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Chapter6
ForceAnalysisofStructuresandMachinesWangMing-luChapter6
ForceAnalysis2SpecializedVocabularyStructures:结构,构造,构[桁]架Truss:构架,桁架,钢梁Joint:接合;榫;接点;联轴节;铰链Section:截口[面,线,点]Frame:框架,框子;【机】架,座身2SpecializedVocabularyStructu3ChapterObjectives.1.Usethemethodofjointstodeterminetheforceinaplanetruss.2.Usethemethodofsectionstodeterminetheforceinaplanetruss.3.Usemultiplefree-bodydiagramstodeterminetheforceinaframeormachine.3ChapterObjectives.1.Usethe46.1Introduction.46.1Introduction.5Structureoftrussinengineering
工程中的桁架结构6.1Introduction.5Structureoftrussinenginee6Structureoftrussinengineering
工程中的桁架结构6.1Introduction.6Structureoftrussinenginee7Structureoftrussinengineering
工程中的桁架结构6.1Introduction.7Structureoftrussinenginee8Structureoftrussinengineering
工程中的桁架结构6.1Introduction.8Structureoftrussinenginee9Structureoftrussinengineering
工程中的桁架结构6.1Introduction.9Structureoftrussinenginee10Truss:arigidstructuresystemcomposedofstraightelements,connectedattheirendsbypins,withoutdeformationundertheactionofforces.桁架:由杆组成,用铰联接,受力不变形的系统。6.2Simpleplanetrusses10Truss:arigidstructure11joint节点element杆件6.2Simpleplanetrusses11jointelement6.2Simpleplan12Theadvantageofthetruss:light,thecapabilityofthematerialcanexertsufficiently.桁架的优点:轻,充分发挥材料性能。Thecharactersofthetruss:桁架的特点:①straightmembers,theweightofthemselvescanbeneglected,theyarealldoubleforceequivalentrods;①直杆,不计自重,均为二力杆;②Thestraightelementsareconnectedattheirendsbyjoints.②杆端铰接;③Allexternalloadsonthetrussactonlyatthejoints.③外力作用在节点上。6.2Simpleplanetrusses12Theadvantageofthetruss:13Themodeloftrussinmechanics力学中的桁架模型(basictriangle)Trianglesensurestability(基本三角形)三角形有稳定性
(a)(b)(c)6.2Simpleplanetrusses13Themodeloftrussinmechan14Thecommonsimplifiedmodelsfortrussinengineeringmechanics工程力学中常见的桁架简化计算模型6.2Simpleplanetrusses14Thecommonsimplifiedmodels156.2Simpleplanetrusses156.2Simpleplanetrusses166.4MethodofjointsP=10kN,determinetheinternalforcesoneveryelements.已知:如图
P=10kN,求各杆内力?[Example][例]Solution:
解:①studythewholestructure,determinethereactionforces:
①研究整体,求支座反力166.4MethodofjointsP=10kN,17②Studythejoints
A,CandDonebyone,determinetheinternalforcesofeverymember.②依次取A、C、D节点研究,计算各杆内力。Weget: (denotethattherodiscompressed)6.4Methodofjoints17②StudythejointsA,CandD18SubstitutingintoWeobtain:Substitutingintoweget:6.4Methodofjoints18SubstitutingintoWeobtain:S19TheanotherequationofthejointDcanbeusedtoverifytheresultofcalculation.节点D的另一个方程可用来校核计算结果ThesolutionofwhichisItequalsto,thecalculationisaccurate.恰与相等,计算准确无误。6.4Methodofjoints19Theanotherequationofthe206.4.3Problems.Dotheproblems6.1-6.25byyourself,andthenIwilltellyoutheanswersofthem.6.4Methodofjoints206.4.3Problems.6.4Methodof21[Example]h,aandParegiven,determinetheinternalforcesontheelement4,5and6.[例]已知:如图,h,a,P,求:4,5,6杆的内力。IISolution:
Studythewholestructure,determinethereactionforces.解:研究整体求支反力①①6.6Methodofsections21[Example]h,aandParegiv22②DrawacutI-I,studytheleft-handsectionofthetruss.选截面I-I,取左半部研究A'From6.6Methodofsections22②DrawacutI-I,studythel23Instruction:说明:MethodofIsolationjoints:Thisisconvenientwhenthestressesinallelementsofthetrusshavetobedetermined.节点法:用于设计,计算全部杆内力Methodofcuts:
Thisisconvenientindeterminingthestressesinindividualmembers,notablyforverifyingresults.截面法:用于校核,计算部分杆内力6.6Methodofsections23Instruction:6.6Methodofs24Beforethecalculation,assumefirstallelementstobeundertension,iftheresultisnegativeitmeanstheelementconcernediscompressed,oppositetothedirectionassumed.
