Leonhardt Cable Stay

Special Report

Cable Stayed BridgesWith Prestressed Concrete

Fritz LeonhardtProf. Dr. Ing.Consulting EngineerStuttgartWest Germany

T he number of cable stayed bridgeswith concrete or steel has increaseddramatically during the last decade. Ref.1 presents a survey of some 200 cablestayed bridges that have been designedor built throughout the world,

Although most of these bridges aremade of steel, many of them could havebeen designed with prestressed con-crete. In fact, by using this material, thedesign, structural detailing and construc-tion method can be simplified, thus pro-ducing a bridge that is economically andaesthetically superior.

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

Note: This paper is based upon the Keynote Lee-hire presented by the author at the FTP Congress inNew Delhi, India, February 16, 1986, and a similarlecture, including steel bridges, at the Symposiumon Strait Crossings in Stavanger, Norway, in Oc-tober 1986.

stand the basic principles of cable staybridge design and construction. Thepurpose of this article is to present thelatest state of the art on cable stayedbridges while elaborating upon thefundamentals and possibilities pertain-ing to such structures. The text willcover highway, pedestrian and railroadbridges using prestressed concrete.

1. Range of Feasibility ofCable Stayed Bridges

There are some misconceptions re-garding 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 m (130 ft) span can bebuilt to be structurally efficient and cost

52

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

effective. Employing prestressed con-crete, the superstructure can be madevery slender using a few cable stays anda deck with a depth of only 25 to 30 cm(10 to 12 in.).

Highway bridges can be built of pre-stressed concrete with spans up to 700 in(2295 ft) and railroad bridges up to about400 m (1311 ft). If composite action be-tween the steel girders and a concretedeck slab is utilized, then spans of about1000 and 600 in (3279 and 1967 ft) forhighway and railroad bridges, respec-tively, 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 m (5900 ft) for six lanes ofroad traffic and two railway tracks with-out encountering any structural or con-struction difficulties.

Many bridge engineers believe thatfor spans above 400 m (1311 i), a sus-pension bridge is preferable. This as-sumption is false. In fact, a cable stayedbridge is much more economical, stifferand aerodynamically safer than a com-parative suspension bridge. The author

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

PCI JOURNALISeptember -October 1987 53

hSuspension Bridge

Cable stayed Bridge" h t. t 5

weight t

50000 width of bridge 38m

46 000 t

1.0 Gip 1

46 000 = 240

30 000 f9 200

0

12300.2.16 yQ

20? 000 5 70o L,^ e ^\ rQ 19 2DD t

1z 30o apt`'

1;^ ocio i 5, e

5 700

0 500 '1000 1500 1800m span

Fig. 2. Comparison of quantity of cable steel for suspension bridges andcable stayed bridges.

showed this was true as early as 1972)In designing a cable stayed bridge

there is first the problem of finding therequired quantity of high strength steelfor the cables. For a bridge with a 1800m (5902 ft) main span and 38 m (125 ft)width, a suspension bridge needs 46000t (50700 tons) of steel whereas a cablestayed bridge only needs 19200 t (21170tons) of steel (see Fig. 2). In the lattercase this represents only about 40 per-cent the amount of steel.

Furthermore, a suspension bridgeneeds a stiffening girder with a bending

stiffness which must be about ten timeslarger than that of the cable stayedbridge. The suspension bridge needsadditional heavy anchor blocks whichcan be extremely costly if the navigationclearance is high and foundation condi-tions are poor. The total cost of such asuspension bridge can easily be 20 to 30percent above the costs of a cable stayedbridge.

Currently, the second Nagoya Har-bour Bridge (in Japan), at 600 m (1967ft), has the longest span of a cable stayedbridge in steel. This structure, which

54

Fig. 3. Nagoya Harbour Bridge, Japan.

was designed by Dr. Ing_ KunioHoshino (a former student of the au-thor), is now under construction. Whencompleted, it will look similar to the firstNagoya Harbour Bridge (see Fig.3). Theauthor is confident that in the near fu-ture similar such spans will be builtusing prestressed concrete.

Range of span is only one importantparameter in designing cable stayedbridges. Special situations such ascurved spans and skew crossings can beeasily solved using stays.

The engineer can choose between alarge variety of configurations: sym-metrical spans with two towers, un-symmetrical spans suspended from onetower, or multi-spans with several towersin between. This is an ideal field forcreativeness in design to satisfy thefunctional requirements of the projectand to obtain an aesthetically pleasingstructure which complements the envir-onment.

2. The Main Girder System

2.1 Development of multi-stay cablesystem

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

one cable at each tower (see Fig.4),leaving long spans requiring a beamwith large bending capacity. Soon threeto five cables were used, decreasing thebending moments of the beam and theindividual cable forces to be anchored.However, structural detailing and con-struction procedures were still difficult.

