搜索
Lesson1CompressionMembersNewWords1.achieveachievement2.eccentricitycenter,中心;eccentric偏心的；eccentricity偏心，偏心距3.inevitableevitable可避免的avoidable;inevitable不可避免的unavoidable4.truss桁架triangulartruss,rooftruss,trussbridge5.bracingbrace支柱，支撑；bracing,支撑，撑杆6.slender细长，苗条；stout;slenderness7.buckle压曲，屈曲；bucklingload8.stockystout9.convincinglyconvince,convincing,convincingly10.stub树桩，短而粗的东西；stubcolumn短柱11.curvature曲率；curve,curvature12.detractordetractdrawortakeaway;divert;belittle，贬低，诽谤；13.convince14.argumentdispute,debate,quarrel,reason,论据（理由）15.crookednesscrook钩状物，v弯曲，crooked弯曲的16.provision规定，条款PhrasesandExpressions1.compressionmember2.bendingmomentshearforce,axialforce3.callupon(on)要求，请求，需要4.criticalbucklingload临界屈曲荷载critical关键的，临界的5.cross-sectionalarea6.radiusofgyration回转半径gyration7.slendernessratio长细比8.tangentmodulus切线模量9.stubcolumn短柱10.trial-and-errorapproach试算法11.empiricalformula经验公式empirical经验的12.residualstress残余应力residual13.hot-rolledshape热轧型钢hot-rolledbar14.lowerbound下限upperbound上限16.effectivelength计算长度2Definition（定义）Compressionmembersarethosestructuralelementsthataresubjectedonlytoaxialcompressiveforces:thatis,theloadsareappliedalongalongitudinalaxisthroughthecentroidofthemembercrosssection,andthestresscanbetakenasfa=P/A,wherefaisconsideredtobeuniformovertheentirecrosssection.受压构件是仅受轴向压力作用的构件，即：荷载是沿纵轴加在其截面形心上的，其应力可表示为…，式中，假定fa在整个截面上均匀分布。Thisidealstateisneverachievedinreality,however,andsomeeccentricityoftheloadisinevitable.然而，现实中从来都不可能达到这种理想状态，因为荷载的一些偏心是不可避免的。Thiswillresultinbending,butitcanusuallyberegardedassecondaryandcanbeneglectedifthetheoreticalloadingconditioniscloselyapproximated.这将导致弯曲，但通常认为它是次要的，如果理论工况是足够近似的，就可将其忽略。Thiscannotalwaysbedoneifthereisacomputedbendingmoment,andsituationofthistypewillbeconsideredinBeam-Columns.但这并非总是可行的，如有计算出的弯矩存在时，这种情形将在梁柱理论中加以考虑。Themostcommontypeofcompressionmemberoccurringinbuildingsandbridgesisthecolumn,averticalmemberwhoseprimaryfunctionistosupportverticalloads.在建筑物和桥梁中最常见的受压构件就是柱，其主要功能就是支承竖向荷载。Inmanyinstancesthesemembersarealsocalledupontoresistbending,andinthesecasesthememberisabeam-column.Compressionmemberscanalsobefoundintrussesandascomponentsofbracingsystems.在许多情况下，它们也需要抵抗弯曲，在此情况下，将它们称为梁柱。受压构件也存在于桁架和支撑系统中。ColumnTheory（柱理论）Considerthelong,slendercompressionmembershowninFig.1.1a.考虑如图1.1.a所示的长柱IftheaxialloadPisslowlyapplied,itwillultimatelyreachavaluelargeenoughtocausethemembertobecomeunstableandassumetheshapeindicatedbythedashedline.如果慢慢增加轴向荷载P，它最终将达到一个足够大的值使该柱变得不稳定(失稳)，如图中虚线所示。