材料力學(xué)知到智慧樹章節(jié)測試課后答案2024年秋山東科技大學(xué)

材料力學(xué)知到智慧樹章節(jié)測試課后答案2024年秋山東科技大學(xué)緒論單元測試

AsteppedshaftACBhavingsolidcircularcrosssectionswithtwodifferentdiametersisheldagainstrotationattheends(seefigure).Iftheallowableshearstressintheshaftis43MPa,whatisthemaximumtorque(T0)maxthatmaybeappliedatsectionC?(Hint:trytoobtainthereactivetorques.)

答案:無

第一章單元測試

AhollowcircularpostABC(seefigure)supportsaloadP1=1700lbactingatthetop.AsecondloadP2isuniformlydistributedaroundthecapplateatB.ThediametersandthicknessesoftheupperandlowerpartsofthepostaredAB=1.25in.,tAB=0.5in.,dBC=2.25in.,andtBC=0.375in.,respectively.

(a)Calculatethenormalstress#ABintheupperpartofthepost.

(b)Ifitisdesiredthatthelowerpartoftheposthavethesamecompressivestressastheupperpart,whatshouldbethemagnitudeoftheloadP2?

(c)IfP1remainsat1700lbandP2isnowsetat2260lb,whatnewthicknessofBCwillresultinthesamecompressivestressinbothparts?

答案:無SupposeABCDisarigidbeam.Asteelcablewiththecross-sectionareaof76.36mm2isaroundapulleywithoutfriction.P=20kN，E=177GPa.DeterminethestressofthesteelcableandtheverticaldisplacementofpointC.

答案:無Drawaxialforcediagramandmaximumnormalstressinthestructure.

答案:無AcircularaluminumtubeoflengthL=400mmisloadedincompressionbyforcesP(seefigure).Theoutsideandinsidediametersare60mmand50mm,respectively.Astraingageisplacedontheoutsideofthebartomeasurenormalstrainsinthelongitudinaldirection.

(a)Ifthemeasuredstrainise=550x106,whatistheshorteningdofthebar?

(b)Ifthecompressivestressinthebarisintendedtobe40MPa,whatshouldbetheloadP?

答案:無Acircularbarofmagnesiumalloyis750mmlong.Thestress-straindiagramforthematerialisshowninthefigure.Thebarisloadedintensiontoanelongationof6.0mm,andthentheloadisremoved.

(a)Whatisthepermanentsetofthebar?

(b)Ifthebarisreloaded,whatistheproportionallimit?

答案:無

第二章單元測試

ThesteelplanetrussshowninthefigureisloadedbythreeforcesP,eachofwhichis490kN.Thetrussmemberseachhaveacross-sectionalareaof3900mm2andareconnectedbypinseachwithadiameterofdp=18mm.MembersACandBCeachconsistofonebarwiththicknessoftAC=tBC=19mm.MemberABiscomposedoftwobars[seefigurepart(b)]eachhavingthicknesstAB/2=10mmandlengthL3m.TherollersupportatB,ismadeupoftwosupportplates,eachhavingthicknesstsp/2=12mm.

(a)FindsupportreactionsatjointsAandBandforcesinmembersAB,BC,andAB.

(b)Calculatethelargestaverageshearstressτp,maxinthepinatjointB,disregardingfrictionbetweenthemembers;seefiguresparts(b)and(c)forsectionalviewsofthejoint.

(c)Calculatethelargestaveragebearingstress#b,maxactingagainstthepinatjointB.

答案:無Aflexibleconnectionconsistingofrubberpads(thicknesst=9mm)bondedtosteelplatesisshowninthefigure.Thepadsare160mmlongand80mmwide.

(a)Findtheaverageshearstraingaverintherubberif

theforceP=16kNandtheshearmodulusfortherubberisG=1250kPa.

(b)Findtherelativehorizontaldisplacementdbetweentheinteriorplateandtheouterplates.

答案:無Ananglebrackethavingthicknesst0.75in.Isattachedtotheflangeofacolumnbytwo5/8-inchdiameterbolts(seefigure).Auniformlydistributedloadfromafloorjoistactsonthetopfaceofthebracketwithapressurep=275psi.ThetopfaceofthebrackethaslengthL=8in.andwidthb=3.0in.