The desired simplification was ob-tained by spacing the cables so closelythat single cables with single anchorheads were sufficient which could eas-ily be placed and anchored. The spacingbecame only 4 to 12 in (13 to 39 ft), al-lowing free cantilever erection withoutauxiliary cables. Simultaneously, thebending moments became very small, ifan extremely small depth of the longi-tudinal edge beams and very stiff cableswere 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 com-pressive chord member. The depth ofthe longitudinal beams in the deckstructure is almost independent of themain span, but it must be stiff enough tolimit local deformations under concen-trated live load and to prevent bucklingdue to the large compressive forcescreated by the inclined cables.

PCI JOURNALSeptember-October 1987 55

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

The stiffness of this new system de-pends mainly on the angle of inclinationand on the stress level of the cables. Fig.5 shows the enormous influence of thestress in such cables on the effectivemodulus of elasticity. Low stresses givea large sag and low stiffness. The stressin the cables should be at least 500 to600 N/mm2 (72500 to 87000 psi). Forlong spans, stiffening ropes (as shown inFig. 6) are needed to prevent an exces-sive change of sag. The simplification ofthe structural design and of the erectionprocess gained by this multi-stay cablesystem should be used whenever suit-able.

2.2 Arrangement of stay cablesIf all the cables are anchored at the

top of 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 islarge. Therefore, it is preferable to dis-tribute the anchorages over a certain

length of the tower head and get asemi-fan arrangement (as shown inFig.8), which also improves the appear-ance of the bridge.

In the author's early bridges acrossthe Rhine River in Dusseldorf, the ar-chitect wanted to have all the cablesparallel and the anchorages equally dis-tributed over the height of the tower.This is called the harp-shaped arrange-ment (see Fig. 9). The system requiresmore steel for the cables, gives morecompression in the deck and producesbending moments in the tower. How-ever, the structure is aestheticallypleasing, especially when looking at thebridge under a skew angle. Dr. UlrichFinsterwalder, the world renownedbridge engineer, prefers this harp ar-rangement with many closely spacedcables. Such a scheme was chosen forthe Dame Point Bridge in Florida (seeFig.10), with a main span of 396 m (1298f3), which is now under construction.

In these multi-stay bridges, the deckis hung up with cables near the tower

56

Y Z f2 E,

Eeff N1mm2eff - o 12 G3

205 000700

180 000 ^; SO 600

steel stressSao

140 000^p0

100 000oti

T

60 000sag

T{C

0 100 200 300 400 fc

Fig. 5. Effective modulus of elasticity depends primarily on steel stress incable which in turn affects the cable sag.

Fig. 6. Stiffening ropes afixed to long cables reduce cable sag.

PCI JOURNAL/September-October 1987 57

Fig. 7. Fan shape arrangement of cables.

rFig. 8. Semi-fan arrangement of cables.

Fig. 9. Harp shape arrangement of cables.

also, to avoid a stiff bearing at the tower.This could cause very large negativebending moments which might be un-acceptable for the small depth of deckgirder used.

Normally, the bridge is supported bycables in two planes along the edges ofthe deck. In some cases (mainly formedium spans), cables in one plane areused along the centerline of the deck. Abox girder with sufficient torsionalrigidity is then needed which requiressome depth so that it can also resist thelarge bending moments. Such a girdermust be supported at the tower to resisttorsion and as a consequence the cablescan begin at a certain distance from thetower, leaving a "window" in the cablenet open. The Brotonne Bridge in

France is such an example (see Fig.11).Of course, other cable configurations

are possible, depending on Iocal condi-tions, like very short side spans. A har-monic arrangement of cables is impor-tant for good appearance and it shouldbe chosen with care and diligence.

2.3 Ratio between main and sidespans

The ratio between side span l andmain span I has an important influenceon the stress changes in the back staycables which holds the tower back to theanchor pier. Live load in the main spanincreases these stresses whereas liveload in the side span decreases them.These stress changes must be kept

58

"Jam 396m 192m

Fig. 10. Dame Point Bridge across St. John's River, Florida, with centralexpansion joint; design by Ulrich Finsterwalder.

458.50_ 55.5DJ. 143 .50 32C,DO I 143, SO 17D.o0 155.50 39

Fig. 11. Semi-fan arrangement of cables leaving a "window' open near thetower; Brotonne Bridge, France.

safely below the fatigue strength of thecables. This fatigue strength is a criter-ion for the allowable ratio 1,/1, which de-pends mainly on the relation betweenIive and dead load, p tog.

