一次超静定理想弹塑性梁的全过程分析

本文研究了集中载荷作用下，一种一次超静定理想弹塑性矩形横截面梁的全部受力变形过程。受力变形可分为四个阶段：弹性阶段、一部分区域产生塑性变形阶段、另外一部分区域也产生塑性变形阶段以及固定端为塑性铰直到形成塑性破损机构阶段。文中推导了各个阶段的挠度曲线方程，建立了求解积分常数和支反力的方程组，利用这些方程计算了部分支反力、各阶段结束时的挠曲线和载荷值以及几种特定载荷下的弯矩图。

ANALYSIS OF THE ENTIRE PROCESS OF AN ELASTIC PLASTIC BEAM WITH ONE DEGREE OF INDETERMINACY

In this paper the entire process of an elastic-perfectly plastic rectangular beam withone degree of indeterminacy subjected tO a concentrated forCe at itS center is stUdied. The processis divided illtO four stages: an elanic State in the whole beam; an elastic-plastic state in a regionof the beam; an elastic-plastic state in tWo regions of the beam, till to forming the mechanism offlow with a plastic hinge at the fixed end. The deflection of the beam axis is derived at the fourstages. EqUations for integral conStantS and the reaction at support are established. Theseequations are used tO calculate the reactions at support, defleCtions, loads and momeds at the endofeach stage.