材料力学双语教学学习资料

1、材料力学双语教学学习资料1第一章绪论Chapter1Introduction1-1材料力学的任务TheTasksofMechanicsofMaterials1.材料力学:MechanicsofMaterials构件:StructuralMembers变形:Deformation4.强度:Strength5.刚度:Rigidity6.稳定性:Stability1-2变形固体的基本假设FundamentalAssumptionsofSolidDeformationBodies连续性假设:Continuity均匀性假设:Homogeneity各向同性假设:Isotropy1.3外力及其分类Exter

2、nalForcesandClassification分布力:DistributedForce集中力:PointForce静载荷:StaticLoad动载荷:DynamicLoad1.4内力、截面法和应力的概念ConceptsofInternalForces，MethodofSectionandStress1.内力:InternalForce2.截面法:MethodofSection截面法的三个步骤：截开，代替，平衡Threestepsofmethodofsection:cutoff,substitute,andequilibrium.4.应力:Stress平均应力：Averagestress应

3、力（全应力）：Wholestres（ssumstress）7.正应力:NormalStress8.剪应力（切应力）：ShearingStress1.5变形与应变DeformationandStrain1线应变:Strain2剪应变:ShearingStrain1.6杆件变形的基本形式BasicTypesofDeformationsofRods1.拉伸或压缩:TensionorCompression2.剪切:Shear3.扭转:Torsion4.弯曲:Bending第二章拉伸、压缩与剪切Chapter2Tension，CompressionandShear2.1轴向拉伸与压缩的概念和实例TheC

4、onceptandExamplesofAxialTensionandCompression拉杆:TensileRod压杆:CompressiveRod受力特点：外力合力的作用线与杆轴线重合CharacteristicoftheExternalForces:Theactinglineoftheresultantofexternalforcesiscoincidedwiththeaxisoftherod.变形特点：杆沿轴向伸长或缩短CharacteristicofDeformation:Rodwillelongateorcontractalongtheaxisoftherod.2.2轴向拉伸或压缩

5、时横截面上的内力和应力InternalForceandStressofAxialTensionorCompressionontheCrossSection1.横截面:CrossSection2.轴力:NormalForce3.轴力图:DiagramofNormalForce2.3直杆轴向拉伸或压缩时斜截面上的应力StressofAxialTensionorCompressionontheSkewSection斜截面:SkewSection2c=acos2at=siifiaaa22.4材料在拉伸时的力学性能MechanicalPropertiesofMaterialswithTensileLoa

6、d标准试件:Specimen低碳钢(CW0.3%):LowCarbonSteel弹性阶段:ElasticRegion屈服阶段:YieldingStage强化阶段:HardeningStage颈缩阶段:NeckingStage7*q比例极限:ProportionalLimit8*q弹性极限:ElasticLimite9*.qs屈服极限:YieldingStress10*.q强度极限:UltimateStressb延伸率:PercentElongation断面收缩率:PercentReductionofArea塑性材料:DuctileMaterials脆性材料:BrittleMaterials铸铁

7、:Castiron2.7失效、安全系数和强度计算Failure,SafetyfactorandStrengthcalculation1*.许用应力:AllowableStress安全系数:SafetyFactor3*.强度条件:StrengthConditionFmaxA4*.强度校核:CheckstrengthN6*.确定许可载荷:DetermineallowableloadFAN2.8轴向拉伸或压缩时的变形DeformationinAxialTensionorCompression弹性变形:ElasticDeformation塑性变形:PlasticDeformation纵向应变:Long

8、itudinalStrainAll-1=-411横向应变:LateralStrainAdd-d=dd5.线弹性变形:LinearElasticDeformation6.泊松比:Poissonsratio7*.弹性模量-E：表示材料抵抗拉压变形的能力E-modulusofelasticity：Indicatesthecapabilityofmaterialsforresistingtensionorcompression8*.抗拉刚度-EA：表示构件抵抗拉压变形的能力EA-theaxialrigidity:Indicatesthecapabilityofconstructivemembersfo

9、rresistingtensionorcompression9*.胡克定律(HookesLaw):当应力不超过材料的比例极限时，应力与应变成正比.Thestressisproportionaltothestrainwithintheelasticregion.二EAL=FNLEA2.12应力集中的概念TheConceptofStressConcentration由于截面尺寸的突然变化，使截面上的应力分布不再均匀，在某些部位出现远大于平均值的应力，称应力集中。Discontinuitiesofcrosssectionmayresultinhighlocalizedorconcentratedst

