集中荷载作用下两端固支梁的弹塑性力学解

The Elastic-plastic Solution of the Beam Fixed at Two Ends Under a Concentrated Load

通过结构对称性分析了两端固支超静定梁在跨中集中荷载作用下的弹塑性加载及变形过程.受力变形可分为弹性和弹塑性两个阶段,在弹塑性阶段,两固支端附近和梁中部同时产生弹塑性变形直至固支端和梁中点同时形成塑性铰而成为塑性流动机构.通过单位荷载法求出了加载过程中的位移公式,可供弹塑性力学教学和工程结构设计参考.

The elastic-plastic loading and deflection process of the hyper-static beam fixed at two ends under a concentrated load is analyzed by use of symmetry. The process is divided into two stages： an elastic state in the whole beam; an elastic-plastic state in the region close to two fixed ends and in the region around the middle of the beam till the formation of plastic flow with three plastic hinges at two fixed ends and in the middle. The formulas of displacement of the beams are derived at the two stages by the unit-load method. The results are applicable to elastic-plastic mechanics teaching as well as engineering structure design.