Homework Problem Statements ME 270 – FSpI

ME270–Homework ©Freeform

Homework Problem Statements ME 270 – FSpI



HomeworkH1.AGiven: When a certain linear spring has a physical length of L = 180 mm, the spring carries a tensile load of F = 150 N. When the same spring has a physical length of L = 160 mm, the spring carries a compressive load of F = 100 N. The stiffness and unstretched length of the spring are represented by k and L0, respectively. Find: For this problem:

a) Determine k and L0 of this spring in SI units.

b) Determine k and L0 of this spring in British gravitational units.


HomeworkH1.BGiven: Block B has a known weight of W. B is placed on a smooth, horizontal surface as a force F is applied to the block. From Newton’s second law, we know that the acceleration, a, of the block is given by , where m is the mass of B. Find: For this problem:

a) What is the mass of the block in terms of slugs?

b) What is the acceleration of the block in terms of as a result of the applied force?

c) What is the acceleration of the block in terms of as a result of the applied force?

Use the following parameter values in your analysis: and .

a = F / m

ft / s2

km / hr2

W = 1000 lb F = 100 lb

Fig.PH01B.M270

B F

smooth


HomeworkH2.AGiven:Threeforcesactingonthebracketasshown.Find: DetermineloadPandtheangleqsuchthattheresultantofthesethree

forcesiszeroinbothxandydirections.Usethefollowingparametervaluesinyouranalysis:F1=800NandF2=600N.

x

y

O

34

F1

F2P = ??

θ = ??

Fig.PH02A.M270

ME270–Homework ©Freeform2021 Fall2021

HomeworkProblemH2.BGiven:Tensionforces�⃗�#$and�⃗�#&actonathree-dimensionalframeatpointB.Find:

a) Determine the unit vector and force vector for �⃗�#$. b) Determine the unit vector and force vector for �⃗�#&. c) Calculate the direction angles and direction cosines for �⃗�#&.

Usethefollowingparametervaluesinyouranalysis:FBO=200lb,FBH=350lb,b=6ft,d=4ft,v=10ftandh=8ft.

z

x

y

d

d

h

vA

B

C

D

EH

b

R

O

Fig.PH02B.M270


HomeworkH3.AGiven:CablesABandAC,carryingtensionsTABandTAC,respectively,areattachedto

theroofpeakofthebuildingatA.Let�⃗�'#and�⃗�'( representtheforcesofcablesABandAC,respectively,onthebuilding.

Find:

a) Write �⃗�'# and �⃗�'( as vectors in terms of their xyz-components. b) Determine the projection of �⃗�'# on the direction of cable AC. Write your answer

as a vector. c) Determine the angle that exists between cables AB and AC.

Usethefollowingparametervaluesinyouranalysis:FAB=600lb,FAC=400lb,q=36.87°,f=53.13°,b=30ft,d=40ftandh=15ft.

φ

z

x

y

A

θ B

C

O

d

b

h

Fig.PH03A.M270


x

y

34

A

B

F

3F

2Fθ

P

HomeworkH3.BGiven:PinPisabletoslidewithinasmooth,angledslot.Threeforces,F,2Fand3F,

areappliedtothepin.Find:

a) Determine the resultant of the three applied forces. Write this resultant in terms of its xy-components. Leave your answer in terms of F.

b) Determine the projection of the resultant found in a) above in the direction AB of the slot. Write your answer as a vector in terms of its xy-components.

Usethefollowingparametervalueinyouranalysis:q=30°.

Fig.PH03B.M270


HomeworkH4.AGiven:BlockEhavingaweightofWEissupportedbycablewrappedoveranideal

pulley.Find:

a) Determine the tensions cables AB and AC. b) Determine the weight of block D.

Usethefollowingparametersinyouranalysis:WE=150lbandq=53.13°.

x

y

B

43

A

C

θ

g

ideal pulley

D

E

Fig.PH04A.M270


HomeworkH4.BGiven:BlockBhavingaweightofWBrestsonasmoothinclinesurface.TheblockissupportedbyaspringwithastiffnessofkandanunstretchedlengthofL0.Find:

a) Determine the final length of the spring. b) If the angle q is increased, will the spring lengthen, shorten or remain unchanged?

Usethefollowingparametersinyouranalysis:k=80lb/in,WB=160lb,L0=15inandq=35°.

