考虑索端刚臂的斜拉桥空间拉索非线性分析

为解决斜拉桥空间拉索在塔和梁上锚固点的刚性连接计算问题,在基于微分法导出考虑垂度效应的非线性空间杆元切线刚度矩阵的基础上,根据索端刚臂在受力后只有刚体运动而本身不变形的特点,将刚臂视为空间矢量,利用空间矢量有限转动公式及微分方法,导出了结构坐标系下刚臂两端的位移之间和杆端力之间的总量及增量关系.最终获得两端带任意刚臂的斜拉索空间杆元切线刚度矩阵表达式,编制了相应的斜拉桥几何非线性有限元计算程序,对经典桁架算例、带刚臂的三杆空间桁架和施工阶段的斜拉桥进行了空间几何非线性分析.计算结果表明:本文方法能解决斜拉桥空间拉索在塔和梁上锚固点的刚性连接计算问题,为斜拉桥进行几何非线性精细分析提供有力工具.

Non-linear Analysis of Spatial Stay Cable with Rigid Arms of Cable-stayed Bridge

In response to the problem of rigid link of anchorage point, which occurs to spatial cable fixed on the girder and the tower of cable-stayed bridge, on the basis of tangent stiffness matrix of nonlinear spatial truss element by differential method, and according to the characteristics of the forced rigid arm without deformation but rigid motion, the relationships between the total amount and increment of the displacement and the end force of ends of rigid arms in global coordinate system were presented by treating rigid arm as the spatial vector and employing its finite rotation formula and differential method. Then, the explicit expressions of nonlinear tangent stiffness matrix of spatial stay cable 3-D truss element with rigid arms on both ends were obtained. A finite element program based on the algorithm was developed to analyze the geometric nonlinear behaviors of cable-stayed bridge. Three examples, including spatial trussed structure with or without rigid arms and a cable-stayed bridge in construction process, were employed to perform spatial geometrical nonlinear analysis. The results show that the new algorithm can solve the rigid link of anchorage point completely, and it provides a powerful tool for refined geometrical nonlinear analysis of cable-stayed bridge.