Determinetheaveragebearingpressureσbbetweentheanglebracketandtheboltsandtheaverageshearstressτaverinthebolts.(Disregardfrictionbetweenthebracketandthecolumn.)

答案:無AbarofsolidcircularcrosssectionisloadedintensionbyforcesP(seefigure).ThebarhaslengthL=16.0in.anddiameterd=0.50in.ThematerialisamagnesiumalloyhavingmodulusofelasticityE=6.4x106psi.

Theallowablestressintensionisσallow=17,000psi,andtheelongationofthebarmustnotexceed0.04in.WhatistheallowablevalueoftheforcesP?

答案:無Aplanetrussissubjectedtoloads2PandPatjointsBandC,respectively,asshowninthefigurepart(a).ThetrussbarsaremadeoftwoL102x76x6.4steelangles[seeTableE-5(b):crosssectionalareaofthetwoangles,A=2180mm2,figurepart(b)]havinganultimatestressintensionequalto390MPa.Theanglesareconnectedtoan12mm-thickgussetplateatC[figurepart(c)]with16-mmdiameterrivets;assumeeachrivettransfersanequalshareofthememberforcetothegussetplate.Theultimatestressesinshearandbearingfortherivetsteelare190MPaand550MPa,respectively.

DeterminetheallowableloadPallowifasafetyfactorof2.5isdesiredwithrespecttotheultimateloadthatcanbecarried.(Considertensioninthebars,shearintherivets,bearingbetweentherivetsandthebars,andalsobearingbetweentherivetsandthegussetplate.Disregardfrictionbetweentheplatesandtheweightofthetrussitself.)

答案:無

第三章單元測試

Drawinternaltorquediagramandmaximumshearstressinthestructure.

答案:無Drawinternaltorquediagram.RadiusofAB=2cm.BCisathinwalltubewithRouter=1cm,Rinner=0.8cm.

答案:無AsshownintheFig,AshaftisloadedatSectionBandC.KnownshearmodulusG.φABistheangleofrotationofSectionBrelativetoSectionA.φBCistheangleofrotationofSectionCrelativetoSectionB.φACistheangleofrotationofSectionBrelativetoSectionA.

Tryto:(1)Plottheinternaltorquediagram;(2)FindoutφAB,φBCandφAC.

答案:無Asthefollowingfigureshown,agearandashaftareconnectedbyakey(bhL20mm10mm100mm).Thetorquethatthekeycantransmitism3kNmKnowingthediameteroftheshaftisd120mm,thepermissibleshearingstressandthepermissiblebearingstressof

thekeyarerespectively55MPaand110MPa.Trytocheckthestrengthofthekey.

答案:無AcopperrodoflengthL=18.0in.istobetwistedbytorquesT(seefigure)untiltheangleofrotationbetweentheendsoftherodis3.0°.Iftheallowableshearstraininthecopperis0.0006rad,whatisthemaximumpermissiblediameteroftherod?

答案:無

第四章單元測試

Plotinternal-forcediagramsofthebeamsshowninthefigure,i.e.shearforceandbendingmomentdiagram.

答案:無CalculatetheshearforceVandbendingmomentMatacrosssectionjusttotheleftofthe1600-1bloadactingonthesimplebeamABshowninthefigure.

答案:無DeterminetheshearforceVandbendingmomentMatthemidpointCofthesimplebeamABshowninthefigure.

答案:無CalculatetheshearforceVandbendingmomentMatacrosssectionlocated0.5mfromthefixedsupportofthecantileverbeamABshowninthefigure.

答案:無DeterminetheshearforceVandbendingmomentMatacrosssectionlocated18ftfromtheleft-handendAofthebeamwithanoverhangshowninthefigure.

答案:無AsimplebeamABsupportstwoconnectedwheelloads

P

and2P

thataredistancedapart(seefigure).Thewheelsmaybeplacedatanydistancexfromtheleft-handsupportofthebeam.

(a)Determinethedistance

x

thatwillproducethemaximumshearforceinthebeam,andalsodeterminethemaximumshearforce

Vmax.

(b)Determinethedistance

x

thatwillproducethemaximumbendingmomentinthebeam,andalsodrawthecorrespondingbending-momentdiagram.(Assume

P=10kN,

d=2.4m,and

L=12m.)

