《英汉双语材料力学》PPT课件

,CHAPTER2SHEAR,材料力学,第二章剪切,CHAPTER2SHEAR,21STRENGTHCALCULATIONABOUTSHEARANDBEARINGOFCONNECTINGMEMBERS,EXCERCISELESSONSOFSHEARANDBEARING,第二章剪切,21连接件的剪切与挤压强度计算,拉压和剪切习题课,Productionoftheshearingstress,SHEAR,剪切,剪应力的产生,21STRENGTHCALCULATIONABOUTSHEARANDBEARINGOFCONNECTINGMEMBERS,1、Characteristicsofloadsanddeformationofconnectingmembers:,1)Connectingmember,Thestructurememberthatconnectsonemembertoanotheriscalledtheconnectingmember.Suchas：bolts、rivets、keysetc.Theconnectingmemberissmall，butitplaystheroleofpassingloads.,Characteristic：Itcanpassgeneralloadsandcanbedismounted.,bolt,SHEAR,21连接件的剪切与挤压强度计算,一、连接件的受力特点和变形特点：,1、连接件,剪切,在构件连接处起连接作用的部件，称为连接件。例如：螺栓、铆钉、键等。连接件虽小，却起着传递载荷的作用。,特点：可传递一般力，可拆卸。,螺栓,rivet,Characteristic:Itcanpassgeneralloads,butcannotbedismounted.forexample,thetrussinabridgeisconnectedbyit.,nogap,Characteristic:Itcanpasstorques.,SHEAR,剪切,铆钉,特点：可传递一般力，不可拆卸。如桥梁桁架结点处用它连接。,无间隙,2)Characteristicsofloadsanddeformation：,Usearivetasanexample：,Characteristicofloads：Therivetissubjectedtotwoequalandoppositeforces.Theactinglinesofthesetwoforcesareveryclose.,Characteristicofdeformation:Twopartssubjectedtotwoequalandoppositeforcestendtoshiftoveroneanotheralongthejunctionplaneoftwoforces.,SHEAR,2、受力特点和变形特点：,剪切,以铆钉为例：,受力特点：构件受两组大小相等、方向相反、作用线相距很近（差一个几何平面）的平行力系作用。,变形特点：构件沿两组平行力系的交界面发生相对错动。,（Resultant）,（Resultant,Shearingplane：Theplanealongwhichtwopartsofthemembertendtoshiftoveroneanother.Suchasnn.,Internalforceonshearingplane：InternalforceShearingforceQ，itsactinglineisparalleltotheshearingplane.,SHEAR,剪切,剪切面：构件将发生相互的错动面，如nn。,剪切面上的内力：内力剪力Q，其作用线与剪切面平行。,3)Threekindsofbreakageatjoint：FailureduetoshearSnipalongtheshearingplaneoftherivet,suchasalongsectionnn.BreakageduetobearingFailduetomutualbearingbetweentherivetandthesteelplateintheirconnectingplane.Breakageduetotension,Thesteelplateisweakenedinthesectioninwhichtherivetholesexistandstressintheweakenedsectionincreasessothatthesteelplateiseasilybrokenduetotensionattheconnectingposition.,SHEAR,剪切,3、连接处破坏的三种形式：剪切破坏沿铆钉的剪切面剪断，如沿nn面剪断。挤压破坏铆钉与钢板在相互接触面上因挤压而使溃压连接松动，发生破坏。拉伸破坏,钢板在受铆钉孔削弱的截面处，应力增大，易在连接处拉断。,2、Practicalcalculationofshear,Methodofthepracticalcalculation：Accordingtopossibilityofbreakageofthemembersomeassumptionsbywhichbasiccharacteristicsubjectedtoforceactionscanbereflectedandcalculationscanbesimplifiedareused.Thencalculateitsnominalstress,determinethecorrespondingpermissiblestressinaccordancewiththeresultofdirecttest.Atlastdothestrengthcalculation.Applyingrange：volumeofthememberisnotlargeandrealstressisquitecomplex.Suchastheconnectingpiecesetc.,Assumptionofpracticalcalculation：Assumethatshearingstressisdistributeduniformlyintheshearingplaneandequaltotheaverageshearingstress.,SHEAR,剪切,二、剪切的实用计算,实用计算方法：根据构件的破坏可能性，采用能反映受力基本特征，并简化计算的假设，计算其名义应力，然后根据直接试验的结果，确定其相应的许用应力，以进行强度计算。