Research on the Refined Main Cable Shape-Finding Algorithm for Long-Span Suspension Bridges

This study aims to address the complexities in the calculation of the tangent stiffness matrix and the issues of divergence in iterative calculations in the shape-finding process of existing suspension bridge main cables. The research investigates the factors influencing the computational errors of existing cable element theories and the convergence or divergence of the main cable shape-finding calculations. First, a nonlinear equation for calculating the height of the cable element is constructed. Subsequently, a formula for cable height calculation is established according to the differential equations of the deformed cable element. Finally, considering the mass conservation principle before and after the cable deformation, a nonlinear system of equations for the configuration of the cable element is derived. Given the symmetric nature of the mid-span structure and loading in most suspension bridges, it is inferred that the point of the lowest slope of the main cable in the completed bridge state serves as the symmetry center of the structure. Consequently, a symmetric main cable shape-finding method is developed. A comparative analysis between the proposed method and existing iterative methods was conducted in terms of calculation accuracy and convergence behavior. The results indicate that the difference in horizontal cable force at the IP point between the two methods is 1.9 kN, and the difference in unstressed length is 2.5 mm. The calculation efficiency of the symmetric main cable shape-finding method is more than twice that of traditional iterative algorithms, with the number of iterations required for convergence generally being lower than that of traditional methods. For initial values that cause divergence in traditional iterative methods, the symmetric main cable shape-finding method achieved convergence within 10 iterations. The derived cable element theory and the symmetric main cable shape-finding calculation method can lay a theoretical foundation for the refined and efficient calculation of the main cable shape-finding process.