具有封闭杆件的刚架在任意荷载作用下的精确解

Analytic Solution of a Rigid Frame with Closed Bars Subjected to Arbitrary Loads

对任意荷载作用下具有封闭杆件的刚架给出用分配系数和传递系数表示的精确解。刚架用弯矩分配法求解时 ,将各结点用假设的刚臂固定 ,求得任意荷载引起的固端弯矩 ,然后求得结点不平衡力矩 ,从而将求任意荷载作用的问题转化为求任意的结点不平衡力矩作用的问题。用弯矩分配法求解时 ,将杆端弯矩 ,表示为无穷多次分配弯矩和传递弯矩之和 ,其表达式为公比小于 1的无穷等比级数的和 ,可方便地求得该和的表达式 ,从而求得任意荷载作用下刚架结构的精确解。文中给出了算例。

In this paper, the analytic solution of a rigid frame with closed bars subjected to arbitrary loads is obtained. The solution is expressed by distribution factors and carried over factors. The moment distribution method is used to solve the rigid frame with closed bars. The fixed end moments and then the unbalanced joint moments are obtained. Hence the structure subjected to the arbitrary unbalanced joint moments instead of the arbitrary loads is considered and studied. The total moments on the ends of the members are obtained by summing up all the distribution moments and the carried over end moments. The total moment on the end of one member is the sum of a infinite series with the common ratio less than one, which is eary to be obtained and is the analytic solution that want to obtain. Numerical example is given in the paper.