Simplified calculation method for deformation of multi-tower cable-stayed bridges with crossed cables

This study explored an analytical method for calculating deformation of a multi-tower cable-stayed bridge (CSB) with crossed cables, which can be used to determine whether the number of crossed cables and tower stiffness are reasonable in the preliminary design. An analytical expression for the longitudinal stiffness constraint imposed on a bridge tower by crossed cables was derived, which could solve the constraint function of crossed cables in the case of different tower heights. An analytical solution for calculating the tower top displacement and midspan deflection of the bridge girder under live loads was obtained and may take into account the effect of tower stiffness, number of main, spans and parameters concerning crossed cables on structural deformations simultaneously. Furthermore, a finite element simulation was performed to verify the accuracy of the proposed equations. The numerical results were consistent with the theoretical results calculated by the equations, demonstrating that the equations can provide accurate estimates of structural deformations required for bridge design in the preliminary design stage.