

1. Range of Feasibility of Cable Stayed Bridges

There are some misconceptions regard-ing the range of feasibility of cablestayed bridges. For example, the state-ment is often made that cable stayedbridges are suitable only for spans from100 to 400 in (about 300 to 1300 ft). Thisstatement is wrong. Pedestrian bridgeswith only about 40 in (130 ft) span can bebuilt to be structurally efficient and cost-

2

Special Report

T

Cable Stayed BridgesWith Prestressed Concrete

Fritz Leonhardt

Prof. Dr. Ing.Consulting EngineerStuttgartWest Germany

Note: This paper is based upon the KeynoteLecture presented by the author at the FIPCongress in New Delhi, India. February 16,1986, and a similar lecture, including steelbridges, at the Symposium on Strait Crossingsin Stavanger, Norway, in October 1986.

effective. Employing prestressed con-crete, the superstructure can be made veryslender using a few cable stays and a deckwith a depth of only 25 to 30 cm (10 to 12in.).

Highway bridges can be built of pre-stressed concrete with spans up to 700 in(2295 ft) and railroad bridges up to about400 in (1311 ft). if composite actionbetween the steel girders and a concretedeck slab is utilized, then spans of about1000 and 600 in (3279 and 1967 ft) forhighway and railroad bridges, respective-ly, can be attained safely.

For the crossing of the Messina Straitsin Italy (see Fig.1), our firm designed anall-steel cable stayed bridge with a mainspan of 1800 in (5900 fit) for six lanes ofroad traffic and two railway tracks with-out encountering any structural or con-struction difficulties.

Many bridge engineers believe that forspans above 400 in (1311 ft), a suspen-sion bridge is preferable. This assump-tion is false. In fact, a cable stayedbridge is much more economical, stifferand aerodynamically safer than a com-parative suspension bridge. The author

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Based on his more than 50 years of experience as aconsulting engineer on specialized structures, theauthor presents a state of the art report on prestressed concrete cable stayed bridges withauthoritative advice on the design-construction intricacies involved with such structures.

Fig. 1. Messina Straits Bridge, linking Sicily and Italian peninsula; design by GruppoLambertini (1982).

showed this was true as early as 19721

In designing a cable stayed bridge thereis first the problem of finding the requiredquantity of high strength steel for thecables. For a bridge with a 1800 m (5902ft) main span and 38 m (125 ft) width, asuspension bridge needs 46000 t (50700tons) of steel whereas a cable stayedbridge only needs 19200 t (21170 tons) ofsteel (see Fig. 2). In the latter case thisrepresents only about 40 percent theamount of steel.

Furthermore, a suspension bridge needsa stiffening girder with a bending stiffness

which must be about ten times larger thanthat of the cable stayed bridge. The sus-pension bridge needs additional heavyanchor blocks which can be extremelycostly if the navigation clearance is highand foundation conditions are poor. Thetotal cost of such a suspension bridge caneasily be 20 to 30 percent above the costsof a cable stayed bridge.

Currently, the second Nagoya HarbourBridge (in Japan), at 600 m (1967 ft), hasthe longest span of a cable stayed bridgein steel. This structure, whichwasdesigned by Dr. Ing. Kunio Hoshino (a

4

Fig. 2. Comparison of quantity of cable steel for suspension bridges and cable stayedbridges.

former student of the author), is nowunder construction. When completed, itwill look similar to the first NagoyaHarbour Bridge (see Fig.3). The author isconfident that in the near future similarsuch spans will be built using prestressedconcrete.

Range of span is only one importantparameter in designing cable stayedbridges. Special situations such as curvedspans and skew crossings can be easilysolved using stays.

The engineer can choose between alarge variety of configurations: symmetri-cal spans with two towers, unsymmetricalspans suspended from one tower, ormulti-spans with several towers inbetween. This is an ideal field for cre-ativeness in design to satisfy the function-al requirements of the project and toobtain an aesthetically pleasing structurewhich complements the environment.

2. The Main GirderSystem2.1 Development of multi-staycable system

Some of the first cable stayed bridges(like the Maracaibo Bridge) had only one

cable at each tower (see Fig.4), leavinglong spans requiring a beam with largebending capacity. Soon three to fivecables were used, decreasing the bendingmoments of the beam and the individualcable forces to be anchored. However,structural detailing and construction pro-cedures were still difficult.

