集中载荷作用下一次超静定梁的弹塑性全过程分析

THE ANALYSIS OF THE ENTIRE ELASTO-PLASTIC PROCESS OF A BEAM WITH ONE DEGREE OF INDETERMINACY UNDER A CONCENTRATED LOAD

对跨中集中载荷作用下一次超静定梁的弹塑性加载和变形全过程进行了分析.根据受力变形特点,集中载荷作用下一次超静定梁的加载过程可分为4个阶段,分别是弹性阶段、固支端附近塑性变形区扩展阶段、固支端和集中载荷作用点附近塑性变形区双扩展阶段、固支端保持为塑性铰同时附近卸载而集中载荷作用点附近塑性变形区继续扩展直至形成第2个塑性铰阶段.在弹性阶段,弯矩内力和挠度与外载荷是线性比例关系,在第2,3两个阶段,弯矩和挠度与外载荷是复杂的非线性关系,在第4阶段,弯矩与外载荷是线性关系但不是比例关系而挠度与外载荷是更为复杂的非线性关系.给出了全过程任意点的弯矩和挠度计算公式,可供结构设计参考应用.

The entire elasto-plastic process of loading and deformation of a beam with one degree of indeterminacy under a concentrated load is analyzed.Based on the deformation feature,the up-loading process can be divided into four stages:the elastic stage,the second stage when the beam region near the fixed end is in the plastic propagation state,the third stage when both the beam regions near the fixed end and near the point where the concentrated load acts are in the plastic propagation state,and the fourth stage when the fixed end behaves as a plastic hinge while the plastic region near the fixed end is unloaded and the plastic region near the mid-point is propagating to the emergence of the second plastic hinge.In the elastic stage,the relation between the moment and the load is proportional,so is that between the deflection and the load.In the second and third stages,the relation between the moment and the load is complicated and nonlinear,so is that between the deflection and the load.In the fourth stage,the relation between the moment and the load is linear but not proportional,while the relation between the deflection and the load is much complicated and nonlinear.The formulas of the moment and the deflection at an arbitrary point at each stage are derived.The formulas can be applied to the engineering structure design.