θ

k

B

g

Fig.PH04B.M270


HomeworkH5.AGiven:BlockEhasamassofmEandissuspendedbythreecables.Find:DeterminethetensionincablesAC,DCandBC.Usethefollowingparametersinyouranalysis:mE=20kg,b=3m,d=4mandh=4m.

x

z

A

B

O

h / 2

gCD

h / 2

h / 3

b / 2

d / 2

d / 2

b / 2

y

E

Fig.PH05A.M270


4 3

5

12

10

10

B D

A

B

g

C

alldimensionsinmeters

x

y

z

HomeworkH5.BGiven:Theweight,W,ofparticleissupportedbythreecablesasshown.All

dimensionsaregiveninfeet.Find:

a) Express the tension in cables AB, AC and AD as the product of their unit vectors and unknown tensions.

b) Determine the tension in cables AB, AC and AD. Leave your answer in terms of W.

Fig.PH05B.M270


y

A

x

d

b

θ

F

C B

HomeworkH6.AGiven:AforceFactsatpointAonthebracketshown.Find:Forthisloading:

a) Calculate the moment about point C due to F. Write your answer as a vector.

b) Calculate the moment about point B due to F. Write your answer as a vector. Usethefollowingparametervaluesinyouranalysis:d=0.8m,b=0.6m,θ=60°andF=900N. Fig.PH06A.M270


x

y

A

TAB

B

z

h

b

D

C h

d

HomeworkH6.BGiven:CableABcarriesatensionofTAB.AngledbarAOissteadiedbythepre-tensionedcableAB,withthetensionforceofABonthebargivenby .Find:Forthisproblem:

a) Write out in terms of its xyz components.

b) Calculate the moment about point D due to .

c) Calculate the moment about point C due to . Usethefollowingparametervaluesinyouranalysis:TAB=1.6kN,b=6m,d=2mandh=4m.

!TAB

!TAB

!

M D !TAB

!

MC !TAB

Fig.PH06B.M270


HomeworkH7.AGiven:Loadingonthemembershown.Find:

a) Determine the magnitude and direction of each force-couple pair. b) Determine the magnitude and direction of the combination of all the force-couple

pairs. Usethefollowingparametervaluesinyourwork:LA=0.5m,LB=0.6mandLC=1m.

LA

Fig.PH07A.M270


HomeworkH7.BGiven:PoleABisfixedintotheground.CablesBCandBDcarrytensionsofTBCandTBD.AloadFisappliedatlocationE.Find:Determineanequivalentforce-couplepairforallloadsatpointE.Usethefollowingparametervaluesinyourwork:TBC=250N,TBD=300N,F=400N,h=0.5m.,b=d=2mandL=3m.

Fig.PH07B.M270


HomeworkH8.AGiven:Theloadingshownmaintainsthebracketinequilibrium.Find:

a) Determine )�⃗�*) b) Determine the reactions at O.

Usethefollowingparametersinyourwork:)�⃗�+)=)�⃗�,) = 200𝑁,d=1m,L=5m,f=15°andq=30°.


HomeworkH8.BGiven:ThebarisloadedasshownandisrestrainedbyapinjointatOandasmooth-slideratA.Find:

a) Determine the reaction on the bar at A and express this as a vector. b) Determine the reaction at O and express as a vector.

Usethefollowingparametersinyourwork:�⃗�+ = �⃗�* = 500𝑙𝑏,d=3ft,L=6ftandθ=36.87°.

Fig.PH08B.M270


A

P

C

B

d

smooth d

2d

3

4

HomeworkH9.AGiven: AnangledbracketispinnedtogroundatendA,withtheotherendofthe

bracketsupportedbyasmoothrolleratC.AhorizontalforcePactsmidwaybetweenBandConthebracket.Assumetheweightofthebrackettobenegligiblecomparedtotheappliedload.

Find: DeterminethereactionsactingonthebracketatendsAandC.Expressyour

answersintermsofP.

Fig.PH09A.M270


A

C

B

idealpulley

D

R

2R

W 4R

4R

g

E

HomeworkH9.BGiven: AT-shapedstructuralmemberisfixedtogroundatendD.Acableis

attachedtopointConthemember,iswrappedaroundanidealpulleyatB,andisconnectedtogroundatendA.Thecablecarriesaknownpre-tensionofT.Bothsectionsofthecablenotincontactwiththepulleyarehorizontal.ThemembersupportsablockofweightWatendE.Assumetheweightofthememberandpulleytobenegligiblecomparedtotheappliedloads.

Find: DeterminethereactionsactingonthememberatendD.Expressyour

answersintermsofW,TandR.

Fig.PH09B.M270


HomeworkH10.AGiven:ThepoleisloadedasshownandisrestrainedbyaballandsocketatO,two

cables(CDandAB)andaloadL.Find:

a) Determine the tensions in cables CD and AB. b) Determine the reactions at O and express as a vector.

Usethefollowingparametersinyourwork:|𝐿| = 210lb,xA=6ft,xE=5ft,xC=3ft,d=4,h=3ftandb=2ft.