The desired simplification was obtainedby spacing the cables so closely that sin-gle cables with single anchor heads weresufficient which could easily be placedand anchored. The spacing became only 4to 12 in (13 to 39 ft), allowing free can-tilever erection without auxiliary cables.Simultaneously, the bending momentsbecame very small, if an extremely smalldepth of the longitudinal edge beams andvery stiff cables were chosen.

This multi-stay cable system can nolonger be defined as a beam girder.Rather, it is a large triangular truss withthe deck structure acting as the compres-sive chord member. The depth of the lon-gitudinal beams in the deck structure isalmost independent of the main span, butit must be stiff enough to limit local defor-mations under concentrated live load andto prevent buckling due to the large com-pressive forces created by the inclinedcables.

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Fig. 3. Nagoya Harbour Bridge, Japan.

The stiffness of this new system de-pends mainly on the angle of inclinationand on the stress level of the cables. Fig. 5shows the enormous influence of thestress in such cables on the effective mod-ulus of elasticity. Low stresses give a largesag and low stiffness. The stress in thecables should be at least 500 to 600N/MM2 (72500 to 87000 psi). For longspans, stiffening ropes (as shown in Fig.6) are needed to prevent an excessivechange of sag. The simplification of thestructural design and of the erectionprocess gained by this multi-stay cablesystem should be used whenever suitable.

2.2 Arrangement of stay cables

If all the cables are anchored at the topof the tower, the structural system iscalled a fan-shaped configuration (seeFig.7). Unfortunately, the concentrationof the anchorages causes structural diffi-culties when the number of cables is large.Therefore, it is preferable to distribute the

anchorages over a certain length of thetower head and get a semi-fan arrange-ment (as shown in Fig.8), which alsoimproves the appearance of the bridge.

In the author’s early bridges across theRhine River in Dusseldorf, the architectwanted to have all the cables parallel andthe anchorages equally distributed overthe height of the tower. This is called theharp-shaped arrangement (see Fig. 9). Thesystem requires more steel for the cables,gives more compression in the deck andproduces bending moments in the tower.However, the structure is aestheticallypleasing, especially when looking at thebridge under a skew angle. Dr. UlrichFinsterwalder, the world renowned bridgeengineer, prefers this harp arrangementwith many closely spaced cables. Such ascheme was chosen for the Dame PointBridge in Florida (see Fig.10), with amain span of 396 m (1298 ft), which isnow under construction.

In these multi-stay bridges, the deck ishung up with cables near the tower

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Fig. 4. Development of structure to multi-stay cable bridge. Note that additional cablesallow beam of superstructure to be progressively more slender.

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also, to avoid a stiff bearing at the tower.This could cause very large negativebending moments which might be unac-ceptable for the small depth of deck gird-er used.

Normally, the bridge is supported bycables in two planes along the edges ofthe deck. In some cases (mainly for medi-um spans), cables in one plane are usedalong the centerline of the deck. A boxgirder with sufficient torsional rigidity isthen needed which requires some depth sothat it can also resist the large bendingmoments. Such a girder must be support-ed at the tower to resist torsion and as aconsequence the cables can begin at a cer-tain distance from the tower, leaving a“window” in the cable net open. TheBrotonne Bridge in France is such an

example (see Fig.11).Of course, other cable configurations

are possible, depending on local condi-tions, like very short side spans. A har-monic arrangement of cables is importantfor good appearance and it should be cho-sen with care and diligence.

2.3 Ratio between main andside spans

The ratio between side span l1 and mainspan l has an important influence on thestress changes in the back stay cableswhich holds the tower back to the anchorpier. Live load in the main span increasesthese stresses whereas live load in the sidespan decreases them. These stresschanges must be kept safely below the

8

fatigue strength of the cables. This fatiguestrength is a criterion for the allowableratio l1/l, which depends mainly on therelation between live and dead load, p to g.

Prestressed concrete bridges allowlonger side spans than steel bridges. Theauthor has published charts in a state ofthe art report for IABSE (1980) fromwhich suitable ratios can be read. For con-crete highway bridges l1/l can be about0.42; for railway bridges the ratio shouldnot be larger than 0.34. The ratio decreas-es with the span length. The magnitude ofthe anchorage forces at the anchor pieralso depends on the ratio l1/l. In particular,short side spans give large anchorageforces.

If there is no need for large free sidespans, then a rather heavy continuousbeam bridge with spans of about 40 m(131 ft) can be used as a long anchoragezone in which all cables act as back stays

and concentrated vertical anchorageforces can be avoided (see Fig.12). Thissolution is especially advantageous if avery long span is hung up to one tower.

