摘要
对均布荷载加载作用下一次超静定梁的弹塑性变形全过程进行了分析.根据受力变形的特点,均布荷载下一次超静定梁的加载过程可分成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,固支端保持为塑性铰而固支端附近塑性变形区卸载阶段,固支端保持为塑性铰而梁中部出现塑性变形区并扩展直至中部某点形成塑性铰阶段.在弹性的第1阶段,弯矩内力、挠度与外荷载是线性比例关系;在第2阶段,弯矩内力、挠度与外荷载是复杂的非线性关系;在第3阶段,弯矩、挠度与外荷载是线性关系但不是比例关系;在第4阶段,弯矩与外荷载的关系与第3阶段相同,但挠度与外荷载是更复杂的非线性关系.给出了弹塑性全过程各阶段任意点的弯矩和挠度计算公式,可供结构设计应用.
The analysis of the entire elastic-plastic deformation process of a beam with one degree of inde- terminacy under uniformly-distributed load was made. Based on the deformation feature, the up-loading process was divided into the following four stages ： 1 ） the elastic stage, 2） the stage that beam region near the fixed end in plastic propagation state, 3 ） the stage that the fixed end as a plastic hinge while the plastic region near the end unloaded, and 4） the stage that the fixed end as a plastic hinge while the plastic region near the mid-point developing until the second plastic hinge occurring in the middle. In the first stage, the relationship between moment and load was proportional, so was that between deflection and the load. In the second stage, the relationship between moment and the load was complicated and nonlinear, so was that between deflection and the load. In the third stage, the relationship between mo- ment and the load was linear but not proportion, so was that between deflection and the load. In the fourth stage, the relationship between moment and the load was the same as that in last stage, while the relationship between deflection and the load was much complicated and nonlinear. The formulae of mo- ment and deflection of arbitrary point at each stage were derived. The formulas can be applied to engi- neering structure design.
出处
《郑州大学学报（理学版）》
CAS
北大核心
2015年第1期119-124,共6页
Journal of Zhengzhou University:Natural Science Edition
关键词
超静定梁
弹塑性
塑性铰
均布荷载
挠度
statically indeterminate beam
elastic-plastic
plastic hinge
uniformly-distributed load
de-flection