Fig.PH10A.M270


HomeworkH10.BGiven:MemberABissupportedbyaball-and-socketjointatendB,andbyasmoothverticalwallatendA,alongwithcableCD.AdownwardverticalloadactsatthemidpointCofmemberAB.TheweightofABcanbeconsideredtobenegligiblecomparedtotheappliedforceP.Find:DeterminethetensionincableCDandthereactiononABatendA.ExpressyouranswerintermsofP.

y

z

x P

A

B

D

C

8d

6d

2d

2d

4d

ball-and-socketjoint


HomeworkH11.AGiven:ThepipestructureshownisattachedtogroundwithafixedconnectionatA.Asetofthreeforcesactsonthestructure.Theweightofthestructureisnegligiblecomparedtotheappliedforcesactingonthestructure.Find:DeterminethereactionsonthestructureatA.Writeyouranswersasvectorsintermsof,atmost,Fandd.

z

y

d

2d

B

D

C

A

x

2F

F

2d

2F

fixedconnection


HomeworkH11.BGiven:ThedoorisloadedatDwithaloadF,andissupportedbyacableCEand

hingesatAandB.ThehingeatBcarriesaloadinthex-directionandthehingeatAdoesNOTcarryaloadinthex-direction.

Find:

a) Determine the tension in cable CE. b) Determine the reactions on the door at hinges A and B.

Usethefollowingparametersinyourwork:)�⃗�)=400N,h=0.20mandd=0.25m.


L / 3

B

w

L / 3 L / 3

F

C D H

x

HomeworkH12.AGiven:Thebeamisloadedasshown.Find:Forthisproblem:

a) Calculate the magnitude and location of the single-force equivalent load. b) Determine the reactions acting on the beam.

Usethefollowingparametervaluesforyourwork:F=20kips,w=6kips/ftandL=9ft.


HomeworkH12.BGiven:Thebeamisloadedwiththedistributedloadasshown.Find:Calculatethemagnitudeandlocationofthesingle-forceequivalentload.Usethefollowingparametervaluesforyourwork:L=4ftandw(x)=0.75x3lb/ft.

L

x

w x( )


HomeworkH13.AGiven:Considertheshadedareashownbelow.Find:Usingthemethodofcompositesections,determinethearea,andthex-andy-componentsforthelocationofthecentroidofthearea.Leaveyouanswersintermsofb.

y

x b b b b

b

b


HomeworkH13.BGiven:Considertheshadedareashownbelow.Find:Usingthemethodofcompositesections,determinethearea,andthex-andy-componentsforthelocationofthecentroidofthearea.LeaveyouanswersintermsofR.

y

x R R

R

R

R


HomeworkH14.AGiven:Theareainthefigure.Find:Determinethearea,andthex-andy-componentsforthelocationofthecentroidofthearea.


HomeworkH14.BGiven:Theshadedareashownliesbetweenastraightlineatx=-2bandthefunctionx2=4by.Find:Youareaskedtofindthecentroidofthisareausingintegration.

a) Carefully define the differential area that you will be using. b) Using this differential area, determine the area, and the x- and y-components for

the location of the centroid of the area. Leave you answers in terms of b.

y

b

x

2b

x2 = 4by

2b


HomeworkH15.AGiven:Thebuoyancyforceonashipistobecalculatedthroughmodelingtheshipas

aprismaticbodywithatriangularcrosssection,asshownbelow.TheweightoftheshipanditscargoisW.Thewaterinwhichtheshipfloatshasamassdensityofρ.

Find:Determinethedraftdoftheship.Leaveyouranswerintermsof,atmost:α,b,g,Wandρ.

b d

α

ship

endviewofship


HomeworkH15.BGiven:Eric isusinga foam“poolnoodle”asa flotationdeviceashe lounges inhisswimmingpool.Thepoolnoodleisathick-walledtubewithdimensionsshownbelow.ErichasaweightofW,whereastheweightof thenoodlecanbeconsideredtobenegligiblecomparedtothewaterthatitdisplaces.Thewaterinthepoolhasamassdensityof .AssumethatthevolumeofthenoodledoesnotchangeappreciablyunderEric’sweightandthebuoyancyforces.Find:AsEricfloatsinthewaterofthepoolwiththenoodlecompletelysubmerged:

a) What is the buoyancy force acting on the noodle?

b) What is the buoyance force acting directly on Eric by the water? Use the following parameters in your analysis: , , ,

and .

ρW

L=6 ft Ro =3 inches Ri =1 inch

W =185 lb ρW =1.94 slugs / ft3

Eric

noodle

Ro

Ri

L

dimensionsofnoodle


HomeworkH16.AGiven:AnangledwatergateissupportedbyapinjointatAandarolleratB.The

gatehasadimensionintothepageofb.Thewaterhasadensityofρ,andtheweightofthegateisnegligiblecomparedtotheweightofthewaterthatitsupports.

