梁侧向屈曲临界荷载分析

来源期刊:中南大学学报(自然科学版)2008年第2期

论文作者:文颖 曾庆元

文章页码:405 - 405

关键词:梁;力矩矢量分析法;侧向屈曲;临界荷载

Key words:beam; vector analysis approach; lateral buckling; critical load

摘    要:揭示梁侧倾分析中弯扭平衡方程的力学意义是梁截面内弯矩等于外弯矩及内扭矩等于外扭矩;提出采用梁截面力矩矢量分析法解决各种荷载类型和不同支承条件下侧向屈曲梁截面弯扭力矩的计算问题;采用伽辽金(Galerkin)法求解梁侧向屈曲平衡方程。研究结果表明:采用力矩矢量分析法可以方便地建立梁侧倾弯扭平衡方程;临界荷载计算值与传统的无穷级数解非常接近,且数值上稍低于无穷级数解,这说明采用伽辽金法进行梁抵抗侧向屈曲设计是偏于安全的。

Abstract: The physical meaning of lateral flexural-torsional equilibrium equations was simple that the external bending moments and twisting forces should balance the internal resisting moments at any cross-section of beam respectively. Therefore, the vector analysis approach was presented to determine the flexural-torsional moments of lateral buckling beams more efficiently under various load types and support conditions. In addition, the lateral buckling loads were obtained by solving the differential equation using Galerkin’s method. The results show that the equations of equilibrium for beam can be formulated directly using the method of couple vector analysis. An illustrative example suggests that the calculated critical load is very close to but lower than the magnitude obtained in an infinite series way. It can be concluded that it is safe to apply the Galerkin’s method to lateral buckling design of beams.

基金信息:教育部高等学校博士点科研基金资助项目

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