Prestressed concrete bridges allowlonger side spans than steel bridges.The author has published charts in astate of the art report for IABSE (1980)from which suitable ratios can he read.For concrete highway bridges 1,ll can beabout 0.42; for railway bridges the ratioshould not be larger than 0.34, The ratiodecreases with the span length. Themagnitude of the anchorage forces at theanchor pier also depends on the ratio1,/I. In particular, short side spans givelarge anchorage lorces.

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 canbe ground anchored over a certainlength or even be joined in an anchorblock. This has been done for theC. F. Casados Bridges in Spain, the Bar-rios de Luna Crossing (see Fig.13)which at 440 m (1443 ft) is currently thelongest span of prestressed concrete,and the Ebro Bridge (see Fig.14) whichhas an inclined tower and back stay ca-bles spreading sidewise into two planes,giving a most interesting impressionfrom the highway.

The inclination of the tower back-wards makes the main cables longer, thebackstay cables shorter and steeper.There is no technical or economical ad-vantage in this but a more thrilling ap-

PCI JOURNAUSeptember-October 1987 59

heavy beam bridge - a light stayed bridge

Fig. 12. Heavy beam bridge used as anchor zone for back stay cables.

90,00

anchor anchor

joint in center _J+ 101.71 440,00 101,71Fig. 13. Back stay cables anchored in ground; Barrios de Luna Bridge, Spain.

jjjj'.anchors on rock -

' 13712 32,00 25,50

146,30 57,6D

I ly, l 11 1 -I l l l Il l 1411 III II I I f H I :III NI ry I I H d {I 6 # -_ ^

y nl'^ I II '1.111 lfl IIIIH 1 'III III h+I H..

tower ^cable5 In median 4m medianbackstay cables

Fig. 14. Back stay cables spread sidewards: Ebro Bridge, Spain.

60

fan shape harp shape

4^ / hh 11

3ti

o ^u `O 2

C ianQ

a 1 harpN good

range

h/{

0,1 0,2 0,3 0,4

Fig. 15. Quantity of cable steel as a function of relativeheight of towers.

pearance. A forward inclination of thetower towards the main span producesuneasy and uncomfortable feelings.Towers should normally be vertical.

3. Optimal Height, Shape andStiffness of the Towers

The cable forces and the requiredquantity of cable steel decrease with theheight of the tower above the road level(see Fig.15). A good range is between021 and 0.251. For bridges with only onetower the height must be related to about1.81. Towers of cable stayed bridgesmust be higher than those fbr suspensionbridges which usually have h/I = 0.10.

The height of the tower also definesthe angle of inclination of the longestcables. This angle should not be smallerthan about 25 degrees because other-wise the deflections will become toolarge.

In the longitudinal direction the tow-

ers should be slender and have a smallbending stiffness, in order to avoid largebending moments to he reacted by thefoundations. If the soil conditions arepoor, then towers can even he hinged atthe foot and fixed only during erection,The towers of some of the author's RhineRiver bridges have such foot hinges.Towers should be built of concrete be-cause concrete towers are much cheaperthan steel towers.

The shape of the towers can be verysimple. Even for large spans up to 500 m(1640 ft), free standing tower legs maybe sufficient if they are fixed and trans-versely connected in the foundationonly i see for example the Kniebriicke inDusseldorf (Fig.16) ] , No transversebracing is needed if the cables are in avertical plane and if the cross section ofthe tower is unsymmetrical with most ofthe load carrying area close to the bridgedeck (see Fig.17). This arrangementbrings the center of gravity close to the

PCI JOURNAL,+ September-October 1987 61

" "1

Fig. 16. The slender free standing towers of Kniebrucke in Dusseldorf, West Germany.

section at top

cable - anchor-zone

cables

Sectionat deck

Fig. 17. Efficient cross section for freestanding towers.

plane of the cables and still gives muchtransverse bending stiffness to carry thewind reactions to the foundation. Suchtower legs should be tapered in both di-rections. Modern climbing forms allowthis tapering without much extra cost.

The bridge deck with the railingsshould run clear through the tower legsand the cable anchorages should beclose to the railings; therefore, veryslender tower shafts become desirable.If the semi-fan cable arrangement isused, then one or two transverse brac-ings between the tower legs are suitable(see Fig.I8). The bracing above the roadlevel should be slender and look lightbetween the thin cables.

For very long spans and especially inregions with strong wind forces, the A-shaped tower is the optimal solution forappearance and wind stability (seeFig.19). In high level bridges, the towerlegs can be joined under the deck levelin order to combine the foundations.The Farb Bridge in Denmark was de-signed in such a way. These A-shapedtowers with the cables sheltering thehighway give a feeling of safety to themotorist and an exciting and pleasingview (see Fig. 20).

