空间主缆悬索桥水平母线鞍座设计位置计算的改进方法

Improved Method for Designing Position Calculation of Horizontal Bus Saddle of Spatial Main Cable Suspension Bridge

摘要: 以空间悬索桥的主缆与索鞍之间存在的几何及力学关系为依据，引入空间斜率作为缆索系统方程的基本参数，利用空间悬索桥索鞍左右两侧主缆切点的空间斜率作为未知量来构建二元非线性方程组，并利用二分法求解上述方程组即可确定空间缆索悬索桥水平母线鞍座的设计位置。改进方法简化了传统求解多元非线性方程组方法的复杂过程，给出了二元非线性方程组的求解区间，无需任何约束条件和迭代初值即可完成计算并保证计算结果收敛。通过对比该方法和传统方法计算出来的索鞍位置，证明该改进方法具有较高的精度。

Abstract: Based on the geometric and mechanical relations between the main cable and the cable saddle of the spatial suspension bridge, the spatial slope is introduced as the basic parameter of the cable system equation, and the spatial slope of the main cable tangential points on the left and right sides of the cable saddle of the spatial suspension bridge is used as the unknown quantity to construct the binary nonlinear equations. The design position of the horizontal bus saddle of the space cable suspension bridge can be determined by solving the above equations with dichotomous method. The improved method simplifies the complicated process of the traditional method of solving multivariate nonlinear equations, and gives the solving interval of binary non-linear equations. It can complete the calculation without any constraints and iterative initial values and ensure the convergence of the calculation results. By comparing the results of saddle position calculated by this method and the traditional method, it is proved that the improved method has higher precision.