先把杆都设为拉力,计算结果为负时,说明是压力,与所设方向相反。6.6Methodofsections246.6Methodofsections253.Thejudgmentsoftheinternalforcesofspecialelements三、特殊杆件的内力判断Ifnoloadactsonatwo-elementjointandthetwoelementsarenotcollinear,theinternalforcesofthemarezero,theyarecalledzeroelements.两杆节点无载荷、且两杆不在一条直线上时,该两杆是零杆。①Ifnoloadactsonathree-elementjointandtwoelementsofthemarecollinear,thethirdisazeroelement.三杆节点无载荷、其中两杆在一条直线上,另一杆必为零杆②6.6Methodofsections253.Thejudgmentsoftheinte26Ifnoloadactsonthefour-elementjointandtwopairsofthemarecollinear,theinternalforcesofeachpairareequalinmagnitude
andofthesamecharacter.四杆节点无载荷、其中两两在一条直线上,同一直线上两杆内力等值、同性。③6.6Methodofsections26Ifnoloadactsonthefour-27[Example3]
Pdareknown,determinetheinternalforcesoftherodsa,b,candd.[例3]
已知Pd,求:a.b.c.d四杆的内力?Solution:fromthejudgmentsofthezeroelement解:由零杆判式6.6Methodofsections27[Example3]Pdareknown,28研究A点:StudythepointA:Again6.6Methodofsections28研究A点:StudythepointA:Again296.6.3Problems.Dotheproblems6.27-6.34byyourself,andthenIwilltellyoutheanswersofthem.6.6Methodofsections296.6.3Problems.6.6Methodof30[Example][例]
Equilibriumofabodysystem物体系统的平衡问题Bodysystem(BS):Asystemcomposedofseveralrigidbodiesconnectedtogetherbyconstraints.物体系统(物系):由若干个物体通过约束所组成的系统。6.7Framesandmachines30[Example]Equilibriumofabo31Externalforces:forceswhichactonthebodysystemfromoutside.外力:外界物体作用于系统上的力叫外力。Internalforces:forcesamongthebodiesofthebodysystem.内力:系统内部各物体之间的相互作用力叫内力。6.7Framesandmachines31Externalforces:forceswhic32Thecharacteristicsoftheequilibriumofabodysystem:物系平衡的特点:
①Thebodysystemisstatic①物系静止②Everybodyinthebodysystemisalsoinequilibrium.②物系中每个单体也是平衡的。
6.7Framesandmachines32Thecharacteristicsofthee33foreverybodythereare3equilibriumequations,sothewholesystemofthebodieshas3n
equations.(nisnumberof
bodiesinthebodysystem)每个单体可列3个平衡方程,整个系统可列3n个方程(设物系中有n个物体)Thegeneralmethodtosolvetheproblemsofthebodysystem:解物系问题的一般方法:fromwholeparts(usualway);frompartswhole(unusualway)
由整体局部(常用),由局部整体(用较少)6.7Framesandmachines33foreverybodythereare3e34[Example]LetOAhorizontal(OA=R,AB=l)andthepressureforcetobeP.[例]
已知:OA=R,AB=l,当OA水平时,冲压力为P时,Determine:①M,②thereactionforcesofpointO,③theinternalforcesoftherodAB,④thesidepressureactingontheleadrail.求:①M=?②O点的约束反力?③AB杆内力?④冲头给导轨的侧压力? Solution:StudythepointB解:研究B
6.7Framesandmachines34[Example]LetOAhorizontal356.7Framesandmachines356.7Framesandmachines36Thenstudythewheel:再研究轮6.7Framesandmachines36Thenstudythewheel:6.7Fra37[thesignofminusmeansthedirectionoftheforcesisoppositetothedirectionindicatedinthediagram][负号表示力的方向与图中所设方向相反]6.7Framesandmachines37[thesignofminusmeansthe38①②③④6.Thestepsandskillsofsolvingproblems:六、解题步骤与技巧
STEPS解题步骤
Selectabodytostudy;
选研究对象
Drawtheforcediagram(forceanalysis);
画受力图(受力分析)
Selectthecoordinates,acenter,andwritedownequilibriumequations;
选坐标、取矩点、列平衡方程。
Solvetheequations,determinetheunknownquantities.
