基于势能原理的双轴对称工字梁弹性侧向屈曲研究

ELASTIC LATERAL BUCKLING OF DOUBLY SYMMETRIC I-BEAMS BASED ON POTENTIAL ENERGY METHOD

该文利用能量方法对考虑腹板畸变的工字梁侧向畸变屈曲、约束畸变屈曲问题进行了初步研究。由于现有的侧向畸变屈曲势能表达式均不能考虑横向分布荷载作用情况,该文首先推导了双轴对称工字梁侧向屈曲总势能一般表达式。该表达式在不考虑腹板畸变时,与经典侧扭屈曲势能表达式等价;在考虑腹板畸变时,可适用于端弯矩、横向集中力及横向分布荷载作用情况。根据所提出的势能表达式并通过合理简化,推导出多跨连续组合梁负弯矩区约束畸变屈曲计算表达式,相应的简化条件及公式均与有限元分析结果进行了比较,验证了合理性。研究成果具有理论和实际意义,为后续侧向畸变屈曲实用设计方法研究提供基础。

Based on potential energy method, a preliminary study of elastic lateral distortional buckling （LDB） and restrained distortional buckling （RDB） of b-beams is presented. Since the existing potential energy expressions of LDB of I-beams cannot reflect the effect of transverse distributed load, a new expression of total potential energy is first derived by using nonlinear elastic theory. The proposed expression is equivalent to the classic potential expression when the distortion of web is suppressed, and accounts for the combined actions of several common loads, such as transverse distributed load, concentrated vertical load and end moments, when the web is flexible. Then, according to the proposed potential energy expression, a RDB equation for continuous composite beams is deduced after some simplifications. Both the simplifications and RDB equations are verified by finite element method. The results of the present study have important theoretical and practical significances, and provide a rational basis for the practical design methods.