变截面悬链线无铰拱应变影响线的解析解

针对变截面悬链线无铰拱应变影响线尚无解析解的现状,通过弹性中心法对其力法方程进行简化,利用Ritter截面变化规律简化变截面悬链线无铰拱的曲线积分,从而推导出变截面悬链线无铰拱应变影响线的闭合解表达式,再将解析结果与有限元分析结果进行对比研究,并对轴力参数展开对比分析。研究结果表明,本文推导得到变截面悬链线无铰拱应变影响线的解析解,数值解析解同有限元结果间最大相对误差小于2%,其轴力影响随矢跨比和测点位置变化而变化,本文公式具有较高的工程精度和计算分析参考价值。

Practical analytical expression to strain influence line of varying cross section catenary fixed arch

In view of the present situation that there is no analytical solution to the strain influence line of the variable-section catenary hingeless arch,this paper simplified the force method equation by using the elastic center method,simplified the curvilinear integral of the variable-section catenary hingeless arch by using the Ritter cross-section variation law,and then derived the closed-form solution expression of the variable-section catenary hingeless arch strain influence line.Then the analytical results are compared with the finite element analysis results.The maximum relative error between the numerical solution and the finite element result is less than 2%.The axial force effect varies with the ratio of the span to the position of the measuring point.The formulas presented in this paper have high engineering accuracy and reference value for calculation and analysis.