Abstract:
In the spatial main cable configuration calculation of suspension bridges, establishing an accurate correspondence between control point displacements and initial forces is a critical challenge. This paper proposes a configuration stiffness matrix method that directly establishes the correspondence between displacement errors and initial force corrections for key control points in a single step. A spatial main cable-hanger collaborative analysis model is established, where both the main cable and hangers are simplified as flexible cables to form a spatial interaction relationship. Based on this model, the unstressed cable length is treated as a variable to establish a complete Jacobi matrix, which is then rigorously eliminated through partial differentiation, yielding the main cable Jacobi matrix and the hanger inverse Jacobi matrix. Force transfer matrices and cumulative transfer matrices are introduced to construct a global equation system, from which the stiffness matrix for three key control points is directly extracted, establishing a linear relationship between control point displacement errors and initial force corrections. The algorithm is implemented in C++ and validated using the Xi'an Bahe Yuanshuo Bridge. The convergence is achieved in 23 iterations with a computation time of 1~2 seconds. The computational results show an excellent agreement with those of BNLAS software and demonstrate strong robustness with respect to the initial value selection, verifying the correctness and engineering applicability of the method proposed.