平面桁架内力求解的“奇怪”现象分析

在所有理论力学教材中,平面任意力系有三个独立的平衡方程,这是众所周知的理论.但在某种情况下,却会出现一些特殊的现象.如用截面法求平面桁架内力的题目中,就出现有人称为“奇怪”的现象,即明明是一平面任意力系,有3个未知力,列出的3个平衡方程也无误,但怎么求解也求解不出结果来,许多学生甚至部分老师对此感到疑惑不解.对此给出了笔者的观点与看法,这实际上涉及到了一个特殊的平面任意力系独立平衡方程的问题.

Analysis of an ＂odd＂ case in determining unknown forces of planar truss

Currently, all theoretical mechanics textbooks state that there are three independ- ent equilibrium equations in a coplanar force system. However, under certain circumstances, there are special cases. For example, using the method of sections to solve for planar internal forces of truss problems （ as given in the two examples in the paper）, is one of these ＂odd＂ cases where no solution can be obtained given three equilibrium equations with three un- known forces in a coplanar force system. Many students and even instructors are puzzled by this. This paper provided the authors＇ point of view on solving this special case of coplanar equilibrium problems.