An Iterative Calculation Method for Suspension Bridge’s Cable System Based on Exact Catenary Theory

Abstract

In this paper, a flexible iterative method capable of considering the effects of slip between the main cable and saddles is presented for the analysis of the cable system in the suspension bridge. In the proposed procedure, nonlinear governing equations were first linearized based on the first-order Taylor expansion, then the tangent stiffness matrix was derived using appropriate numerical methods. Using the proposed flexible iterative procedure which is built upon the framework of Newton-Raphson method, the main cable’s unstrained length and equilibrium forces which satisfy the configuration and mechanical property under bridge’s completion state is obtained according to the main cable’s initial geometry parameters, saddles parameters and hangers arrangement. Based on form-finding analysis, the method is also proposed to calculate the main cable’s internal forces and displacements during the erection of stiffening girder; the reliability and efficiency of the method is demonstrated by two typical numerical examples. Furthermore, the proposed method is used as a pro-processing tool in the finite element analyses of a cable structure. Finally, a numerical example (Yingwuzhou Yangtze River Bridge) is reported to illustrate the advantages of the proposed method, including the accurate predictions of the main cable’s unstrained length and the excursion of the saddles, which is crucial for choosing appropriate saddles parameters.