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1、Chapter4AxialForce,Shear,andBending-moment4-1Introduction1.BeamsInmanyinstancesinstructuralandmachinedesign,membersmustresistforcesappliedlaterallyortransverselytotheiraxes.Suchmembersarecalledbeams.Hereonlythecasesthatallloadsactandthedeflectionsoccurinthesameplane----planeofbending----areco
2、nsidered.梁的轴线受载后将变成曲线----elasticcurve.此种变形称为弯曲变形.2.ClassificationofbeamsSimplysupportedorsimplebeamCantileverorfixedbeamOverhangingbeam通常梁有各方面的简化:(1)构件的简化:有时不考虑横截面的具体形状,并忽略构造上的枝节,如键槽、销孔、阶梯等,简化为一直杆.(2)载荷的简化:载荷作用范围小时,处理为集中力或集中力偶,若连续作用,则处理为分布载荷.(3)支座的简化:fixedsupport,oreitherpinsorrollers.所以,除了上述
3、的三种梁外,还有continuousbeams,restrainedbeams,属于静不定问题.4-2Directapproach:axialforce,shear,bendingmoment要求得梁上某处的内力,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:左上右下为正,反之为负.如图.3.BendingmomentinbeamsFrom∑M=0,onehasbendingmomentMactingonthecrosszsectionofthebeam.Thebendingmomentistheresultantmomentofstressesdistributedoverthecrosssectionandisnumericallyequaltotheexternalmomentactingontheisolatedsegment,butitisoppositeind
6、irection.上面关于P,V,M正负的规定,使得在求解内力时,无论研究左段还是研究右段都将得到一样的结果.4-3ShearandBending-MomentDiagrams剪力,弯矩随轴截面位置的变化曲线分别称为剪力图与弯矩图.本节以例题为主,介绍如何求梁的内力以及梁的内力图的画法.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
