材料力学课件13组合变形.ppt

1、5 . 组合变形的 应力与强度计算,The stresses and strength of combined deformations,In engenering the strength of combined deformations often need to be calculated . The steps are as follows :,(1) 确定危险截面 , 用截面法计算危险截面上的内力 .,组合变形杆件强度计算的步骤 :,(2) 确定危险截面上的危险点 , 分析危险点的应力状态 .,Determine the dangerous cross section of the

2、bar , and using section method to get the internal forces on this section .,Determine the dangerous point on the cross section , and analysis the state of stress at this point .,(3) 根据适当的强度准则计算组合变形杆件的强度 .,强度计算包含三个方面的内容 (The calculation of strength for a bar involes three parts ) :,a. 校核强度 (Examine t

3、he strength of the bar ),b. 计算许可载荷 (Determine the maximum laodings acted on the bar ),c. 计算许可截面尺寸 (Determine the minimum cross section of the bar ),Calculate the strength of the bar acoording to certain strength criterion .,5.1 拉弯扭组合变形 (Generially combined deformations ),Suppose the internal forces

4、on the dangerious section are N T M . The dangerious point will be point A or B . Its state of stress is shown in follows figure .,For the ductile materials :,Very important formulas,If the cross section of the bar is not circular .,5.2 拉弯组合变形 (Combined deformation of tension and bending ),T = 0,The

5、 dangerious point is a simple state of stress .,拉弯组合中的最大正应力的计算,T = 0,The dangerious point is a simple state of stress .,(2) 强度准则 ( Strength criterion ),如图的集中荷载 P 可在立柱端面中线上移动，要使立柱横截面上不产生拉应力，偏心量 e 允许的最大值为多少？,Example :,5.4 弯扭组合变形 (Combined deformations of bending and torsion),N = 0,The dangerious point

6、 is a plane state of stress .,强度准则 ( Strength criterion ),For the circular section , we can get :,AB 段承受弯扭组合变形,最大弯矩,扭矩,故轴径 d 应满足,Example : Determine the diameter of bar AB using the fourth criterion . Known the allowed stress of the material .,5.5 斜 弯 曲 ( Skew bending ),The dangerious section is A .

7、 The moments on section A are :,(1) 斜弯曲概念 ( Concept of skew bending ),For example , a beam acted by a force P shown in right figur . The beam will be bending along two directions y and z . This bending is called skew bending .,The dangerious points are C and D . The stresses at C and D are :,Tension

8、 stress,compression stress,斜弯曲问题一般出现在矩形、工字形等截面的梁中。,(3) Circular and regular-polygon cross section,For the circular and regular-polygon cross section , there is no skew bending . The bending is plane bending !,(a) Circular cross section,Especially for two moments on the cross section shown follows ,

9、the result will be attained :,(b) Regular-polygon cross section,Dangerious point is A or B .,Especially for two moments on the cross section shown follows , the result will be attained :,平移 P1 到 B， A 截面承受弯扭组合荷载：,平移 P2 到 B， A 截面承受拉弯组合荷载：,P1 = 2 kN,P2 = 3 kN,L = 400 mm,a = 300 mm,d = 50 mm,危险点应力状态,扭转切

10、应力,例 求图示结构 A 截面危险点的第三强度相当应力。,拉伸正应力,P1 = 2 kN,P2 = 3 kN,L = 400 mm,a = 300 mm,d = 50 mm,弯曲正应力,例 求图示结构 A 截面危险点的第三强度相当应力。,5.6 斜弯曲和基本变形的组合问题 ( Combined deformations of Skew bending and other basic deformations ),For example , deformation of the column shown follows is combined with skew bending and comp

11、ression .,例 如图的集中荷载 P 可在立柱端面上平行移动，要使立柱横截面上不产生拉应力， P 应该限制在什么样的区域内？,压缩正应力,最大弯曲拉应力,不产生拉应力的条件,截面核心 ( kern of cross-section ),特别注意: 圆形截面和正多边形梁斜弯曲问题如何处理？,结论 圆形截面和正多边形梁问题不能按斜弯曲方式处理。,5.7 杆件弯曲的一般情况,正多边形的横向荷载通过截面形心，则总是产生平面弯曲。,(1) 平面弯曲,实体杆件的横向荷载通过截面形心，并沿形心惯性主轴方向，则产生平面弯曲。,薄壁杆件的横向荷载通过弯曲中心，并沿形心惯性主轴方向，则产生平面弯曲。,(2) 斜弯曲,杆件的横向荷载通过弯曲中心，但不沿形心惯性主轴方向，则将产生斜弯曲。,(3) 弯扭