解方程求出未知数
6.7Framesandmachines38①②③④6.Thestepsandskills39
[Example1]Allelementsareconnectedwitheachotherbyjoints,thebottomBisinsertedintotheearth,P=1000N,AE=BE=CE=DE=1m,theweightoftheelementsarenegligible.DeterminetheinternalforcesofthememberACandthereactionforcesofthepointB.
[例1]
已知各杆均铰接,B端插入地内,P=1000N,AE=BE=CE=DE=1m,杆重不计。求AC杆内力?B点的反力?6.7Framesandmachines39[Example1]Allelement40Writedowntheequations
列方程为:④
Solvingthem,weobtain:解方程得③SelectthecoordinatesystemBxywiththepointBasthegivencentre;选坐标、取矩点、Bxy,B点②Drawtheforcediagram;受力如图①Solution:解:Studythewholerigidstructure;选整体研究6.7Framesandmachines40Writedowntheequations④41①StudytheelementCD;再研究CD杆②Drawtheforcediagram;受力如图6.7Framesandmachines41①StudytheelementCD;再研究CD杆42Solvingthem,wefind:解方程求未知数④③SelectpointEasthegivencenter,writedowntheequation:取E为矩心,列方程6.7Framesandmachines42Solvingthem,wefind:④③Sele43[Example2]LetP=100N,AC=1.6m,BC=0.9m,CD=EC=1.2m,AD=2mABishorizontal,EDisvertical,BDisperpendiculartotheincline.Determineandthereactionforceoftheconstraints.[例2]
已知:P=100N.AC=1.6m,BC=0.9m,CD=EC=1.2m,AD=2m且AB水平,ED铅垂,BD垂直于斜面;
求
?和支座反力?Solution:解:
Studythewholerigidstructure;
研究整体
Drawtheforcediagram;
画受力图6.7Framesandmachines43[Example2]LetP=100N,AC=1.644Selectacoordinatesystem,writedowntheequations
选坐标列方程6.7Framesandmachines44Selectacoordinatesystem,45AgainstudytheelementAB,drawtheforcediagramasabove;再研究AB杆,受力如图6.7Framesandmachines45AgainstudytheelementAB,466.7Framesandmachines466.7Framesandmachines47[Example4]Consideracontinuousbeam,P=10kN,Q=50kN,CEis
vertical,neglecttheweightofthebeam.DeterminethereactionforcesofthepointsA,BandD.(wefindthenumberoftheunknownquantitiesislargerthanthree,sowecannotsolveitbystudyingthewholerigidstructure,itmustbedividedintoseveralparts.)