10、resses.理论应力集中系数K：TheoreticalStress-concentrationFactor-K2.13剪切和挤压的实用计算PracticalCalculationofShearandBearing1*.剪切：Shear剪切面：ShearingPlane3*.剪切面上的内力-剪力：InternalForceinShearingPlane-ShearingForce剪切的实用计算：PracticalCalculationofShearFT=STA挤压的实用计算：PracticalCalculationofBearingFQbsAbsbs挤压强度条件：工作中的挤压应力不应超过许用挤

11、压应力。Strengthconditionofbearing：Workingbearingstressshouldnotexceedtheallowablebearingstress.第三章扭转ChapterThreeTorsion3.1扭转的概念和实例ConceptandExamplesofTorsion电动机:Generator涡轮:Turbine3*.扭转的受力特点：杆件的两端作用着大小相等，方向相反，且作用面垂直于杆件轴线的力偶。Characteristicofloads:Shaftisloadedbyatorsionalcoupleinplanesthatareperpendicul

12、artotheaxisoftheshaft.4*.变形特点：杆件的任意两个横截面发生绕轴线的相对转动。Characteristicofdeformation:anytwocrosssectionswilltwistalongtheaxis.5*.轴:Shaft3.2外力偶矩的计算扭矩和扭矩图CalculationoftheexternaltorqueInternaltorqueandItsdiagram1扭转外力偶矩的计算：Calculationoftheexternaltorque2*.扭矩：InternalTorque符号规定：Signconvention4*.右手螺旋法则:Rightha

13、ndscrewrule5*.扭矩图：DiagramofInternalTorque3.3纯剪切PureShear薄壁圆筒的扭转实验：Experimentofthin-walledcirculartubeundertorsion变形特点:Charactersofdeformations：截面间的距离不变;所有横截面的位置不变;所有纵向线转过了一个角度匕。Distancesbetweenthesectionsremainunchanged,Allcrosssectionsremainunchanged,Allthegeneratinglinesrevolvethroughanangle/.3*.切

14、应力互等定理：Theoremofcomplementaryshearingstresses4*.切应变：Shearingstrain5*剪切虎克定律：Hookeslawofshear6*.剪切弹性模量G：Modulusofelasticityofshearing第四节圆轴扭转时的应力Stressesinaroundshaftundertorsion）1*.Ip（极惯性矩）-polarmomentofinertia2*.Wp（抗扭截面系数）sectionmodulusintorsion3.5圆轴扭转时的变形扭转角:Theangleoftwist2*.抗扭刚度GIp：thetorsionalrig

15、idity3*.扭转的刚度条件:Rigidityconditionintorsion单位长度扭转角：TheangleoftwistperunitlengthExercisesAbracket（支架）isshowninthefigure，Thecross-sectionareaofthesteelbarABisA1=6cm2；thecross-sectionareaofthewoodenbarBCisA2=300cm2，KnowingtheallowablestressofsteelisQ=140MPa,theallowabletensilestressofwoodisQL=8MPa,andth

16、eallowablecompressivestressofwoodisQY=4MPa.TrydeterminetheallowableloadPofthebracket.4.Atensilebarandtwocoverboardsareboltedtogetherasshown.Eachcoverboardhasathicknessof8mm.AllthepartsaremadefromthesamematerialandhavetheallowablestresseslandhavethetJ=80MPa,=160MPa.Thethicknesssameb=60MPa,tbsofthebar

17、8=15mm,thetensileforceF=120KN.Trytodesignthediameterdofthebolt.thewidthbofthetensilebar.2.Awoodentenon(榫)jointisshowninthefigure.Knowingthatthequantitiesarea=b=12cm，h=35cm，c=4.5cmandP=40KN.Trytodeterminetheshearingstressandbearingstressforthejoint.hh5构件在外力作用下抵抗破坏的能力称为.；构件在外力作用下抵抗变形的能力称为.；构件在外力作用下保持原

18、有平衡状态的能力称为。(PleasefillintheblankswithproperwordsinEnglish.)aA3TwoAboardsareboltedtogetherPasshown.Eachboardhasathickness(5)of2mm,andawidth(b)of15mm.Thediameterdoftheboltis4mm.AllthepartsaremadefromthesamematerialandhavethesameallowablestressesIn=160MPa,b=100MPa,t=300MPa.TrytodesignthetensilebsforceF

19、.6杆件的基本变形一般、四种。(PleasefillintheblankswithproperwordsinEnglish.)第四章弯曲内力ChapterFourInternalForcesinBending4-1弯曲的概念和实例4-1TheConceptsandExamplesinBending1梁：beam2轴线：axis3.纵向对称面：longitudinalplaneofsymmetry4*.平面弯曲：planebending5.弯曲的受力特点：作用于杆件上的外力或外力偶矩矢垂直于杆件轴线。Characteristicsofloads:externalforcesorexternalt

