超静定连续梁弹塑性过程分析的单位荷载法

Unit-Load Method of Elastic-Plastic Process Analysis of Statically Indeterminate Continuous Beam

讨论了分析超静定连续梁弹塑性受力和变形全过程的单位荷载法,运用该方法分析了集中荷载作用下一次超静定两跨连续梁的弹塑性加载和变形全过程.根据受力变形的特点,集中荷载作用下两跨连续梁的弹塑性加载过程可分为四个阶段,分别是弹性阶段、集中荷载作用点附近塑性区扩展阶段、集中荷载作用点保持为塑性铰而附近区域线性卸载阶段、两跨连接点附近塑性区扩展直至形成第二个塑性铰阶段.给出了加载过程中各阶段的弯矩内力和竖向位移随外荷载而变化的解析公式.研究结果表明:在相同的单跨荷载工况下,连续梁的变形过程不同于单跨一次超静定梁,其塑性铰形成顺序不同,静定结构形成顺序不同,但塑性极限破坏荷载相同.

The unit-load method to analyze the entire elastic-plastic process of loading and deformation was discussed on statically indeterminate continuous beam. By the method,the entire elastic-plastic process of loading and deformation was analyzed for two span continuous beam with one degree of indeterminacy under a concentrated load. Based on the deformation feature,the up-loading process of two span continuous beam under a concentrated load can be divided into four stages： elastic stage,plastic propagating stage around the point where the concentrated load is exerted,the stage in which the point where the concentrated load is exerted behaves as a plastic hinge while the region around the point is unloading,the stage in which the plastic region around the conjunctive point of two spans propagates until the second plastic hinge occurs. The analytic formulas of moment and deflection varying with external load were derived for each stage. The results show that the elastic-plastic process of continuous beam is different from that of one span beam at the same load condition. The order of forming plastic hinge and static structure is different,but the plastic-limit load is the same.