Find:DeterminethereactionforceonthegateatsupportB.Leaveyouranswerintermsof,atmost:d,b,gandρ.

A

2d

d

B

d


HomeworkH16.BGiven:AwatergateissupportedbyapinjointatAandacable-pulleysystematB.AcounterweightCisattachedtotheendofthecable.Thegatehasadimensionintothepageofb.Thewaterhasadensityofρ,andtheweightofthegateisnegligiblecomparedtotheweightofthewaterthatitsupports.Find:DeterminetheweightofCrequiredtoholdthegateinequilibrium.Leaveyouranswerintermsof,atmost:d,b,gandρ.

A

B

d 4

3

d

GC


HomeworkH17.AGiven: AnL-shapedarmispinnedtogroundatendB,withendAincontactwith

blockC.CoefficientsofstaticfrictionμsAandμsCexistsonthesurfacesbetweenthearmandblockC,andbetweenblockCandground,respectively.AforceFisappliedtothearminanattempttopreventslidingmotionofC,wheretheforcePactstotherightonC.Theweightsofthearmandblockcanbeconsideredtobenegligiblecomparedtotheotherforcesactingonthesystem.

Find: DeterminetheminimumforceFneededtopreventblockCfromsliding.Forthisproblem,usethefollowingparameters:L=6ft,h=4ft,P=90lbandμsA=μsC=0.4.


g

A

5

12

2µS µS

B

G

HomeworkH17.BGiven: ApersonhavingaweightofWisattemptingtopullacrateofweightWCto

theleft.Find: DeterminethemaximumweightWCsuchthatthecratecanbemoved.Use

.WriteyouranswerintermsW. HINT:Drawindividualfreebodydiagramsforthepersonandthecrate.

µS = 0.4


g

h

3h

G

A

B

FC

D 2h 2h

h

HomeworkH18.AGiven: AblockhavingaweightofWanditscenterofmassatGissupportedby

light-weightlegsatAandB.ThecoefficientofstaticfrictionofμSexistsbetweenthelegsandground.

Find:

a) Determine the smallest applied force F required to move the block.

b) For the force F found above, is the block in a state of impending tipping or impending slipping?

Forthisproblem,usethefollowingparametervalue:μs=0.60.


HomeworkH18.BGiven: AblockhavingaweightofWanditscenterofmassatGrestsonapanel

whenθ=0.AmomentMisslowlyappliedtothepanel,slowlyincreasingtheangleθ.ThecoefficientofstaticfrictionofμSexistsbetweenthelegsandground.

Find:

a) Determine the angle θ at which the block begins to move relative to the panel.

b) For the angle θ found above, is the block in a state of impending tipping or impending slipping with respect to the panel?

Forthisproblem,usethefollowingparametervalue:μs=0.70.

d

θ

2d

g

d d

3d

M

G

A B


HomeworkH19.AGiven: BlockAhavingaweightofWisattachedtoacable,withtheotherendofthe

cableattachedtoafixedsupport.Thecableispulledoveradrumthatisabletoslidealongasmoothhorizontalguide.AhorizontalforcePisappliedtothedrumtoholdthesysteminequilibrium.Thecoefficientofstaticfrictionbetweenthecableandthedrumisknowntobeμs.Assumethatthecableremainstaut.

Find: DeterminethemaximumforcePforwhichthesystemcanremainin

equilibrium.LeaveyouranswerintermsofW.Forthisproblem,usethefollowingparameters:μs=0.35.


R

A

2R 2R

B C

O M

R

P

D

HomeworkH19.BGiven: Theband-brakesystemshownbelowhasabandwrappedaroundadrum,

withacounter-clockwisetorqueMbeingappliedtothedrumandthedrumrotatingataconstantrate.ThebandistensionedbyarmAC,withtheloadPactingatendCofthearm.ThecoefficientofkineticfrictionbetweenthebandandthedrumisμK.ConsidertheweightofarmACtobenegligiblecomparedtoP.

Find: DeterminethecoupleMactingonthedrum.Writeyouranswerintermsof

P,RandμK.


HomeworkH20.AGiven: AdiskhavingaweightofWandanouterradiusofRrestsonarough,

horizontalfloor.AforceFactsatthecenterofthediskandpressesthediskagainstawedgeatsurfaceB,withthewedgealsobeingsupportedbyasmoothwallatsurfaceA.AverticalforcePactsonthewedge.ThecoefficientofstaticfrictionatsurfacesBandCisμs.Theweightofthewedgecanbeconsideredtobenegligiblecomparedtotheotherforcesactingonthesystem.

