基于抽象翘曲位移函数的箱形梁剪力滞效应分析  

Analysis of Shear Lag Effects in Box Girders Based on Abstract Warping Displacement Functions

作　　者：姚晓东 张元海[1] YAO Xiaodong;ZHANG Yuanhai(School of Civil Engineering,Lanzhou Jiaotong University, Lanzhou 730070,P.R.China)

机构地区：[1]兰州交通大学土木工程学院,兰州730070

出　　处：《应用数学和力学》2018年第12期1351-1363,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51468032; 51268029)~~

摘　　要：针对薄壁箱梁剪力滞问题,基于抽象的翘曲位移函数,通过对控制微分方程的形式进行分析研究,构造出剪力滞翘曲位移函数的基本形式;对翼板引入边界约束影响的修正系数,然后通过能量变分原理推导出了箱形梁剪力滞的控制微分方程及其解析解.根据有限元结果确定翼板边界约束影响修正系数的具体值,以带翼板的简支箱形梁分别作用集中荷载和均布荷载为数值算例,进行了计算分析.分析结果表明:采用该文方法计算的结果与有限元结果总体吻合良好,并且该文的计算结果也反映出了翼板应力小于顶板应力的分布规律,从而验证了该文分析方法的正确性.In view of the shear lag problem in thin-walled box girders,based on the abstract warping displacement functions,the form of the control differential equation was studied. The basic form of the shear lag warping displacement function was constructed. The correction coefficient of the boundary constraint influence on the flanges was introduced,and then the control differential equation of shear lag was deduced under the energy variational principle. According to the finite element results,the value of the boundary constraint correction coefficient for the flanges was determined. A simply supported box girder with flanges was calculated and analyzed under uniform and concentrated loads,respectively. The analytical results are in good agreement with the finite element results. Moreover,the flange stresses are less than the corresponding top plate stresses. The comparison verifies the correctness of the proposed analytical method.

关 键 词：剪力滞效应 薄壁箱梁 能量变分 翘曲位移函数 解析解 边界约束修正系数 

分 类 号：O39[理学—工程力学]