确定悬索桥主缆成桥线形的参数方程法

Parameter equation methods for determination of main cable's profile of suspension bridges

假设悬索桥主缆自重沿弧长均匀分布,加劲梁、桥面等其余恒载沿水平均匀分布,导出了悬索桥主缆成桥线形的参数方程解。然后由边界条件及连续性条件,建立了确定主缆成桥线形的非线性方程组。根据中跨方程组可求出成桥状态主缆张力水平分量和中跨端点处对应的参数,再由中跨与边跨主缆张力水平分量相等的假定,根据边跨方程组来确定边跨端点处的参数。这样,主缆吊点坐标计算最终被转换成求解一个非线性方程。本文采用拟牛顿法求解非线性方程组,采用对分法求解非线性方程,算例结果表明本文方法具有适合程序计算、收敛速度快、计算精度较高的特点。

Suppose the self-weight of main cable distributing uniformly along the curve length, and those of stiffening girder and bridge deck distributing uniformly along the horizontal length, the general solution of the main cable's profile formula after completion is derived. Then the nonlinear equation group of the main cable's profile is determined according to the boundary conditions and deformation compatibility condition. The horizontal component of the cable tension force and the corresponding parameters at the end points of the mid-span are derived according to the mid-span equations. After that, the parameters at the end point of the side-span are solved according to the equality of the horizontal components of the cable tension force between the mid-span and the side-span. Thus through solving a nonlinear equation, the coordinates of hanging points can be obtained. The quasi-Newton method is used to solve the nonlinear equation group and bisection method is used to solve the nonlinear equation. The result of the example shows that this method is easy for programming and has a rapid convergence. Also the results are of pretty high accuracy.