ANALYTICAL STUDIES OF A CABLE STAYED GIRDER BRIDGE

Abstract The paper deals with the linear and nonlinear behavior of a cable stayed girder bridge subjected to static and dynamic conditions of load. Particular reference is given to a bridge designed by the Division of Bay Toll Crossings for the Southern Crossing of San Francisco Bay, California. The loads and displacements considered are symmetrical to a vertical plane which includes the central longitudinal axis of the roadway girder. The orientations of the cables and of the diamond-shaped towers are in three dimensional space and are taken into account. A linear theory and a nonlinear theory are presented for determining the effects of static conditions of loads on the bridge. The linear theory is employed in determining influence lines for various parameters of the bridge, and in determining the maximum effects caused by specified live loads, temperature changes, and differential movements. The influence lines are based on the direct application of Muller-Breslau's principle to structures composed of finite elastic elements. The linear theory also is employed for obtaining the effects of selected cases of live load distributions. Special attention is given to the distributions forces and moments in the towers and the girder, and of the forces in the cables. The nonlinear theory is general and is employed for static and dynamic conditions of load. For static conditions of load, the theory is employed for determining, (1) the camber of the girder and the dimensions of each unstressed segment of the bridge, (2) the displacements, forces, and moments at each section of the bridge for various stages of erection, and (3) the influence of possible overloads of vehicular traffic on the nonlinear behavior of the bridge. The dimensions of the unstressed segments are required for fabrication and to determine camber. The camber is required to insure that all conditions at dead load, prescribed by the designers, are obtained after erection. The other studies of nonlinear behavior are needed to determine possible modes of failure during and after erection. For use in the nonlinear theory, nonlinearforce-deformation relations and tangent stiffnesses are required for the kinds of members encountered in the analytical model. The kinds encountered are (1) axial-flexual members which lie in three dimensional space, and (2) catenaries. For the axial-flexural members, the influences of eccentricities are taken into account.