基于板-梁理论的单轴对称箱形钢梁组合扭转分析

An Analysis of Combined Torsion of Uniaxial Symmetric Box Steel Beams Based on Plate-beam Theory

以端部作用一个集中扭矩的单轴对称箱形截面悬臂梁为研究对象,基于板-梁理论研究其扭转变形和截面扭转角.依据Timoshenko梁和Kirchhoff板力学模型,引入腹板翘曲变形偏移值m,求出单轴对称箱形钢梁扭转的总应变能和扭转刚度;根据端部作用集中扭矩的荷载,建立箱形钢梁的总势能方程,并求得单轴对称钢箱梁组合扭转最大扭转角的理论解.借助大型通用有限元分析软件ANSYS,依据扭转参数K,计算6组不同尺寸的钢梁在端部集中扭矩作用下的最大扭转角.与板-梁理论的理论解进行对比,最大误差为3.37%,证明了理论解的正确性.

Taking an uniaxial symmetric box-section cantilever beam with a concentrated torque acting on the end as the research object,this paper aims to study torsional deformation and the torsion angle of the section through using Plate-beam theory.According to the mechanical model of Timoshenko beam and Kirchhoff plate,web deformation offset value m is introduced to obtain torsional total strain energy and torsional stiffness of uniaxially symmetric box steel beams.The total potential energy equation of the box-shaped steel beams is built in line with loads of concentrated torques acting on the end.And theoretical solution for the maximum torsion angle of the combined torsion of uniaxially symmetric steel box beams is obtained.With the help of ANSYS,a large-scale general finite element analysis software,the maximum torsion angle of 6 groups of steel beams with different sizes under the action of concentrated torque at the end is calculated according to the torsion parameter K.Compared with the theoretical solution of the Plate-beam theory,the maximum error is 3.37%,which proves the correctness of the theoretical solution.