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

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.