Find: DeterminethelargestforcePthatcanbeappliedtothewedgewithout

movingthedisk.Whatistheimpendingmotionofthesystematthisvalueoftheload:doesthedisksliponthewedgeoronthefloor?

Forthisproblem,usethefollowingparameters:W=200lb,R=3ft,F=300lb,μs=0.5andθ=15°.


µS

d

5

12

F

d d

P

O

B

A µS

C

HomeworkH20.BGiven: TheL-shapedarmOAispinnedtogroundatendO.EndAissupportedbya

wedge,withthecoefficientofstaticfrictionbetweenthewedgeandthearm,andbetweenthewedgeandgroundbeingμS.AverticalforceFactsonthearmasshown.AhorizontalforcePisappliedtothewedgetoholdthewedgeinplace.Considertheweightsofthewedgeandarmtobenegligiblecomparedtotheotherforcesactingonthesystem.

Find: DeterminethelargestforcePforwhichthesystemremainsinequilibrium.

ExpressyouranswersintermsoftheappliedforceF.Forthisproblem,usethefollowingparameter:μs=0.3.


HomeworkH21.AGiven: ConsiderthetrussshownbelowwiththeloadingonjointsBandC.Find: Usethemethodofjointstodeterminetheloadcarriedbyeachmemberin

thetruss.Identifyeachmemberaseitherbeingintension,incompressionorcarryingzeroload.LeaveyouranswersintermsofP.

Forthisproblem,usethefollowingparameters:h=0.8mandb=0.6m.

A CB

D

P

x

y

h

b b

P


HomeworkH21.BGiven: ConsiderthetrussshownbelowwiththeloadingonjointsDandE.Find: Usethemethodofjointstodeterminetheloadcarriedbyeachmemberin

thetruss.Identifyeachmemberaseitherbeingintension,incompressionorcarryingzeroload.

Forthisproblem,usethefollowingparameters:θ=30°,h=4ft,b=5ft,F=30kipsandP=50kips.

A

C

B

D

F

P

E H

θ

h

h

b

x

y


HomeworkH22.AGiven: ConsiderthetrussshownbelowwiththeloadingonjointsD,HandK.Find: UsethemethodofsectionstodeterminetheloadcarriedbymembersCE,

EHandHR.Identifyeachmemberaseitherbeingintension,incompressionorcarryingzeroload.

Forthisproblem,usethefollowingparameters:b=3ft,h=4ft,F=100kNandP=160kN.

A

C

B

D

EH

h

b

K

h

h

R

F

F

P P

x

y


A

C

B

D

E H

K

S

F

P

F

Q

R

b

h

h

h

h

x

y

HomeworkH22.BGiven: ConsiderthetrussshownbelowwiththeloadingonjointsD,K,SandU.Find: Forthisproblem:

a) Identify all zero-force members in the truss. b) Determine the load carried by members EK, EH and HD. Identify each

member as either being in tension, in compression or carrying zero load.

Forthisproblem,usethefollowingparameters:h=3m,b=6m,F=20kN,P=40kNandQ=36kN.


ACB

b

P

x

y

F

Q

D E

H

I J K L

M N

b b b b

h

h

HomeworkH23.AGiven: ConsiderthetrussshownbelowwiththeloadingonjointsC,DandQ.Find: Forthisproblem:

a) Determine the external reactions acting on the truss at supports A and H. b) Identify all zero-force members in the truss.. c) Determine the load carried by members BC, CJ and MN. Identify each

member as either being in tension, in compression or carrying zero load.

Forthisproblem,usethefollowingparameters:h=12ft,b=16ft,F=20kips,P=30kipsandQ=25kips.


BC

ED

H I

J

2P

K

L

M

2d

P

2d

d

d

d

d

d A

HomeworkH23.BGiven: ConsiderthetrussshownbelowwiththeloadingonjointM.Find: Forthisproblem:

a) Identify all zero-force members in the truss.

b) Determine the load carried by members HJ, HK, HI and EI of the truss. Identify each member as either being in tension, in compression or carrying zero load. Leave your answers in terms of P.


HomeworkH24.AGiven: Aframeismadeofcircular-arc-shapedmembersACandBC.Thesemembers

arejoinedtogetheratCwithapinjoint,andarepinnedtogroundatendsAandB.AloadFisappliedatjointC,andloadsFandPactatpointDonmemberBC.

Find: DeterminethereactionsontheframeatpinsAandB.Writeyouranswersas

vectorsintermsoftheirxycomponents.LeaveyouranswersintermsofFandP.

