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1、52EffectiveLengthofCompressionMembers52.1Introduction52.2IsolatedColumns52.3FramedColumns—AlignmentChartMethodAlignmentChartMethod•RequirementsforBracedFrames•SimplifiedEquations.toAlignmentCharts52.4ModificationstoAlignmentChartsDifferentRestrainingGirderEndConditions•Considerati
2、onofPartialColumnBaseFixity•ColumnsRestrainedbyTaperedRectangularGirders52.5FramedColumns—AlternativeMethodsLeMessurierMethod•LuiMethod•RemarksLianDuan52.6CrossingFrameSystemCaliforniaDepartment52.7LatticedandBuilt-UpMembersofTransportationLatticedMembers•Built-UpMembersWai-FahC
3、hen52.8TaperedColumnsPurdueUniversity52.9Summary52.1Introduction*TheconceptofeffectivelengthfactororKfactorplaysanimportantroleincompressionmemberdesign.AlthoughgreateffortshavebeenmadeinthepastyearstoeliminatetheKfactorincolumndesign,Kfactorsarestillpopularlyusedinpracticeforro
4、utinedesign[1].Mathematically,theeffectivelengthfactorortheelasticKfactorisdefinedas2PpEIK==e(52.1)2PLPcrcrwherePeisEulerload,elasticbucklingloadofapin-endedcolumn,Pcriselasticbucklingloadofanend-restrainedframedcolumn,Eismodulusofelasticity,Iismomentofinertiaintheflexuralbuckling
5、plane,andLisunsupportedlengthofcolumn.*MuchofthematerialofthischapterwastakenfromDuan,L.andChen,W.F.,Chapter17:Effectivelengthfactorsofcompressionmembers,inHandbookofStructuralEngineering,Chen,W.F.,Ed.,CRCPress,BocaRaton,FL,1997.©2000byCRCPressLLCFIGURE52.1Isolatedcolumns.(a)End
6、-restrainedcolumns;(b)pin-endedcolumns.Physically,theKfactorisafactorthat,whenmultipliedbyactuallengthoftheend-restrainedcolumn(Figure52.1a),givesthelengthofanequivalentpin-endedcolumn(Figure52.1b)whosebucklingloadisthesameasthatoftheend-restrainedcolumn.Itfollowsthattheeffectiv
7、elengthKLofanend-restrainedcolumnisthelengthbetweenadjacentinflectionpointsofitspureflexuralbucklingshape.Practically,designspecificationsprovidetheresistanceequationsforpin-endedcolumns,whiletheresistanceofframedcolumnscanbeestimatedthroughtheKfactortothepin-endedcolumnstrengthequ
8、ations.TheoreticalKfactorisdeterminedfromanelas