62

Fig. 18. Tower shapes for two planes of cables.

m-00_ I high level bridge

tower sections

1V

River bridgelow level sea -high level

Fig. 19. A-shaped towers for two cable planes_


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

For bridges with cables in one plane itis best to design a slender single towerin the median strip and to protect thecables and the tower with strong guard-rails (see Fig. 21) as was done for theRhine Bridge in Bonn, the BrotonneBridge in France, the Sunshine SkywayBridge in Tampa, Florida and otherbridges. Tower shapes for such bridgesare 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 Statewas influenced by the wind tunnel testsconducted at the NFL of Ottawa (1968).These tests were done to find the opti-mal aerodynamic shape for the author'sdesign of the Burrard Inlet Bridge inVancouver for 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. How-ever, during the design of the Parana

f

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

Bridges in Argentina for highway plusrailway traffic, it was conceived that thisaerodynamic shape was useless when400 m (1311 ft) long freight trainswere on the bridge. Through dynamictests it was learned that multi-stay cablebridges have very strong damping coefficients and do not need the same goodaerodynamic shape as suspensionbridges do. Therefore, the cross sectioncould be simplified further.

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

and for widths up to about 20 m (66 ft), avery simple solid concrete slab withoutan edge beam is the best solution (see

Fig. 24). The thickness of the slab de-pends primarily on the transversebending moments which can be in-creased towards the towers to respond tothe increasing longitudinal normalforces.

Dr. Finsterwalder had proposed suchslender slabs as early as 1967 for his de-sign of the Great Belt Bridge and lateralso for the Pasco-Kennewick Bridge.The thickness of the slab was so small inrelation to the span that the safetyagainst buckling under high longitudi-nal compressive forces was subse-quently questioned especially in thecase of high deflections under concen-


Fig. 22. Tower shapes for one plane of cables.

4coble%

22.50 m

Fig. 23. Cross section of Pasco-Kennewick Bridge (1972), Washington State.

50 -60cm

15 20 m

Fig. 24. Cross section with solid slab only for highway bridges with spans up to 150 m(490 ft).

66

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

trated live load and the possibility thatone cable could break in an accident.

This buckling safety was meanwhilestudied by Professor Renee Walther inLausanne, Switzerland. Second ordertheory calculations were checked bytests with a relatively large model.Buckling safety could now be checkedreliably. It was found that a certainamount of longitudinal reinforcement isrequired for obtaining sufficient ductil-ity in such thin slabs.

Professor Walther became the firstengineer to build a highway bridge 15 m(49 ft) wide across the upper RhineRiver in Diepoldsau with a slab only 50cin (20 in.) thick for a main span of 97 m(318 ft) with no edge beams (see Fig.25). He even reduced the slab thicknessat the edges to 36 cm (14 in.).

For wider bridges, B>2() ni (66 $),transverse T beams are, of course, moreeconomical (see Fig. 26). The spacing ofthe beams should not be Iarger than 4 to

25-30m

t ,y

1+- 4=6m^

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

PCI JOURNALiSeptember-October 1987 67

27, 53 -

1,37 12,16 0,45 12,16 1,37

prefab. stab 280rnm+50mm special layer

8 0.4' 2% 2%O.CB

2.33 r 1.75 L165A

Steel cross girder @3,8m

28,Q m

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

6 m (13 to 20 ft) and the slab on topshould always span longitudinally tomake good use of the longitudinal com-pressive forces from the cables. Thecross beams can he cast in place or pre-fabricated and end in a thick edge beamwith a depth of not more than 1.0 to 1.5m (3.2 to 4.9 ft), giving ample bucklingsafety and keeping the curvature of thedeflection line under concentrated loadswithin allowable limits even for spansup to 5{l0 m (1640 ft).

Such cross sections are especiallysuitable for composite structures, usingsteel cross girders between concreteedge beams which the author designedfor the East Huntington Bridge. Its 274m (898 ft) span hung up to one towercorresponds to a span of about 500 m(1639 ft) if suspended from two towers.In the proposed design (conducted bythe author's consulting firm) of the Sun-shine Skyway Bridge (see Fig. 27) in1980, a 2 m (6.6 ft) deep steel edge beamwas used to simplify the erection pro-cess and to allow the use of prefabri-cated deck slabs.

Soon thereafter, this type of sectionwas chosen for the Annacis Bridge inCanada with a main span of 465 m (1525ft) together with some advanced details.The project was built in 26 monthswhich is remarkable considering the

structure is 1000 m (3286 ft) long. Thisefficiency shows the ease and simplicityof the erection method.