20、hecouplevectorperpendiculartotheaxisoftherod.6*.弯曲的变形特点：杆件的轴线由直线变为曲线。Characteristicsofdeformations:theaxisoftherodchangeintocurvefromoriginalstraightlines.7*.弯曲变形：杆件在垂直于杆轴线的外力或两个外力偶的作用下，杆的轴线由直线变为曲线，这种变形称为弯曲变形。BENDING:Theactionoftheexternalforceorexternalthecouplevectorperpendiculartotheaxisoftherodm

21、akestheaxisoftherodchangeintocurvefromoriginalstraightlines,thisdeformationiscalledbending.4-2受弯杆件的简化4-2SimplificationofBendingRods集中力：concentratedforce分布力：distributedload均布载荷：uniformload支座：support5*.简支粱：simplesupportedbeam6*.外伸梁：overhangingbeam7*.悬臂梁：cantileverbeam4-3剪力和弯矩4-3ShearingForceandBending

22、Moment弯曲内力：internalforcesinbending2*.剪力：shearingforce3*.弯矩：bendingmoment内力的正负规定：signconventionsfortheinternalforces4-4剪力方程和弯矩弯矩方程剪力图和弯矩图4-4TheEquationsofShearingForceandBendingMomentTheDiagramsofShearingForceandBendingMoment1*.剪力方程：equationofshearingforce2*.弯矩方程：equationofbendingmoment3*.剪力图：diagram

23、ofshearingforce4*.弯矩图：diagramofbendingmoment4-5载荷集度、剪力和弯矩间的关系4-5RelationsamongtheIntensityofDistributedLoad,ShearingForceandBendingMoment1*.微分关系：differentialrelations2*.规律法：methodofregulation3*.控制截面法：methodofcontrolsections水平直线：horizontalstraightline斜直线：inclinedstraightline突变：suddenchange增函数：increas

24、ingfunction减函数：decreasingfunction盆状抛物线：basin-likecurve坟状抛物线：tomb-likecurve折向与P相反：flexibleoppositetoP第五章弯曲应力ChapterFiveStressesinBending5-1纯弯曲5-1PureBending横力弯曲：transversebending2*.纯弯曲：purebending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。Hypothesisofplanesection:Thecrosssectionsremainstillplanes,andonl

25、yrotatethroughsomeanglesaroundtheirneutralaxesafterdeformation.4*.中性层：neutrallayer5*.中性轴：neutralaxis纵向对称轴：longitudinalaxisofsymmetry5-2纯弯曲时的正应力5-2NormalStressinPureBending几何关系：geometricrelation物理关系：physicsrelation静力关系：staticrelation4*.抗弯刚度EIz:flexuralrigidity5-3横力弯曲时的正应力5-3NormalStressinTransverseBe

26、nding1.抗弯截面系数W：sectionfactorofbending2*.弯曲的强度条件：strengthconditioninbending5-4弯曲切应力5-4ShearingStressinBending1矩形截面梁：thebeamwithrectangularsection2工字形截面梁：wide-flangebeam3翼缘：flange4腹板：web5静矩：staticmoment6*.惯性矩：momentofinertia6焊接：melt7铆接：rivet5-6提高弯曲强度的措施5-6MeasuresofIncreasingStrengthinBending1合理安排梁的受力

27、情况：arrangetheloadsofbeamreasonably2跨度：span3梁的合理截面：reasonablesectionofbeams4*.等强度梁：equalstrengthbeams第六章弯曲变形ChapterSixDeformationsinBending6-1工程中的弯曲变形问题6-1TheProblemsofDeformationDuetoBendinginEngineering1车床主轴：principalaxisoflathe2振动：vibrate3噪声：noise6-2挠曲线的微分方程6-2Thedifferentialequationofdeflectioncu

28、rve挠曲线：deflectioncurve2*.挠度：deflection3*.转角：angleofrotationorslope切线：tangent逆时针：counter-clockwise顺时针：clockwise曲率：curvature曲率半径：radiusofcurvature6-3积分法求弯曲变形6-3DeterminetheDeformationsinBendingbyIntegration1*.微分方程：differentialequation边界条件：boundarycondition连续性条件：continuitycondition积分常数：integralconstant

