The Formulas for Solving the Cable-free Cable Length Based on Newton-raphson

Based on the catenary theory of stayed cables, a method for calculating the cable length of cable-stayed bridge without stress is proposed. The constraint equations of the cable's characteristic parameters under the known terminal tension state are established, and the formulas for solving the cable-free cable length are given. By using this method, the cable-free cable length of Fengdu Changjiang No.2 Bridge was calculated, and the results were compared with the results of Ernst equivalent modulus method and Levenberg-Marquardt iterative solution. A comparative analysis proves the reliability and effectiveness of the method.