In these composite structures, theconcrete must remain the main struc-tural material. The deck slab has to carrythe compressive chord forces. If for verylong spans these thrust forces becometoo large for the normal deck slab, thenits thickness should be increased to-wards the tower or a concrete edgebeam should be added. However, thesteel section should remain small inorder to avoid creep problems.

If the bridge is hung up with cables inthe median only, then a box girder isneeded. The cross section of the Bro-tonne Bridge (see Fig. 28) has become astandard for this type. The requiredamount of torsional rigidity depends onthe width of the deck and the length ofthe main span. Smaller cross-sectionalareas of the box may often be sufficientand this would allow sections like thatshown in Fig. 29, which is simpler toconstruct and has a smaller depth andsimple cable anchorages.

For railroad bridges, especially forhigh speed trains, large mass is neededto get a good dynamic behavior. There-fore, the DB German Federal Rail-ways carry the 40 cm (15 in.) deepballast over their modem bridges and

68

i,50 6,50 ^1^0 5.50 1,50

5,60 -- 4.00 --- 4,00 5.60 --

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

prefer thick concrete deck slabs. Withhigh strength cables it is not difficultand also not too costly to carry suchheavy dead loads over long spans (seeFig. 30).

Edge beams 1.5 to 2.0 m (4.9 toi.6 ft) deep should he sufficient to

satisfy deflection limits if the cables arenot too flat. For very long spans and se-vere deformation limits, a flat box sec-tion may be needed (see Fig. 31). Thecables of such railroad bridges shouldhave angles of inclination above 30 de-grees.

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

PCI JCURNALJSeptember-Oclober 1987 69

14,00

Fig. 30. Cross section of railroad bridges for spans up to 140 m (459 ft).

Fig. 31. Cross section of railroad bridges with spans longer than 140 m (459 ft).

liveload ______________ii ii 11111111 I I liii LI..L.i._II1.1I 111111111111

L 0,45 1 0.45Fig. 32. Deflection line showing large angular changes at the endsof side spans.

70

Fig. 33. Continuity to a short approach span avoids largeangular changes.

5. Situation at the Ends ofCable Stayed Bridges

The sudden change from an elasticsupport to a stiff support at the ends ofthe side spans causes large bendingmoments and consequently a large an-gular change of the deflection line (seeFig. 32). These angular changes are un-acceptable for railroad bridges.

The difficulties can easily be avoidedif the edge beams continue with an in-creasing depth into a small approachspan (see Fig. 33). The length and thebending stiffness of this smootheningtransition span must be well designed toavoid large bending moments.

This transition span can also be usedto counteract the uplift forces of the backstay cables by its weight or even by bal-last concrete within its depth. It also al-lows the distribution of the anchoragesfor the back stays over a certain lengthbehind the axis of the anchor pier.

6. Cables and TheirAnchorages

6.1 Cables and Their ProtectionThe cables are the most important

members of this system. They must besafe against fatigue, durable and wellprotected against corrosion especially

in an aggressive environment. The besttype of cable must be chosen and not thecheapest. It is unwise to save a few per-cent of steel and to later have to replaceropes with broken or corroded wiresafter only 8 to 12 years as was the case inthe Knhlbrand and Maracaibo Bridges.

Regarding the choice of cables, testresults and practical experience of morethan 30 years are available. The follow-ing is the author's opinion based on ex-perience and judgment.

There is no doubt that bundles ofparallel wires or parallel long lay strandsdeserve preference due to their highand constant modulus of elasticity. Thequality of the wires or strands must bewell controlled because very differentqualities are on the market. Wires with adiameter of 7 mm of St 1470/1670 N/mm2are generally used, the number of wiresper cable can be 337, giving a maximumultimate force of Pq = 21.7 MN or 2170tons. Applying the rather high factor ofsafety of 22, the allowable cable force isabout P = 10.0 MN or 1000 tons. Itwould be better to choose a lower safetyfactor, Le., 1.7, but instead refer it to the0.2 percent yield strength.

Strands are available of St 1500/1700Nlmm2 with a diameter of 12.7, 15.7 and17.8 mm (0.5, 0.6 and 0.7 in.). The big-gest bundles have 91 strands, yielding toP = 31.4 MN or 14 MN allowable force.

The wires or strands are closely

PCI JOURNAUSeptember-October 1987 71

rig, s4. Section through cable with strands.

packed together to minimize the diam-eter for the protecting pipe (see Fig. 34).These cables should only be used forwide and heavy bridges; normallysmaller cables lead to a reasonablespacing and can he easier handled.

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 tinder transverse pres-

DEAD END Circular shim -- Locking plate Wires

Button head PE:"pipe ,LIVE END -- Steel pipe

Fig. 35. HIAM anchorage of BBR.

