lecture 17 bending stress：讲座17弯曲应力

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1、EGR236PropertiesandMechanicsofMaterialsSpring2013Lecture17:BendingStressToday:--Homeworkquestions:--NewTopics:--SomemoreShear-MomentDiagrams--StressinBeamssubjectedtoBending--MomentofInertia--Homework:ReadSection6:3-4WorkProblemsfromChap6:37,73,75,80Followingtoday'sclassyoushouldbea

2、bleto:--Statewherethemaximumstresseswillbefoundinabeamsubjectedtobendingloads.--Beabletocalculatethemaximumstressinabeamcausedbyabendingload--Understandthedifferencebetweencompressiveandtensilebendingstress.Beams:Wheneverthereisaninternalbendingmoment,M,actingonthecrosssectionofabea

3、m,thiswillsetupnormalstressesinthebeam.FBL-xxMVVFAThestresssetupbysuchabendingmomenttendstobemaximumasyoureachtheouterfibersofthebeam.Thereisalsoalocationinthecrosssectionwherethestressdropstozeroalongwhatiscalledtheneutralaxis.σcompNeutralAxisMVVMσtenTheneutralaxisrunsthroughthecen

4、troidoftheareaofthecrosssection.Thestressincreaseslinearlywiththedistancefromtheneutralaxis.Sothefartherawayaportionofthecrosssectionisfromthecentroid,thelargerwillbethenormalstressduetobending.σcompNeutralAxisMVVMσtenOnonesideoftheneutralaxisthestresseswillbetensile.Ontheothersidet

5、hestresseswillbecompressive.ThemagnitudeofthesenormalstressesaregivenbyaformulaknownastheflexureformulawhereMistheresultantinternalbendingmoment,cisthedistancefromtheneutralaxisIisthemomentinertiaofthecrosssectionabouttheneutralaxisNotethatthenegativesignisanindicationofwhetherthest

6、ressistensileorcompressive.Negativemeansacompressivestress.Procedureforanalysisofbeamssubjectedtobending.1)Determinetheinternalreactions.FindthedistributionofVandMalongthelengthofbeam.ThisisusuallydonebydrawingtheShearandMomentdiagrams.2)DeterminetheSectionProperties.Thismayincluden

7、eedingtoa)locatetheneutralaxisthroughthecentroidoftheareab)determinethemomentofinertiaaboutthecentroid3)DeterminethemaximumnormalcompressiveandtensilestressesbyuseoftheflexureformulaExample1:AT-shapedbeambuiltfromtwowoodenboardshastheloadingshownbelow.Determinethemaximumcompressivea

8、ndtensilestressinth