29、s5*.转角方程：equationofangleofrotation6*.挠曲线方程：equationofdeflectioncurve刚度条件：rigiditycondition镗床：boringmachine镗刀：boringtool6-4叠加法求弯曲变形6-4DeterminetheDeformationsinBendingbytheMethodofSuperposition1*.叠加法：themethodofsuperposition桥式起重机：overheadtravelingcrane6-5简单超静定梁6-5IndeterminateSimpleBeams1静定梁：statical

30、lydeterminatebeam2超静定梁：staticallyindeterminatebeam3变形协调方程：equationofcompatibilityofdeformations6-6提高弯曲刚度的一些措施6-6MeasuresofIncreasingRigidityinBending1增大抗弯刚度：increaseflexuralrigidity2减少跨度或增加支承：decreasespanorincreasesupports3减小弯矩：decreasebendingmoment4选择合理的截面形状：selectthereasonablesectionsExercisesAcan

31、tileverbeamAB.Thedistributedloadof3kN/mextendsover0.8mofthebeamandthe1kNloadisappliedatpointE.Plotthediagramsofsharingforceandbendingmoment.Theallowablestressofthewoodenbeamshowninthefigureisd=10MPa.Trytodeterminethemaximumdiameterdofthecircularholeincasethatthestrengthofthebeamissatisfied(neglectin

32、gstressconcentrations).3DeterminetheangleofrotationofpointAandthedeflectionofpointCbythemethodofsuperposition.第七章应力和应变分析强度理论ChapterSevenStressandStrainAnalysisStrengthTheories7-1应力状态概述7-1ConceptsoftheStateofStress1一点的应力状态：过一点有无数的截面，这一点的各个截面上应力情况的集合，称为这点的应力状态。Thestateofstressatapoint:Therearecountles

33、ssectionsthroughapoint.Thegatheringofstressesinallsectionsiscalledthestateofstressatthispoint.2单元体：构件内的点的代表物，是包围被研究点的无限小的几何体，常用的是正六面体。Element:Delegateofapointinthemember.Itisaninfinitesimalgeometricbodyenvelopingthestudiedpoint.Incommonuseitisacorrectitudecubicbody.3主单元体：各侧面上剪应力均为零的单元体。Principalelem

34、ent:Theelementinwhichtheshearingstressesinsideplanesareallzero.4主平面：剪应力为零的截面。PrincipalPlanes:Theplanesonwhichtheshearingstressesarezero.5主应力：主平面上的正应力。Principalstresses:Normalstressesactingontheprincipleplanes.主应力排列规定；按代数值大小Q123Conventionoftheorderforthreeprincipalstresses:Inmagnitudeofthealgebraicva

35、lue.三向应力状态：三个主应力都不为零的应力状态。Stateofthetriaxialstress(threedimensionalstateofstress):Stateofstressthatallthethreeprincipalstressesarenotequaltozero.二向应力状态：一个主应力为零的应力状态。stateofthebiaxialstress(planestateofstress):stateofstressthatoneprincipalstressisequaltozero.单向应力状态：一个主应力不为零的应力状态stateoftheuniaxialstre

36、ss(unidirectionalstateofstress):stateofstressthatoneprincipalstressisnotequaltozero.7-2二向应力状态分析解析法7-2AnalysisoftheStateofPlaneStressAnalyticalMethod任意斜截面上的应力：stressesactinginarbitraryinclinedplane2正负规定：q截面外法线同向为正；ar绕研究对象顺时针转为正；a逆时针为正。SignStipulate：Qispositiveifitsdirectionisthesamewithoneoftheextern

37、alnormallineofthesection；Taispositiveifitmaketheelementrotateclockwise；Acounterclockwiseangleaisconsideredtobepositive.7-3二向应力状态分一图解法7-3AnalysisoftheStateofPlaneStressGraphicalMethod应力圆：stresscircle单元体与应力圆的对应关系Correspondingrelationbetweentheelementandstresscircle应力圆的半径o两半径夹角2a；且转向a面上的应力9/工丿o应力圆上一点(%

38、,)a面的法线两面夹角a一致。stressa，ta)inaplaneoapoint(g，t)onthestresscircumferenceaanormallineofaplaneoradiusofthestresscircleangleabetweentwosectionsoangle2abetweentworadiuses；Andthedirectionofrotationisthesame.7-10强度理论概述7-10ConceptsofStrengthTheories*1.材料的破坏形式：屈服断裂：Typesoffailureofmaterials：yieldrupture强度理论：是

39、关于“构件发生强度失效起因”的假说。theoriesofstrength：someassumptionsaboutthecauseofthestrengthfailureofmaterials.7-11四种常用强度理论7-11FourCommonUsedStrengthTheories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。Theoryofthemaximumtensilestress(thefirststrengththeory):Thistheoryconsidersthemaincauseofrupturetobe

