预张力悬索桥及其静力学性能分析

为从理论上获得预张力悬索桥的力学特性,利用大位移不完全广义势能变分原理,建立了预张力悬索桥的一般基础微分方程.在进一步引入假设条件下,导出了基于古典挠度理论的平衡微分方程.通过对微分方程的解析,讨论了预张力悬索桥的静力学特性及其与普通悬索桥的区别.结合算例悬索桥的数值分析表明,预张力悬索桥由于抗风索的存在,以及结构中建立的预张力,在提高结构刚度、减小加劲梁弯矩等方面具有一定的优越性.

Determination of initial cable force of cantilever casting concrete arch bridge using stress balance and influence matrix methods

Cantilever casting concrete arch bridge using form traveller has a broad application prospect.However,it is difficult to obtain reasonable initial cable force in construction stage.In this study,stress balance and influence matrix methods were developed to determine the initial cable force of cantilever casting concrete arch bridge.The stress balance equation and influence matrix of arch rib critical section were established,and the buckle cable force range was determined by the allowable stress of arch rib critical section.Then a group of buckle cable forces were selected and substituted into the stress balance equation,and the reasonable initial buckle cable force was determined through iteration.Based on the principle of force balance,the initial anchor cable force was determined.In an engineering application example,it is shown that the stress balance and influence matrix methods for the determination of initial cable force are feasible and reliable.The initial cable forces of arch rib segments only need to be adjusted once in the corresponding construction process,which improves the working efficiency and reduces the construction risk.It is found that the methods have great advantages for determining initial cable force in cantilever casting construction process of concrete arch bridge.

用牛顿迭代法探讨悬索桥端点张力

悬索计算难点在于垂度的非线性方程如何解,文章采用数值分析中的Newton迭代法进行计算。分别从传统人工、卡西欧计算器、Mathematica、GeoGebra等4种不同计算手段求得相同结果的思维过程出发,为提升学生运用数学工具解决物理问题的能力提供可行性的办法。