答案:[{"id":16770873,"url":"/zhs/teacherExam_h5/CHILDQUESTION/202305/6e838d296f5b487f9e3cae56c8a8e695.jpg","name":"圖片1.jpg","suffix":"jpg","dataType":"2","videoSize":"","interfaceDataId":746835199}]AbeamoflengthLisbeingdesignedtosupportauniformloadofintensityq(seefigure).Ifthesupportsofthebeamareplacedattheends,creatingasimplebeam,themaximumbendingmomentinthebeamisqL2

/8.However,ifthesupportsofthebeamaremovedsymmetricallytowardthemiddleofthebeam(aspictured),themaximumbendingmomentisreduced.

Determinethedistanceabetweenthesupportssothatthemaximumbendingmomentinthebeamhasthesmallestpossiblenumericalvalue.Drawtheshear-forceandbending-momentdiagramsforthiscondition.

答案:[{"id":16770872,"url":"/zhs/teacherExam_h5/CHILDQUESTION/202305/5c0b63bc15c34a63a17cf0a2ad8a5af6.jpg","name":"圖片1.jpg","suffix":"jpg","dataType":"2","videoSize":"","interfaceDataId":746834983}]Thecantileverbeamshowninthefiguresupportsaconcentratedloadandasegmentofuniformload.Drawtheshear-forceandbending-momentdiagramsforthiscantileverbeam.

答案:[{"id":16770871,"url":"/zhs/teacherExam_h5/CHILDQUESTION/202305/7ae947bf317a49eba3ccf2a327ea5013.jpg","name":"圖片1.jpg","suffix":"jpg","dataType":"2","videoSize":"","interfaceDataId":746834725}]ThesimplebeamABshowninthefiguresupportsaconcentratedloadandasegmentofuniformload.Drawtheshear-forceandbending-momentdiagramsforthisbeam.

答案:[{"id":16770869,"url":"/zhs/teacherExam_h5/CHILDQUESTION/202305/17853b1f7e0743b2941c563ec326b99b.jpg","name":"圖片1.jpg","suffix":"jpg","dataType":"2","videoSize":"","interfaceDataId":746834413}]

AbeamABCDwithaverticalarmCEissupportedasasimplebeamatAandD(seefigure).AcablepassesoverasmallpulleythatisattachedtothearmatE.OneendofthecableisattachedtothebeamatpointB.Thetensileforceinthecableis1800lb.Drawtheshear-forceandbending-momentdiagramsforbeamABCD.

答案:[{"id":16770868,"url":"/zhs/teacherExam_h5/CHILDQUESTION/202305/a3621f2030e047ea9867a6147b09befd.jpg","name":"圖片1.jpg","suffix":"jpg","dataType":"2","videoSize":"","interfaceDataId":746833985}]AsimplebeamABisloadedbytwosegmentsofuniformloadandtwohorizontalforcesactingattheendsofaverticalarm(seefigure).Drawtheshear-forceandbending-momentdiagramsforthisbeam.

答案:[{"id":16770867,"url":"/zhs/teacherExam_h5/CHILDQUESTION/202305/47b4af11ffa441a985f1d4e4e2e2ceca.jpg","name":"圖片1.jpg","suffix":"jpg","dataType":"2","videoSize":"","interfaceDataId":746833567}]AbeamABCwithanoverhangatoneendsupportsauniformloadofintensity12kN/mandaconcentratedmomentofmagnitude3kN.matC(seefigure).Drawtheshear-forceandbending-momentdiagrams

forthisbeam.

答案:[{"id":16770865,"url":"/zhs/teacherExam_h5/CHILDQUESTION/202305/55823e39ad1044c885a2a436035d6f99.png","name":"圖片1.png","suffix":"png","dataType":"2","videoSize":"","interfaceDataId":746833113}]ThebeamABshowninthefiguresupportsauniformloadofintensity3000N/mactingoverhalfthelengthofthebeam.Thebeamrestsonafoundationthatproducesauniformlydistributedloadovertheentirelength.Drawtheshear-forceandbending-momentdiagramsforthisbeam.

答案:[{"id":16770864,"url":"/zhs/teacherExam_h5/CHILDQUESTION/202305/110e1f0b5c9842348774f840df507320.png","name":"圖片1.png","suffix":"png","dataType":"2","videoSize":"","interfaceDataId":746832941}]AsimplebeamABsubjectedtocouples

M1

and3M1

actingatthethirdpointsisshowninthefigure.Drawtheshear-forceandbending-momentdiagramsforthisbeam.