Thememberissaidtohavebuckled,andthecorrespondingloadiscalledthecriticalbucklingload.这时认为构件已经屈曲，相应的荷载称为临界屈曲荷载。Ifthememberismorestocky,astheoneinFig.1.1b,alargerloadwillberequiredtobringthemembertothepointofinstability.如果该构件更粗短些，如图1.1b所示，则需要更大的荷载才能使其屈曲。Forextremelystockymembers,failuremaybebycompressiveyieldingratherthanbuckling.对特别粗短的构件，破坏可能是由受压屈服引起而非由屈曲引起。Forthesestockymembersandformoreslendercolumnsbeforetheybuckle,thecompressivestressP/Aisuniformoverthecrosssectionatanypointalongthelength.对这些短柱以及更细长的柱，在其屈曲前，在其长度方向上任意点处横截面上的压应力P/A都是均匀的。Asweshallsee,theloadatwhichbucklingoccursisafunctionofslenderness,andforveryslendermembersthisloadcouldbequitesmall.我们将会看到，屈曲发生时的荷载是长细程度的函数，非常细长的构件的屈曲荷载将会很低。Ifthememberissoslender(aprecisedefinitionofslendernesswillbegivenshortly)thatthestressjustbeforebucklingisbelowtheproportionallimit—thatis,thememberisstillelastic—thecriticalbucklingloadisgivenby如果构件如此细长（随后将会给出细长程度的精确定义）以致即将屈曲时的应力低于比例极限—即，构件仍是弹性的，临界屈曲荷载如下式给出：322LEIPcr(1.1)whereEisthemodulusofelasticityofthematerial,Iisthemomentofinertiaofthecross-sectionalareawithrespecttotheminorprincipalaxis,andListhelengthofthememberbetweenpointsofsupport.式中E为材料弹性模量，I为关于截面副主轴的惯性矩，L为支座间的距离。ForEq1.1tobevalid,themembermustbeelastic,anditsendsmustbefreetorotatebutnottranslatelaterally.Thisendconditionissatisfiedbyhingesorpins.要使方程1.1成立，构件必须是弹性的，且其两端必须能自由转动，但不能侧向移动。ThisremarkablerelationshipwasfirstformulatedbySwissmathematicianLeonhardEulerandpublishedin1975.此著名公式是瑞士数学家欧拉于1975年提出的。ThecriticalloadissometimesreferredtoastheEulerloadortheEulerbucklingload.ThevalidityofEq.1.1hasbeendemonstratedconvincinglybynumeroustests.因此有时将临界荷载称为欧拉荷载或欧拉临界荷载。欧拉公式的有效性（正确性）已由许多试验充分证实。ItwillbeconvenienttorewriteEq.1.1asfollows:方程1.1可方便地写为2222222)/(rLEALEArLEIPcr(1.1a)whereAisthecross-sectionalareaandristheradiusofgyrationwithrespecttotheaxisofbuckling.TheratioL/ristheslendernessratioandisthemeasureofacompressionmember’sslenderness,withlargevaluescorrespondingtoslendermembers.式中A为截面面积，r为关于屈曲轴的回转半径，L/r为长细比，它是对受压构件细长程度的一种度量，该值越大，构件越细长。Ifthecriticalloadisdividedbythecross-sectionalarea,thecriticalbucklingstressisobtained:如果将屈曲荷载除以截面面积，便可得到以下屈曲应力：22)/(rLEAPFcrcr(1.2)Thisisthecompressivestressatwhichbucklingoccurabouttheaxiscorrespondingtor.这便是绕相应于r的轴发生屈曲时的压应力。SincebucklingwilltakeplaceassoonastheloadreachesthevaluebyEq.1.1,thecolumnwillbecomeunstableabouttheprincipleaxiscorrespondingtothelargestslendernessratio.Thisusuallymeanstheaxiswiththesmallermomentofinertia.由于一旦荷载达到式1.1之值，柱将在与最大长细比对应的主轴方向变得不稳定（失稳），通常该轴是惯性矩较小的轴。Thus,theminimummomento