适用：构件体积不大，真实应力相当复杂情况，如连接件等。,实用计算假设：假设剪应力在整个剪切面上均匀分布，等于剪切面上的平均应力。,1)Shearingplane-AQ：Shiftingplane.Shearingforce-Q：Internalforceontheshearingplane.,2)Nominalshearingforce-：,3)Strengthconditionofshear：,Workingstressshouldnotexceedthepermissiblestress.,SHEAR,where,剪切,1、剪切面-AQ：错动面。剪力-Q：剪切面上的内力。,2、名义剪应力-：,3、剪切强度条件（准则）：,工作应力不得超过材料的许用应力。,3、Practicalcalculationsofbearing,1)BearingforcePjy：Theresultantforceactingonthetouchingplane.,Bearing：Thephenomenonthatthereispressureonthepartialareaofamember.Bearingforce：Theresultantforceactingonthebearingplane，designatedbyPjy.,Assumption：Bearingstressesaredistributeduniformlyovertheeffectivebearingplane.,SHEAR,三、挤压的实用计算,1、挤压力Pjy：接触面上的合力。,剪切,挤压：构件局部面积的承压现象。挤压力：在接触面上的压力，记Pjy。,假设：挤压应力在有效挤压面上均匀分布。,2)Bearingarea：AreaoftheprojectionplaneofthetouchingplaneinthedirectionperpendiculartoPjy,3)Strengthconditionofbearing：Workingbearingstressshouldnotexceedthepermissiblebearingstress,Bearingarea,SHEAR,2、挤压面积：接触面在垂直Pjy方向上的投影面的面积。,3、挤压强度条件（准则）：工作挤压应力不得超过材料的许用挤压应力。,剪切,挤压面积,4、Applications,SHEAR,1)Checkthestrength,2)Selectthecrosssectionarea,3)Determinetheexternalload,四、应用,剪切,Example1Awoodentenonjointisshowninthefigure.Knowingthatthequantitiesarea=b=12cm，h=35cm，c=4.5cmandP=40KN.Trytodeterminetheshearingstressandbearingstressforthejoint.,Solution：Freebodydiagramisshowninthefigure,：Shearingstressandbearingstress,Shearingforceis,Bearingforceis,SHEAR,例1木榫接头如图所示，a=b=12cm，h=35cm，c=4.5cm,P=40KN，试求接头的剪应力和挤压应力。,解：受力分析如图,剪应力和挤压应力,剪切面和剪力为,挤压面和挤压力为：,剪切,Solution：Freebodydiagramofthekeyisshowninthefigure,Example2Agearandashaftareconnectedbyakey（bhL=2012100).Thetorquethatthekeycantransmitism=2KNm.Knowingthediameteroftheshaftisd=70mm，thepermissibleshearingstressandthepermissiblebearingstressofthekeyarerespectively=60MPaandjy=100MPa.Trytocheckthestrengthofthekey.,SHEAR,解：键的受力分析如图,例2齿轮与轴由平键（bhL=2012100）连接，它传递的扭矩m=2KNm，轴的直径d=70mm，键的许用剪应力为=60MPa，许用挤压应力为jy=100MPa，试校核键的强度。,剪切,Accordingtotheabovecalculation,strengthconditionsofthekeyaresatisfied.,Checkthestrengthofshearandbearing,SHEAR,综上，键满足强度要求。,剪应力和挤压应力的强度校核,剪切,Solution：Freebodydiagramofthekeyisshowninthefigure,Example3Agearandashaftareconnectedbyakey（b=16mm,h=10mm).Thetorquethatthekeycantransmitism=1600Nm.Knowingthediameteroftheshaftisd=50mm，thepermissibleshearingstressandthepermissiblebearingstressofthekeyarerespectively=80MPaandjy=240MPa.Trytodesignthelengthofthekey.,SHEAR,解：键的受力分析如图,例3齿轮与轴由平键（b=16mm，h=10mm，）连接，它传递的扭矩m=1600Nm，轴的直径d=50mm，键的许用剪应力为=80MPa，许用挤压应力为jy=240MPa，试设计键的长度。