考虑恒载效应的拱形梁静力近似解

应用虚功原理,推导了考虑恒载效应影响时拱形梁在活载作用下的非线性微分方程,得到了方程的近似闭合解。根据方程的解,讨论了恒载大小及结构自身刚度(矢高、跨度、惯性矩及惯性半径等)不同因素在考虑恒载效应时对拱形梁静力特性的影响。通过与Takabatake得到的直梁解析解结果及作者在其他文献提出的有限元方法对拱形梁分析结果的比较,验证了本文非线性微分方程及其求解公式。结果表明,本文给出的非线性微分方程对于拱形梁和直线梁具有通用性,初始恒载的存在减小了拱形梁在活载作用下的静力反应,这种影响与恒载的大小及结构自身的刚度有关,对轻型结构的设计提出了一些建议。

Approximate solutions of static arch beams considering static loads effect

A nonlinear differential equation considering static load effect is formulated from the virtual work principle,for static arch beams and the approximate closed-form solution of the equation is given. Based on the solution, the effects of various physical factors, including the magnitude of static loads, the rise and span of the arch beam, the sectional inertia moment and inertia radius, on the static characteristics of the arch beam are discussed. The equation and solution are validated through a comparison with the analytical solution for a straight beam given by Takabatake and the numerical results for arch beams based on finite element method, which are presented in other articles by the author. The differential equation can be applied to both arch and straight beams. The initial static loads have a deterrent effect on the static responses of the arch beam subjected to dynamic loads, which relates to the magnitude of static loads and the stiffness of the structure. In addition, some suggestions for the design of light weight structures are proposed.