ME 211 Homework 10 Solutions

ME 211 Homework 10 Solutions - Problem#114.5...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem#114.5 ME211HomeworkSet#10Solutions 11142008 Twohemisphereshavinganinnerradiusof2ftandwallthicknessof0.25in.arefitted together,andtheinsidegaugepressureisreducedto10psi.Ifthecoefficientofstatic firctioniss=0.5betweenthehemsipheres,determine(a)thetorqueTneededto initiatetheroationoftheotphemisphererelativetothebottomone,(b)thevertical forceneededtopullthetophemisphereoffthebottomone,and(c)thehorizontal forceneededtoslidethetophemisphereoffthebottomone. 1.)DrawtheFBDandbreakthepiecedownintopartsofwhichyoucanfindthearea andthecentroid. 2.)Determinethenormalforce 3.)Determinetheforceoffriction Part(a)Therequiredtorque:Inordertoinitiaterotationofthetwohemispheres relativetoeachother,thetorquemustovercomethemomentproducedbythe frictionforceaboutthecenterofthesphere. T = F f r = 2880 (2 + 0.125 /12) = 18190lb * ft = 18.2kip * ft Part(b)Therequiredverticalforce:Inordertojustpullthetwohemispheres apart,theverticalforcePmustovercomethenormalforce. Part(c)Therequiredhorizontalforce:Inordertojustcausethetwo hemispherestosliderelativetoeachother,thehorizontalforceFmustovercome thefrictionforce. Problem#214.7 Apressurevesselheadisfabricatedbygluingthecircularplatetotheendofthe vesselasshown.Ifthevesselsustainsaninternalpressureof450kPa,determine theaverageshearstressintheglueandthestateofstressinthewallofthevessel. 1.) DrawaFBD 2.)Writetheequilibriumequationintheydirection 3.)NowuseCylindricalPressureVesselEquations Problem#314.10 Aboilerisconstructedof8mmsteelplatesthatarefastenedtogetherattheirends usingabuttjointconsistingoftwo8mmcoverplatesandrivetshavingadiameter of10mmandspaced50mmapartasshown.Ifthesteampressureintheboileris 1.35MPa,determine(a)thecircumferentialstressintheboiler'splateapartfrom theseam,(b)thecircumferentialstressintheoutercoverplatealongtherivetline aa,and(c)theshearstressintherivets. 1.)DrawtheFBDofsectionsbothcircumferentiallyandalongtherivetlineaa Part(a)Determinethecircumferentialstressintheboilersplateapartfromthe seam Pr 1.35(10 6 )(0.75m) 1 = = = 126.56(10 6 ) t (0.008m) 1 = 127MPa Part(b)Determinethecircumferentialstressintheoutercoverplatealongthe rivetlineaa 126.56(10 6 )(0.04)(0.008) = 1 '(2)(0.04)(0.08) 1 '= 63.3MPa Part(c)Determinetheshearstressintherivets.Firstyoumustdeterminethe forceintherivets,andthendividethatbytheareathatitactstodeterminethe shearstress F y = 0 = Fb - 63.3(10 6 )[(0.008)(0.04)] Fb = 20.25kN Fb ( avg ) b = = 258MPa 2 (0.01) 4 Problem#414.28 Thechimneyissubjectedtotheuniformwindpressureofp=25lb/ft^2.Itistobe constructedwith1=ft=thickbrickwalls.Ifthebricksandmortarhaveaspecific weightof145lb/ft^3,determinethesmallestouterdiameterdofthechimneyso thatnotensilestressisdevelopedinthematerial.Thewindloadingcanbe approximatedbyw=pa. 1.)FirstdrawtheFBD 2.)Findthesectionproperties 2 [d - (d - 2) 2 ] = (d -1) 4 I = [d 4 - (d - 2) 4 ] = (d 3 - 3d 2 + 4d - 2) 64 8 A= 3.)Applythenormalstressequationtodeterminethediameter B = 0 = N Mc + A I d 11250d( ) 2 -4350 (d -1) + 3 (d -1) (d - 3d 2 + 4d - 2) 8 0 = 4350d 3 - 85997.78d 2 + 17400d - 8700 d = 5.65 ft 0= Problem#514.38 Thesolidrodissubjectedtotheloadingshown.Determinethestateofstressat pointB,andshowtheresultsonadifferentialvolumeelementlocatedatthispoint. 1.)DrawtheFBD,theshearforceandmomentdiagramstodeterminethemaximum moment 2.)Findtheinternalforcesandmoments F F F x = 0 = N x -10 = 0 = Vy + 10 = 0 = Vz = 0 = Tx + 0.200 -10(0.03) N x = 10.0kN y Vy = -10.0kN z Vz = 0.0kN M M M x Tx = 0.10kN * m y =0 13.5MPa My = 0 z = 0 = M z -10(0.03) -10(0.15) M z = 1.80kN * m 3.)Findthesectionproperties A = (0.032 ) = 0.9(10-3 )m 2 Ix = Iy = (0.034 ) = 0.2025(10-6 )m 4 4 J = (0.034 ) = 0.405(10-6 )m 4 2 (QB ) y = 0 (QB ) z = 4(0.03) 1 [ (0.032 )] = 18.0(10-6 ) 3 2 4.)FindtheNormalStress = N Mz y Myz - + A Iz Iy 10.0(10 3 ) 1.80(10 3 )(0.03) B = - +0 -3 -6 0.900(10 ) 0.2025(10 ) B = -81.3MPa = 81.3MPa(C) 1.)Findtheshearstress.Thetransverseshearstressinthezandydirectionsand thetorsionalshearstresscanbeobtainedusingtheshearformulaandthetorsion VQ It formulas, T twist = J v = ( xz ) B = twist + Vi 0.100(10 3 )(0.03) + 0 = 2.36MPa ( xz ) B = -6 0.405(10 ) ( xy ) B = Vy = 0 ...
View Full Document

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.

Ask a homework question - tutors are online