Anchor headNutBearing plate

Neoprene damper

FTension ringConnection pipe

Stay tube

Grout cap L7ransition pipe

Fig. 36. VSL anchorage for strands.

72

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

sure inside the cone of the socket.Hereby, stress amplitudes of o- = 300Nlmm2 (43500 psi) can be resisted withover 2 million cycles (according to thelatest Swiss publications). Japanesetests confirmed these favorable values ofthe HIAM anchorage.

Since the number of wires in one an-chorage has influence, special testingmachines had to be developed to testthese big bundles at full size with pul-sating forces up to 700 t (772 tons). TheSwiss firm VSL has developed an an-chorage (see Fig. 36) holding up to 91strands with wedges, yielding a fatigueamplitude of Av = 200 N/mm2 (290000psi). The Freyssinet group and Dywidaghave anchorages for strands with similarqualities.

For corrosion protection, a polyethyl-ene (PE) pipe around the wire bundle isthe optimal solution. The PE is maderesistant against ultraviolet rays byadding 2.5 percent of carbon black.

More than 40 years of experience hasshown that this material is durable intropical regions as well as in polluted airof an industrial environment. The fewcases in which PE pipes were damagedby cracking have been traced to causeswhich can safely be avoided. Of course,quality control, sound judgment or theretention of a consultant are necessary.

The PE pipe can be pulled over thebundle or applied by extrusion. Itshould be at least 7 mm (0.275 in.) thick.PE is impermeable to vapor and givesfull corrosion protection. Therefore, thematerial to fill the voids inside the pipein order to take moisture and oxygenout, must not have anti-corrosive qual-ities. Usually, cement grout is injectedafter the cable is under dead Ioadstresses because cement grout is thecheapest filling material and also hasgood corrosion protection characteris-tics. However, this injection procedureis not always liked on the site. In the


Cable in PE pipeRubber sleeve

Thick steel pipe

Height forprotection / Neoprene pad

(damperl

HIAM Anchor, fixed, adjustment in tower

Fig. 38. Standard cable anchorage at the deck.

future, the cables will most likely befilled in the factory with a rubberlikedeformable material.

The PE pipe must be tightly and reli-ably fixed to the anchor socket so thatthe cable can be finished in the factory,

Fig. 39. Crossing of cable anchorages intower head.

rolled on reels (see Fig. 37) for shipping,and easily handled at the bridge site.These advantages cannot be obtainedwith steel pipes around the bundlewhich must in addition get painted forprotection.

The only disadvantage of the PE pipeis its black color, which detracts fromthe good appearance of the bridge in itsenvironment. Therefore, the cables ofsome bridges have been wrapped with atape ofa brighter color like ivory or winered. The tapes of PVC used at thePasco-Kennewick Bridge deterioratedafter about 6 years. Later, Tedlar tapesof polyvinyl fluoride were used forwhich a 20 year life is expected. Thiswrapping does not cost much but it em=bellishes the bridge as can be seen fromthe color photos of the East HuntingtonBridges

6.2 AnchoragesThe anchorages must be designed to

allow adjustment of length and replac-ing a cable damaged by an accidentwithout interrupting the traffic. They mustfurther be designed to prevent bendingstresses in the wires or strands at thesocket due to change of sag or due toslight oscillations. The anchorage

74

easyaccess

main side span

neoprene pad

sleeve\ __-

steel pipe

crosssection

prestress - bars or loops

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

should further comprise dampers toprevent resonance oscillations of the ca-bles caused by wind eddies (followingthe von Karman effect).

The anchorage at the deck structurewhich the author designed for thePasco-Kennewick Bridge in 1972 hasmeanwhile become the accepted solu-tion (see Fig. 38). A strong steel pipe isencased in the concrete with the correctangle of inclination. The diameter islarge enough to thread the anchor socketof the cable through the pipe and placeshims or turn the anchor nut on, which

allows length adjustment. The steelpipe extends about 1.2 m (3.9 ff) abovethe road level to protect the cableagainst aberrant vehicles. On its topthere is a thick soft neoprene pad, whichacts as a damper and stops flexuralmovements of the cable. The top issealed with a rubber sleeve.

At the tower head, cables runningover a saddle like in a suspension bridgeshould be avoided because their re-placement would be rather difficult. It ispreferable to anchor the cable at eachside individually and to design devices

PCI JOURNAL September-October 1987 75

il`IIA_____ iII^ IIYVII

I.

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

to carry the horizontal component of thecable forces through the tower. Thesimplest solution is shown in Fig. 39 inwhich the cables cross each other, againin steel pipes. This is easy if there aresingle cables towards the main span andtwin cables for the short side span.

