复合荷载作用下钢梁弯扭屈曲临界弯矩研究

基于由完备的复合荷载作用下钢梁弯扭屈曲总势能方程推导的平衡微分方程，采用Galerkin法推导了考虑横向荷载作用点高度和横截面不对称参数的复合荷载作用下钢梁弯扭屈曲临界弯矩的计算式，建立了等效弯矩系数的计算理论。依据等效弯矩系数的计算理论确定了7种常见工况的等效弯矩系数理论计算式并给出了6种特殊工况的Cb实用计算式，从Cb计算式的计算精度、适用范围和形式三个方面对国内外文献的Cb计算式进行对比，验证了等效弯矩系数理论的正确性并提出了Cb计算式的选用准则，最后通过2个数值算例验证了复合荷载作用下钢梁临界弯矩Mcr计算式的正确性和Cb计算式选用准则的合理性。结果表明：考虑了横向荷载作用点高度和横截面不对称参数的复合荷载作用下钢梁弯扭屈曲临界弯矩的计算式形式简单、物理意义明确且便于计算；Cb实用计算式的适用范围广且精度高；等效弯矩系数的选用准则合理、有效。

Research on critical moment of flexural-torsional buckling for steel beam subjected to combined loads

Based on the complete total potential energy of flexural-torsion buckling for steel beam subjected to combined loads, the equilibrium differential equation is obtained. The closed-formed formula of critical moment, considering both the height of load and the monosymmetry section constants, is deduced by employing Galerkin method. The theory of equivalent moment factor is also proposed. Based on the proposed equivalent moment factor theory, theoretical formulas of Cb for seven conventional load conditions and practical formulas of Cb for six special load conditions are derived. The practical Cb formulas are compared, about accuracy, application range and form, with those formulas in current literatures. The theory of equivalent moment factor is verified and the criteria on Cb formula is proposed. Two numerical examples are presented to verify the proposed Mcr formula and the criteria on Cb formulas. The results shown that the closed-formed formula of critical moment, considering both the height of load and the monosymmetry section constants, is of simple form, clear physical significance and easy application. The practical Cb formula is of wide application range and high accuracy. The criteria on Cb formula is reasonable and effective.