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1、MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 16-12,6-15(b),7-2,7-3(c,d),7-5MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 2本 讲 内 容第七章 应力状态
2、分析 叠加法二：逐段分析求和法MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 3ABC例1:求图示外伸梁C点的挠度和转角ABCABCqaqa2/2仅考虑BC段变形（刚化AB）仅考虑AB段变形(刚化BC)二、逐段变形效应叠加法总挠度和转角MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATER
3、IALS MECHANICS OF MATERIALS B U A A B U A APage 4逐段变形效应叠加法：静定梁的任一横截面的总位移，等于各梁段单独变形(其余梁段刚化)在该截面引起的位移的代数和或矢量和。进一步讨论ABCABCABCqaqa2/2MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U
4、 A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 6AB段的变形：仅考虑BC段变形：ABCMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 7例3：E常数,，,求PA BCE FA BCE FA BCE FA BC 对称性在变形分析中的应用：对称性在变形分析中的应用：P/2CFBMECHA
5、NICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 8例5：EI=常数，求ABCFABCBC刚化FBCAFFaw32.BC扭转(AB刚化)3.BC弯曲(AB刚化)1.AB弯曲(BC刚化）MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U
6、A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 10二、梁的合理刚度设计EIz弯曲刚度，Pk广义力(P,m,q)梁的弯曲变形与梁的受力、支持条件及截面的弯曲刚度EI有关1、可以采用提高弯曲强度的某些措施，例如合理安排约束、改善 梁的受力等方法，来提高梁的弯曲刚度。2、但梁的合理刚度设计与合理强度设计不尽相同。MECHANICS OF MATERIALS MECHANIC
7、S OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 11三、提高梁刚度的主要措施 合理安排梁的约束；改善梁的受力情况；适当增加梁的约束，变静定梁为静不定梁。1、减小M的数值：2、提高I/A选择合理的截面形状：3、减小跨长l4、提高材料弹性模量选择E大的材料5、整体提高EI更大范围内使EI提高不同于提高Wz/A不同于提高不同于提高(M/W)max是局部加强MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A
8、A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 13（1）强度是局部量，刚度是整体量（积分）2.与梁的合理强度设计的不同点 辅梁、等强度梁是合理强度设计的有效手段，提高梁的刚度须整体加强 小孔显著影响强度，但对刚度影响甚微MECHANICS OF MAT
9、ERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 15跨度微小改变，将导致挠度显著改变例如 l 缩短 20，dmax 将减少 48.8%梁跨度的合理选取MECHANICS OF MAT
10、ERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 167-1 7-1 引引 言言7-2 7-2 平面应力状态应力分析平面应力状态应力分析第七章 应力状态分析7-4 7-4 复杂应力状态的最大应力复杂应力状态的最大应力7-3 7-3 极值应力与主应力极值应力与主应力7-6 7-6 应变分析与电测应力应变分析与电测应力7-5 7-5 广义胡克定律广义胡克定律7-7 7-7 复合材料应力应变关系简介复合材料应力应变关系简介MECH
11、ANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 18低碳钢和铸铁的扭转实验 低碳钢和铸铁的扭转实验低碳钢 低碳钢 铸 铸 铁 铁容易由实验建立强度条件。与拉伸
12、断口有何不同，为什么？拉伸与扭转强度条件是否有关联？MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 19单向受力状态：max 纯剪切状态：max 杆件的基本变形形式：轴向拉伸与压缩扭转 纯弯MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATER
13、IALS B U A A B U A APage 20 螺旋桨轴:FFMA A微体A采用拉伸强度条件、扭转强度条件，还是其它强度条件？MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 21 工字梁 工字梁:c,d 点处:单向应力；a 点处:纯剪切；b 点处:,联合作用d复杂应力状态下，如何建立强度条件？分别满足?做实验?MECHANICS OF MATERIALS MECHANICS OF M
14、ATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 22一、应力分析的解析法：符号规定：拉伸为正；使微体顺时针转者为正 以x轴为始边，指向沿逆时针转者为正xyxxxyyynyxdAxy7-2 平面应力状态应力分析MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANIC
15、S OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 24xyxxxyyyn 当 时，此时对应单向应力状态 当 时，此时对应纯剪切应力状态 MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 25解：问 可取何值（
16、x轴向左）例 求图示，已知单位：MPaMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 26二、应力分析的图解法在 平面上，的轨迹？斜截面应力公式对斜截面应力公式进行变换圆 应力圆MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B
17、 U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 28三、应力圆的绘制及应用o(x+y)/2R绘制方法1：为半径作圆为圆心，以缺点：需用解析法计算圆心坐标和半径没有反映应力圆上的点与微体截面方位的对应关系MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIAL
18、S MECHANICS OF MATERIALS B U A A B U A APage 29oDExxyyC(x+y)/2F(x-y)/2绘制方法2（实际采用）分析设x面和y面的应力分别为故DE中点坐标由于为圆心，DE为直径。MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMEC
19、HANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 31l l 点面对应：点面对应：应力圆上某一点的坐标值对应着微体某 应力圆上某一点的坐标值对应着微体某一方向截面上的正应力和切应力 一方向截面上的正应力和切应力应力圆点与微体截面应力对应关系HCMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 32l l 二倍角对应：二
20、倍角对应：半径转过的角度是方向面旋转角度的两倍 半径转过的角度是方向面旋转角度的两倍 微体互垂截面，对应应力圆同一直径两端 微体互垂截面，对应应力圆同一直径两端 微体平行对边 微体平行对边,对应 对应应力圆 应力圆同一点 同一点2Cl 转向对应：转向对应：半径旋转方向与方向面法线旋转方向一致 半径旋转方向与方向面法线旋转方向一致；MECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A AMECHANICS OF MATERIALS MECHANICS OF MATERIALS B U A A B U A APage 33 几种简单受力状态的应力圆xx单向受力状态xy纯剪切受力状态oR=x双向等拉 ox/2R=x/2C o C圆心坐标：半径：