集中载荷作用下双模量矩形截面梁的弹性解  

Elastic Solution of Bimodulous Rectangular Cross-section Beam Under Concentrated Load

作　　者：李苗苗 吴晓[2] LI Miaomiao;WU Xiao(Department of Civil Architecture,Changde Vocational Technical College,Changde 415000,Hunan,China;College of Mechanical Engineering,Hunan University of Arts and Science,Changde 415000,Hunan,China)

机构地区：[1]常德职业技术学院土建系,湖南常德415000 [2]湖南文理学院机械工程学院,湖南常德415000

出　　处：《工程与试验》2024年第3期12-14,20,共4页Engineering and Test

摘　　要：利用弹性理论的半逆解法研究了双模量矩形截面梁的弯曲变形,推导出了集中载荷作用下双模量简支矩形截面梁的应力及位移表达式。研究分析表明,对于集中载荷作用下双模量简支矩形截面梁,弹性理论给出了集中载荷作用下双模量简支矩形截面梁拉伸区、压缩区的轴向位移及竖向位移表达式,这说明双模量梁截面任意点的弯曲挠度都不相同,而材料力学方法仅能推导出集中载荷作用下双模量简支矩形截面梁的中性轴竖向位移表达式。双模量简支矩形截面梁中性轴处竖向位移对模量比变化很敏感,原则上建议计算双模量简支矩形截面梁中性轴处竖向位移应采用弹性理论。The bending deformation of bimodulous rectangular cross-section beam is studied by using the semi-inverse method of elastic theory.The expressions of stress and displacement of bimodulous simply supported rectangular cross-section beam under concentrated load are derived.The analysis shows that the expressions of axial displacement and bending deflection in tension and compression zones of bimodulous simply supported rectangular cross-section beam under concentrated load are given by elastic theory.This shows that the bending deflection at any point of the bimodulous beam section is different.However,the material mechanics method can only derive the expression of the neutral axial deflection curve of a bimodulous simply supported rectangular cross-section beam under concentrated load.The bending deflection at the neutral axis of a bimodulous simply supported rectangular cross-section beam is sensitive to the change of the equivalent modulus ratio.In principle,the elastic theory is suggested to be used to calculate the bending deflection at the neutral axis of a bimodulous simply supported rectangular cross-section beam.

关 键 词：集中载荷 双模量 弹性理论 应力 挠曲线 

分 类 号：O341[理学—固体力学]