If only a short or even no side span ispractical, then the back stay cables can beground anchored over a certain length oreven be joined in an anchor block. Thishas been done for the C. F. CasadosBridges in Spain, the Barrios de LunaCrossing (see Fig.13) which at 440 m(1443 ft) is currently the longest span ofprestressed concrete, and the Ebro Bridge(see Fig.14) which has an inclined towerand back stay cables spreading sidewiseinto two planes, giving a most interestingimpression from the highway.

The inclination of the tower backwardsmakes the main cables longer, the back-stay cables shorter and steeper. There isno technical or economical advantage inthis but a more thrilling appearance. A

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10

forward inclination of the tower towardsthe main span produces uneasy anduncomfortable feelings. Towers shouldnormally be vertical.

3. Optimal Height, Shapeand Stiffness of the Towers

The cable forces and the required quan-tity of cable steel decrease with the heightof the tower above the road level (seeFig.15). A good range is between 0.2l and0.25l. For bridges with only one tower theheight must be related to about 1.81.Towers of cable stayed bridges must behigher than those for suspension bridgeswhich usually have h/l = 0.10.

The height of the tower also defines theangle of inclination of the longest cables.This angle should not be smaller thanabout 25 degrees because otherwise thedeflections will become too large.

In the longitudinal direction the towers

should be slender and have a small bend-ing stiffness, in order to avoid large bend-ing moments to be reacted by the founda-tions. If the soil conditions are poor, thentowers can even be hinged at the foot andfixed only dwing erection. The towers ofsome of the author’s Rhine River bridgeshave such foot binges. Towers should bebuilt of concrete because concrete towersare much cheaper than steel towers.

The shape of the towers can be verysimple. Even for large spans up to 500 in(1640 ft), free standing tower legs may besufficient if they are fixed and transverse-ly connected in the foundation only [ seefor example the Kniebrucke in Dusseldorf(Fig.16)]. No transverse bracing is neededif the cables are in a vertical plane and ifthe cross section of the tower is unsym-metrical with most of the load carryingarea close to the bridge deck (see Fig.17).This arrangement brings the center ofgravity close to the plane of the cables andstill gives much transverse bending stiff-

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ness to carry the wind reactions to thefoundation. Such tower legs should betapered in both directions. Modem climb-ing forms allow this tapering withoutmuch extra cost.

The bridge deck with the railings shouldrun clear through the tower legs and thecable anchorages should be close to therailings; therefore, very slender towershafts become desirable. If the semi-fancable arrangement is used, then one ortwo transverse bracings between thetower legs are suitable (see Fig.18). Thebracing above the road level should beslender and look light between the thincables.

For very long spans and especially inregions with strong wind forces, theAshaped tower is the optimal solution forappearance and wind stability (seeFig.19). In high level bridges, the towerlegs can be joined under the deck level inorder to combine the foundations. TheFarb Bridge in Denmark was designed insuch a way. These A-shaped towers withthe cables sheltering the highway give afeeling of safety to the motorist and anexciting and pleasing view (see Fig. 20).

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Fig. 16. The slender free standing towes of Kniebrücke in Düsseldorf, West Germany.

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For bridges with cables in one plane it isbest to design a slender single tower in themedian strip and to protect the cables andthe tower with strong guardrails (see Fig.21) as was done for the Rhine Bridge inBonn, the Brotonne Bridge in France, theSunshine Skyway Bridge in Tampa,Florida and other bridges. Tower shapesfor such bridges are shown in Fig. 22.

4. Development of CrossSection of Deck Structures

The cross section which the authorselected in 1972 for the first long span

cable stayed bridge using precast pre-stressed concrete, namely, the Pasco-Kennewick Bridge (see Fig. 23) over theColumbia River in Washington State wasinfluenced by the wind tunnel tests con-ducted at the NPL of Ottawa (1968).These tests were done to find the optimalaerodynamic shape for the author’s designof the Burrard Inlet Bridge in Vancouverfor a span length of 760 m (2492 ft).

The wind nose and the slight inclina-tion of the bottom face gave the lowestwind coefficients and, therefore, thebest provision for wind stability.However, during the design of the Parana

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Fig. 20. View of A-shaped tower as motorist approaches bridge. There isan inherent feeling of comfort and safety.

