Application of Exact Element-Method on Calculation of Form-Finding and Unstressed Length of Cable

Abstract

The problem of form-finding for the suspended cable is actually the problem of determining all key points' coordinates on main cable, which are by equilibrium relation on the horizontal force, main cable sagitta and lifting point force under the precondition of determining the endpoint's boundary conditions of cable segment. According from the static equilibrium relationship of cable element, based on the analysis of its analytical solution process, in this paper, the cable elements are divided into two types in accordance withthe vertical distribution load along the arc length and along the string length , the corresponding shape curve of cable element is the parabola and the catenary, and with parabolic results as its initial value for the iteration of nonlinear solution, then cable element eventually converge for the catenary. And based on the exact coordinates results ,the calculation method of the length without stress is presented ， and compiled corresponding computational procedures. By comparing the results of form-finding and the cable-length in non-stress according to program compiled and the results from the finite element software and the measured value of Aizhai suspension bridge, compared with the nonlinear finite element method,it confirmed the method requireing smaller dividing element density, the convergence speed is quicker and the results can ensure the precision.