泊松比在薄壁箱梁约束扭转和横向内力分析中的影响

Influence of Poisson’s ratio on analyzing restrained torsion and transverse internal force of thin-walled box girders

为准确分析薄壁箱梁的约束扭转效应和横向内力,结合弹性力学中平面问题的几何和物理条件,提出基于乌曼斯基第二理论分析约束扭转时应考虑泊松比对弹性模量的修正,基于框架分析法分析畸变横向内力时应考虑泊松比对各板件横向弯曲刚度的修正。结合箱梁数值算例,不考虑泊松比或按工程中常用的材料选取不同的泊松比,详细分析了泊松比对约束扭转效应和横向弯矩的影响。研究结果表明:考虑泊松比时,扭转翘曲正应力和横向弯矩与有限元结果吻合良好;与不考虑泊松比时的计算结果进行比较,当泊松比为0.37时,扭转翘曲正应力可提高28.41%,反对称荷载下的横向弯矩可减少24.97%。因此,约束扭转分析时应考虑泊松比对弹性模量的修正,横向内力分析时应考虑泊松比对横向弯曲刚度的修正。

This paper investigated the restrained torsion effect and transverse internal force of thin-walled box girders,considering geometric and physical conditions of plane problem in elasticity.Correction of Poisson’s ratio on elastic modulus was taken into account when analyzing restrained torsion based on Umanskii’s second theory.Correction of Poisson’s ratio on the transverse bending stiffness of each slab was taken into account when analyzing transverse internal force considering distortion based on a frame analysis method.The influence of Poisson’s ratio on the restrained torsion effect and the transverse bending moment was analyzed through numerical examples of box girderswith overlooking Poisson’s ratio or selecting that according to commonly used engineering materials.The results show that when poisson’s ratio is considered,torsion warping normal stresses and transverse moments are in good agreement with the finite element results.Compared with the calculated results when Poisson’s ratio is overlooked,torsion warping normal stresses increase by 28.41%and transverse bending momentwith dissymmetric loaddecrease by 24.97%when Poisson’s ratio is 0.37.Therefore,correction of Poisson’s ratio on elastic modulusshould be taken into account in the analysis of restrained torsion,and correction of Poisson’s ratio on transverse bending stiffness should be taken into account in the analysis of transverse internal force.