Bridges in Argentina for highway plus rail-way traffic, it was conceived that this aer-dynamic shape was useless when 400 m(1311 ft) long freight trains were on thebridge. Through dynamic tests it waslearned that multi-stay cable bridges havevery strong damping coefficients and donot need the same good aerodynamic shapeas suspension bridges do. Therefore, thecross section could be simplified further.

The following can be concluded:For spans up to about 150 m (492 ft)

and for widths up to about 20 m (66 ft), avery simple solid concrete slab without anedge beam is the best solution (see Fig.

24). The thickness of the slab depends pri-marily on the transverse bendingmoments which can be increased towardsthe towers to respond to the increasinglongitudinal normal forces.

Dr. Finsterwalder had proposed suchslender slabs as early as 1967 for hisdesign of the Great Belt Bridge and lateralso for the Pasco-Kennewick Bridge. Thethickness of the slab was so small in rela-tion to the span that the safety againstbuckling under high longitudinal com-pressive forces was subsequently ques-tioned especially in the case of highdeflections under concentrated live load

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Fig. 21. Tower in median of Rhine Bridge in Bonn-Nord,West Germany.

16

and the possibility that one cable couldbreak in an accident.

This buckling safety was meanwhilestudied by Professor Renee Walther inLausanne, Switzerland. Second order the-ory calculations were checked by testswith a relatively large model. Bucklingsafety could now be checked reliably. Itwas found that a certain amount of longi-tudinal reinforcement is required forobtaining sufficient ductility in such thinslabs.

Professor Walther became the first engi-neer to build a highway bridge 15 in (49ft) wide across the upper Rhine River inDiepoldsau with a slab only 50 cm (20in.) thick for a main span of 97 in (318 ft)with no edge beams (see Fig. 25). He evenreduced the slab thickness at the edges to36 cm (14 in.).

For wider bridges, B>20 in (66 ft),transverse T beams are, of course, moreeconomical (see Fig. 26). The spacing ofthe beams should not be larger than 4 to 6

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Fig. 25. Bridge across the Rhine at Diepoldsau, West Germany. Span = 97 m (318 ft).

Fig. 26. Cross section with transverse beams for width greater than 20 m (66 ft) andspans up to 500 m (1640 ft).

m (13 to 20 ft) and the slab on top shouldalways span longitudinally to make gooduse of the longitudinal compressive forcesfrom the cables. The cross beams can becast in place or prefabricated and end in athick edge beam with a depth of not morethan 1.0 to 1.5 m (3-2 to 4.9 ft), givingample buckling safety and keeping thecurvature of the deflection line under con-centrated loads within allowable limitseven for spans up to 500 m (1640 ft).

Such cross sections are especially suit-able for composite structures, using steelcross girders between concrete edgebeams which the author designed for theEast Huntington Bridge. Its 274 m (898ft) span hung up to one tower correspondsto a span of about 500 m (1639 ft) if sus-pended from two towers. In the proposeddesign (conducted by the author’s con-sulting firm) of the Sunshine SkywayBridge (see Fig. 27) in 1980, a 2 m (6.6 ft)deep steel edge beam was used to simpli-fy the erection process and to allow theuse of prefabricated deck slabs.

Soon thereafter, this type of section waschosen for the Annacis Bridge in Canadawith a main span of 465 m (1525 ft)together with some advanced details. Theproject was built in 26 months which isremarkable considering the structure is1000 m (3286 ft) long. This efficiency

shows the ease and simplicity of the erec-tion method.

In these composite structures, the con-crete must remain the main structuralmaterial. The deck slab has to carry thecompressive chord forces. If for very longspans these thrust forces become too largefor the normal deck slab, then its thick-ness should be increased towards thetower or a concrete edge beam should beadded. However, the steel section shouldremain small in order to avoid creep prob-lems.

If the bridge is hung up with cables inthe median only, then a box girder is need-ed. The cross section of the BrotonneBridge (see Fig. 28) has become a stan-dard for this type. The required amount oftorsional rigidity depends on the width ofthe deck and the length of the main span.Smaller cross-sectional areas of the boxmay often be sufficient and this wouldallow sections like that shown in Fig. 29,which is simpler to construct and has asmaller depth and simple cable anchor-ages.

For railroad bridges, especially for highspeed trains, large mass is needed to get agood dynamic behavior. Therefore, theDB - German Federal Railways - carry the40 cm, (15 in.) deep ballast over theirmodem bridges and prefer thick concrete

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Fig. 27. Cross section of Sunshine Skyway Bridge, Florida, showing composite structure(not built).

deck slabs. with high strength cables it isnot difficult and also not too costly tocarry such heavy dead loads over longspans (see Fig. 30).

