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对双集中荷载作用下一次超静定梁的弹塑性加载全过程进行了分析.根据变形特点可把加载过程分成四个阶段.第一阶段是常规的弹性阶段,第二阶段是固支端附近单个塑性变形区扩展的阶段,第三阶段是固支端和一个集中荷载附近两个塑性变形区同时扩展的阶段,第四阶段是固支端保持为塑性铰从而引起固支端附近区域卸载而梁中间的塑性变形区继续扩展直至形成第二个塑性铰的阶段.在第一阶段,弯矩内力和挠度与外荷载均是线性比例递增关系;在第二、第三两个阶段,弯矩和挠度与外荷载是不同的非线性关系;在第四阶段,弯矩与外荷载是非比例的线性关系,但挠度与外荷载却是复杂的非线性关系.给出了加载各阶段的弯矩及挠度计算公式,具有理论意义,也可供对应的结构设计应用.
The whole process of elasto-plastic loading of a statically indeterminate beam under double concentrated load is analyzed. According to the deformation characteristics, the loading process can be divided into four stages. The first stage is the conventional elastic stage, the second stage is near the fixed branch The third stage is the stage of simultaneous expansion of two plastic deformation zones near the fixed branch and a concentrated load. In the fourth stage, the fixed branch is kept as a plastic hinge so as to cause the area near the branch ends to be unloaded The plastic deformation zone in the middle of the beam continues to expand until the second plastic hinge is formed.In the first stage, the internal forces and deflections of the bending moment are linearly and proportionally increasing with respect to the external loads. In the second and third stages, And the deflection and the external load are different non-linear relations; in the fourth stage, the bending moment and the external load are non-proportional linear relationship, but the deflection and the external load is a complex non-linear relationship. And deflection formula, with theoretical significance, but also for the corresponding structural design and application.