[例4]
已知:连续梁上,P=10kN,Q=50kN,CE铅垂,不计梁重求:A,B和D点的反力(看出未知数多余三个,不能先整体求出,要拆开)
6.7Framesandmachines47[Example4]Consideraconti48解:①研究起重机Solution:①studythecrane6.7Framesandmachines48解:①研究起重机Solution:①studythe49②Thenstudythebeam
CD②再研究梁CD6.7Framesandmachines49②ThenstudythebeamCD②再研50③再研究整体③Studythewholerigidstructure:6.7Framesandmachines50③再研究整体③Studythewholerig51
Aladderplacedonthesmoothhorizontalsurfaceisinequilibrium,F=60kN,l=3m,α=45o,computethereactionforcesonpinCandsurface[solution]Firstly,drawtheFBDsofthewholeandeachpart,findoutthenumberofunknowns.6.7FramesandmachinesSampleproblem551 Aladderplacedonthesmoo52FromtheFBDsabove,wecanmaketheprocedureofsolvingtheproblem,thatis:
FA,FBFcx,Fcyverify6.7Framesandmachines52FromtheFBDsabove,wecan536.7Framesandmachines536.7Framesandmachines546.7Framesandmachines546.7Framesandmachines55Verify:Ifthefollowingequationsaresatisfied,thenyourresultsarecorrect.6.7Framesandmachines55Verify:Ifthefollowingequa56Sampleproblem6
Thestructureshowninthefigureleft,AB=BC=1m,EK=KD,P=1732kN,Q=1000kN,neglectallthegravityforces,computethereactionforcesandforceinleverDC6.7Framesandmachines56Sampleproblem6 Thestruct57[solution]DrawtheFBDs,findoutthepathofsolution:[FBDofthewhole] Coplanarcommonforcesystem
3equations
5unknowns
cannotdeterminealltheunknowns6.7Framesandmachines57[solution]DrawtheFBDs,fi58[FBDofDEandCD] Coplanarcommonforcesystem
3equations
3unknowns
resolvableHeretheleverDCisaleversubjectedtwoforces.6.7Framesandmachines58[FBDofDEandCD] Coplanar59[FBDofDEandCD] Coplanarcommonforcesystem
3equations
4unknowns
cannotdeterminealltheunknownsFromtheFBDsabove,wecanfindoutthepathofsolutionasfollowing:6.7Framesandmachines59[FBDofDEandCD] Coplanar60[Pathofsolution]Fex,Fey,FDFAx,FAy,MAFBDofthewholeVerify6.7Framesandmachines60[Pathofsolution]Fex,Fey616.7Framesandmachines616.7Framesandmachines62Verify--omitted6.7Framesandmachines62Verify--omitted6.7Framesan63Sampleproblem7
Astructureshownasthefigureleft,l=2R,BD=2l,computetheexternalreactionforcesatpinAandB.6.7Framesandmachines63Sampleproblem7 Astructur64[solution]DrawtheFBDs,findoutthepathofsolution:[FBDofthewhole] Coplanarcommonforcesystem
3equations
4unknowns6.7Framesandmachines64[solution]DrawtheFBDs,fi65[FBDoftheBC-Wheel] Coplanarcommonforcesystem
3equations
4unknowns IfFBxhasbeenknown,then 3equations,3unknown.6.7Framesandmachines65[FBDoftheBC-Wheel] Copla66[FBDoftheACB] Coplanarcommonforcesystem
3equations
4unknowns IfFAxhasbeenknown,then 3equations,3unknown.6.7Framesandmachines66[FBDoftheACB] Coplanarc67[Pathofsolution]FAx,FBxFBy,FCy,FcxFByFAy6.7Framesandmachines67[Pathofsolution]FAx,FBx686.7Framesandmachines686.7Framesandmachines696.7Framesandmachines696.7Framesandmachines70Theend70TheendChapter6
ForceAnalysisofStructuresandMachinesWangMing-luChapter6
ForceAnalysis72SpecializedVocabularyStructures:结构,构造,构[桁]架Truss:构架,桁架,钢梁Joint:接合;榫;接点;联轴节;铰链Section:截口[面,线,点]Frame:框架,框子;【机】架,座身2SpecializedVocabularyStructu73ChapterObjectives.1.Usethemethodofjointstodeterminetheforceinaplanetruss.2.Usethemethodofsectionstodeterminetheforceinaplanetruss.3.Usemultiplefree-bodydiagramstodeterminetheforceinaframeormachine.3ChapterObjectives.1.Usethe746.1Introduction.46.1Introduction.75Structureoftrussinengineering
