悬链线解答在斜拉索数值分析中的应用

斜拉桥和斜拉索是几何非线性明显的结构。随着斜拉桥跨径的飞速增长,斜拉索的长度也大大增加,目前最长的斜拉索的水平投影长度已超过500 m,这大大超出了常用斜拉索的长度,原有理论的计算精度值得研究。由弹性悬链线静力解析解可推导出弹性悬链线单元,得到单元的刚度矩阵和单元的节点力向量,集成后得到结构的平衡方程。根据该方法,编制了弹性悬链线单元的有限元程序并进行实例计算。该程序可以一根索的任何一个参数值(如索端张拉力或测量预应力状态下的索长)为已知条件来确定索的状态,结果表明,该程序所需单元少、结果精度高,可方便应用于工程实践。建议超大跨度斜拉桥拉索的受力分析采用基于悬链线单元的分析方法。

Application of Catenary Solution in Numerical Analysis of Stayed Cables

Cable-stayed bridges and stayed cables are geometrically obvious nonlinear structures.The length of stayed cables in use has been rising to accommodate the increasing spans of cabled-stayed bridges.The longest cable has reached over 500 m,much longer than ordinary cables.The increasing length of stayed cables in use makes it necessary to study the character of long stayed cable.The stiffness matrix and node force vector of the elastic catenary element can be gained,and the equilibrium equation of the structure can be assembled,based on static analytical solutions of the elastic catenary.In this paper,the relationship between the stressed length(or end tension forces) and the unstressed length of cables is derived.The corresponding iterative procedure also is presented.With this approach,a finite element program on the elastic catenary element is developed.Two examples are investigated.The finite element program leads to high precision as the solution with only a few elements that also meets engineering requirements.The authors therefore recommended using the catenary element in analyses of stayed cables.