弯矩分配传递极限公式在薄板弯曲问题中的应用

Application of bending moment distribution and carryover limit formula to plate bending problems

用传统的弯矩分配法求解任意荷载作用下的薄板弯曲问题,将杆端弯矩表示为多次分配弯矩和传递弯矩之和,得到了当分配传递次数无穷大时其表达式为公比小于1的无穷等比级数的和的形式,并求得了该和的表达式即极限公式.该极限公式便于编程电算,可方便地应用于任意荷载作用下的薄板弯曲问题.

The conventional bending moment distribution method was adopted to solve the plate bending problem. The total moment on the ends of the member was obtained by summing up of infinitely distributed and carriedover bending moments, and the expression is the sum of an infinite series with the common ratio less that 1. Further deduction of the expression forms a limit formula. The formula can be easily programmed, providing another convenient method for the bending problem of plates under arbitrary loads.