斜拉桥轴向力效应的半解析法

A Simplified Method for the Calculation of Effect of Axial Force in a Cable--Stayed Bridge

本文以梁的振型函数为位移试函数,基于最小势能原理,采用拉氏乘子法强制满足桥墩处主梁的位移条件,对斜拉桥拉索的轴力,塔架和主梁的弯炬、轴力及挠曲位移作了计算。文中考虑了梁、塔的轴向力对挠度的影响(即梁—柱效应),采用牛顿迭代法修正求解。由于利用了梁振型函数的正交性,刚阵形成简单。计算实例表明,只需取试函数的前几项迭代3～5次,便可得到较满意的解答。本法计算量、未知量均很少,可在微机上求解。

Based on the priniciple of minimum potential energy and Lagrangian approach, the axial force of cable, moment of beam and moment of pylon are calculated by using the vibration mode func- tion. In this paper, the effect of axial force on deflection is analyzed by using Newton method to modify the solution. Because of the orthogo- nality of vibration mode functions, the formation of the stiffness matrix is straight forward. Numerical results show that the convergence and accuracy is good and the problem can be solved in a microcom- puter.