ME 211 Homework 8 Solutions

ME 211 Homework 8 Solutions - Problem#111.8...

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Unformatted text preview: Problem#111.8 ME211HomeworkSet#8Solutions 10312008 Thesolidshaftasadiameterof0.75in.Ifitissubjectedtothetorquesshown, determinethemaximumshearstressdevelopedinregionsCDandEFoftheshaft.The bearingsatAandFallowfreerotationoftheshaft. 25lb*ft 40lb*ft 20lb*ft 35lb*ft 1.)DeterminethetorqueinregionsCDandEF. 2.)Determinethemaximumshearstressbyapplyingthetorsionformulatothe segmentCD. 3.)Determinethemaximumshearstressbyapplyingthetorsionformulaforthe segmentEF. Problem#211.9 Asteeltubehavinganouterdiameterof2.5inisusedtotransmit35hpwhen turningat2700rev/min.Determinetheinnerdiameterdofthetubetothenearest 1/8iniftheallowableshearstressisallow=10ksi. 1.) Converttheturningspeedtorad/s 2.)Determinethetorqueontheshaft 3.)Utilizetheshearstressequationtodeterminethediameter Usethediameterequalto2.5in. *Problem#311.18 Thecouplingisusedtoconnectthetwoshaftstogether.Assumingthattheshear stressintheboltsisuniform,determinethenumberofboltsnecessarytomakethe maximumshearstressintheshaftequaltotheshearstressinthebolts.Eachbolt hasadiameterd. 1.)DrawtheFBKofthetorqueshaft 2.)Writetheequilibriumequation Intheequationbelow,n=numberofbolts,F=shearforceineachbolt 3.)Shearstressinthebolt 4.)Shearstressintheshaft 5.)Asstatedintheproblem,theshearstressinthebarisequaltotheshearstressin thebolts Problem#411.37 TheA36steelassemblyconsistsofatubehavinganouterradiusof1in.andawall thicknessof0.125in.UsingarigidplateatB,itisconnectedtothesolid1in diametershaftAB.Determinetherotationofthetube'sendCifatorqueof200lb*in isappliedtothetubeatthisend.TheendAoftheshaftisfixedsupported. 1.)DrawtheFBD 2.)UsetheangleoftwistequationtodeterminetheangleoftwistatBduetobarAB. B = TAB L 200lb * in(10in) = = 0.001852rad JG 4 6 (0.5) (11.0)(10 ) 2 3.)DeterminetheangleoftwistinbarBC C / B = TCB L -200lb * in(4in) = = -0.0001119rad 4 JG 4 6 (1 - 0.875 )(11.0)(10 ) 2 4.)AddtheanglesoftwisttogethertodeterminetototalangleoftwistfromAtoC. *Problem#511.42 The60mmdiametersolidshaftismadeofA36steelandissubjectedtothe distributedandconcentratedtorsionalloadingsshown.Determinetheangleof twistatthefreeendAoftheshaftduetotheseloadings. 1.)DrawtheFBDtofindtorqueineachrod 2.)Usethetwistangleformula 2.)Partoftheequationcanbesolvedusingtheintegrationformulasincethereisa nonconstanttorque Problem#611.50 ThebronzeC86100pipehasanouterdiameterof1.5inandathicknessof0.125in. ThecouplingonitatCisbeingtightenedusingawrench.Iftheappliedforceis F=20lbs,determinethemaximumshearstressinthepipe. 1.)DrawtheFBD 2.)Writetheequilibriumequationsintermsoftorques. 3.)Applycompatability,thetotalangleoftwistmustbezero. 4.)Usingtheresultsfromsteptwoandthree,solveforTAandTB. TA = 106.67lb * in TB = 133.33lb * in 5.)WiththetorquesatAandBdetermined,theequationforthemaxshearstress canbeused.Todeterminethemax,thelargertorquemustbeused. max = TB c 133.33(0.75) = = 389 psi J 4 4 (0.75 - 0.625 ) 2 Problem#711.65 Thecontourofthesurfaceoftheshaftisdefinedbytheequationy=e^ax,whereais aconstant.IFtheshaftissubjectedtoatorqueTatitsends,determinetheangleof twistofendAwithrespecttoendB.TheshearmodulusisG. 1.)DeterminetheangleoftwistutilizinganintegraltodetermineJ(x)overthe contour. Problem#812.1 ThebeamissubjectedtoamomentM.Determinethepercentageofthis momentthatisresistedbythestressesactingonboththetopandbottom boards,AandB,ofthebeam. 1.)DrawtheFBD 2.)Utilizethesectionpropertytodeterminetheareamomentofinertia.The equationforasquarecrosssectionisshownbelow. I= 1 1 (0.2)(0.2 3 ) - (0.15)(0.15 3 ) = 91.14583(10-6 )m 4 12 12 3.)Determinethebendingstressbyapplyingtheflexureformula = My I M(0.1) = 1097.143M -6 91.14583(10 ) M(0.075) D = = 822.857M -6 91.14583(10 ) E = 4.)ApplytherelationshipbetweenforceandstresstodeterminetheforcesonAand B.Utilizetheareaofatrapazoidinsteadofhavingtotaketheintegraloverthearea. F= dA = (AreaTrap) F = 822.857M(0.2mm)(0.025mm) 1 + (1097.143M - 822.857M)(0.2mm)(0.025mm) 2 F = 4.800M 5.)Mulitplytheforcebythedistancebetweenthecentroidsofforceofeach trapazoid. M'= F(0.17169mm) = 4.800M(0.17619mm) = 0.8457M %= M' *100% = 84.6% M Problem#912.12 Thecontrollevelisusedonaridinglawnmower.Determinethemaximum bendingstressintheleveratsectionaaifaforceof20lbisappliedtothe handle.TheleverissupportedbyapinatAandawireatB.Sectionaais square,0.25inby0.25in. 1.)DrawtheFBDofthecontrolleverexposingthecrosssectionataa. 2.)Determinethemomentatthecrosssectionaatouseinthemaxbending stressequation 3.)Utilizethemaximumbendingstressequation,andsetcequaltotheplace wherethemaximumbendingstresswilloccur. ...
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This note was uploaded on 05/12/2010 for the course MECHENG 211 taught by Professor ? during the Fall '07 term at University of Michigan.

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