《【材料课件】第五章 弯曲应力教学提纲》由会员分享，可在线阅读，更多相关《【材料课件】第五章 弯曲应力教学提纲（144页珍藏版）》请在金锄头文库上搜索。
1、1,CHAPTER 5 STRESSES IN BENDING,2,第五章 弯曲应力,材料力学,3,51 FORWORD 52 NORMAL STRESS ON THE CROSS SECTION OF THE BEAM IN PLANAR BENDING 53 SHEARING STRESS ON THE CROSS SECTION OF THE BEAM IN PLANAR BENDING 54 STRENGTH CONDITIONS OF THE NORMAL STRESS AND SHEARING STRESS OF THE BEAM REASONABLE SECTION OF THE
2、 BEAM 55 PLANAR BENDING OF UNSIMMETRIC BEAMBENDING CENTER OF THE OPENED THIN-WALLED SECTION 56 LIMIT BENDING MOMENT OF A MATERIAL WITH PLASTICITY CONSIDERED,CHAPTER 5 STRESSES IN BENDING,4,51 引言 52 平面弯曲时梁横截面上的正应力 53 梁横截面上的剪应力 54 梁的正应力和剪应力强度条件 梁的合理截面 55 非对称截面梁的平面弯曲开口薄壁截面的弯曲中心 56 考虑材料塑性时的极限弯矩,第五章 弯曲应力
3、,5 引言,弯曲应力,1、弯曲构件横截面上的（内力）应力,There are only normal stresses in the section under plane bending beam of pure bending (There is only M and no Q in the cross section). There are shearing stresses in the section under plane bending beam of transverse bending. (There are Q and M in the cross section).,2、
4、Study method,Such as：,STRESSES IN BENDING,平面弯曲时横截面s 纯弯曲梁(横截面上只有M而无Q的情况) 平面弯曲时横截面t 剪切弯曲(横截面上既有Q又有M的情况),弯曲应力,2、研究方法,纵向对称面,P1,P2,例如：,Deformation of some portion of the beam in which there are only bending moment and no shearing stress is called pure bending. Such as portion AB.,P,P,a,a,A,B,Q,M,x,x,Pure
5、 Bending:,STRESSES IN BENDING,P,P,Pa,某段梁的内力只有弯矩没有剪力时，该段梁的变形称为纯弯曲。如AB段。,弯曲应力,P,P,a,a,A,B,Q,M,x,x,纯弯曲(Pure Bending):,P,P,Pa,52 NORMAL STRESS ON THE CROSS SECTION OF THE BEAM IN PLANAR BENDING,1.Experiment of pure bending of the beam,Lateral lines(a b、c d）keep l straight lines and rotate through some a
6、ngles after deformation, longitudinal straight lines change into curves with upper fibers constructed and lower fibers elongated, lateral lines are still normal to longitudinals lines after deformation.,（1）Geometric law of the deformation：,1、 NORMAL STRESS ON THE CROSS SECTION OF THE BEAM IN PLANAR
7、BENDING,Neutral axis,STRESSES IN BENDING,52 平面弯曲时梁横截面上的正应力,1.梁的纯弯曲实验,横向线(a b、c d）变形后仍为直线，但有转动；纵向线变为曲线，且上缩下伸；横向线与纵向线变形后仍正交。,（一）变形几何规律：,一、 纯弯曲时梁横截面上的正应力,弯曲应力,There are only normal stresses on cross sections.,Hypothesis of plane section：The cross sections remain still planes and only rotate through som
8、e angles around their neutral axes after deformation.,（May be proved by symmetry and the method of infinite division）,Neutral layer：A layer at a certain height inside the beam in which the longitudinal fibers are neither to be elongated nor to be shortened and they are neither subject to tension nor
9、 compression.This layer is called the neutral layer Neutral axis：The intersection of the neutral layer with any cross section.,STRESSES IN BENDING,2. Two concepts:,3. Deduction:,横截面上只有正应力。,平面假设：横截面变形后仍为平面，只是绕中性轴发生转动，距中性轴等高处，变形相等。,（可由对称性及无限分割法证明）,3.推论,弯曲应力,2.两个概念,中性层：梁内一层纤维既不伸长也不缩短，因而纤维不受拉应力和压应力，此层纤维
10、称中性层。 中性轴：中性层与横截面的交线。,4. Geometric equation：,STRESSES IN BENDING,4. 几何方程：,弯曲应力,（2）Physical relation：,Assume there is no extrusion between the longitudinal fibers, therefore，an arbitrary point in the beam is at an uniaxial stressed state.,（3）Static relations：,STRESSES IN BENDING,（二）物理关系：,假设：纵向纤维互不挤压。
11、于是，任意一点均处于单项应 力状态。,弯曲应力,（三）静力学关系：,（Symmetric plane）, (3),STRESSES IN BENDING,弯曲应力,（对称面）, (3),STRESSES IN BENDING,Circular section,（四）最大正应力：,弯曲应力, (5),Solution：Plot the diagram of M and determine the bending moment of the section,STRESSES IN BENDING,Example 1 The simply supported beam subjected to un
12、iformly distributed load is shown in the figure. Try to determine：(1）the normal stresses at points 1、2 on the section 11；（2）the maximum normal stress on this section； (3) knowing maximum normal stress in the whole beam；（4）as E=200GPa，determine the radius of curvature of section 11.,例1 受均布载荷作用的简支梁如图所
13、示，试求： （1）11截面上1、2两点的正应力； （2）此截面上的最大正应力； （3）全梁的最大正应力； （4）已知E=200GPa，求11截面的曲率半径。,弯曲应力,解：画M图求截面弯矩,Determine the stress,STRESSES IN BENDING,弯曲应力,求应力,Determine the radius of curvature,STRESSES IN BENDING,求曲率半径,弯曲应力,53 SHEARING STRESS ON THE CROSS SECTION OF THE BEAM,1、Shearing stresses on the cross secti
14、on of the beam with rectangular sections,Fig. a,Fig. b,Fig. c,STRESSES IN BENDING,1)、Two assumptions： Shearing stresses are all parallel to the shearing force；Shearing stresses are equal at the same distance to the neutral axis.,2)、Researching method;the free body is in equilibrium. Take an infinite
15、simal segment of the beam as shown in figure b； Take a small block from the infinitesimal segment as shown in figure c，the equilibrium equation is,53 梁横截面上的剪应力,一、 矩形截面梁横截面上的剪应力,1、两点假设： 剪应力与剪力平行；矩中性轴等距离处，剪应力 相等。,2、研究方法：分离体平衡。 在梁上取微段如图b； 在微段上取一块如图c，平衡,弯曲应力,Q(x)+d Q(x),M(x),y,M(x)+d M(x),Q(x),dx,图a,图b,图c,Q(x)+d Q(x),M(x),y,M(x)+d M(x),Q(x),dx,Fig.a,Fig.b,Fig.c,From the theory of the conjugate shearing stress,STRESSES IN BENDING,弯曲应力,Q(x)+d Q(x),M(x),y,M(x)+d M(x),Q(x),dx,