答案:[{"id":16770861,"url":"/zhs/teacherExam_h5/CHILDQUESTION/202305/e0906f57bdfa44779338806e48eef022.png","name":"圖片1.png","suffix":"png","dataType":"2","videoSize":"","interfaceDataId":746832487}]ThecantileverbeamABshowninthefigureissubjectedtoaconcentratedloadPatthemidpointandacounterclockwisecoupleofmoment

M1=PL/4atthefreeend.Drawtheshear-forceandbending-momentdiagramsforthisbeam.

答案:[{"id":16770856,"url":"/zhs/teacherExam_h5/CHILDQUESTION/202305/aee66052bd624da0b478a7e185d81c59.png","name":"圖片1.png","suffix":"png","dataType":"2","videoSize":"","interfaceDataId":746832005}]

第五章單元測試

AsimplysupportedwoodbeamABwithspanlengthL=4mcarriesauniformloadofintensityq=5.8kN/m(seefigure).

(a)Calculatethemaximumbendingstressσmaxduetotheloadqifthebeamhasarectangularcrosssectionwithwidthb=140mmandheighth=240mm.

答案:無Afreight-caraxleABisloadedapproximatelyasshowninthefigure,withtheforcesPrepresentingthecarloads(transmittedtotheaxlethroughtheaxleboxes)andtheforcesRrepresentingtherailloads(transmittedtotheaxlethroughthewheels).Thediameteroftheaxleisd=82mm,thedistancebetweencentersoftherailsisL,andthedistancebetweentheforcesPandRisb=220mm.CalculatethemaximumbendingstressσmaxintheaxleifP=50kN.

答案:無Arailroadtie(orsleeper)issubjectedtotworailloads,eachofmagnitudeP=175kN,actingasshowninthefigure.Thereactionqoftheballastisassumedtobeuniformlydistributedoverthelengthofthetie,whichhascross-sectionaldimensionsb=300mmandh=250mm.

CalculatethemaximumbendingstressσmaxinthetieduetotheloadsP,assumingthedistanceL=1500mmandtheoverhanglengtha=500mm.

答案:無DeterminethemaximumtensilestressσtandmaximumcompressivestressσcduetotheloadPactingonthesimplebeamAB(seefigure).Dataareasfollows:P=6.2kN,L=3.2m,d=1.25m,b=80mm,t=25mm,h=120mm,andh1=90mm.

答案:無AcantileverbeamAB,loadedbyauniformloadandaconcentratedload(seefigure),isconstructedofachannelsection.Findthemaximumtensilestressσtandmaximumcompressivestressσcifthecrosssectionhasthedimensionsindicatedandthemomentofinertiaaboutthezaxis(theneutralaxis)isI=3.36in.4(Note:Theuniformloadrepresentstheweightofthebeam.)

答案:無Abeamhavingacrosssectionintheformofanunsymmetricwide-flangeshape(seefigure)issubjectedtoanegativebendingmomentactingaboutthezaxis.Determinethewidthbofthetopflangeinorderthatthestressesatthetopandbottomofthebeamwillbeintheratio4:3,respectively.

答案:無Determinetheratiosoftheweightsofthreebeamsthathavethesamelength,aremadeofthesamematerial,aresubjectedtothesamemaximumbendingmoment,andhavethesamemaximumbendingstressiftheircrosssectionsare(1)arectanglewithheightequaltotwicethewidth,(2)asquare,and(3)acircle(seefigures).

答案:無AsteelbeamABCissimplysupportedatAandBandhasanoverhangBCoflengthL=150mm(seefigure).Thebeamsupportsauniformloadofintensityq=4.0kN/moveritsentirespanABand1.5qoverBC.Thecrosssectionofthebeamisrectangularwithwidthbandheight2b.Theallowablebendingstressinthesteelisσallow=60MPa,anditsweightdensityisγ=77.0kN/m3.

(a)Disregardingtheweightofthebeam,calculatetherequiredwidthboftherectangularcrosssection.

(b)Takingintoaccounttheweightofthebeam,calculatetherequiredwidthb.

