黄金分割算法在简支桥梁设计计算中的应用

移动荷载作用下,简支桥梁横截面上弯矩的变化为二元函数Z=f(x,y),本文给出了绝对最大弯矩Zm ax的极值点x*、y*的判别方法:利用数学中的黄金分割算法搜索梁的绝对最大弯矩对应的最危险横截面位置x*;利用力学中的影响线理论判别该截面发生最大弯矩时的最危险荷载位置y*,计算该横截面的最大弯矩得到梁的绝对最大弯矩.该算法易于编写计算程序,以计算机为工具,适用于任意有限多个平行移动荷载在桥梁上移动,对于桥梁的设计计算与安全评估,有一定的实用价值.

Application of Golden Divisional Method on Design of Simply Supported Bridge

The bending moment on simply supported beam acted by moving loads varies with two variables Z=f(x,y).In this article,golden divisional method was used to search the most dangerous section x~* and theory of influence line was used to search the worst load position y~*.The absolute maximum bending moment was got by calculating the corresponding maximum bending moment in x~* section.By using computer,the method can be used to any finite parallel moving loads,so it is very useful to bridge design and safety evaluation.