3 Cable-stayed bridges and Suspension bridges are the most economic longitudinal schemes for long span bridges. This is a consequence of the structural behaviour of these bridge types, in which the axial behaviour is the main structural response rather than the flexural behaviour.Advantages of Cable-stayed bridges against Suspension bridges:Cable-stayed bridges are stiffer than suspension bridges under non-symmetrical live loads and under wind loadThe amount of cables required for the stays of a cable-stayed bridge is smaller than that required for the bearing cables of a suspension bridgeDisadvantages of Cable-stayed bridges against Suspension bridges:The horizontal components of the axial forces in the stay cables introduce large axial compressions in the deck in the sections close to the piers. Additional flexural stiffness must be provided to the deck in order to avoid buckling. Due to this fact, for very long bridges, suspension bridges are cheaper than cable-stayed bridges.
4 STRUCTURAL BEHAVIOUR UNDER PERMANENT LOADS: The vertical deflection at the anchorages of the stay cables in the main span due to dead load and superimposed dead load are counterweight with those due to the prestressing of the stay cables.The bending moment diagram in the deck in the main span is similar to that in a continuous bridge with supports at the sections where the stay cables are anchored on the deckThe prestressing of the back stays is established in order to cancel the bending moments in the towers in permanent stateModelling: The prestressing of the stay cables can be modelled through imposed shortening of the stays (or imposed temperature change).
6 STRUCTURAL BEHAVIOUR UNDER LIVE LOADS: The efficiency of the cable-staying system under live loads is achieved by limiting the horizontal displacement of the tower crown, which in turn is achieved by:providing enough flexural stiffness to the towers (expensive unless continuous bridges)providing enough axial stiffness to the back staysanchoring the back stays in fix points or points that have relatively small displacementsIn addition, once the horizontal displacement of the tower crowns is limited:The larger the axial stiffness of the stay cables in the main span, the larger the efficiency of the cable-staying systemThe smaller the flexural stiffness of the deck, the larger the efficiency of the cable-staying system
7 LONGITUDINAL STAY CABLE ARRANGEMENT: There are three different longitudinal arrangements:harp systemfan systemintermediate system
8 LONGITUDINAL STAY CABLE ARRANGEMENT: HARP SYSTEM:Better aesthetical appearance, specially when the cable-staying system is arranged in two different vertical planesThe tower crown is less restricted to displacements and, therefore, the efficiency of this cable-staying system is smaller than othersAn appropriate efficiency of the cable-staying system is achieved by mean of both providing enough flexural stiffness to the towers and anchoring the back-stays to points in which the deflections are restricted.
9 LONGITUDINAL STAY CABLE ARRANGEMENT: FAN SYSTEM:Higher efficiency of the cable-staying systemSmaller slope with the vertical alignment → Higher efficiency → Smaller cross-sectional area → Smaller amount of stay cables → Smaller costSmaller slope with the vertical alignment → Smaller axial load in the deck → → Smaller amount of additional flexural stiffness in the deck to avoid buckling → Smaller costDisadvantages: Lack of space for anchoring the stay cables in the tower crown + Superposition of stay cables when they are arranged in two different vertical planes (aesthetics)
10 LONGITUDINAL STAY CABLE ARRANGEMENT: INTERMEDIATE SYSTEM:The stay cable anchorages are located in the top of the tower but in a larger area that in a fan systemAdvantages of the fan arrangement, with a slightly smaller efficiency (significantly larger than the harp arrangement)Enough space available for anchoring the stay cables in the top of the towerSuperposition of stay cables when they are arranged in two different vertical planes (aesthetics)
11 LONGITUDINAL STAY CABLE ARRANGEMENT: LONGITUDINAL SPACING BETWEEN ANCHORAGES OF STAY CABLES:The smaller the spacing → the smaller the bending moments in permanent stage → the smaller the design bending moments for the deck → the smaller the required depth of the deck → the smaller the cross sectional area of the stay cables → The smaller the costThe smaller the spacing → the smaller the bending moments during construction
12 TRANSVERSE STAY CABLE ARRANGEMENT: There are three different transverse arrangements:single cable-staying planedouble cable-staying planedouble cable-staying plane converging at the top of the towers
13 TRANSVERSE STAY CABLE ARRANGEMENT: SINGLE CABLE-STAYING PLANE:The cable-staying system contribute to the shear and bending responseThe cable-staying system does not contribute to the torsional response. All the torsional response is resisted by the deck → single/multiple box girdersGood appearance (aesthetics). The stay cables are not seen one over other onesThe anchorages are located in the middle-axis of the deck
14 TRANSVERSE STAY CABLE ARRANGEMENT: DOUBLE CABLE-STAYING PLANE:The cable-staying system contribute to the shear, the bending, and the torsional responseAll the torsional response may be resisted by the cable staying system → thin transverse slab with two main eccentric longitudinal ribs where the anchorages are locatedSuperposition of stay cables (aesthetics).
15 TRANSVERSE STAY CABLE ARRANGEMENT: DOUBLE CABLE-STAYING PLANE CONVERGING AT THE TOP OF THE TOWERS:The cable-staying system contribute to the shear, the bending, and the torsional responseAll the torsional response may be resisted by the cable staying system → thin transverse slab with two main eccentric longitudinal ribs where the anchorages are locatedSuperposition of stay cables (aesthetics).The torsional stiffness of the entire structural system is enhancedAdditional axial response of the towers under transverse wind loading
17 TOWERS:Single towerH-shape towerH-shape tower with an horizontal bracing (better resistance under transverse horizontal loads)A-shape tower (D: clearance when 2 cable-staying planes)Inverted-Y-shape tower (A: larger space for anchorages)Diamond-shape tower (appropriate when the deck in very high over the ground)
20 SINGLE-, TWO-, THREE- AND MULTIPLE-SPAN CABLE-STAYED BRIDGES: In single- and two-span bridges a larger tower high / span length ratio is requiredIn two-span bridges with similar span lengths a tower with a high flexural stiffness is required to guarantee the efficiency of the cable-staying system under live loadIn multiple-spans, three effective systems can be used to guarantee the efficiency of the cable-staying system:Stay cable bracing the top of all of the towersStay cable from the top of each tower to the bottom of the adjacent towersTowers with a high flexural stiffness
23 REFERENCES:CHEN, W. F. AND DUAN L Bridge Engineering. CRC Press LLCHAMBLY, E.C Bridge Deck Behaviour. Spon Press.PARKE G, HEWSON N ICE manual of bridge engineering. ICE.MANTEROLA, J. BRIDGES. (6 Volumes, in Spanish). ETSICCP, Madrid