Edge beams 1.5 to 2.0 m (4.9 to 6.6 ft)deep should be sufficient to satisfy deflec-

tion limits if the cables are not too flat.For very long spans and severe deforma-tion limits, a flat box section may beneeded (see Fig. 31). The cables of suchrailroad bridges should have angles ofinclination above 30 degrees.

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Fig. 28. Cross section of Brotonne Bridge, France, showing cables in the median.

Fig. 29. Stender cross section for cables in the median with simple anchorage (BrotonneBridge, France).

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5. Situation at the Endsof Cable Stayed Bridges

The sudden change from an elastic sup-port to a stiff support at the ends of theside spans causes large bending momentsand consequently a large angular changeof the deflection line (see Fig. 32). Theseangular changes are unacceptable for rail-road bridges.

The difficulties can easily be avoided ifthe edge beams continue with an increas-ing depth into a small approach span (seeFig. 33). The length and the bending stiff-ness of this smoothening transition spanmust be well designed to avoid largebending moments.

This transition span can also be used tocounteract the uplift forces of the backstay cables by its weight or even by ballastconcrete within its depth. It also allowsthe distribution of the anchorages for theback stays over a certain length behind theaxis of the anchor pier.

6. Cables and TheirAnchorages6.1 Cables and Their Protection

The cables are the most important mem-bers of this system. They must be safeagainst fatigue, durable and well protect-ed against corrosion - especially in an

aggressive environment. The best type ofcable must be chosen and not the cheap-est. It is unwise to save a few percent ofsteel and to later have to replace ropeswith broken or corroded wires after only 8to 12 years as was the case in theKohlbrand and Maracaibo Bridges.

Regarding the choice of cables, testresults and practical experience of morethan 30 years are available. The followingis the author’s opinion based on experi-ence and judgment,

There is no doubt that bundles of paral-lel wires or parallel long lay strandsdeserve preference due to their high andconstant modulus of elasticity. The quali-ty of the wires or strands must be wellcontrolled because very different qualitiesare on the market. Wires with a diameterof 7 mm of St 1470/1670 N/mm2 are gen-erally used, the number of wires per cablecan be 337, giving a maximum ultimateforce of Pu = 21.7 MN or 2170 tons.Applying the rather high factor of safetyof 2.2, the allowable cable force is aboutP ≈ 10.0 MN or 1000 tons. It would bebetter to choose a lower safety factor, i.e.,1.7, but instead refer it to the 0.2 percentyield strength.

Strands are available of St 1500/1700N/mm2 with a diameter of 12.7, 15.7 and17.8 mm (0.5, 0.6 and 0.7 in.). The big-gest bundles have 9l. strands, yielding toPu = 31.4 MN or 14 MN allowable force.

The wires or strands are closelypacked

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Fig. 33. Continuity to a short approach span avoids large angular changes.

together to minimize the diameter for theprotecting pipe (see Fig. 34). These cablesshould only be used for wide and heavybridges; normally smaller cables lead to areasonable spacing and can be easier han-dled.

With regard to the high stress changesof back stay cables, special anchorageshave been developed which avoid thedamaging effect of hot metal filling insockets which is generally used for ropeanchors.

The Swiss firm BBR developed theHIAM (high amplitude) anchorage (seeFig. 35) using their button heads at theends of the wires or strands to set a coldsteel ball filling under transverse pressureinside the cone of the socket, Hereby,stress amplitudes of _o = 300 N/mm2

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Fig. 34. Section through cable with strands.

Fig. 35. HIAM anchorage of BBR.

Fig. 36. VSL anchorage for strands.

(43500 psi) can be resisted with over 2million cycles (according to the latestSwiss publications). Japanese tests con-firmed these favorable values of theHIAM anchorage.

Since the number of wires in oneanchorage has influence, special testingmachines had to be developed to test thesebig bundles at full size with pulsatingforces up to 700 t (772 tons). The Swissfirm VSL has developed an anchorage(see Fig. 36) holding up to 91 strands withwedges, yielding a fatigue amplitude of∆σ = 200 N/mm2 (290000 psi). TheFreyssinet group and Dywidag have anchor-ages for strands with similar qualities.

For corrosion protection, a polyethylene(PE) pipe around the wire bundle is theoptimal solution. The PE is made resistantagainst ultraviolet rays by adding 2.5 per-cent of carbon black.

