考虑轴向位移的压弯Π形梁剪力滞分析

摘要

In the longitudinal displacement function of cross section,the axial displacement of cross section was introduced to describe the section deformation state of Π shaped girder under axial compression and bending.Based on energy variation method,the governing differential equations coupled with axial displacement,vertical displacement and shear lag displacement were deduced,and the displacement solution ofΠshaped girder under axial compression and bending and its corresponding boundary conditions were obtained.Combined with ANSYS software,the simply supported girder and cantilever girder were analyzed by using solid element,the derived displacement solutions and its boundary conditions,and the validity and reliability of the method were verified.The results show that the shear lag effect makes the separation between neutral axis and centroidal axis on the section of Π shaped girder,and the section no longer rotates around the centroidal axis.Under the action of bending,the shear lag decreases the flexural stiffness of the section of simply supported girder and the section within quarter span on the cantilever fixed side,and increases the flexural stiffness of the section within three quarter span on the cantilever free side.Under the action of axial compression and bending,the shear lag caused by axial compression decreases the flexural stiffness of the section near the end of simply supported girder,and increases the flexural stiffness of the section near cantilever free end.%在截面纵向位移函数中引入截面轴向位移,以描述压弯作用下Π形梁截面的变形状态.基于能量变分法导出轴向位移、竖向位移和剪力滞位移之间相互耦合的控制微分方程组,求得压弯作用下Π形梁的位移解及其相应的边界条件.结合ANSYS软件,利用实体单元和导出的位移解及其边界条件分别对简支梁和悬臂梁进行分析,验证其有效性和可靠性.结果表明:剪力滞效应使得Π形梁中性轴和形心轴相互分离,截面不再绕形心轴转动;在弯曲作用下,剪力滞使简支梁截面弯曲刚度减小,悬臂梁固定端一侧1/4跨度内截面弯曲刚度减小,悬臂梁自由端一侧3/4跨度内截面弯曲刚度增加;在压弯作用下,轴向压力引起的剪力滞使简支梁梁端附近截面弯曲刚度减小,悬臂梁自由端一侧截面弯曲刚度增加.