基于板-梁理论的集中荷载下带侧向弹性支撑矩形钢管混凝土翼缘工字形梁的弯扭屈曲分析  

Flexural-Torsional Buckling Analysis of I-shaped Beam with Concrete-Filled Rectangular Tubular Flange and Lateral Elastic Bracing Under Concentrated Load Based on Plate-Beam Theory

作　　者：张文福[1,2] 严威 刘迎春[1] 章丛俊[2] 赵文艳[1] 黄斌 邓世林[1] 李洋[1] 杭昭明 ZHANG Wenfu;YAN Wei;LIU Yingchun;ZHANG Congjun;ZHAO Wenyan;HUANG Bin;DENG Shilin;LI Yang;HANG Zhaoming(School of Civil Engineering and Architecture,Northeast Petroleum University,Daqing 163318,China;School of Architecture Engineering,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]东北石油大学土木建筑工程学院,黑龙江大庆163318 [2]南京工程学院建筑工程学院,南京211167

出　　处：《建筑钢结构进展》2021年第6期61-70,共10页Progress in Steel Building Structures

基　　金：国家自然科学基金(51178087、51578120);南京工程学院校级科研基金(YKJ201617)。

摘　　要：基于板-梁理论和能量变分原理,建立集中荷载下跨中布置侧向弹性支撑的矩形钢管混凝土翼缘工字形简支梁的弯扭屈曲总势能方程,其中位移和转角模态试函数选用6项三角级数形式。引入无量纲参数并依据势能驻值原理,获得弯扭屈曲无量纲临界弯矩解析解。采用1stOpt数学优化分析软件,拟合矩形钢管混凝土翼缘工字形简支梁无量纲临界弯矩计算公式,并与ANSYS有限元解进行对比。结果表明:拟合的无量纲临界弯矩计算公式具有可靠的精度,误差在5%以内,可为工程设计提供参考。Based on the plate-beam theory and energy variational method,the total potential energy equation of flexural-torsional buckling of I-shaped beam with concrete-filled rectangular tubular flange and lateral elastic bracing under concentrated load is established.The modal trial functions of the lateral displacement and torsional angle are expressed by the first six terms of the trigonometric function.By introducing dimensionless parameters and according to the principle of potential energy standing,the analytical solution of the dimensionless critical moment is obtained.The 1 stOpt mathematical optimization analysis software is used to retrieve the dimensionless bending moment of I-shaped simply supported beam with concrete-filled rectangular tubular flange.The finite element method is used to validate this formula.The results show that the formula of dimensionless critical moment has higher accuracy and the error is less than 5%,which can provide a reference for future engineering design.

关 键 词：侧向弹性支撑 弯扭屈曲 板-梁理论 能量变分法 矩形钢管混凝土翼缘 模态试函数 

分 类 号：TU398[建筑科学—结构工程]