AB

x

y

CD

R

F F

P

R / 2 R / 2


A

B

F

b

3R / 2

R

C

D

E

b

HomeworkH24.BGiven: TheframeshownismadeupofthecurvedmemberABandtheL-shaped

memberBD,withthetwomembersjoinedbyapinjointatB.AforceFactstotheleftatpointDontheframe.Considerallsurfacestobesmooth.

Find: DeterminethereactionsontheframeatsupportpointsAandC.Also,what

isthecontactforcememberABonmemberBD?Forthisproblem,usethefollowingparameters:R=2ft,b=1ftandF=1300lb.


A

h

B

C

D

M

b b b b

y

x

F P

E

HomeworkH25.AGiven: ConsidertheframemadeupofmembersCD,ACandBE.AmomentMacts

onmemberCDasshown,inadditiontoloadsPandFactingonmemberAC.Find: DeterminetheloadcarriedbymemberBE,aswellasthereactionsonthe

frameatthesupportpointsAandD.Forthisproblem,usethefollowingparameters:b=0.2m,h=0.6m,F=800kN,P=600kNandM=500N-m.


y

xA

h

B

C

D

ER

H

d

ideal pulley

e b

HomeworkH25.BGiven: AframeismadeupofmembersADandBEthatarepinnedtogetheratjoint

C.AnidealpulleyisattachedtoendEofmemberBE.AcableispulledoverthepulleythatsupportsblockH,whereHhasaweightofW.

Find: DeterminethereactionsontheframeatsupportpointAandB.Also,

determinethereactionforceofmemberADonmemberBEatjointC.LeaveyouranswersintermsofW.

Forthisproblem,usethefollowingparameters:h=18in,d=4in,R=4in,b=6inande=18in.


y

x

B C

D

HK

w

R

RRR

R

HomeworkH26.AGiven: ConsidertheframeshownbelowthatismadeupofanL-shapedmemberBD

andacurvedmemberDK.AlineloadwactsonsectionBRofmemberBD.Find: Forthisproblem:

a) Determine the reactions on the frame at supports B and K. b) Determine the internal reactions on a section of the frame at H on the curved

member DK.

Forthisproblem,usethefollowingparameters:w=400lb/ftandR=3ft.


x

b

P

d

y

z

D

C

L

B

O

HomeworkH26.BGiven: AsocketwrenchisusedtoloosenaboltwithaloadPactingonendCofthe

wrench’shandle.Find: DeterminetheinternalresultantsonsectionOBatlocationBonthesocket

OD.Forthisproblem,usethefollowingparameters:L=7in,b=4inandP=120lb.


A B C

L / 2

2P P

M V (x)

M (x)

x

x

L / 2

HomeworkH27.AGiven: Cantileveredbeamloadedwithtwoforces2PandPatBandC,respectively,

alongwithacoupleMatB.Find: Constructtheshearforceandbendingmomentdiagramsforthisbeam.Forthisproblem,usethefollowingparameters:L=10ft,M=40kip-ftandP=20kips.


L / 2

x

V (x)

M (x)

L / 2

2P P

MC

x

x

A B C

HomeworkH27.BGiven: Cantileveredbeamloadedwithtwoforces2PandPatBandC,respectively,

alongwithacoupleMCatC.Find: Constructtheshearforceandbendingmomentdiagramsforthisbeam.Forthisproblem,usethefollowingparameters:L=10ft,MC=40kip-ftandP=30kips.


A L B

x

p(x)

V (x)

M (x)

x

x

p0

HomeworkH28.AGiven: Cantileveredbeamwithlinearly-varyinglineloadp(x)actingalongits

length.Find: Constructtheshearforceandbendingmomentdiagramsforthisbeam.Forthisproblem,usethefollowingparameters:p0=15kN/mandL=3m.


V (x)

M (x)

x

x

x

2w

2d d

A B

C

w

HomeworkH28.BGiven: Beamwiththelineloadingshown.Find: Constructtheshearforceandbendingmomentdiagramsforthisbeam.Forthisproblem,usethefollowingparameters:w=10kips/ftandd=4ft.


V (x)

M (x)

x

x

x

w

ABC

L / 3

F

D

L / 3 L / 3

HomeworkH29.AGiven: CantileveredbeamwiththelineloadingappliedbetweenAandC,anda

concentratedloadFactingatD.Find: Usingthegraphicaltechnique,constructtheshearforceandbending

momentdiagramsforthisbeam.Forthisproblem,usethefollowingparameters:w=8kips/ft,F=25kipsandL=6ft.


