分段抛物线求解缆索线形的直接方法

Direct Solution Procedure Obtaining the Line Shape of Cable with Segmentation Parabolic Function

假设悬索桥主缆在相邻两吊杆之间的缆索段自重沿桥跨径方向均匀分布,均布荷载集度与该段索长度有关,则每段索可假设为满足抛物线方程.忽略缆索抗弯性能,各缆索段端点处水平力相等,索拉力沿索端点处切线方向.根据节点力平衡,并考虑到位移条件,得到以各段端点高差及水平力为未知量的耦合方程组.通过解算方程组并修正矩阵参数直接得到主缆线形坐标及水平力,进一步对各段抛物线积分得到主缆的有应力和无应力长度.该方法不需要迭代,因此计算速度快.算例结果表明该方法计算精度很高,可以用于悬索桥设计与施工计算.

Assuming self-weight of cable segments uniform distributed with coordinate axis, the cable segments curve can be denoted as parabolic function. Based on the force equalization of nodes, and considering the displacement coordination conditions, the parameter equations are established, in which the height differences and horizontal force are considered as unknown quantifies. To be worth presenting, the equations can be solved directly. So the unknown quantities can be obtained quickly. The fact that calculation result meets well with exact solution indicates the method can be used for design and construction control for cable bridges.