More than 40 years of experience has

shown that this material is durable in trop-ical regions as well as in polluted air of anindustrial environment. The few cases inwhich PE pipes were damaged by crack-ing have been traced to causes which cansafely be avoided. Of course, quality con-trol, sound judgment or the retention of aconsultant are necessary.

The PE pipe can be pulled over the bun-dle or applied by extrusion. It should be atleast 7 mm (0.275 in.) thick. PE is imper-meable to vapor and gives full corrosionprotection. Therefore, the material to fillthe voids inside the pipe in order to takemoisture and oxygen out, need not haveanti-corrosive qualities. Usually, cementgrout is injected after the cable is underdead load stresses because cement grout isthe cheapest filling material and also hasgood corrosion protection characteristics.However, this injection procedure is notalways liked on the site. In the future, the

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Fig. 37. Cables in polyethylene pipe on reels for transport.

cables will most likely be filled in the fac-tory with a rubberlike deformable materi-al.

The PE pipe must be tightly and reliablyfixed to the anchor socket so that the cable

can be finished in the factory, rolled onreels (see Fig. 37) for shipping, and easilyhandled at the bridge site. These advan-tages cannot be obtained with steel pipesaround the bundle which must in additionget painted for protection.

The only disadvantage of the PE pipe isits black color, which detracts from thegood appearance of the bridge in its envi-ronment. Therefore, the cables of somebridges have been wrapped with a tape ofa brighter color like ivory or wine red. Thetapes of PVC used at thePasco-Kennewick Bridge deterioratedafter about 6 years. Later, Tedlar tapes ofpolyvinyl fluoride were used for which a20 year life is expected. This wrappingdoes not cost much but it embellishes thebridge as can be seen from the color pho-tos of the East Huntington Bridge.5

6.2 Anchorages

The anchorages must be designed toallow adjustment of length and replacinga cable damaged by an accident withoutinterrupting the traffic. They must furtherbe designed to prevent bending stresses inthe wires or strands at the socket due tochange of sag or due to slight oscillations.The anchorage should further comprise

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Fig. 38. Standard cable anchorage at the deck.

Fig. 39. Crossing of cable anchorages intower head.

dampers to prevent resonance oscillationsof the cables caused by wind eddies (fol-lowing the Von Kaman effect).

The anchorage at the deck structurewhich the author designed for thePasco-Kennewick Bridge in 1972 hasmeanwhile become the accepted solution(see Fig. 38). A strong steel pipe isencased in the concrete with the correctangle of inclination. The diameter is largeenough to thread the anchor socket of thecable through the pipe and place shims orturn the anchor nut on, which allows

length adjustment. The steel pipe extendsabout 1.2 m (3.9 ft) above the road level toprotect the cable against aberrant vehi-cles. On its top there is a thick soft neo-prene pad, which acts as a damper andstops flexural movements of the cable.The top is sealed with a rubber sleeve.

At the tower head, cables running over asaddle like in a suspension bridge shouldbe avoided because their replacementwould be rather difficult. It is preferableto anchor the cable at each side individu-ally and to design devices to carry the hor-

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Fig. 40. Cable anchorage inside tower with box section.

izontal component of the cable forcesthrough the tower. The simplest solutionis shown in Fig. 39 in which the cablescross each other, again in steel pipes. Thisis easy if there are single cables towardsthe main span and twin cables for theshort side span.

Since the concrete towers usually haveshafts with a box section, it is practical toarrange the anchorages inside this boxsection as shown in Fig. 40. The horizon-tal component of the cables is taken up inthe longitudinal box walls by prestressedbus. All anchorages are easily accessible.Them must be sufficient space for apply-ing a jack to adjust the cable length,which can be done here much easier thanat the deck anchorages. At the end of thesteel pipe there is again the neoprene padand the sleeve.

For the Annacis Bridge, the prestressingwas avoided by placing short steel beams

inside the box section which take the hor-izontal component of the cable forces (seeFig. 41). These beams must be wellanchored for unbalanced horizontal forcesduring erection or for the case in which acable must be exchanged, The tower boxmust be wide enough to allow access andhandling of the jacks. All these solutionsmake the erection very simple if prefabri-cated flexible cables with slender anchorsockets are used.

