带悬臂板薄壁箱梁极惯性矩的合理计算方法

Rational Method for Computing Polar Inertia Moment of Thin-walled Box Girders with Cantilever Slab

分析带悬臂板箱梁横截面上各项剪应力及其合成的扭矩,导出极惯性矩和翘曲系数的表达式并论证计算极惯性矩时考虑悬臂板的必要性。在约束扭转控制微分方程基础上,给出简支箱梁跨中作用集中扭矩荷载时各广义位移和内力的初参数解。结合数值算例,分别按考虑和不考虑悬臂板情况计算极惯性矩,将求得的全截面翘曲正应力与通用有限元软件ANSYS壳单元计算结果进行比较,分析不同极惯性矩计算结果对广义位移和内力的影响。结果表明:计算极惯性矩考虑悬臂板时求得的翘曲正应力比不考虑时更接近ANSYS壳单元的计算结果,证实考虑悬臂板更合理;计算极惯性矩时是否考虑悬臂板,对箱梁扭转角和广义翘曲位移的影响较小,但对双力矩和二次扭矩有明显影响,不考虑悬臂板时跨中截面的双力矩和二次扭矩分别减小22%和39%。

The expressions of the polar inertia moment and the warping coefficient of box girders with cantilever slab were derived,followed by the demonstration of the necessity for considering cantilever slabs in calculating the polar inertia moment through the analysis of shear stresses and the resultant torques.Initial parameter solution to the generalized displacement and internal force of a simply supported box girder subjected to concentrated torsion load at mid-span section was given based on the governing differential equation of restrained torsion.A numerical example was provided to calculate the polar inertia moment with and without cantilever slab respectively.The results of the calculated warping normal stresses on the whole cross section were compared with those obtained by the shell element in the general finite element software ANSYS.The influence of diffe-rent values of the polar inertia moment on the generalized displacement and internal force was studied.The results show that the warping normal stresses calculated with cantilever slab are closer to those from ANSYS,validating the reasonability of considering cantilever slab.Whether or not the cantilever slab is considered in calculating the polar inertia moment has little effect on the torsion angle and generalized warping displacement,but has remarkable effect on bi-moment and secondary torque.The bi-moment and secondary torque of the midspan section decrease by 22% and 39% respectively when the cantilever slab is not considered.