,剪切,Strengthconditionsoftheshearingstressandthebearingstress,Accordingtotheabovecalculation,SHEAR,剪切,剪应力和挤压应力的强度条件,综上,Solution：Freebodydiagramisshowninthefigure,Example4Arivetedtie-inactedbyforceP=110kNisshowninthefigure.Knowingthethicknessist=1cm，widthofitisb=8.5cm.Thepermissiblestressis=160MPa.Diameteroftherivetisd=1.6cmandthepermissibleshearingstressis=140MPa，thepermissiblebearingstressisjy=320MPa.Trytocheckthestrengthoftheriveting.(Assumetheforceactedoneachrivetisequal.）,SHEAR,解：受力分析如图,例4一铆接头如图所示，受力P=110kN，已知钢板厚度为t=1cm，宽度b=8.5cm，许用应力为=160MPa；铆钉的直径d=1.6cm，许用剪应力为=140MPa，许用挤压应力为jy=320MPa，试校核铆接头的强度。（假定每个铆钉受力相等。）,剪切,Thesections22and33ofthesteelplatearethecriticalsections.,Thestrengthconditionsofshearandbearing,Therefore，thetie-inissafe.,SHEAR,钢板的2-2和3-3面为危险面,剪应力和挤压应力的强度条件,综上，接头安全。,剪切,1、Internal-forceandaxial-forcediagramsoftherodintensionandcompression,1)ExpressionofAxialforce?,2)Methodtodetermineaxialforce?,3)Positiveandnegativeofaxialforce?,Exerciselessonsoftensionandcompressionandshear,Whydoweplottheaxial-forcediagram?Whatshouldwepayattentionwhenwedoit?,4)Axial-forcediagram：ExpressedbythediagramofN=N(x)?,SHEAR,一、轴向拉压杆的内力及轴力图,1、轴力的表示?,2、轴力的求法?,3、轴力的正负规定?,剪切,拉压和剪切习题课,为什么画轴力图?应注意什么?,4、轴力图：N=N(x)的图象表示?,Simplemethodtodetermineaxialforces:Taketheleftpartofthesectionxastheobject,theaxialforceonthesectionxcanbecalculatedbyfollowingformula:,Where“P()”and“P()”expressthesumofleftdirectionforcesandthesumofrightdirectionforcesoftheleftpartofthesectionx.Taketherightpartofthesectionxastheobject,theaxialforceN(x)ofpointxcanbecalculatedbythefollowingformulate:Where“”and“”denotethesumofrightdirectionforcesandthesumofleftdirectionforcesoftherightpartofsectionx.,SHEAR,轴力的简便求法:以x点左侧部分为研究对象,x点的轴力N(x)由下式计算:,其中“P()”与“P()”为x点左侧向左的所有外力与向右的所有外力。以x点右侧部分为研究对象，x点的轴力N(x)由下式计算：其中“P()”与“P()”为x点右侧向右的所有外力与向左的所有外力。,剪切,Example1Forces5P,8P,4PandPareactedatpointsA,B,CandDontherodrespectively，theirdirectionsareshowninthefigure.Trytoplottheaxial-forcediagramoftherod.,A,B,C,D,O,2P,SHEAR,例1图示杆的A、B、C、D点分别作用着5P、8P、4P、P的力，方向如图，试画出杆的轴力图。,剪切,A,B,C,D,O,2P,Positiveandnegativeofstress?,1)Stressonthecrosssection:,2、Stressoftherodintensionorcompression,Criticalsectionandmaximumworkingstress?,2)Stressontheinclinedsection,Saint-Venantprinciple?,Stressconcentrations?,SHEAR,应力的正负规定?,1、横截面上的应力:,二、拉压杆的应力,危险截面及最大工作应力?,2、拉压杆斜截面上的应力,Saint-Venant原理?,应力集中?,剪切,3、Strengthdesigncriterion：,1)Strengthdesigncriterion,Checkstrength：,Designthecrosssectionarea：,Designtheload：,SHEAR,三、强度设计准则（StrengthDesignCriterion）：,1、强度设计准则?,校核强度：,设计截面尺寸：,设计载荷：,剪切,1)Elasticlawoftherodwithequalaxialforces,2)Elasticlawwithvariableinternalforces,3)Elasticlawinuniaxialstressedstate,4、Deformationandstrainoftherodintensionorcompression,SHEAR,1、等轴力拉压杆的弹性定律,2、变内力拉压杆的弹性定律,3、单向应力状态下的弹性定律,四、拉压杆的变形及应变,剪切,4)Possionsratio（orlateraldeformationfactor）,5)Theenlarged-deformationdiagramandthemethodtodeterminethedisplacement,SHEAR,4、泊松比（或横向变形系数）,剪切,5、小变形放大图与位移的求法,Assemblestressinitialstress,Temperaturestress,Equilibriumequations；Geometricequationscompatibilityequationsofdeformation；Physicalequationselasticlaws；Complementaryequations：gettingfromgeometricequationsandphysicalequations；Solvingthecombinedequationsincludingofequilibriumequationsandcomplementequations.,6)Thestepstosolvethestaticallyindeterminateproblem,SHEAR,装配应力预应力,温度应力,剪切,平衡方程；几何方程变形协调方程；物理方程弹性定律；补充方程：由几何方程和物理方程得；解由平衡方程和补充方程组成的方程组。,6、超静定问题的处理方法步骤：,5、Mechanicalpropertiesofthematerialsintensionandcompression,3)Unloadedlaw；Coldhardening；Cold-drawntimeeffect.,1)Elasticlaw,4)Residualrelativeelongation,5)Permanentrelativereductionofarea,SHEAR,2)Limitstress,6)Permissiblestress,五、材料在拉伸和压缩时的力学性能,3、卸载定律；冷作硬化；冷拉时效。,1,、弹性定律,剪切,4、延伸率,5、面缩率,1)Practicalcalculationofshear,6、Practicalcalculationofshearandbearingoftheconnectingmemberoftherodsintensionandcompression,2)Practicalcalculationofbearing,SHEAR,1、剪切的实用计算,六、拉(压)杆连接部分的剪切与挤压强度计算,剪切,2、挤压的实用计算,Bearingarea,SHEAR,Checkthestrength,Designthedimension,Designtheexternalload,剪切,挤压面积,Example2TherodsAB、CD、EFandGHinthestructureareshowninthefigureEachofthemconsiststwoofrolledunequal-legssteels.Knowing=170MPa，E=210GPa.RodsACandEGmaybeseenasrigidrod.TrytoselectthesectiondimensionofeachrodandtodeterminethedisplacementsofpointsA、DandC.,P=300kN,0.8m,3.2m,1.8m,1.2m,2m,3.4m,A,B,C,D,F,H,q0=100kN/m,Solution：Determinetheinternalforce.Thefreebodydiagramisshowninthefigure.,E,G,SHEAR,例2结构如图，AB、CD、EF、GH都由两根不等边角钢组成，已知材料的=170MPa，E=210GPa。AC、EG可视为刚杆，试选择各杆的截面型号和A、D、C点的位移。,剪切,P=300kN,0.8m,3.2m,1.8m,1.2m,2m,3.4m,A,B,C,D,F,H,q0=100kN/m,解：求内力，受力分析如图,E,G,D,q0=100kN/m,E,G,A,C,NG,NC,NA,NE,ND,=ND,P=300kN,Determinetheareabystrengthcondition,SHEAR,剪切,D,q0=100kN/m,E,G,A,C,NG,NC,NA,NE,ND,=ND,P=300kN,由强度条件求面积,Determinethetypesoftherodsreferencetothetable,Determinethedeformation,SHEAR,剪切,试依面积值查表确定型钢号,求变形,Determinethedisplacement.Thedeformationisshowninthefigure.,A,B,D,F,H,E,G,C,C1,A1,E1,D1,G1,SHEAR,求位移,变形图如图,剪切,A,B,D,F,H,E,G,C,C1,A1,E1,D1,G1,Example3DiametersofrodACandBDinthestructureshowninthefigurearerespectivelyd1=25mm,d2=18mm.Knowing=170MPa，E=210GPa.RodABmaybeseenasarigidrod.Tryto(1)checkthestrengthofeachrodandtodeterminethedisplacementsAandBofpointsAanB.(2)determinethedisplacementFofpointFwhentheforcePisactedonpointA.F=Aisagenerallaw,whichiscalledtheoremofconjugatedisplacement.,A,B,C,D,P=100kN,1.5m,3m,2.5m,F,Solution：DeterminetheinternalforceThefreebodydiagramisshowninthefingure.,SHEAR,例3结构如图，AC、BD的直径分别为:d1=25mm,d2=18mm,已知材料的=170MPa，E=210GPa,AB可视为刚杆，试校核各杆的强度;求A、B点的位移A和B。(2)求当P作用于A点时,F点的位移F，F=A是普遍规律：称为位移互等定理。,剪切,A,B,C,D,P=100kN,1.5m,3m,2.5m,F,解：求内力，受力分析如图,Checkthestrength,Determinet