40、themaximumtensilestress.Thememberwillruptureasthemaximumtensilestressreachesthestrengthlimitinaxialtension.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Theoryofthemaximumtensilestrai(nthesecondstrengththeory):Thistheoryconsidersthemaincauseofrupturetobethemaximumtensilestrain.The

41、memberwillruptureasthemaximumtensilestrainreachesthelimitstraininaxialtension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。Theoryofthemaximumshearingstress(thethirdstrengththeory):Thistheoryconsidersthemaincauseofrupturetobethemaximumshearingstress.Thememberwillruptureasthemaximumshea

42、ringstressreachesthelimitshearingstressinaxialtension.畸变能密度(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的形状改变比能时，构件就破坏了。Theoryofthedistortionalenergydensity(thefourthstrengththeory):Thistheoryconsidersthemaincauseofyieldtobethedistortionalstrainenergy.Thememberwillruptureasthedistortionalstrainener

43、gyreachesthedistortionalstrainenergyofyieldinaxialtension相当应力：equivalentstress断裂准则：criterionofrupture屈服准则:criterionofyield第八章组合变形ChapterEightCompositeDeformation8-1组合变形和叠加原理8-1CompositeDeformationandSuperpositionPrinciple叠加原理的步骤：Thestepsforprincipleofsuperposition外力分析：外力向形心简化并沿形心主惯性轴分解Analysisofexte

44、rnalforces：Externalforcesarereducedalongthecentroidofsectionandresolvedalongprincipalaxesofinertia.内力分析：求每个外力分量对应的内力方程和内力图，确定危险面。Analysisofinternalforces：Determinetheinternalforceequationanditsdiagramcorrespondingtoeachexternalforcecomponentandthecriticalsection.应力分析：画危险面应力分布图，叠加，建立危险点的强度条件。Analysis

45、ofstresses：Plotthedistributiondiagramofthestressinthecriticalsection，dothesuperpositionofthestressesandestablishthestrengthconditionofthecriticalpoint.第九章压杆稳定ChapterNineStabilizationofCompressiveColumns9-1压杆稳定性的概念9-1ConceptsofStabilityofCompressedColumns1.失稳：lossofstability2.稳定与不稳定平衡:stableandinstab

46、leequilibrium3.临界压力：criticalpressure9-2两端铰支细长压杆的临界压力9-2CriticalPressureofTheSlenderCompressedColumnWithTwoHingedEnds1.欧拉公式:Eulersformula理想压杆：材料绝对理想；轴线绝对直；压力绝对沿轴线作用。Idealcompressivecolumn:thematerialisabsolutelyideal；theaxisisabsolutelystraight；thecompressiveforceisabsolutelyalongtheaxisofthecolumn.9

47、-3其它支座条件下细长压杆的临界压力9-3CriticalPressureofTheSlenderCompressedColumnWithOtherEndConditions长度系数(约束系数)：lengthcoefficient(orconstraintcoefficient)两端铰支:twohingedends一端固定另一端自由:onefixedendandonefreeend两端固定:twofixedends一端固定另端铰支:onefixedendandonehingedend9-4欧拉公式的适用范围经验公式9-4ApplicationRangeofEulersFormulaEmpiri

48、calFormula1.临界应力:压杆处于临界状态时横截面上的平均应力。Criticalstress:averagestressinthecrosssectionofthecompressivecolumninthecriticalstate.*2.柔度(或长细比)：flexibility(orslendernessratio)大柔度杆的临界应力由欧拉公式来求;小柔度杆的临界应力就是它的屈服极限;中柔度杆的临界应力由经验公式来求ThecriticalstressofthelargeflexibilitycolumniscalculatedbyEulersformula.Thecriticals

49、tressofsmallflexibilitycolumnisitsyieldlimit.Thecriticalstressofthemiddleflexibilitycolumnmaybedeterminedbytheempiricalformula.9-5压杆的稳定校核9-5StabilityCheckofCompressedColumn稳定安全因数：safetycoefficientofstability稳定条件：stabilitycondition9-6提高压杆稳定性的措施9-6MethodtoImproveStabilityofCompressedColumn选择合理的截面形状:choosereasonablesectionofthecolumn:改变压杆的约束条件:changeconstraintconditionofthecolumn合理选择材料:choosereasonablematerial.第十章动载荷ChapterTenDynamicLoad10-1概述10-1Introduction静载荷:staticloadsTheloadsdontchangewi