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Lectures (5) Strength of Materials I_1

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Lectures (5) Strength of Materials I_1

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  1. Asst.Prof.Dr.ThakerSalehDawood

  2. ShearingForce&BendingMomentDiagrams Usually,weclassifystructuralmembersbasedonthetypesofloadsthey support.Forexample,aRodmemberhasacircularcrosssection.However, barscanhaveanytypeofcrosssection.Onlyaxialload,whichcanbeeither tensionorcompressivebutnottorsionorbending,affectstherodandbar. However,beamscanhaveanycrosssectionandcanwithstandanykindof load,includingtension,compression,torsion,bending,andshear. ClassificationofBeams: Beamsareclassifiedaccordingtothewayinwhichtheyaresupported. SeveraltypesofbeamsfrequentlyusedareshowninFigure.ThedistanceL showninthevariouspartsofthefigureiscalledthespan: Asst.Prof.Dr.ThakerSalehDawood

  3. Asst.Prof.Dr.ThakerSalehDawood

  4. Typesofloadsonthebeam:seefigurebelow Concentratedload:Whenaloadisappliedoveraverysmallareaitmaybe idealizedasaconcentratedload,whichisasingleforce. Distributedload:Whenaloadisspreadalongtheaxisofabeam,itis representedasadistributedload,suchastheloadw LinearlyVaryingLoad:Avaryingloadhasanintensitythatchangeswith distancealongthe axis. Couple:ThecoupleofmomentM1actingontheoverhangingbeam. Asst.Prof.Dr.ThakerSalehDawood

  5. Whenabeamissubjectedtotransverseloads,theinternalforcesinany section ofthebeamwillgenerallyconsistofashearforceVandabendingcoupleM. Consider,forexample,asimplysupportedbeamABcarryingtwoconcentrated loadsandauniformlydistributedload(seeFigurebelow). Asst.Prof.Dr.ThakerSalehDawood

  6. TodeterminetheinternalforcesinasectionthroughpointCwefirstdrawthefree- bodydiagramoftheentirebeamtoobtainthereactionsatthesupports.Passinga sectionthroughC,wethendrawthefreebodydiagramofAC(seeFigurebelow), fromwhichwedeterminetheshearforceVandthebendingcoupleM. Asst.Prof.Dr.ThakerSalehDawood

  7. Shearforce(V),whichequalsthealgebraicsummationofalltheforcesthatexist perpendicularlyononesideofthesection. Bendingmoment(M),whichequalsthealgebraicsummationofthemoments causedbyalltheperpendicularforcesaffectonesideof the section. Theshearatanygivenpointofabeamispositivewhentheexternalforces(loads andreactions)actingonthebeamtendtoshearoffthebeamatthatpointas indicatedinFigure: Thebendingmomentatanygivenpointofabeamispositivewhentheexternal forcesactingonthebeamtendtobendthebeamatthatpointasindicatedin Figure: Asst.Prof.Dr.ThakerSalehDawood

  8. Asst.Prof.Dr.ThakerSalehDawood

  9. BasicRelationshipbetweentheRateofLoading,ShearForceandBendingMomentBasicRelationshipbetweentheRateofLoading,ShearForceandBendingMoment Asimplebeamwithavaryingloadindicatedby w(x)issketchedinFigure.BasicRelationship BetweentheRateofLoadingw(x),ShearForceV andBendingMomentMForanyvalueof x: • Theslopeofshearingforcediagramatanypoint equaltointensityofdistributedloadatthatpoint. • Theslopeofbendingmomentdiagramatany pointequaltoshearingforceatthatpoint. • WhenV=0,Mismaximumorminimum. 9 Asst.Prof. Dr.ThakerSalehDawood

  10. Example1: DrawtheshearandmomentdiagramsforthebeamshowninFigure Asst.Prof.Dr.ThakerSalehDawood 10

  11. Example2: DrawtheshearandmomentdiagramsforthebeamshowninFigure M (kN.m) Asst.Prof.Dr.ThakerSalehDawood 11

  12. Example3: DrawtheshearandmomentdiagramsforthebeamshowninFigure Asst.Prof.Dr.ThakerSalehDawood 12

  13. Example4:DrawtheshearandmomentdiagramsforthebeamshowninFigureExample4:DrawtheshearandmomentdiagramsforthebeamshowninFigure Solution: Findthereactionforces ΣMA=0 (12x1)+(6x3)-4RB+(10x5)=0 ΣFy=0 -12-6–10+RA+RB=0 RB=20kN RA=8kN Asst.Prof.Dr.ThakerSalehDawood 13

  14. PartAD:(0≤𝑥 ≤2) ΣFy=0 8-6x =Vx ΣMsec.=0 2 2 6𝑥 8x+( )–Mx=0 8x+(6𝑥)=Mx 2 2 PartDB:(2≤𝑥 ≤4) ΣFy=0 8-12-3(x-2)-Vx=0 2–3x=Vx ΣMsec.=0 2 3(𝑥−2) 8x-12(x-1)- –Mx=0 2 Mx=12–4x–1.5(𝑥− 2)2 Asst.Prof.Dr.ThakerSalehDawood 14

  15. PartBC:(5≤𝑥 ≤5) ΣFy=0 8-12–6+20-Vx = 0 Vx = 10 ΣMsec.=0 8x-12(x-1)–6(x-3)+20(x-4)=Mx Mx=10x-50 Asst.Prof.Dr.ThakerSalehDawood

  16. Asst.Prof.Dr.ThakerSalehDawood

  17. Endoflecture5 Asst.Prof.Dr.ThakerSalehDawood

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