STATIC AND DYNAMIC STUDY OF CABLE-STAYED BRIDGES

Abstract

Cable-stayed bridges are structural systems in which inclined cables emanate from one or more points of supporting towers and hold large span stiffening girders of the bridge deck at intermediate locations between the main supports. Modern cable-stayed bridges are found to fulfil the engineering requirement of optimum structural use of materials involved in their construction for a span range of 90-370 m. These bridges possess a good aesthetical appeal. A wide acceptance of the concept of the cablestayed bridge has faced organisational as well as tech nological problems in the past. The present study aims at advancing the understanding about the analysis proce dure and the static and dynamic behaviour of such bridges through investigation of the influence of certaJJi impor tant parameters and experimental verification of the ana lytical results. The specific objectives of the present investigation ares (a) To determine the effects of parameters like nonlinear axial-flexural interaction, prestressing of the cables, and soil-structure interaction on the behaviour of the bridge under symmetric vertical loads. (ii) (b) To investigate the behaviour of the bridge under eccentric vertical as well as lateral loads with and without soil-structure interaction effects. (c) To work out the influence of geometrical para meters of the bridge, like side to main span ratio, tower height to main span ratio etc., on its lateral load behaviour. (d) To study the free vibration mode shapes in the principal directions of the bridge and to com pute the dynamic response to a specified base motion. (e) To verify some of the analytical results by comparison with experimental results of a small size laboratory structure. Radiating type bridge structures having six cables on each side of the tower legs with (a) a main span and two side spans (referred to as a 3~span system) and (b) with anchor piers added at mid points of the side spans (ref erred to as a 5-span system) have been chosen for the present investigations. Parametric lateral load studies have been made on the three span structure having three equivalent cables, in place of six. Appropriate two dimensional and three dimensional mathematical models have been developed to take into acc ount the actual conditions of transfer of forces between (iii), the superstructure and the substructure. In the three dimensional models, the lateral stiffness of the transverse girders has been replaced by equivalent diagonal members. The stiffness matrix method has been used for sta tic analysis and for obtaining deflection influence coeffi cients. For free vibration analysis, the inverse iteration technique coupled with approximation to the RayleigL Quo tient has been used to find the fundamental period and associated modeshape. The higher periods and modes have been obtained by Wilkinson's deflation technique. As an illustration of seismic response calculations, maximum probable response of a bridge has been evaluated for a spe cified ground motion spectrum in the traffic direction. Experimental studies under static and dynamic load ing conditions have been made on a small size laboratory model of aluminium alloy. The laboratory structure has been scaled down from a major bridge proposed in India, using a scale factor of 1/200. The analytical results of this laboratory structure have been obtained after taking due care to represent the actual conditions of rotational and torsional fixity available at the base of the subs tructure and to represent actual tensile stiffness of aluminium wires used as cables. A comparison of analyti cal and experimental values of the laboratory structure has been made. (iv) The main conclusions arrived at from the study are the following: The three span system is appreciably more flexible than the five span system. The effect of axial-flexural interaction is to increase the overall flexibility of the system. The increase is seen to be within 10# for the five span system, but the increase in the axial forces in main girder elements is seen to be significant. The mutual sharing of eccentric vertical loads by the main girders is moderate as seen from the study of the bridge under vertical loads applied to one of the main girders. The forces and deformations in the unloaded side lie generally between 10 to 2% of those on the loaded side. Other effects of eccentric loading are the horizontal bend ing and twisting of the deck near the centre of main span which must be considered in the design. Under the action of lateral forces, the deck tends to act as a horizontal girder with cables carrying only negligible axial forces. Axial forces and moments in the main girder elements are significantly effected by the ratio of the side span to centre span. The ratio of tower height to centre span has significant effect on twisting and hori zontal bending of the main girders and axial forces, shears and moments in the tower and the substructure. The ratio of cable stiffness to girder torsional stiffness effects (v) horizontal bending and twisting of tower legs. The effects of increasing the width of deck is to decrease the horizon tal bending of the deck. The effect of soil-structure interaction, even when soil is soft, is seen to be negligible on the superstructure forces but the substructure forces are significantly increased. Most of the lower modes of free vibration are charac terised by the deflections of the deck in the vertical plane, Experimentally, it does not appear possible to induce a pure mode in the superstructure due to cable vibrations. Comparison of analytical and experimental results is generally good which proves the adequacy of the analyses adopted.