基于修正翘曲位移函数的薄壁箱梁剪力滞效应分析

Analysis on shear lag effect in thin-walled box girders based on modified warping displacement function

为完善薄壁箱梁剪力滞效应研究,构造余弦函数作为剪力滞效应下纵向翘曲位移分布形态的描述,考虑弯曲剪力流分布对薄壁箱梁弯曲曲率和顶底板纵向翘曲位移的影响,引入顶板悬臂板纵向翘曲位移差函数修正系数及内力平衡因子,基于能量变分法,推导了薄壁箱梁剪力滞效应作用下应力与挠度计算微分方程.针对单箱单室简支箱梁和连续箱梁算例,将理论分析方法得到的应力和挠度计算值与有限元结果和实测值进行对比分析.结果表明,按理论分析方法得到的薄壁箱梁纵向应力值不仅与有限元结果、实测值吻合良好,而且能真实地反映顶板悬臂板应力分布形态.集中荷载和均布荷载作用下,考虑剪力滞效应影响的方法使得薄壁简支箱梁跨中挠度分别增加了25. 34%和19. 22%,与有限元结果的误差分别为1. 31%和1. 83%,精度较高.该理论分析方法可以准确预测薄壁箱梁在任意荷载作用下的截面应力与挠度分布.

To improve the analysis on the shear lag effect in thin-walled box girders,a cosine-function was contrasted to describe the distribution pattern of the longitudinal warping displacement under the shear lag effect.The effect of the shear flow distribution on the bending curvature of the thin-walled box girder and the difference function of the longitudinal warping displacement in top and bottom flanges were investigated,and the correction factor on the difference function of the longitudinal warping displacement in the top cantilever flanges were introduced.The internal force equilibrium was considered and the internal force balance factor was given.Based on the energy variation method,the differential equations for the normal stress and the vertical displacement were deduced.The examples of simply supported and continuous single-cell thin-walled box girder were chosen.The normal stress and the deflection calculated by the theoretical analysis method were compared with those of the finite element method(FEM)and the experimental study.The results show that normal stress values of the flanges obtained from the theoretical analysis method is in good agreement with the FEM and experimental results,and can reflect the normal stress distribution pattern of top cantilever flanges.Under the concentrated load and the uniformly distributed load,the deflection at the mid-span calculated by the theoretical analysis method considering the shear lag effect increase by 25.34%and 19.22%,respectively,and the errors between the results of the theoretical analysis method and those of the FEM are 1.31%and 1.83%,respectively,exhibiting the high precision of the theoretical analysis method.This theoretical analysis method can accurately predict the distribution of the normal stress over the cross-section and the displacement under arbitrary load.