空间自锚式悬索桥水平母线索鞍预偏量计算的改进方法

Improved Method for Calculating the Pre Deflection of the Horizontal Busbar Saddle of a Space Self Anchored Suspension Bridge

摘要: 针对现有求解预偏量方法迭代复杂，收敛慢的问题，提出一种改进的空间悬索桥水平母线索鞍预偏量计算方法。作者在前期的研究过程中，建立了全新的空间主缆线形方程，在此基础上对索鞍成桥状态和空缆状态的力学与几何关系进行分析，推导出一个七阶非线性方程组，运用牛顿–拉弗森算法推导了雅可比矩阵，确定了初始值的选取方法，求解非线性方程组得到了水平母线索鞍预偏量。通过一个算例证明该计算方法能够满足空间悬索桥施工的精度要求，计算更加简便，迭代更加便捷，收敛较快，为空间悬索桥的建设提供有效的理论依据。

Abstract: Aiming at the problems of complex iteration and slow convergence of existing methods for solving pre deflection, an improved method for calculating the pre deflection of the horizontal busbar saddle of a spatial suspension bridge is proposed. In the preliminary research process, the author established a new spatial main cable linear equation. A seven element nonlinear equation system was derived, and the Newton Raphson algorithm was used to provide the iterative format, solving steps, and Jacobian matrix for the solution. Through a numerical example, it is proven that this calculation method can meet the accuracy requirements of space suspension bridge construction, with simpler calculations, more convenient iterations, and faster convergence, providing effective theoretical basis for the construction of space suspension bridges.