薄壁箱梁畸变的Galerkin解法  

Galerkin Methods for Distortion of Thin-Walled Box Girders

作　　者：王兆南 张元海[1] WANG Zhaonan;ZHANG Yuanhai(School of Civil Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学土木工程学院,兰州730070

出　　处：《工业建筑》2022年第3期112-116,207,共6页Industrial Construction

基　　金：国家自然科学基金项目(51968040)。

摘　　要：为揭示简支薄壁箱梁的畸变效应和跨内横隔板数量对箱梁畸变的影响,在改进的箱梁畸变分析理论的基础上,建立了以箱梁腹板竖向挠度为未知量的畸变控制微分方程,采用Galerkin解法进行求解。分析了矩形截面箱梁以畸变角为未知量和以腹板畸变挠度为未知量的畸变扇性坐标、畸变翘曲惯性矩之间的联系。通过算例,采用解析法研究了简支箱梁跨内横隔板数量对箱梁畸变的影响。结果表明:Galerkin解法求解箱梁跨内横隔板数量对畸变变形的影响较为直观,当箱梁在跨内设置3道横隔板时,腹板的竖向挠度可减小到不设跨内横隔板时挠度的98.84%,跨内横隔板数量多于3道时,限制箱梁畸变变形的效果并不明显;本文方法计算的箱梁畸变挠度和有限元结果较为接近,与修正后的相关文献算式计算结果吻合较好。To investigated the distortion effect and the influence of diaphragms in the span on the distortion of the simply supported thin-walled box girder. Based on the improved distortion analysis theory of box girder, the distortion control differential equation with the web vertical deflection as the unknown quantity was established and solved by Galerkin methods. The relationship between distortion sector coordinates and distortion warping moment inertia of rectangular cross section box girder with distortion angle and web distortion deflection as unknown quantity were analyzed. Through an example, the influence of the number of diaphragms on the distortion deformation of simply supported box girder was studied by analytical method. The results show that the influence of the number of diaphragms on the distortion deformation of box girder by Galerkin methods is more intuitive. When end diaphragms existence, three diaphragms set in the box girder, the web vertical deflection can be reduced to 98.84% of that only end diaphragms. When there are more than three diaphragms in the box girder, the effect of limiting the distortion deformation of box girder can not be significantly improved. The distortion deflection calculated by proposed method is close to the finite element results, and is in good agreement with the calculated results of the modified relevant literature formulas.

关 键 词：薄壁箱梁 畸变 GALERKIN解法 横隔板 畸变挠度 

分 类 号：U441[建筑科学—桥梁与隧道工程]