机械设计05弯曲剪切和扭转.ppt

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1、05Bending,ShearandTorsionShigley,Fig.4-15Theneutralplanepassesthroughthecentroidofthecrosssectionalarea.Stress(strain)iszeroattheneutralplane.BendingofStraightBeams:DeformedBeamsDeformedBeamsThematerialisisotropic,homogeneousandlinearelastic.Thebeamisinitiallyst

2、raight.Planecrosssectionsremainplaneduringbending(i.e.,thedeformationduetotransverseshearisignored).Thebeamaxesaretheprincipalaxesofthesection,i.e.,Iyz=0.Thebeamwouldfailbybendingratherthanbycrushing,wrinkling(localbuckling)orglobalbuckling.Assump-tions2Thereisa

3、tleastonesetofcoordinatesystemaboutwhichIyz=0.TheaxisaboutwhichIyz=0iscalledtheprincipalaxis.Ifthesectionissymmetricaboutanaxis,thisaxisisaprincipalaxis.Formostshapes,thereareonlytwomutuallyperpendicularprincipalaxes.StraightBeams:MomentsofInertiaDefinitionPrinc

4、ipalAxis3UnderAllLoadsUnderN:UnderMyUnderMzIfIyz≠0,StraightBeams:NormalStressesNormalStressNotes4UnderMzStraightBeams:NormalStressDistributionEquation5dxbShearStressinBeams:ShearStressForequilibriumofbeamelement6ShearStressinBeams:FirstMomentofAreaShearStressina

5、BeamForbuiltupsectionShearStressFirstMomentofAreaNoteShearFlowbisthewidthofthecrosssectionattheparticulardistancey1.IisthesecondmomentofareaoftheentiresectionaboutN.A.y1=the1stmomentofareaoftheisolatedareaisthedistancefromtheneutralaxis(N.A.)tothecentroid(C.G.)o

6、ftheisolatedarea(Forceperunitlength)7ShearStressinaNarrowRectangularBeamFreeBodyDiagramShearStressparabolicA:Areaoftheshadedarea.A0:Areaoftheentirecrosssection8IBeam:ShearStresstxyShearStressForWideBeams9IBeam:ShearStresstxzintheFlangeShearStresstxzqinWeb10Examp

7、leAlongbeamismadeofthreeplanks,nailedtogether.Knowingthatthespacingbetweennailsis25mmandthattheverticalshearinthebeamisV=500N,determinetheshearforceineachnail.Problem11Example:SolutionStrategyIfthebeamwereonepiece,therewouldbeshearstress(shearflow)betweenthecapa

8、ndtheweb.SolutionStrategyThenailswillcarrytheforceresultedfromtheshearstress.12Example:SolutionShearflowqonthelowersurfaceoftheupperplank.IShearFlowShearForceinEachNa