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1、Chapter4AxialForce,Shear,andBending-moment4-1Introduction1.BeamsInmanyinstancesinstructuralandmachinedesign,membersmustresistforcesappliedlaterallyortransverselytotheiraxes.Suchmembersarecalledbeams.Hereonlythecasesthatallloadsactandthedeflectionsoccurinthesameplane----planeofbending----areco
2、nsidered.梁的軸線受載后將變成曲線----elasticcurve.此種變形稱為彎曲變形.2.ClassificationofbeamsSimplysupportedorsimplebeamCantileverorfixedbeamOverhangingbeam通常梁有各方面的簡化:(1)構(gòu)件的簡化:有時(shí)不考慮橫截面的具體形狀,并忽略構(gòu)造上的枝節(jié),如鍵槽、銷孔、階梯等,簡化為一直桿.(2)載荷的簡化:載荷作用范圍小時(shí),處理為集中力或集中力偶,若連續(xù)作用,則處理為分布載荷.(3)支座的簡化:fixedsupport,oreitherpinsorrollers.所以,除了上述
3、的三種梁外,還有continuousbeams,restrainedbeams,屬于靜不定問題.4-2Directapproach:axialforce,shear,bendingmoment要求得梁上某處的內(nèi)力,依然可用截面法.梁平衡,局部也平衡.1.AxialforceinbeamsFrom∑F=0onecanxgettheaxialforcePThelineofactionoftheaxialforcewillalwaysbedirectedthroughthecentroidofthebeam’scross-sectiontoavoidbending.2.Shearinb
4、eamsFrom∑F=0,onehasinternalforceyVwhichiscalledtheshearorshearforceactingatrightanglestotheaxisofthebeam.Theshearistheresultantofstressesdistributedoverthecrosssectionandisnumericallyequaltothealgebraicsumofalltheverticalcomponentsoftheexternalforcesactingontheisolatedsegment,butitisoppositei
5、ndirection.Senseoftheshearforce:左上右下為正,反之為負(fù).如圖.3.BendingmomentinbeamsFrom∑M=0,onehasbendingmomentMactingonthecrosszsectionofthebeam.Thebendingmomentistheresultantmomentofstressesdistributedoverthecrosssectionandisnumericallyequaltotheexternalmomentactingontheisolatedsegment,butitisoppositeind
6、irection.上面關(guān)于P,V,M正負(fù)的規(guī)定,使得在求解內(nèi)力時(shí),無論研究左段還是研究右段都將得到一樣的結(jié)果.4-3ShearandBending-MomentDiagrams剪力,彎矩隨軸截面位置的變化曲線分別稱為剪力圖與彎矩圖.本節(jié)以例題為主,介紹如何求梁的內(nèi)力以及梁的內(nèi)力圖的畫法.Example4-1Constructaxial-force,shear,andbending-momentdiagramsforthecantileverloadedwithaninclinedforceattheend;seethefigure.Solution:1.Calculatereac
7、tions2.CalculateP,V,M.Studyleftsegment:M(x)∑Fx=0P(x)=P∑Fy=0V(x)=P∑MCz=0,PL-Px+M(x)=0M(x)=-PL+Px3.DrawtheP,V,MdiagramsExample4-2Plotshearandabending-momentdiagramsforasimplebeamwithauniformlydistributedload;seeFig..Solution:1Calculatethereacti