B

w

C

L / 2 L / 2

M

PD

V (x)

M (x)

x

x

HomeworkH29.BGiven: Cantileveredbeamwiththelineloadingwactingoveritslength,a

concentratedforceatCandaconcentratedcoupleMactingatendD.Find: Usingthegraphicaltechnique,constructtheshearforceandbending

momentdiagramsforthisbeam.Forthisproblem,usethefollowingparameters:w=5kips/ft,M=75kips-ft,P=100kipsandL=4ft.


HomeworkH30.AGiven: CurvedstructuralmemberABispinnedtogroundatendA.Acablehavinga

cross-sectionalareaofAconnectsDonthestructuralmembertogroundatC.

Find: Forthisproblem:

a) Determine the tension in the cable.

b) Determine the axial stress and strain in the cable.

Forthisproblem,usethefollowingparameters:R=0.5ft,A=1.5in2,P=10ksiandE=30x106psi.

P

A

R

R / 2 R

C

D

O

B


HomeworkH30.BGiven: Arigidplatformissupportedbyrods(1)and(2),withtherodshavingequal

cross-sectionalareasofA.Theplatform,inturn,supportsacratehavingaweightofW.Considertheweightoftheplatformandrodstobenegligiblecomparedtotheweightofthecrate.

Find: Determinethestressineachrod.Forthisproblem,usethefollowingparameters:a=2ft,b=3ft,A=4in2andW=2000lb.

A

a b

W

B

D

C

L2L1 (1)

(2)


B

L / 2

H

P

L

C D

L / 22P

HomeworkH31.AGiven: TheframeshownbelowismadeupofmembersBDandCH,withthetwo

memberspinnedtogetheratC,andpinnedtogroundatendsHandDofthemembers.MemberCHhasacross-sectionalareaofAandismadeofamaterialhavingaYoung’smodulusofEandayieldstrengthofσYP.LoadsactatjointsBandContheframe.


a) Determine the axial stress and strain in rod CH. b) Has the material in rod CH failed due to yielding? If not, what is the factor

of safety for this loading against yielding? Forthisproblem,usethefollowingparameters:E=200GPa,σYP=250MPa,P=50kN,L=2mandA=80mm2.


HomeworkH31.BGiven: Arodismadeupofmembers(1),(2)and(3)withthesemembershaving

diametersofd,2dand3d,respectively.Allmembersoftherodaremadeupofanaluminumalloy6061-T6.


a) Determine the stress and strain in each member of the rod. b) Has the material failed due to yielding in any of the three members? If not,

what is the factor of safety for this loading against yielding? Forthisproblem,usethefollowingparameters:d=3inandP=50kips..

B

P

C

(1)

L L 2L

3d

(2) (3)

D H

2dd

P3P


HomeworkH32.AGiven: Itisdesiredtopunchofholeinasheetofmetal,withthesheetmetalhaving

athicknessoft.Theshapeoftheholeisrectangular,withsemi-circularends,asshownbelow.Thepunchingresistanceofthematerialinshearisknowntobeτres.

Find: DeterminethepunchingforcePrequiredtopunchthehole.

Forthisproblem,usethefollowingparameters:L=2in,r=0.5in,t=0.06inandτres=40ksi.

platesemi − circular ends

L

2r


A

hC

D

B

h

b b

W

HomeworkH32.BGiven: AnL-shapedbracketispinnedtogroundatBwithadouble-shearpin

connection,withthepinatBhavingadiameterofD.ThebracketisheldinpositionbywireCDhavingadiameterdasitsupportsacrate.ThecratehasaweightofW.Theweightofthebracketcanbeassumedtobenegligibleascomparedtotheweightofthecrate.

Find: DeterminethetensilestressinwireCDandtheshearstressinthepinatB.Forthisproblem,usethefollowingparameters:b=0.3m,h=0.4m,d=10mmandW=2kN.


A

2d

BC

T

d d

3T

2( )1( )

HomeworkH33.AGiven: Acircularcross-sectionedshaftismadeupofcomponents(1)and(2).

Component(1)hasatubularcrosssection,withinnerandouterdiametersofdand2d,respectively.Component(2)hasasolidcrosssectionwithadiameterofd.Components(1)and(2)arejoinedbyarigidconnectoratBwith(1)beingattachedtoafixedwallatendA.RigidconnectorCisattachedtoendCofcomponent(2).Torques3TandTactonconnectorsBandC,respectively,asshown.


a) Determine the torque load on each of the components as a result of the applied torques.

b) What is the maximum shear stress in the shaft? At what location(s) does this maximum stress exist?

LeaveyouranswersintermsofTandd.


