Leonhardt Cable Stay

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Leonhardt Cable Stay

Text of 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


  • 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


    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


  • 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


  • Y Z f2 E,

    Eeff N1mm2eff - o 12 G3

    205 000700

    180 000 ^; SO 600

    steel stressSao

    140 000^p0

    100 000oti


    60 000sag


    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 o