工程中的桁架结构6.1Introduction.5Structureoftrussinenginee76Structureoftrussinengineering
工程中的桁架结构6.1Introduction.6Structureoftrussinenginee77Structureoftrussinengineering
工程中的桁架结构6.1Introduction.7Structureoftrussinenginee78Structureoftrussinengineering
工程中的桁架结构6.1Introduction.8Structureoftrussinenginee79Structureoftrussinengineering
工程中的桁架结构6.1Introduction.9Structureoftrussinenginee80Truss:arigidstructuresystemcomposedofstraightelements,connectedattheirendsbypins,withoutdeformationundertheactionofforces.桁架:由杆组成,用铰联接,受力不变形的系统。6.2Simpleplanetrusses10Truss:arigidstructure81joint节点element杆件6.2Simpleplanetrusses11jointelement6.2Simpleplan82Theadvantageofthetruss:light,thecapabilityofthematerialcanexertsufficiently.桁架的优点:轻,充分发挥材料性能。Thecharactersofthetruss:桁架的特点:①straightmembers,theweightofthemselvescanbeneglected,theyarealldoubleforceequivalentrods;①直杆,不计自重,均为二力杆;②Thestraightelementsareconnectedattheirendsbyjoints.②杆端铰接;③Allexternalloadsonthetrussactonlyatthejoints.③外力作用在节点上。6.2Simpleplanetrusses12Theadvantageofthetruss:83Themodeloftrussinmechanics力学中的桁架模型(basictriangle)Trianglesensurestability(基本三角形)三角形有稳定性
(a)(b)(c)6.2Simpleplanetrusses13Themodeloftrussinmechan84Thecommonsimplifiedmodelsfortrussinengineeringmechanics工程力学中常见的桁架简化计算模型6.2Simpleplanetrusses14Thecommonsimplifiedmodels856.2Simpleplanetrusses156.2Simpleplanetrusses866.4MethodofjointsP=10kN,determinetheinternalforcesoneveryelements.已知:如图
P=10kN,求各杆内力?[Example][例]Solution:
解:①studythewholestructure,determinethereactionforces:
①研究整体,求支座反力166.4MethodofjointsP=10kN,87②Studythejoints
A,CandDonebyone,determinetheinternalforcesofeverymember.②依次取A、C、D节点研究,计算各杆内力。Weget: (denotethattherodiscompressed)6.4Methodofjoints17②StudythejointsA,CandD88SubstitutingintoWeobtain:Substitutingintoweget:6.4Methodofjoints18SubstitutingintoWeobtain:S89TheanotherequationofthejointDcanbeusedtoverifytheresultofcalculation.节点D的另一个方程可用来校核计算结果ThesolutionofwhichisItequalsto,thecalculationisaccurate.恰与相等,计算准确无误。6.4Methodofjoints19Theanotherequationofthe906.4.3Problems.Dotheproblems6.1-6.25byyourself,andthenIwilltellyoutheanswersofthem.6.4Methodofjoints206.4.3Problems.6.4Methodof91[Example]h,aandParegiven,determinetheinternalforcesontheelement4,5and6.[例]已知:如图,h,a,P,求:4,5,6杆的内力。IISolution:
Studythewholestructure,determinethereactionforces.解:研究整体求支反力①①6.6Methodofsections21[Example]h,aandParegiv92②DrawacutI-I,studytheleft-handsectionofthetruss.选截面I-I,取左半部研究A'From6.6Methodofsections22②DrawacutI-I,studythel93Instruction:说明:MethodofIsolationjoints:Thisisconvenientwhenthestressesinallelementsofthetrusshavetobedetermined.节点法:用于设计,计算全部杆内力Methodofcuts:
Thisisconvenientindeterminingthestressesinindividualmembers,notablyforverifyingresults.截面法:用于校核,计算部分杆内力6.6Methodofsections23Instruction:6.6Methodofs94Beforethecalculation,assumefirstallelementstobeundertension,iftheresultisnegativeitmeanstheelementconcernediscompressed,oppositetothedirectionassumed.