Since the concrete towers usuallyhave shafts with a box section, it is prac-tical to arrange the anchorages insidethis box section as shown in Fig. 40. Thehorizontal component of the cables istaken up in the longitudinal box wallsby prestressed bars. All anchorages areeasily accessible. There must be suffi-cient space for applying a jack to adjustthe cable length, which can be donehere much easier than at the deck an-chorages. At the end of the steel pipethere is again the neoprene pad and thesleeve.

For the Annacis Bridge, the pre-stressing was avoided by placing short

steel beams inside the box sectionwhich take the horizontal component ofthe cable forces (see Fig. 41). Thesebeams must be well anchored for unbal-anced horizontal forces during erectionor for the case in which a cable must beexchanged. The tower box must be wideenough to allow access and handling ofthe jacks. All these solutions make theerection very simple if prefabricatedflexible cables with slender anchorsockets are used.

7. Dynamic Behavior andAerodynamic Stability

The cable stayed bridges with con-crete decks and highly stressed cables[Efn > 180000 N/mm2 (26,100,000 psi)]have a very favorable dynamic behavior.The deflections under live load are ex-tremely small because the effectivedepth of the large cantilever truss

76

ÂL4Sd6îY.d4C^.H.VA'.6'.O .^QiASO'.6îQ60î8î6^^6fiY.4G6'r62G5y^6'G^ ^l4L9q

- t

B a 10 H

H

B 10 H+i

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

formed by the cables is much larger thanfor beam girders.

Most important is the fact that the in-crease of amplitudes due to resonanceoscillation is prevented by systemdamping caused by the interference ofthe many cables. This is an advantage ofthe multi-cable system. Measurementsat the Tjbrn Bridge in Sweden showedthat the damping increases with in-creasing amplitudes and the logarithmicdecrement gets well above 0.10.

This damping is very favorable for thewind stability. Current theories whichcalculate critical wind speeds do notadequately represent the actual be-havior and have only limited validity.The same is true for wind tunnel testswith sectional models in which only aconstant damping factor is applied.More tests should be made of actualbridges to improve our theories basedon observed facts.

From our present knowledge we cansay that there is no danger by wind withconcrete bridges hung up with cables in

two planes along the edges, if the fol-lowing geometrical relations are ob-served (see Fig. 42);

1.B >10H2. For B < 10 H, a wind nose should

be added.3. B -- 1130 L. This means that the

width of the bridge should not betoo small in relation to the mainspan. If this ratio gets smaller, thenA-shaped towers and wind shapingof the cross section 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 Encar-nacion, Argentina (see Fig. 43), whichhas to be safe against tornados with theirenormous uplift forces. A rather heavybox girder and A-shaped towers wereselected to get the required safety.H. Cabjolsky reported on this bridge atthe FIP Congress (1986) in New Delhi.

Bridges hung up with cables in oneplane along the center line have almost

PCI JOURNAL'September-October 1987 77

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

no 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 length be-comes larger than 20 B. Unsymmetricaland inclined wind forces can causetrouble. Temporary wind noses or ropesto submerged anchor blocks can preventdangerous oscillations.

8. Prestressing ofCable Stayed Bridges

For bridges with cables along bothedges longitudinal prestressing of thedeck structure is needed only over acertain length in the middle of the mainspan, if towers stand on both sides. Thehorizontal thrust forces of the cables arezero in 1/2; there may even be tensiondue to restraint forces caused by bear-ings and unsymmetrical live load. Fur-ther, there are bending moments due to

concentrated live load. In slabs asshown in Fig. 24, the longitudinal ten-dons can be distributed over the widthof the bridge with some concentrationnear the edges. In cross sections likeFig. 26, all tendons can be placed in theedge beams.

The longitudinal thrust in the deckdue to the cable forces increases to-wards the towers, causing so much com-pression that no additional prestressingis needed there. However, towards theends of the side spans, this thrust de-creases and the bending moments in-crease; consequently, longitudinal pre-stressing is needed. Since the bendingmoments are mainly caused by local liveload with maxima conditions rarelyhappening, partial prestressing will besufficient.

Transverse prestressing is desirablefor widths between 10 to 15 m (33 to 49ft) 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

78

be used against transverse bending andtransverse normal forces caused by thecable forces. The degree of prestressingnay be chosen for no tension in the con-crete due to dead load plus 20 to 40 per-cent live load depending upon theweights of national live load specifica-tions which vary considerably through-out the world.

For bridges hung up by one row ofcables along the centerline with a boxgirder, more longitudinal prestressing isneeded, because the large bendingstiffness of these girders cause large pos-itive and negative bending moments.The tendons may be placed in the topand bottom slabs. Transverse pre-stressing is needed for the transversebending moments and to counteract tor-sional stresses which can be rather largetowards the towers. A high degree ofprestressing is suggested here, becausethe torsional rigidity gets almost lost, assoon as cracks due to tensile stressesoccur (see Chapter 7 in Ref 4).

