英汉双语材料力学8资料.ppt

英汉双语材料力学8CHAPTER 8 STHENGTH THEORIESCHAPTER 8 STHENGTH THEORIES81 Concepts of strength theories82 Four strength theories and their equivalent stresses83 Mohrs strength theory and its equivalent stress8-4 8-4 Applications of strength theories32第八章第八章第八章第八章 强度理论强度理论强度理论强度理论81 强度理论的概念强度理论的概念82 四个强度理论及其相当应力四个强度理论及其相当应力83 莫尔强度理论及其相当应力莫尔强度理论及其相当应力8-4 8-4 强度理论的应用强度理论的应用431 1、Opening words：8 CONCEPTS OF STRENGTH THEORIES1)、Investigation of the tensile,compressive and torsional tests of cast iron and low-carbon steelMLow-carbon steelCast ironPPTension of cast iron PCompression of cast iron2)、How will the member rupture in Combined deformations？MP54一、引子：一、引子：8 强度理论的概念强度理论的概念1、铸铁与低碳钢的拉、压、扭试验现象是怎样产生的？M低碳钢铸铁PP铸铁拉伸 P铸铁压缩2、组合变形杆将怎样破坏？MP652 2、Theories of strength：Some assumptions about the cause of the strength failure of materials.3、Types of failure of materials：yield；rupture1)、Galileo planted the seed of the first strength theory；2)、Mariottos statement about the rupture of material due to excessive deformation is the flush of the second strength theory；3)、C.Duguet proposed the theory of the maximum shearing stress；4)、Maxwell brought forward the theory of the maximum distortional energy theory early,which was known after his letters were published.76二、强度理论：是关于“构件发生强度失效（failure by lost strength）起因”的假说。1、伽利略播下了第一强度理论的种子；三、材料的破坏形式：屈服；断裂。2、马里奥特关于变形过大引起破坏的论述，是第二强度理论的萌芽；3、杜奎特（C.Duguet)提出了最大剪应力理论；4、麦克斯威尔最早提出了最大畸变能理论（maximum distortion energy theory）；这是后来人们在他的书信出版后才知道的。8782 FOUR STRENGTH THEORIES AND THEIR EQUIVALENT STRESSES1 1、Theory of the maximum tensile stress（the first strength）：）：This theory considers the main cause of rupture to be the maximum tensile stress.The member will rupture as the maximum tensile stress reaches the strength limit in axial tension.1)、Criterion of rupture：2)、strength condition：3)、Application range：May be applied to the members with the failure form of brittle rupture.9882 四个强度理论及其相当应力四个强度理论及其相当应力一、最大拉应力（第一强度）理论：一、最大拉应力（第一强度）理论：认为构件的断裂是由最大拉应力引起的。当最大拉应力达到单向拉伸的强度极限时，构件就断了。1、破坏判据：2、强度准则：3、实用范围：实用于破坏形式为脆断的构件。1092、Theory of the maximum tensile strain（the second strength）：）：This theory considers the main cause of rupture to be the maximum tensile strain.The member will rupture as the maximum tensile strain reaches the limit strain in axial tension 1)、Criterion of failure：2)、Strength condition：3)、Application range：May be applied to the members with the failure form of brittle rupture.1110二、最大伸长线应变（第二强度）理论：最大伸长线应变（第二强度）理论：认为构件的断裂是由最大伸长线应变引起的。当最大伸长线应变达到单向拉伸试验下的极限应变时，构件就断了。1、破坏判据：2、强度准则：3、实用范围：实用于破坏形式为脆断的构件。12113 3、Theory of the maximum shearing stress（the third strength）：）：This theory considers the main cause of rupture to be the maximum shearing stress.The member will rupture as the maximum shearing stress reaches the limit shearing stress in axial tension.1)、Criterion of failure：3)、Application range：May be applied to the members with the failure form of plastic yield.2)、Strength condition：1312三、最大剪应力（第三强度）理论：三、最大剪应力（第三强度）理论：认为构件的屈服是由最大剪应力引起的。当最大剪应力达到单向拉伸试验的极限剪应力时，构件就破坏了。1、破坏判据：3、实用范围：实用于破坏形式为屈服的构件。