答案:無AsimplebeamoflengthL=5mcarriesauniformloadofintensityq=5.8andaconcentratedload22.5kN(seefigure).Assumingσallow=110MPa,calculatetherequiredsectionmodulusS.Thenselectan200mmwide-flangebeam(Wshape)fromTableE-1(b)AppendixE,andrecalculateStakingintoaccounttheweightofthebeam.Selectanew200mmbeamifnecessary.

答案:無Calculatethemaximumshearstressσmaxandthemaximumbendingstressσmaxinawoodbeam(seefigure)carryingauniformloadof22.5kN/m(whichincludestheweightofthebeam)ifthelengthis1.95mandthecrosssectionisrectangularwithwidth150mmandheight300mm,andthebeamis(a)simplysupportedasinthefigurepart(a)and(b)hasaslidingsupportatrightasinthefigurepart(b).

答案:無AcantileverbeamoflengthL=2msupportsaloadP=8.0kN(seefigure).Thebeamismadeofwoodwithcross-sectionaldimensions120mmx200mm.

CalculatetheshearstressesduetotheloadPatpointslocated25mm,50mm,75mm,and100mmfromthetopsurfaceofthebeam.Fromtheseresults,plotagraphshowingthedistributionofshearstressesfromtoptobottomofthebeam.

答案:無AsteelbeamoflengthL=16in.andcross-sectionaldimensionsb=0.6in.andh=2in.(seefigure)supportsauniformloadofintensityq=240lb/in.,whichincludestheweightofthebeam.

Calculatetheshearstressesinthebeam(atthecrosssectionofmaximumshearforce)atpointslocated1/4in.,1/2in.,3/4in.,and1in.fromthetopsurfaceofthebeam.Fromthesecalculations,plotagraphshowingthedistributionofshearstressesfromtoptobottomofthebeam.

答案:無Alaminatedplasticbeamofsquarecrosssectionisbuiltupbygluingtogetherthreestrips,each10mmx30mmincrosssection(seefigure).Thebeamhasatotalweightof3.6NandissimplysupportedwithspanlengthL=360mm.

Consideringtheweightofthebeam(q)calculatethemaximumpermissibleCCWmomentMthatmaybeplacedattherightsupport.(a)Iftheallowableshearstressinthegluedjointsis0.3MPa.(b)Iftheallowablebendingstressintheplasticis8MPa.

答案:無Asimplysupportedwoodbeamofrectangularcrosssectionandspanlength1.2mcarriesaconcentratedloadPatmidspaninadditiontoitsownweight(seefigure).Thecrosssectionhaswidth140mmandheight240mm.Theweightdensityofthewoodis5.4kN/m3.

CalculatethemaximumpermissiblevalueoftheloadPif(a)theallowablebendingstressis8.5MPa,and(b)theallowableshearstressis0.8MPa.

答案:無AwoodbeamABCwithsimplesupportsatAandBandanoverhangBChasheighth=300mm(seefigure).ThelengthofthemainspanofthebeamisL=3.6mandthelengthoftheoverhangisL/3=1.2m.Thebeamsupportsaconcentratedload3P=18kNatthemidpointofthemainspanandamomentPL/2=10.8kN.matthefreeendoftheoverhang.Thewoodhasweightdensity5.5kN/m3.

(a)Determinetherequiredwidthbofthebeambaseduponanallowablebendingstressof8.2MPa.(b)Determinetherequiredwidthbaseduponanallowableshearstressof0.7MPa.

答案:無Asimplebeamwithanoverhangsupportsauniformloadofintensityq=1200lb/ftandaconcentratedloadP=3000lbat8fttotherightofAandalsoatC(seefigure).Theuniformloadincludesanallowancefortheweightofthebeam.Theallowablestressesinbendingandshearare18ksiand11ksi,respectively.SelectfromTableE-2(a),AppendixE,thelightestI-beam(Sshape)thatwillsupportthegivenloads.

答案:無AsshownintheFigure,abeammadeofcastironandhasaTshapecrosssection.yandZCaretheneutralaxisofitscrosssection,withyc216mm，Izc1.112108mm4.

(1)Plottheshearforceandbendingmomentdiagram;

(2)If[σt]=60MPa,[σc]=160MPa,findthemaximumnormalstress(bothtensileandcompressive),andcheckthestrengthofthebeam.

答案:無DeterminethedistanceytothecentroidCofthecompositeareashowninthefigure.

