含多个边裂纹的矩形截面阶梯形轴压柱的屈曲行为分析

采用Rayleigh-Ritz能量法推导了带多个边裂纹的矩形截面阶梯柱弹性后屈曲过程的控制方程，提出了一个带裂纹轴压柱弹性屈曲全过程的平衡路径模型，同时更正了相关文献中认为裂纹对柱的临界力肯定有影响的错误结论，并针对某一简支阶梯柱，通过数值计算得到了4种裂纹状态下的屈曲前后的平衡路径曲线。分析结果表明：当横向干扰挠度大于一定程度时，裂纹才对轴压柱的临界荷载有影响；当横向干扰挠度小于一定程度时，裂纹只对轴压柱的后屈曲过程有影响，而对临界荷载无影响。

Analysis for Buckling Behavior of Multi-step Rectangular Section Compressive Columns with Arbitrary Number of Side-cracks

The governing equation for the post-buckling process of a multi-step rectangular section compressive column with arbitrary number of side-cracks was derived by using Rayleigh-Ritz energy method. Moreover, an analytical model of the equilibrium path of whole buckling process was suggested for the cracked compressive column, where the crack closure and fracture condition were considered. Thus the unreasonable conclusions in some relevant references that cracks had certainly effects on critical load were corrected. As an example, the equilibrium path curves of four states of cracks were obtained numerically for a simply supported three-steps columns. The analytical results show that when an excessive lateral interfering deflection appears, the cracks will have effects on critical load; when the lateral interfering deflection is small, the cracks will have no effects on critical load but have effects on post-buckling process.