2、强度准则：14134、Theory of the maximum torsional(shearing)strain energy(the fourth strength）：）：This theory consider the main cause of yield to be the distortional strain energy.The member will rupture as the distortional strain energy reaches the distortional strain energy of yield in axial tension 1)、Criterion of failure：2)、Strength condition:3)、Application range：May be applied to the members with the failure form of plastic yield.1514四、形状改变比能（第四强度）理论：四、形状改变比能（第四强度）理论：认为构件的屈服是由形状改变比能引起的。当形状改变比能达到单向拉伸试验屈服时形状改变比能时，构件就破坏了。1、破坏判据：2、强度准则3、实用范围：实用于破坏形式为屈服的构件。161583 MOHRS STRENGTH THEORY AND ITS EQUIVALENT STRESS Mohr thought the maximum shearing stress is the main cause of failure of materials,but the friction force in the sliding section is not neglected.(Law of Mohr friction）,Combining the factors of the maximum shearing stress and the maximum normal stress Mohr obtained his strength theory.171683 莫尔强度理论及其相当应力莫尔强度理论及其相当应力 莫尔认为：最大剪应力是使物体破坏的主要因素，但滑移面上的摩擦力也不可忽略（莫尔摩擦定律）。综合最大剪应力及最大正应力的因素，莫尔得出了他自己的强度理论。1817Approximate envelopeEnvelope of circles of limit stress1 1、Two concepts：1)、Circle of limit stress：2)、Limit curve：Envelope of circles of limit stress.O t ts Circle of limit stress1918近似包络线极限应力圆的包络线O t ts 极限应力圆一、两个概念：一、两个概念：1、极限应力圆：2、极限曲线：极限应力圆的包络线（envelope）。20191)、Criterion of failure：2)、Strength condition：yaaot LO1O2Derivation of the critical condition of Mohr,s theory O3 1 3MKLPN2 2、Mohrs strength theory：If the stress circle of an arbitrary point Contacts with the limit curve,the material will yield or break due to shearing.2120 yaaot LO1O2莫尔理论危险条件的推导莫尔理论危险条件的推导2、强度准则：1、破坏判据：O3 1 3MKLPN二、莫尔强度理论：二、莫尔强度理论：任意一点的应力圆若与极限曲线相接触，则材料即将屈服或剪断。22213、Equivalent stress：（：（unified form of strength conditions）where，requivalent stress3)、Application range：May be applied to the members with the failure form of plastic yield and the brittle members（rock、concrete and so on.）with different limit strength of tension and compression in complex stressed state.2322三、相当应力：（强度准则的统一形式）。三、相当应力：（强度准则的统一形式）。其中，r相当应力。3、实用范围：实用于破坏形式为屈服的构件及其拉压极限强度不等的处于复杂应力状态的脆性材料的破坏（岩石、混凝土等）。242384 APPLICATIONS OF STRENGTH THEORIES1 1、Steps of calculation of strength：1)、Analysis of external forces：Determine the value of the request external forces2)、Analysis of internal forces：Plot the diagram of the internal forces and determine the critical section.3)、Analysis of stresses：Plot the diagram of stress distribution in the critical section,determine the critical point,plot the element and determine the principal stresses.4)、Analysis of strength：Select the proper theory of strength，calculate the equivalent stress and then do the calculation of strength.252484 强度理论的应用强度理论的应用一、强度计算的步骤：一、强度计算的步骤：1、外力分析：确定所需的外力值。2、内力分析：画内力图，确定可能的危险面。3、应力分析：画危面应力分布图，确定危险点并画出单元体，求主应力。4、强度分析：选择适当的强度理论，计算相当应力，然后进行 强度计算。