A

2d

B C

3T d2TT

3d

D1( )

2( )3( )

HomeworkH33.BGiven: Acircularcross-sectionedshaftismadeupofsolidshaftcomponents(1),

(2)and(3),havingdiametersof3d,2dandd,respectively.(1)and(2)arejoinedwiththerigidconnectorB,(2)and(3)arejoinedbyrigidconnectorCand(1)isattachedtoafixedwallatitsleftend.Arigidconnectorisattachedtotherightendof(3).Torques2T,3TandTactonconnectorsB,CandD,asshown.


a) Determine the torque load on each of the components as a result of the applied torques.

b) What is the maximum shear stress in the shaft? At what location(s) does this maximum stress exist?

LeaveyouranswersintermsofTandd..


HomeworkH34.AGiven: Atubularcross-sectionshafthasinnerandouterdiametersofdianddo,

respectively.Theshaftisfixedtoarigidwallatitsleftend,andanaxialtorqueTisappliedtotherightend.ThematerialmakinguptheshafthasashearmodulusofG.


a) Determine the maximum shear stress in the shaft. Where on the shaft’s cross section does this maximum shear stress exist?

b) Make a sketch of the shear stress on the cross section of the tube. c) Determine the maximum shear strain in the shaft. Where on the shaft’s cross

section does this maximum shear strain exist? Forthisproblem,usethefollowingparameters:di=2in,do=4in,T=30kip-ftandG=11x103ksi.

z

T

y

do di

L

do

di

crosssec'onoftube


HomeworkH34.BGiven: Circularcross-sectionedshafts(1)and(2)arecoupledthroughapairof

meshinggearsBandC,whererB>rC.EndDofshaft(2)isconnectedtoafixedwall,whereasatorqueofTisappliedtoendAofshaft(1).Bothshaftshavesolidcrosssectionswithadiameterofd.

Find: Forthisproblem,determinethemaximumshearstressinthesystem.In

whichshaftdoesthismaximumshearstressoccur,andwhereonthecrosssectiondoesitoccur?

Expressyouranswersintermsoftheparametersdefinedinthefigure.

TA

L2

A

rCL1

gear B

x

(2)

(1)

rBD

gear C

d

d

bearing support bearing support

bearing support

T


x

x

M x( )

x

V x( )

A

B

C

2w

w

d d d

HomeworkH35.AGiven: Considerthebeamloadedasshownbelow.Thebeamhasatubularcross

sectionwithinnerandouterradiiofR/2andR,respectively.Find: Forthisproblem:

a) Determine the location(s) for which pure bending exists on the cross section of the beam.

b) For the location(s) found in a) above, determine the maximum normal stress.

Forthisproblem,usethefollowingparameters:d=3ft,w=15kips/ftandR=4in.


AB

w

L / 2 L / 2

x

M x( )

x

x

V x( )

HomeworkH35.BGiven: Considerthebeamloadedasshownbelow.Thebeamhasarectangular

crosssectionwithcross-sectiondimensionsofbxh,wherebisthedimensionintothepage.




Forthisproblem,usethefollowingparameters:L=5m,w=20kN/m,b=0.1mandh=0.3m.


x

x

M x( )

x

AB

O

C

2w

w

d 2d

V x( )

HomeworkH36.AGiven: Considerthebeamloadedasshownbelow.Thebeamhasarectangular





Forthisproblem,usethefollowingparameters:d=6ft,w=4kips/ft,b=2ftandh=4ft.


x

x

M x( )

x

AB

w

d

V x( )

P

d d

C D

HomeworkH36.BGiven: Considerthebeamloadedasshownbelow.Thebeamhasarectangular





Forthisproblem,usethefollowingparameters:d=1m,P=10kN,w=30kN/m,b=0.3mandh=0.3m.


ZO

Y

R / 2R

HomeworkH37.AGiven: Considerthegreyedareashownbelow.Find: Usingthemethodofcompositesections,determinetheY-positionofthe

centroidforthisareaandthesecondareamomentforthesectionaboutitscentroidforbendingabouttheZdirection.


ZO

Y

R / 2

R

HomeworkH37.BGiven: Considerthegreyedareashownbelow.Find: Usingthemethodofcompositesections,determinetheY-positionofthe

centroidforthisareaandthesecondareamomentforthesectionaboutitscentroidforbendingabouttheZdirection.


Z

Y

R

α α

R

HomeworkH38.AGiven: Considerthegreyedareashownbelow.Find: Usingintegration,determinetheY-positionofthecentroidforthisareaand

thesecondareamomentforthesectionaboutitscentroidforbendingabouttheZdirection.


Z

Y

a a

2a2a

3a

HomeworkH38.BGiven: Considerthegreyedareashownbelow.Find: Usingintegration,determinetheY-positionofthecentroidforthisareaand

thesecondareamomentforthesectionaboutitscentroidforbendingabouttheZdirection.

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Homework Problem Statements ME 270 – FSpI