纯弯下简支角钢梁静态和动态不稳定性分析

Static and dynamic instability of angle section beams under pure bending

主要涉及角钢梁在纯弯状态下的非线性屈曲失稳.角钢自由两肢翘曲变形曲线采用悬臂梁在均布满荷载、悬臂端受弯矩和悬臂端集中力作用下的三种典型变形曲线,应用能量法研究了在上述三类假定下简支角钢梁在纯弯矩作用下的静状和动态非线性失稳.同时也应用ANSYS建立了有限元模型对角钢梁纯受弯时非线性失稳状态进行了模拟分析.通过本研究提出的结论、他人实验结果和有限元分析的数据比较,三者吻合较好,证明了提出假定与分析方法的准确性.结果表明:纯弯下简支角钢梁在动力非线性失稳下的极限弯矩是静力状态下极限弯矩的71%,动力状态突加荷载下的纵向的曲率和翘曲变形约是静力状态下的两倍.

This paper presents a study on the nonlinear buckling behavior of angle section beams subjected to pure bending. Analytical solutions for both static and dynamic instabilities of angle section beams subjected to pure bending about its weak axis are derived using energy methods. Nonlinear finite element model using the code ANSYS is developed to simulate nonlinear snapthrough instability of angle section beams under pure bending. The optimization assumption about flattening shape of the leg is proposed, through comparison of the presented solutions（the critical moment, the bending curvature and buckling deformation）, experimental results, and the finite element analysis results. The numerical results show that the dynamic instability of angle section beams under the action of a sudden step moment occurs at about 71% of the corresponding critical static moment, but the deformations of the longitudinal curvature and buckling at the critical dynamic state are almost twice of those corresponding to the static instability case.