剪切变形对双模量梁弯曲正应力的影响  

Effects of shear deformation on bending normal stress of bimodulous beam

作　　者：吴晓[1] 罗佑新[1] 

机构地区：[1]湖南文理学院机械工程学院,湖南常德415000

出　　处：《湖南文理学院学报（自然科学版）》2016年第1期55-59,共5页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：湖南省"十二五"重点建设学科资助项目(湘教发2011[76])

摘　　要：利用静力方程确定了矩形截面双模量梁的中性轴位置,得到了矩形截面双模量梁的弯曲剪应力计算公式。在考虑剪切变形影响的情况下,利用矩形截面双模量梁的弯曲剪应力计算公式,导出了等矩形截面双模量梁弯曲正应力计算公式。通过算例分析了矩形截面双模量梁的长高比变化时,剪切变形对等矩形截面双模量梁弯曲正应力的影响。研究结果表明:当矩形截面双模量梁的长高比小于一定值时,剪切变形会对矩形截面双模量梁弯曲正应力产生较大的影响;拉压弹性模量相差较大的双模量材料梁弯曲应力的计算,应采用双模量材料力学理论进行分析计算,而采用经典材料力学理论进行分析计算是不合适的。Using the static equilibrium equation of bimodulous beam with rectangular cross section, the location of the neutral axis is determined and the calculation formula of the bending shear stress is obtained. On the basis of the effects of shear deformation and the calculation formula of the bending shear stress, the calculation formula of the bending normal stress on the bimodulous beam with rectangular cross section is deduced. The examples show that the shear deformation affects the bending normal stress when the length-height ratio of the bimodulous beam with rectangular cross section changes, and there is greater effect when the ratio is smaller than a certain value. The conclusion is that the bending stress of bimodulous beam with a larger difference elastic modulus of tension and compression was calculated, and the bending stress of the beam should be calculated and analyzed by using the bimodulous material mechanics theory because it is inappropriate for using the classical material mechanics theory.

关 键 词：剪切变形 双模量 梁 弯曲 正应力 长高比 

分 类 号：O341[理学—固体力学]