答案:無

第六章單元測試

Awide-flangebeam(W12x35)supportsauniformloadonasimplespanoflengthL=14ft(seefigure).Calculatethemaximumdeflectionδmaxatthemidpointandtheanglesofrotationθatthesupportsifq=1.8k/ftandE=30x106psi.

答案:無Calculatethemaximumdeflectionδmaxofauniformlyloadedsimplebeam(seefigureonthenextpage)ifthespanlengthL=2.0m,theintensityoftheuniformloadq=2.0kN/m,andthemaximumbendingstressσ=60MPa.Thecrosssectionofthebeamissquare,andthematerialisaluminumhavingmodulusofelasticityE=70GPa.

答案:無Acantileverbeamwithauniformload(seefigure)hasaheighthequalto1/8ofthelengthL.Thebeamisasteelwide-flangesectionwithE=28x106psiandanallowablebendingstressof17,500psiinbothtensionandcompression.Calculatetheratioδ/Lofthedeflectionatthefreeendtothelength,assumingthatthebeamcarriesthemaximumallowableload.

答案:無ObtainaformulafortheratioδC/δmaxofthedeflectionatthemidpointtothemaximumdeflectionforasimplebeamsupportingaconcentratedloadP(seefigure).Fromtheformula,plotagraphofδC/δmaxversustheratioa/Lthatdefinesthepositionoftheload(0.5<a/L<1).Whatconclusiondoyoudrawfromthegraph?

答案:無DerivetheequationofthedeflectioncurveforacantileverbeamABsupportingaloadPatthefreeend(seefigure).Also,determinethedeflectionδBandangleofrotationθBatthefreeend.

答案:無DeterminetheangleofrotationθBanddeflectionδBatthefreeendofacantileverbeamABhavingauniformloadofintensityqactingoverthemiddlethirdofitslength(seefigure).

答案:無ThecantileverbeamACBshowninthefigurehasflexuralrigidityEI=2.1x106k-in.2CalculatethedownwarddeflectionsδCandδBatpointsCandB,respectively,duetothesimultaneousactionofthemomentof35k-in.appliedatpointCandtheconcentratedloadof2.5kappliedatthefreeendB.

答案:無AsimplebeamABsupportsauniformloadofintensityqactingoverthemiddleregionofthespan(seefigure).DeterminetheangleofrotationθAattheleft-handsupportandthedeflectionδmaxatthemidpoint.

答案:無AbeamABCDEhassimplesupportsatBandDandsymmetricaloverhangsateachend(seefigure).ThecenterspanhaslengthLandeachoverhanghaslengthb.Auniformloadofintensityqactsonthebeam.(a)Determinetheratiob/LsothatthedeflectionδCatthemidpointofthebeamisequaltothedeflectionsδAandδEattheends.(b)Forthisvalueofb/L,whatisthedeflectionδCatthemidpoint?

答案:無AcantileverbeamABissubjectedtoaconcentratedloadPandacoupleM0actingatthefreeend(seefigure).ObtainformulasfortheangleofrotationθBandthedeflectionδBatendB.

答案:無DeterminetheangleofrotationθBandthedeflectionδBatthefreeendofacantileverbeamABwithauniformloadofintensityqactingoverthemiddlethirdofthelength(seefigure).

答案:無CalculatethedeflectionsδBandδCatpointsBandC,respectively,ofthecantileverbeamACBshowninthefigure.AssumeM0=36k-in.,P=3.8k,L=8ft,andEI=2.25x109lb-in.2

答案:無ObtainformulasfortheangleofrotationθAatsupportAandthedeflectionδmaxatthemidpointforasimplebeamABwithauniformloadofintensityq(seefigure).

答案:無DerivetheequationofthedeflectioncurveforasimplebeamABloadedbyacoupleM0attheleft-handsupport(seefigure).Also,determinethemaximumdeflectionδmax.

答案:無

第七章單元測試

Solvetheprecedingproblemforanelementinplanestresssubjectedtostresses=100MPa,σy=80MPa,andτxy=28MPa,asshowninthefigure.Determinethestressesactingonanelementorientedatanangleθ=30°fromthexaxis,wheretheangleθispositivewhencounterclockwise.Showthesestressesonasketchofanelementorientedattheangleθ.