7. Dynamic Behavior andAerodynamic Stability

The cable stayed bridges with concretedecks and highly stressed cables [Eeff >180000 N/mm2 (26,100,000 psi)] have avery favorable dynamic behavior. Thedeflections under live load are extremelysmall because the effective depth of thelarge cantilever truss formed by the cables

26

Fig. 41. Cable anchorage by means of a steel beam insideconcrete tower.

is much larger than for beam girders.Most important is the fact that the

increase of amplitudes due to resonanceoscillation is prevented by system damp-ing caused by the interference of the manycables. This is an advantage of themulti-cable system. Measurements at theTjörn Bridge in Sweden showed that thedamping increases with increasing ampli-tudes and the logarithmic decrement getswell above 0. 10.

This damping is very favorable for thewind stability. Current theories which cal-culate critical wind speeds do not ade-quately represent the actual behavior andhave only limited validity. The same istrue for wind tunnel tests with sectionalmodels in which only a constant dampingfactor is applied. More tests should bemade of actual bridges to improve ourtheories based on observed facts.

From our present knowledge we can saythat there is no danger by wind with con-crete bridges hung up with cables in twoplanes along the edges, if the following

geometrical relations are observed (seeFig. 42):

I. B ≥ 10H2. For B < 10 H, a wind nose should be

added.3. B ≥ 1/30 L. This means that the width

of the bridge should not be too smallin relation to the main span. If thisratio gets smaller, then A-shaped tow-ers and wind shaping of the cross sec-tion must be used.

The A-shaped tower gives a triangularshape of the cable planes and the deck,which increases the torsional rigidity.

The author was a consultant in the de-sign of the bridge at Posadas Encarnacion,Argentina (see Fig. 43), which has to besafe against tornados with their enormousuplift forces. A rather heavy box girderand A-shaped towers were selected to getthe required safety. H. Cabjolsky reportedon this bridge at the FIP Congress (1986)in New Delhi.

Bridges hung up with cables in oneplane along the center line have almost no

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Fig. 42. Geometrical relations for obtaining wind stability withcables at beam edges.

damping for torsional oscillations.Caution is recommended because thiscase has not been sufficiently studied.

Caution must also be taken for someerection stages mainly during free can-tilevering on both sides of the towersespecially if the cantilever lengthbecomes larger than 20 B. Unsymmetricaland inclined wind forces can cause trou-ble. Temporary wind noses or ropes tosubmerged anchor blocks can preventdangerous oscillations.

8. Prestressing of CableStayed Bridges

For bridges with cables along bothedges longitudinal prestressing of thedeck structure is needed only over a cer-tain length in the middle of the main span,if towers stand on both sides. The hori-zontal thrust forces of the cables are zeroin l/2; there may even be tension due torestraint forces caused by bearings andunsymmetrical live load. Further, there

are bending moments due to concentratedlive load. in slabs as shown in Fig. 24, thelongitudinal tendons can be distributedover the width of the bridge with someconcentration near the edges. In cross sec-tions like Fig. 26, all tendons can beplaced in the edge beams.

The longitudinal thrust in the deck dueto the cable forces increases towards thetowers, causing so much compression thatno additional prestressing is needed there.However, towards the ends of the sidespans, this thrust decreases and the bend-ing moments increase; consequently, lon-gitudinal prestressing is needed. Since thebending moments are mainly caused bylocal live load with maxima conditionsrarely happening, partial prestressing willbe sufficient.

Transverse prestressing is desirable forwidths between 10 to 15 m (33 to 49 ft)mainly at the ends of the side spans,where the spreading out of the cableforces over the width of the deck causestransverse tension. For wider bridges,transverse prestressing should generally

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Fig. 43. Erection of Posadas Encarnacion Bridge, Argentina.

be used against transverse bending andtransverse normal forces caused by thecable forces. The degree of prestressingmay be chosen for no tension in the con-crete due to dead load plus 20 to 40 per-cent live load depending upon the weightsof national live load specifications whichvary considerably throughout the world.

For bridges hung up by one row ofcables along the centerline with a boxgirder, more longitudinal prestressing isneeded, because the large bending stiff-ness of these girders cause large positiveand negative bending moments. The ten-dons may be placed in the top and bottomslabs. Transverse prestressing is neededfor the transverse bending moments andto counteract torsional stresses which canbe rather large towards the towers. A highdegree of prestressing is suggested here,because the torsional rigidity gets almostlost, as soon as cracks due to tensilestresses occur (see Chapter 7 in Ref. 4).