先把杆都设为拉力,计算结果为负时,说明是压力,与所设方向相反。6.6Methodofsections246.6Methodofsections953.Thejudgmentsoftheinternalforcesofspecialelements三、特殊杆件的内力判断Ifnoloadactsonatwo-elementjointandthetwoelementsarenotcollinear,theinternalforcesofthemarezero,theyarecalledzeroelements.两杆节点无载荷、且两杆不在一条直线上时,该两杆是零杆。①Ifnoloadactsonathree-elementjointandtwoelementsofthemarecollinear,thethirdisazeroelement.三杆节点无载荷、其中两杆在一条直线上,另一杆必为零杆②6.6Methodofsections253.Thejudgmentsoftheinte96Ifnoloadactsonthefour-elementjointandtwopairsofthemarecollinear,theinternalforcesofeachpairareequalinmagnitude
andofthesamecharacter.四杆节点无载荷、其中两两在一条直线上,同一直线上两杆内力等值、同性。③6.6Methodofsections26Ifnoloadactsonthefour-97[Example3]
Pdareknown,determinetheinternalforcesoftherodsa,b,candd.[例3]
已知Pd,求:a.b.c.d四杆的内力?Solution:fromthejudgmentsofthezeroelement解:由零杆判式6.6Methodofsections27[Example3]Pdareknown,98研究A点:StudythepointA:Again6.6Methodofsections28研究A点:StudythepointA:Again996.6.3Problems.Dotheproblems6.27-6.34byyourself,andthenIwilltellyoutheanswersofthem.6.6Methodofsections296.6.3Problems.6.6Methodof100[Example][例]
Equilibriumofabodysystem物体系统的平衡问题Bodysystem(BS):Asystemcomposedofseveralrigidbodiesconnectedtogetherbyconstraints.物体系统(物系):由若干个物体通过约束所组成的系统。6.7Framesandmachines30[Example]Equilibriumofabo101Externalforces:forceswhichactonthebodysystemfromoutside.外力:外界物体作用于系统上的力叫外力。Internalforces:forcesamongthebodiesofthebodysystem.内力:系统内部各物体之间的相互作用力叫内力。6.7Framesandmachines31Externalforces:forceswhic102Thecharacteristicsoftheequilibriumofabodysystem:物系平衡的特点:
①Thebodysystemisstatic①物系静止②Everybodyinthebodysystemisalsoinequilibrium.②物系中每个单体也是平衡的。
6.7Framesandmachines32Thecharacteristicsofthee103foreverybodythereare3equilibriumequations,sothewholesystemofthebodieshas3n
equations.(nisnumberof
bodiesinthebodysystem)每个单体可列3个平衡方程,整个系统可列3n个方程(设物系中有n个物体)Thegeneralmethodtosolvetheproblemsofthebodysystem:解物系问题的一般方法:fromwholeparts(usualway);frompartswhole(unusualway)
由整体局部(常用),由局部整体(用较少)6.7Framesandmachines33foreverybodythereare3e104[Example]LetOAhorizontal(OA=R,AB=l)andthepressureforcetobeP.[例]
已知:OA=R,AB=l,当OA水平时,冲压力为P时,Determine:①M,②thereactionforcesofpointO,③theinternalforcesoftherodAB,④thesidepressureactingontheleadrail.求:①M=?②O点的约束反力?③AB杆内力?④冲头给导轨的侧压力? Solution:StudythepointB解:研究B
6.7Framesandmachines34[Example]LetOAhorizontal1056.7Framesandmachines356.7Framesandmachines106Thenstudythewheel:再研究轮6.7Framesandmachines36Thenstudythewheel:6.7Fra107[thesignofminusmeansthedirectionoftheforcesisoppositetothedirectionindicatedinthediagram][负号表示力的方向与图中所设方向相反]6.7Framesandmachines37[thesignofminusmeansthe108①②③④6.Thestepsandskillsofsolvingproblems:六、解题步骤与技巧
STEPS解题步骤
Selectabodytostudy;
选研究对象
Drawtheforcediagram(forceanalysis);
画受力图(受力分析)
Selectthecoordinates,acenter,andwritedownequilibriumequations;
选坐标、取矩点、列平衡方程。
Solvetheequations,determinetheunknownquantities.
