恒载效应对拱形梁的影响分析

ANALYSIS OF THE EFFECT OF DEAD LOADS ON STATIC ARCH BEAMS

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。根据所得方程,利用Galerkin方法讨论了恒载大小及结构自身刚度(矢高、跨度、惯性矩、惯性半径等)等不同因素在考虑恒载效应时对拱形梁静力特性的影响。通过与直梁解析解结果及作者在其它文献中提出的有限元方法对拱形梁分析结果的比较,验证了该文非线性微分方程及其求解公式。结果表明:该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。

A nonlinear differential equation with the effect of dead loads taken into account is formulated by the virtual work principle. Based on the equation, the effect of key physical factors, including the magnitude of dead loads, the height and span of the arch beam, the moment of inertia and the radius of inertia, etc, on the static characteristics of the arch beam, are discussed by using the Galerkin method. The equation is validated through comparing with the analytical solution for a straight beam presented by Takabatake and the numerical results for arch beams, which are presented, based on finite element method, in other articles by the author. The conclusion shows the differential equation can be applied to both arch and straight beams, the initial dead loads have a deterrent effect on the static responses of the arch beams with live loads, and such an effect relates to the magnitude of dead loads and the stiffness of the structures. In addition, some suggestions for the design of lightweight structures are proposed.