集中力活载作用下悬索桥变形及内力的解析算法

Analytical Method for Deformation and Internal Force of Suspension Bridge under Concentrated Live Load

悬索桥作为一种柔性结构,活载下的响应是长期以来被研究的重点内容。该文针对悬索桥提出了一种集中力活载作用下结构变形及内力的解析计算方法。以已知成桥状态参数和活载参数为基础,首先分析了主缆变形、主梁变形、主缆和主梁的关系、桥塔变形。随后建立了4类控制方程,分别为各段主缆的无应力长度守恒、各根吊杆的力与变形协调、各跨跨径及高差闭合和主梁的受力平衡,从而使得控制方程的总数与基本未知数的总数相等。最后将控制方程合并成一个目标函数,并进行规划求解。找到基本未知量的取值,使得全部控制方程同时成立,进而推导出所有其他参数,并表达出结构变形后的状态。以一座主跨1 080 m的悬索桥作为算例,验证了方法的可行性和有效性。活载作用下变形及内力的结果都具有良好的精度,与有限元的结果相一致。

As a flexible structure,the response of suspension bridges under live load has been the focus of research for a long time.This paper presented an analytical calculation method for structural deformation and internal force of suspension bridges under concentrated live load.Based on the known bridge state parameters and live load parameters,the deformation of the main cable,the deformation of the main beam,the relationship between the main cable and the main beam,and the deformation of the bridge tower were analyzed successively.Then,four kinds of governing equations were established,involving the conserved unstrained length of each main cable,the coordinated force and deformation of each suspender,the closed span and height difference,and the balanced force of the main beam,so that the total number of the governing equations was equal to the total number of basic unknown parameters.Finally,the governing equations were combined into an objective function and solved programmatically.The values of the basic unknown parameters were found to make all the governing equations valid at the same time,and then all the other parameters were deduced.The state of the structure after deformation was expressed.Finally,a suspension bridge with a main span of 1080 m was taken as an example to verify the feasibility and effectiveness of the method.The results of deformation and internal force under live load were in good agreement with those of the finite element method.