解方程求出未知数
6.7Framesandmachines38①②③④6.Thestepsandskills109
[Example1]Allelementsareconnectedwitheachotherbyjoints,thebottomBisinsertedintotheearth,P=1000N,AE=BE=CE=DE=1m,theweightoftheelementsarenegligible.DeterminetheinternalforcesofthememberACandthereactionforcesofthepointB.
[例1]
已知各杆均铰接,B端插入地内,P=1000N,AE=BE=CE=DE=1m,杆重不计。求AC杆内力?B点的反力?6.7Framesandmachines39[Example1]Allelement110Writedowntheequations
列方程为:④
Solvingthem,weobtain:解方程得③SelectthecoordinatesystemBxywiththepointBasthegivencentre;选坐标、取矩点、Bxy,B点②Drawtheforcediagram;受力如图①Solution:解:Studythewholerigidstructure;选整体研究6.7Framesandmachines40Writedowntheequations④111①StudytheelementCD;再研究CD杆②Drawtheforcediagram;受力如图6.7Framesandmachines41①StudytheelementCD;再研究CD杆112Solvingthem,wefind:解方程求未知数④③SelectpointEasthegivencenter,writedowntheequation:取E为矩心,列方程6.7Framesandmachines42Solvingthem,wefind:④③Sele113[Example2]LetP=100N,AC=1.6m,BC=0.9m,CD=EC=1.2m,AD=2mABishorizontal,EDisvertical,BDisperpendiculartotheincline.Determineandthereactionforceoftheconstraints.[例2]
已知:P=100N.AC=1.6m,BC=0.9m,CD=EC=1.2m,AD=2m且AB水平,ED铅垂,BD垂直于斜面;
求
?和支座反力?Solution:解:
Studythewholerigidstructure;
研究整体
Drawtheforcediagram;
画受力图6.7Framesandmachines43[Example2]LetP=100N,AC=1.6114Selectacoordinatesystem,writedowntheequations
选坐标列方程6.7Framesandmachines44Selectacoordinatesystem,115AgainstudytheelementAB,drawtheforcediagramasabove;再研究AB杆,受力如图6.7Framesandmachines45AgainstudytheelementAB,1166.7Framesandmachines466.7Framesandmachines117[Example4]Consideracontinuousbeam,P=10kN,Q=50kN,CEis
vertical,neglecttheweightofthebeam.DeterminethereactionforcesofthepointsA,BandD.(wefindthenumberoftheunknownquantitiesislargerthanthree,sowecannotsolveitbystudyingthewholerigidstructure,itmustbedividedintoseveralparts.)
[例4]
已知:连续梁上,P=10kN,Q=50kN,CE铅垂,不计梁重求:A,B和D点的反力(看出未知数多余三个,不能先整体求出,要拆开)
6.7Framesandmachines47[Example4]Consideraconti118解:①研究起重机Solution:①studythecrane6.7Framesandmachines48解:①研究起重机Solution:①studythe119②Thenstudythebeam
CD②再研究梁CD6.7Framesandmachines49②ThenstudythebeamCD②再研120③再研究整体③Studythewholerigidstructure:6.7Framesandmachines50③再研究整体③Studythewholerig121
Aladderplacedonthesmoothhorizontalsurfaceisinequilibrium,F=60kN,l=3m,α=45o,computethereactionforcesonpinCandsurface[solution]Firstly,
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