ME 211 Homework 9 Solutions

# ME 211 Homework 9 Solutions - Problem#16.20...

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem#16.20 ME211HomeworkSet#9Solutions 1172008 Locatethecentroidybarofthechannel'scrosssectionalarea. 1.)DrawtheFBDandbreakthepiecedownintopartsofwhichyoucanfindthearea andthecentroid. 2.)Determinetheareaandthecentroidofeachindividualpiece(1,2,and1) Area1 = 6in(4in) y1 = 3in Area1 y = 72in 3 Area2 = 12in(2in) y 2 = 1in Area2 y 2 = 24in 3 3.)DeterminethesummationoftheareasandthesummationsofAreaxybar Area = Area + Area = 24in Area = 48in Area y = 72in + 24in Area y = 96in 1 2 2 3 3 x x x x 3 2 + 24in 2 4.)Solveforybarofthewholepiece Area y y= Area x x 96in 3 = = 2in 3 48in Thecentroidis2inchesfromthetopor4inchesfromthebottom. Problem#26.73 Determineybar,whichlocatesthecentroidalaxisx'forthecrosssectionalareaofthe Tbeam,andthenfindthemomentsofinertiaIx'andIy'. 1.) Tofindthecentroid,usetwosections 2.)Nowfindthemomentofinertiaaboutthisaxis 3.)Nowabouttheyaxis(Note:symmetrygetsridofAd^2term) 1 1 IY = 12 (250mm)(50mm) 3 + 12 (50mm)(300mm) 3 IY = 2604166.667mm 4 + 112500000mm 4 IY = 115104166.7mm 4 IY = 115(10 6 ) mm 4 Problem#36.83 Determinethemomentofinertiaofthebeam'scrosssectionalareawithrespectto thex'axispassingthroughthecentroidCofthecrosssection.Neglectthesizeofthe cornerweldsatAandBforthecalculation,ybar=104.3mm. 1.)DrawtheFBDandbreakthebarintosegmentstoallowtheuseofsectionsto determinethecentroid 2.)Themomentofinertiaaboutthex'axisforeachsegmentcanbedetermined usingtheparallelaxistheorem, Findthemomentofinertiaofeachsegement Segment 1 2 3 3.)Thetotalmomentofinertia Ai(mm2) (17.52) 15(150) (252) (dy)i(mm) 113.2 20.7 79.3 (Ibarx')i(mm4) (/4)(17.52) (Ady2)i(mm4) (Ix')i(mm4) 12.329(106) 12.402(106) 5.183(106) 12.654(106) . (1/12)15(1503) 0.964(106) (/4)(254) 12.347(106) Problem#412.9 ThealuminummachinepartissubjectedtoamomentofM=75N*m.Determinethe maximumtensileandcompressivebendingstressesinthepart. 1.)Firstfindthecentroidandtheareamoment 2.)Tensiononbottom,compressionontop Problem#512.21 Determinethesmallestallowablediameteroftheshaft,whichissubjectedtothe concentratedforces.ThesleevebearingsatAandBsupportonlyverticalforces, andtheallowablebendingstressisallow=22ksi. 1.)DrawtheFBD,theshearforceandmomentdiagramstodeterminethemaximum moment 2.)Findthemaximummomentfromthemomentgraphabove 3.)Findthediameterbyapplyingthebendingstressequationwiththeallowable bendingstressequalto22(103)psi. Problem#612.23 DeterminethemagnitudeofthemaximumloadPthatcanbeappliedtothebeamif thebeamismadeofamaterialhavinganallowablebendingstressof(allow)C=16ksi incompressionand(allow)t=18ksiintension. 1.)DrawtheFBDofthewholebeam,Figure(a),asectionthatyieldsthemax moment,andacrosssection. 2.)Firstfindthecentroidandtheareamoment 3.)Checkcompressionfirst Compression = M MAX c 5P(12in / ft)(2.75in) = = 16,000 psi I 124.33in 4 P = 12,056lbs = 12.1kip 4.)Checktension Tension = M MAX c 5P(12in / ft)(9in - 2.75in) = = 18,000 psi I 124.33in 4 P = 5968lb = 5.97kip Tensionwasthecriticalvalue. Problem#712.24 ThestrutCDontheutilitypolesupportsthecablehavingaweightof600lbs. DeterminetheabsolutemaximumbendingstressinthestrutifA,B,andCare assumedtobepinned. 1.)DrawtheFBD 2.)WritetheequilibriumequationsaboutthestrutCDtosolvefortheforces 4.)Usetheforcesjustfoundtodeterminetheshearforceandmomentdiagrams 5.)Usethemaxmomentfromthemomentgraphaboveinthebendingstress equationtosolveforthemaxbendingstress. Problem#814.11 Thescrewoftheclampexertsacompressiveforceof500lbsonthewoodblocks. Determinethemaximumnormalstressdevelopedalongsectionaa.Thecross sectionthereisrectangular,0.75in.by0.50in. 1.)DrawtheFBD 2.)Determinetheareaofthecrosssection 3.)Determinemaximumstressinthecrosssection.Inthissituation,thereis bothnormalstressandbendingstress Problem#914.17 Determinethemaximumandminimumnormalstressinthebracketatsectiona whentheloadisappliedatx=0. 1.)DrawtheFBDofthecontrolleverexposingthecrosssectionataa. 2.)Determinethesectionproperties 3.)Determinethestressinthecrosssection ...
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