基于固端弯矩相等原则的等效荷载法

为提高工程结构力学分析的效率，提出了一种基于固端弯矩相等原则的计算方法。首先，基于固端弯矩相等的原则，研究在对称集中荷载和三角形分布荷载作用下单跨超静定梁的等效荷载施加方法，并导出梁在非常规荷载作用下固端弯矩的实用计算公式。然后，将超静定单跨梁的荷载形式推广至更任意的集中荷载和分布荷载等情况，并探讨了任意多集中荷载作用下单跨超静定梁的等效荷载施加方法和通用计算公式。最后，通过多跨连续梁和框架结构算例验证了所提方法具有较好的计算效果。算例结果表明，基于提出的等效荷载法可快速得到单跨超静定梁的固端弯矩，从而可高效准确地确定结构的真实内力分布。研究成果表明了利用等效荷载实现高效求解的可行性，它为力矩分配法及其它力学分析问题提供了一条高效便捷的思路。

Equivalent load method based on the equivalence principle of the bending moments of fixed ends

In order to improve the efficiency of the analysis of structural mechanics in engineering, an equivalent load method is proposed based on the equal principle of the fixed-end moments in this paper. Firstly, based on the equal principle of the fixed-end moments, the equivalent load method used for the mechanical analysis of a single-span indeterminate beam under symmetrical concentrated load and triangular distributed load was investigated. And practical formulas were deduced for the single-span indeterminate beams under uncommon loads. Secondly, without loss of generality, the load modes on the single-span indeterminate beams were extended to the arbitrary concentrated load and arbitrary distributed load, and the general formulas for the proposed method were discussed in detail. Lastly, numerical examples about a multi-span continuous beam and a frame structure under uncommon load were used to verify the effectiveness of the proposed method. The results show that the fixed-end moments of single-span indeterminate beams can be obtained efficiently by the proposed method, which can be used to calculate the real internal forces of beams with convenience and accuracy. The study indicates that the mechanical analysis can be carried out efficiently by the equivalent load method, which provides a highly efficient way for the moment distribution method and the analysis of other mechanical problems.