等截面抛物线无铰拱挠度影响线实用解析解

为解决弧长微分表达式复杂导致抛物线拱挠度解析计算繁琐的难题,采取有简单弧长微分表达式的近似曲线拟合抛物线的方法,通过以沿曲线的曲率和为量化指标评价3种曲线(直线)的拟合度,最终得出悬索线拟合度最优的结论。在此基础上,利用基本力学原理,推导出抛物线无铰拱挠度影响线解析计算公式,最后应用于实例,并与有限元分析结果进行对比。算例结果表明,公式计算与有限元分析结果最大相差不超过1%,具有非常高的工程精度,可用于工程实践。

Practical analytical solution of deflection influence line of clamped parabolic arch bridges with uniform section

In order to overcome the complexity in determining deflection of a parabolic arch using the analytical expression of arch length in differential form,an approximate curve that has a simple differential expression of its arc length to fit a parabola is considered to be the best way.Ultimately,the best fitting suspension curve is obtained according to the values of the curvature sum of three kinds of curves.On this basis,the analytical formula for calculating deflection influence line of clamped parabolic arch bridges with uniform section is derived based on fundamental mechanics principles,and then applied to an example.The results are compared with finite element analysis results.Numerical results show that the values obtained by the analytical formula are different from the finite element results by less 1%.Thus the analytical formula satisfies the engineering requirement and can be used in engineering practice.