考虑剪切变形时薄壁箱梁的挠曲分析

FLEXURAL ANALYSIS OF THIN-WALLED BOX GIRDERS WITH SHEAR DEFORMATION

为分析剪切效应对薄壁箱梁受力特性的影响,利用微板的面内剪切及平衡微分方程,分别推导出不考虑和考虑薄壁箱梁各板面内剪切效应的弯曲位移函数。选取剪切效应引起的附加挠度作为广义位移,通过定义的剪切广义力矩及剪切翘曲位移函数,将剪切变形状态从全梁挠曲变形状态中分离出来,作为独立的变形状态进行分析。为满足全截面翘曲应力的自平衡条件,引入两个截面特性参数对广义剪切翘曲位移函数进行了修正。数值算例表明,按该文推导的薄壁箱梁剪切弯曲位移函数计算的两跨连续梁跨中截面应力与实测值及有限元值吻合良好。挠度计算表明:剪切效应使得该箱梁在集中和均布荷载作用下跨中挠度分别增大27%和24%。

In order to analyze the influence of shear effect on mechanical characteristics of thin-walled box girders, the paper uses the shear equilibrium differential equation of microplate to derive the bending displacement function for thin-walled box girders, which accounts for the in-plane shear effect of girder plates. The additional deflection induced by shear effect is adopted as the generalized displacement of a thin-walled box girder. By defining the generalized moment and warping displacement function, the shear deformation state is separated from the whole flexural deformation state and treated as a fundamental deformation state. Considering the self-equilibrium of shear warping stress, the paper introduces two sectional characteristic parameters in the generalized warping displacement function. The numerical example of a two-span continuous box girder shows that the stresses at the mid-span cross section calculated by applying the shearing and bending displacement function are in a good agreement with test results and those by finite element method. The shear effect increases the mid-span deflection of the box girder under concentrated and uniformly distributed loads by 27% and 24%, respectively.