答案:無Anelementinplanestressissubjectedtostressesσx=4750psi,σy=1200psi,andτxy=950psi,asshowninthefigure.Determinethestressesactingonanelementorientedatanangleθ=60°fromthexaxis,wheretheangleθispositivewhencounterclockwise.Showthesestressesonasketchofanelementorientedattheangleθ.

答案:無SolveProblemforanelementinplanestresssubjectedtostressesσx=5700psi,σy=2300psi,andτxy=2500psi,asshowninthefigure.Determinethestressesactingonanelementorientedatanangleθ=50°fromthexaxis,wheretheangleθispositivewhencounterclockwise.

答案:無ThestressesactingonelementAinthewebofatrainrailarefoundtobe40MPatensioninthehorizontaldirectionand160MPacompressionintheverticaldirection(seefigure).Also,shearstressesofmagnitude54MPaactinthedirectionsshown.Determinethestressesactingonanelementorientedatacounterclockwiseangleof52°fromthehorizontal.

答案:無Anelementinplanestressfromthefuselageofanairplaneissubjectedtocompressivestressesofmagnitude27MPainthehorizontaldirectionandtensilestressesofmagnitude5.5MPaintheverticaldirection(seefigure).Also,shearstressesofmagnitude10.5MPaactinthedirectionsshown.Determinethestressesactingonanelementorientedataclockwiseangleof35°fromthehorizontal.

答案:無Solvetheproblems,thenormalandshearstressesactingonelementsareasshowninthefollowingfigures,Determinethestressesactingonanelementorientedataclockwiseangleof45°.

答案:無Anelementinplanestressisorientedataknownangleθ(seefigure).Onthisinclinedelement,thenormalandshearstresseshavethemagnitudesanddirectionsshowninthefigure.Determinethenormalandshearstressesactingonanelementwhosesidesareparalleltothexyaxes,thatis,determineσx,σy,andτxy.Showtheresultsonasketchofanelementorientedatθ=0°.

答案:無

答案:無Apropellershaftsubjectedtocombinedtorsionandaxialthrustisdesignedtoresistashearstressof56MPaandacompressivestressof85MPa(seefigure).

(a)Determinetheprincipalstressesandshowthemonasketchofaproperlyorientedelement.

(b)Determinethemaximumshearstressesandassociatednormalstressesandshowthemonasketchofaproperlyorientedelement.

答案:無Anelementinplanestressissubjectedtostressesnormalstressesσx,σy,andshearstressτxy,asshowninthefigure.

(a)Determinetheprincipalstressesandshowthemonasketchofaproperlyorientedelement.

(b)Determinethemaximumshearstressesandassociatednormalstressesandshowthemonasketchofaproperlyorientedelement.

(1)σx=2500psi,σy=1020psi,andτxy=-900psi

(2)σx=16.5MPa,σy=-91MPa,andτxy=-39MPa

(3)σx=2150kPa,σy=375kPa,andτxy=-460kPa

(4)σx=40MPa,σy=160MPa,andτxy=54MPa

(5)σx=27MPa,σy=5.5MPa,andτxy=10.5MPa

(6)σx=-46MPa,σy=-13MPa,andτxy=21MPa

(7)σx=-108MPa,σy=58MPa,andτxy=-58MPa

答案:無Atapointonthesurfaceofamachinecomponentthestressesactingonthexfaceofastresselementareσx=42MPaandτxy=33MPa(seefigure).Whatistheallowablerangeofvaluesforthestressσyifthemaximumshearstressislimitedtoτ0=35MPa?

答案:無Anelementinplanestressissubjectedtostressesσx=50MPaandτxy=42MPa(seefigure).Itisknownthatoneoftheprincipalstressesequals33MPaintension.(a)Determinethestressσy.(b)Determinetheotherprincipalstressandtheorientationoftheprincipalplanes,thenshowtheprincipalstressesonasketchofaproperlyorientedelement.

答案:無Anelementinuniaxialstressissubjectedtotensilestressesσx=49MPa,asshowninthefigureUsingMohr’scircle,determine:

(a)Thestressesactingonanelementorientedatanangleθ=27°fromthexaxis(minusmeansclockwise).(b)Themaximumshearstressesandassociatednormalstresses.Showallresultsonsketchesofproperlyorientedelements.

答案:無Anelementinbiaxialstressissubjectedtostressesσx=48MPa