基于刚性支承连续梁法的悬索桥成桥状态解析算法  

Analytical algorithm for completed state of suspension bridge based on rigid supported continuous beam method

作　　者：朱伟华 刘国坤 颜东煌 许红胜 ZHU Wei-hua;LIU Guo-kun;YAN Dong-huang;XU Hong-sheng(School of Civil Engineering,Hunan City University,Yiyang 413000,Hunan,China;School of Civil Engineering,Changsha University of Science and Technology,Changsha 410001,Hunan,China;School of Architecture Engineering,Hunan Institute of Engineering,Xiangtan 411104,Hunan,China)

机构地区：[1]湖南城市学院土木工程学院,湖南益阳413000 [2]长沙理工大学土木工程学院,湖南长沙410001 [3]湖南工程学院建筑工程学院,湖南湘潭411104

出　　处：《长安大学学报（自然科学版）》2024年第1期58-67,共10页Journal of Chang’an University(Natural Science Edition)

基　　金：国家自然科学基金项目(51878073);湖南省研究生科研创新项目(CX20190649)。

摘　　要：为解决悬索桥合理成桥状态平衡态计算闭合问题,系统提出成桥状态的解析算法。首先,根据余能定理推导基于刚性支承连续梁成桥状态目标函数,考虑索塔压缩变形,基于悬链线理论建立缆索体系非线性方程组;然后,考虑加劲梁无应力曲率,根据加劲梁弯曲变形微分方程组,构建多节点力作用下的加劲梁位形计算非线性方程组;进而,根据成桥状态下刚性支承连续梁位形,设立加劲梁各吊点最优化控制目标函数;最后,基于吊索体系联立缆索体系与加劲梁体系的力学模型非线性方程组,实现基于刚性支承连续梁的成桥状态各构件力学参数化求解,并将推导的解析算法与有限元模型的研究结果进行对比分析。结果表明:解析算法计算结果由于计算过程的闭合条件,与有限元模型计算结果基本吻合,对于关键参数吊索力及主缆线形计算差值率控制在0.1%以内,加劲梁弯矩极值差值率约为-0.34%;推导的解析算法为精细化合理成桥状态闭合方法,可作为悬索桥合理成桥状态设计的可靠方法。To solve the problem of calculating and closing the equilibrium state of suspension bridge,an analytical algorithm of completed state of suspension bridge was proposed.First of all,according to the complementary energy theorem,the state objective function of the rigid supported continuous beam was derived and the compression deformation of the tower was considered,nonlinear equations of the cable system was established based on the catenary theory.And then the unstressed curvature of the stiff girder was considered,according to the differential equations of bending deformation of stiffening beams,the nonlinear equations for calculating the configuration of stiffening beams under multi-node forces was constructed.Furthermore,according to the configuration of the rigid supported continuous beam,an optimization objective function for each suspension point of the stiff girder was established.Finally,based on the nonlinear equations of the mechanical models of the cable system and the stiffening beam system,the mechanical parameterization solution of each member in the bridge state based on the rigid supported continuous beam was realized.The derived analytical algorithm was compared with the research results of FEM.The results show that because of the closure condition of the calculation process,the calculation results of the analytical algorithm are in good agreement with the results of the finite element model.The difference rate of calculation of the key parameters,the suspension cable force and the main cable shape are controlled within 0.1%,and the difference rate of the maximum bending moment of the stiff girder is approximately-0.34%.The derived analytical algorithm is a refined and reasonable closure method of the bridged state,which can be used as a reliable method for the design and calculation of the rational completed state of suspension bridges.11 figs,26 refs.

关 键 词：桥梁工程 悬索桥 解析算法 合理成桥状态 刚性支承连续梁 悬链线理论 目标函数 

分 类 号：U448.25[建筑科学—桥梁与隧道工程]