摘要
复合荷载作用下单向受弯简支梁的弹性临界弯矩对简支梁的稳定设计非常重要。文章基于总势能公式,围绕复合荷载作用下简支梁的弹性弯扭屈曲进行了研究,针对简支梁在复合荷载作用下的弹性临界弯矩计算公式适用范围有限的情况,通过采用瑞利—里兹法主要推导了单个集中荷载、满跨均布荷载和端弯矩单独作用以及组合作用下简支梁的弹性临界弯矩和对应参数的计算方法,并与现有的计算方法进行了对比分析。结果表明:推导的弹性临界弯矩计算公式在形式上与传统公式完全一致,但参数C1、C2、C3不再是简单荷载下的具体数值,而是通用计算公式,不仅可适用于简单荷载,也可适用于复合荷载;一系列的算例表明,文中所给公式的计算结果与传统计算方法所得结果最大偏差为5.5%,精度较高且适用范围广。
The elastic critical moment of one-way flexural simply supported beam under combined loads is very important to the stable design of simply supported beam. The article is based on the total potential energy formula of Tong Genshu, studied around elastic flexural-torsional buckling of simply supported beam under combined loads, for the case of the scope of formula of the elastic critical moment of simply supported beam limited under combined loads, using Rayleigh-Ritz method to derive calculation method for critical simply supported beam bending moment and its parameters in the single concentrated loads, uniformly distributed load and end moment effect, making comparative analysis with the existing calculation method. The result shows：~ The critical moment formula derived in this article is fully consistent with the traditional formula in the form, however, the parameters CC2 C3 is no longer a specific value under the simple load, but the general formula, not only for simple load, but also be used in the composite load. A series of examples show that the maximum deviation of the results of the formula in this article and the traditional formula is 5.5 % high precision and wide range of application.
出处
《山东建筑大学学报》
2016年第3期249-253,258,共6页
Journal of Shandong Jianzhu University
关键词
弹性弯扭屈曲
简支梁
总势能公式
临界弯矩
复合荷载
elastic flexural-torsional buckling
simply supported beam
total potential energy equation
critical moment
combined loads
