基于翘曲位移函数的框筒结构剪力滞后效应研究

Research on shear lag effect of frame tube structure based on warping displacement function

将框筒结构进行等效连续化,并对翼缘和腹板采用相同的最大纵向位移差函数。根据剪力滞后效应的特征,分别假定翼缘和腹板的翘曲位移函数为二次和三次抛物线。利用能量变分原理,推导出结构的控制微分方程和边界条件方程,并对水平集中力和水平均布荷载作用时进行求解。为了研究Timoshenko剪切变形和腹板翘曲函数对剪力滞后的影响,分别推导出相应的微分方程,并进行求解。研究结果表明:该计算方法可以正确地分析框筒的剪力滞后效应,且独立函数少,求解方便;分析框筒剪力滞后效应时可以不考虑Timoshenko剪切变形的影响;腹板采用线性翘曲函数时不能真实反映腹板的滞后现象,虽然可以反映翼缘的滞后情况,但计算的滞后程度偏小。

This study used equivalent continuous for the frame tube structure and assumed the same maximum longitudinal displacement difference function for the flange and the web.According to the characteristic of shear lag effect,the warping displacement function of flange was assumed and webs were assumed to be quadratic and cubic parabola respectively.By using the energy variational principle,the governing differential equations and boundary condition equations were deduced and then solved under horizontal concentrated force and horizontal uniform load.In order to study the influence of Timoshenko shear deformation and web warping function on the shear lag,the corresponding differential equations were deduced and solved.Through the example analysis,the following conclusions were drawn:the calculation method can correctly analyze the shear lag effect of the frame tube and has few independent function for convenient solution;Timoshenko shear deformation cannot be considered when analyzing the shear lag effect of frame tube;adopting linear warping function in the web cannot be used to reflect the hysteresis phenomenon of the web,although it can reflect the shear lag of the flange;and the lag degree of calculation is relatively small.