If segmental construction with prefabri-cated elements is chosen with no longitu-dinal reinforcement across the joints, thena rather high degree of prestressing isimperative in the longitudinal direction.This prestressing prevents partial openingof these joints due to differential shrink-age and creep which is caused by frequenthigh temperature of the deck slab (sun-shine) and often by a different thicknessof the members (web thicker than bottomslab, etc.). The high degree of prestressingis especially needed if unbonded externaltendons are used and no reinforcementcrosses the joints, in order to get therequired safety for the ultimate limit state.

9. Construction MethodsThe common construction method for

multi-stay cable bridges is free cantilever-ing from the tower towards both sides.

The final cables are used to support onesegment after the other. Since full symme-try of loadings can usually not be secured,the tower must be stiffened under the deck

by struts or by retaining cables from thetower head to suitable anchor points.

For cross sections like those shown inFigs. 24 and 26, casting the segments inplace is preferred because the joints canbe secured by overlapping longitudinalreinforcement which helps to preventcracks due to unforeseen restraint forces.Such reinforcement also aids in securingthe required safety for the ultimate loadcondition. A part of the edge or edgebeam with the anchor steel pipe in the cor-rect position can be prefabricated andfixed to the cantilevering steel girder car-rying the forms. The construction headcan be sheltered against the weather.

For bridges with box girders, prefabri-cated segments can be used with matchcast joints but using a paste in the jointwhich compensates for differential short-ening during the curing and hardeningperiod. Prefabricated segments can alsobe mounted, leaving a gap for overlappinglongitudinal reinforcement by means ofsteel hinges on the webs, which allowadjustment for the correct positioning ofthe segment. This has been done success-fully at the Parana Bridge in PosadasEncarnacion (see Fig. 43).

Bridges with a deck of compositebeams allow the simplest and quickesterection. The grid of steel cross girdersand light steel edge girders, including thecable anchors, are installed with light der-ricks and then the prefabricated concreteslabs are placed, leaving gaps for overlap-ping reinforcement and shear connectorswhich are closed by cast-in-place con-crete. The Annacis Bridge in Vancouver,British Columbia, is a good example.

The cables in PE pipes have recentlybeen pulled up to the towers from thereels standing on the deck or even fromboats without any auxiliary cables usingonly curved saddles with rollers in orderto prevent excessive bending. The haulingequipment must be strong enough to pullthe cable socket into the deck anchor. Thelast stretch is done by a hydraulic jackwhich can resist the full dead load cableforce.

PCI JOURNAL 29

During the last ten years, constructionmethods have shown major progresstowards simplification and reducing erec-tion equipment. The construction must,however, be well planned using step bystep calculations for the alignment,forces, exact lengths and angles consider-ing temperature and creep influences,which depend on seasonal, climatic andeven daily conditions. The old rule mustbe observed that all measurements shouldbe made early in the morning before thesun rises. Special expertise is still needed,which is rather rare, since most universi-ties do not teach such essentials for prac-tical work.

10. Closing RemarksDue to limited space, the author had to

omit several subjects which are importantfor a modem design of a cable stayedbridge. For example, in multispan bridges,the best arrangement of bearings and jointsor provisions against seismic damage arenot covered. Also, codes of practice andproject specifications, which often are notup to date with respect to the latest researchand experience, are not mentioned.

Nevertheless, the author hopes that hehas demonstrated how simple the crosssections and the details of these bridgescan be if our collective experience and

knowledge gained during the past thirtyyears is well exploited. The author is con-fident that such cable stayed bridges ofprestressed concrete will have a wide fieldof application in the future in countriesthroughout the world to serve the needs ofhuman society.

But in our work, let us always search forgood quality, durability, ease of inspectionand maintenance and especially let us notforget the aesthetics of a structure as itaffects the environment.

REFERENCES1. Leonhardt, F., and Zellner, W.,

“Vergleiche zwischen Hange- undSchragkabelbruken fur Spannweitenfiber 600 in, “ Band 32 derlVBH-Abhandlugen, Zurich, 1972.

2. Leonhardt, F., and Zellner, W., “CableStayed Bridges,” IABSE Surveys, S13/80, Zurich, 1980.

3. Saul, R., Svensson, H., Andes H. P.,and Selchow, H. J., “Die SunshineSkyway Brucke in Florida, USA,”Bautechnik, Hefte 7 - 9, Berlin, 1984.

4. Leonhardt, F., Vorlesungen fiberMassivbau, Ted 4, Springer Verlag,Berlin, 1984. 5. Grant, A., “Design andConstruction of the East HuntingtonBridge,” PCI JOURNAL, V. 32, No. 1,January-February, 1987, pp. 20-29.

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