2625 2 2、Rules to select strength theories:decide according to the form of failure.1)、Brittle materials：As the minimum principal stress is larger than or equal to zero the first theory may be applied；As the minimum principal stress is smaller than zero and the maximum principal stress is larger than zero Mohrs theory may be applied；As the maximum principal stress is smaller than or equal to zero the third or fourth theory may be applied；2)、Ductile material：As the minimum principal stress is larger than or equal to zero the first theory may be applied；For the other stressed state the third or fourth theory may be applied.4)、Forms of failure are relative with temperature、speed of deformation etc.3)、In simple deformation：Apply the strength condition corresponding to the simple deformation.Such as in torsion we may apply:2726二、强度理论的选用原则：依破坏形式而定。二、强度理论的选用原则：依破坏形式而定。1、脆性材料：当最小主应力大于等于零时，使用第一理论；3、简单变形时：一律用与其对应的强度准则。如扭转，都用：2、塑性材料：当最小主应力大于等于零时，使用第一理论；4、破坏形式还与温度、变形速度等有关！当最小主应力小于零而最大主应力大于零时，使用莫尔理论。当最大主应力小于等于零时，使用第三或第四理论。其它应力状态时，使用第三或第四理论。2827Solution：Stressed state at the critical point A is shown in the figure：Example 1 A circular rod made of cast iron is subjected to the loads T=7kNm,P=50kN as shown in the figure.Its diameter is d=0.1m,=40MPa.Try to check the strength of the rod according to the theory of the first strength.SafePPTTAA t t2928解：危险点A的应力状态如图：例例1 直径为d=0.1m的圆杆受力如图,T=7kNm,P=50kN,为铸铁构件，=40MPa,试用第一强度理论校核杆的强度。故，安全。PPTTAA t t3029As sx yxyA Solution：From generalized Hookes law we get:This container does not satisfy the third strength theory and is not safe.Example 2 As a circular thin-walled tube is subjected to the maximum internal pressure,tested x=1.8810-4,y=7.3710-4.Knowing for steel E=210GPa，=170MPa,Possions ratio is=0.3.Check itsstrength according to the third strength theory.3130例例2 薄壁圆筒受最大内压时,测得x=1.8810-4,y=7.3710-4,已知钢的E=210GPa，=170MPa,泊松比=0.3，试用第三强度理论校核其强度。解：由广义虎克定律得:As sx yxyA所以，此容器不满足第三强度理论。不安全。3231Solution：Plot the diagramof Mohrtheory yaaot LO1O2Critical diagram of Mohr,s theory O3 1 3MKLPNa aExample 3 For a structural member made of cast iron,bL=400MPa，by=1200MPa.As a point with with the of plane stress yields according to Mohrs strength theory,the maximum shearing stress is 450MPa.Try to determine the principal stresses at the point.3332破坏判据：例例3 一铸铁构件 bL=400MPa，by=1200MPa，一平面应力状态点按莫尔强度理论屈服时，最大剪应力为450MPa，试求该点的主应力值。解：做莫尔理论分析图 yaaot LO1O2莫尔理论危险图莫尔理论危险图O3 1 3MKLPNa a3433Sowing the above simultaneous equations,we get:Sowing the above simultaneous equations,we get:That isCriterion of failure:3534解解上述联立方程得上述联立方程得：3635 Chapter 8 Exercises 1.When establishing the strength conditions in the complex stress state,why can we determine the allowable stress of a material according to the results of the simple-tension test?2.The first and the second strength theories are only suitable for brittle materials and the third and the fourth strength theories are only suitable for plastic materials.Can we say like this?Why?3.Try to write out the expressions of the equivalent stress of a circular shaft in torsion according to the four strength theories.Solution:36 第八章第八章 练习题练习题 一、在建立复杂应力状态下的强度条件时，为一、在建立复杂应力状态下的强度条件时，为什么可以根据简单拉伸的试验结果来确定材料的许什么可以根据简单拉伸的试验结果来确定材料的许用应力？用应力？二、第一和第二强度理论只适用于脆性材料；二、第一和第二强度理论只适用于脆性材料；第三和第四强度理论只适用于塑性材料。这种说法第三和第四强度理论只适用于塑性材料。这种说法是否正确，为什么？是否正确，为什么？三、试按四个强度理论写出圆轴扭转时的相当三、试按四个强度理论写出圆轴扭转时的相当应力表达式。应力表达式。解：解：373839此课件下载可自行编辑修改，仅供参考！此课件下载可自行编辑修改，仅供参考！感谢您的支持，我们努力做得更好！谢谢感谢您的支持，我们努力做得更好！谢谢