弯曲梁柱结构平面外失稳的研究

研究了两节梁组成的弯曲梁在受竖向集中载荷作用下的平面外稳定问题,通过建立每节梁临界状态下弯曲和扭转变形微分方程,根据变形协调关系,得出了一端固定一端悬臂的弯曲梁平面外失稳的特征方程,并以等截面等长度梁构成的弯曲梁为对象,探讨了弯曲梁上拱和上翘对其平面外稳定性的影响,以及抗扭刚度对稳定性的影响。结果表明,同样的载荷作用幅度和梁高度,采用上拱的弯曲梁比直梁具有更高的侧向稳定性,并且存在一个最佳的弯曲角度,而上翘弯曲梁的侧向稳定性要低于直梁的侧向稳定性。当弯曲梁上翘时,增大抗扭刚度可以提高侧向稳定性,弯曲梁上拱时,增大抗扭刚度却会降低其侧向稳定性。

THE OUT-OF-PLANE STABILITY OF A BENDING BEAM

The out-of-plane stability of a bending beam, which is made up with 2 beams and loaded by concentrated vertical loads, is studied. Differential equations of each beam with both bending deflection and torsinal deformation is established in critical condition. According to compatibility conditions of deformation, the characteristic equation is obtained for out-of-plane stability of the cantilever bending beam. By analyzing bending beam consisting of 2 similar beams, the stability characters of upwards-bent and downwards-bent beam are discussed. The effect of torsional stiffness on stability is studied. Under the same load and beam length, downwards-bent beam has higher lateral stability than straight beam, but the upwards-bent beam has lower lateral stability. There exists a best bending angle to obtain the highest stability. The increase of torsional stiffness will lead to the increase of the lateral stability for upwards-bent beam, but reduce the lateral stability for downwards-bent beam.