If segmental construction with prefab-ricated elements is chosen with no lon-gitudinal reinforcement across thejoints, then a rather high degree of pre-stressing is imperative in the longitudi-nal direction. This prestressing preventspartial opening of these joints due todifferential shrinkage and creep whichis caused by frequent high temperatureof the deck slab (sunshine) and often bya different thickness of the members(web thicker than bottom slab, etc.). Thehigh degree of prestressing is especiallyneeded if unbonded external tendonsare used and no reinforcement crossesthe joints, in order to get the requiredsafety for the ultimate limit state.

9. Construction MethodsThe common construction method for

multi-stay cable bridges is free canti-levering from the tower towards bothsides.

The final cables are used to supportone segment after the other. Since full

symmetry of loadings can usually not besecured, the tower must be stiffenedunder the deck by struts or by retainingcables from the tower head to suitableanchor points.

For cross sections like those shown inFigs. 24 and 36, casting the segments inplace is preferred because the joints canbe secured by overlapping longitudinalreinforcement which helps to preventcracks due to unforeseen restraintforces. Such reinforcement also aids insecuring the required safety for the ul-timate load condition, A part of the edgeor edge beam with the anchor steel pipein the correct position can be prefabri-cated and fixed to the cantilevering steelgirder carrying the forms. The construc-tion head can be sheltered against theweather.

For bridges with box girders, prefab-ricated segments can be used withmatch cast joints but using a paste in thejoint which compensates for differentialshortening during the curing and hard-ening period. Prefabricated segmentscan also be mounted, leaving a gap Foroverlapping longitudinal reinforcementby means of steel hinges on the webs,which allow adjustment for the correctpositioning of the segment. This hasbeen done successfully at the ParanaBridge in Posadas EncarnaciOn (see Fig.43).

Bridges with a deck of compositebeams allow the simplest and quickesterection. The grid of steel cross girdersand light steel edge girders, includingthe cable anchors, are installed with lightderricks and then the prefabricated con-crete slabs are placed, leaving gaps foroverlapping reinforcement and shearconnectors which are closed by cast-in-place concrete. The Annacis Bridge inVancouver, British Columbia, is a goodexample.

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 usingonl y curved saddles with rollers in order

PCI JOURNAUJSeptember-October 1987 79

to prevent excessive bending. Thehauling equipment must be strongenough to pull the cable socket into thedeck anchor. The last stretch is done bya hydraulic jack which can resist the fulldead load cable force.

During the last ten years, constructionmethods have shown major progress to-wards 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 consid-ering temperature and creep influences,which depend on seasonal, climatic andeven daily conditions. The old rule mustbe observed that all measurementsshould be made early in the morningbefore the sun rises. Special expertise isstill needed, which is rather rare, sincemost universities do not teach such es-sentials for practical work.

10. Closing RemarksDue to limited space, the author had

to omit several subjects which are im-portant for a modern design of a cablestayed bridge. For example, in multi-span bridges, the best arrangement ofbearings and joints or provisions againstseismic damage are not covered. Also,codes of practice and project specifica-tions, which often are not up to datewith respect to the latest research andexperience, are not mentioned.

Nevertheless, the author hopes thathe has demonstrated how simple thecross sections and the details of thesebridges can be if our collective experi-ence and knowledge gained during thepast thirty years is well exploited. Theauthor is confident that such cablestayed bridges of prestressed concretewill have a wide field of application inthe future in countries throughout theworld to serve the needs of human soci-ety.

But in our work, let us always searchfor good quality, durability, ease of in-spection and maintenance and espe-cially let us not forget the aesthetics of astructure as it affects the environment.

REFERENCES1. Leonhardt, F., and Zellner, W., "Verg-

leiche zwischen Hange- andSchragkabelbrucken fur SpannweitenCher 600 m, " Band 32 der IVBH-Abhandlugen, Zurich, 1972.

2. Leonhardt, F., and Zellner, W., "CableStayed Bridges," IABSE Surveys, S 13/80,Zurich, 1980.

3. Saul, H., Svensson, H., Andra H. P., andSelchow, H. J., "Die Sunshine SkywayBriicke in Florida, USA," Bautechnik,Hefte 7 9, Berlin, 1984.

4, Leonhardt, F., Vorlesungen Ober Mastic-ban, Teil 4, Springer Verlag, Berlin, 1984.

5. Grant, A., "Design and Construction of theEast Huntington Bridge," PCI JOURNAL,V. 32, No. 1, January-February, 1987, pp.20-29.

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Documents

Leonhardt Cable Stay