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1、Geometricconstructionanalysisofstructure 2 1purposeofanalyzinggeometricconstructionofstructures stableandunstablestructuralsystemsinordertowithstandandtransmitload thegeometricshapeofastructuresystemisvariableunderloads thestructuralsystemcannotbeusedasastructure itshouldberealizedthatallphysicalbod
2、iesdeformwhensubjectedtoloads thedeformationinmostengineeringstructuresunderserviceconditionsaresosmallthattheireffectonthegeometricconstructionanalysisofthestructurescanbeneglected Forsimplicitywecallastructureasasystem Forinstance framedstructuresarenamedframedsystems Accordingtotheshapeandlocatio
3、noftheirmembers framedsystemscanbeclassifiedintotwocategories 1 GeometricallystablesystemUndertheactionoftheloads thesystemstillmaintainsitsshapeandremainsitslocationifthesmalldeformationsofthemembersareneglectedasshowninFig 2 1 2 GeometricallyunstablesystemUndertheactionoftheloads thesystemwillchan
4、geitsshapeanditslocationifthesmalldeformationsofthemembersareneglectedasshowninfig 2 2Correspondingtogeometricallystableandunstablesystem thereareinternallystableandunstablesystemsaswell Astructureisconsideredtobeinternallystable orrigid ifitmaintainsitsshapeandremainsarigidbodywhendetachedfromthesu
5、pports Conversely astructureistermedinternallyunstableifitcannotmaintainitsshapeandmayundergolargedisplacementsundersmalldisturbanceswhennotsupportedexternally Purposeofanalyzinggeometricconstructionofstructuresisasfollowing Toestimatewhetherornotasystemisgeometricallystable soastodeterminewhetherth
6、esystemcanbeusedasastructureornot Todiscussgeometricconstructionrulesofstablesystems 2 2theconceptofdegreesoffreedomandrestraints Intheanalyzinggeometricconstructionofstructures itisveryfeasibletoconsideronepartofthemembersorjointsofasystemasanobjectwhichpossessesdegreesoffreedom whereasotherpartoft
7、hemembersorjointsofthesystemasrestraintswhichrestrictsthemovementoftheobject Therelationshipofthesetwopartsarethenanalyzedandwhetherornotthesystemwillbedetermined Accordingly theconceptofdegreesoffreedomandrestraintsofasystemisdiscussedfirstofall 2 2 1thedegreesoffreedomThedegreesoffreedomofasystema
8、rethenumbersofindependentmovementswhicharerequiredtolocatethesystemfully obviously arigidbodyhasthreedegreesoffreedominaplanarcoordinatesystem sixdegreesoffreedominathreedimensionalcoordinatesystem e g thepositionofmemberABmaybedeterminedbythreeparametersXa Yaand 1 ThedegreesoffreedomofajointThemove
9、mentofapointinaplanarcoordinatesystemcandecomposedintotwotranslationsinanydifferentdirectionsi e apointpossessestwoindependentmovingstylesortwoindependentcoordinatesareneededtolocateitspositioninaplanarcoordinatesystem Soajointhastwodegreesoffreedominaplanarcoordinatesystem infigtheparametersXa Yawi
10、lllocatejointA n 2 2 ThedegreesoffreedomoffreedomofarigidbodyThemovementofarigidbodyinplanarcoordinatesystemcanbedecomposedtotwotranslationsinanydifferentdirectionsandarotationaboutsomepointinthesystem i e arigidbodypossessesthreeindependentmovingstylesorthreeindependentcoordinatesareneededtolocatei
11、tspositioninaplanarcoordinatesystem Therefore arigidbodyhasthreedegreesoffreedominaplanarcoordinatesystem thepositionofmemberABmaybedeterminedbythreeparametersXa Yaand n 3 2 2 2Restraintsthedevicesorconnectionswhichcanreducethedegreesoffreedomofasystemaredefinedasrestraints Thenumberofthedegreesoffr
12、eedomofasystemreducedbythedeviceorconnectionisnamedthenumberofitsrestraints Therearetwokindsofrestraints supportrestraintsandconnectingrestraintsbetweenrigidbodies 1 Supportrestraints TherollersupportcanrestrictthetranslationofjointAinthedirectionperpendiculartoitsmovingsurfacebutcannotpreventitstra
13、nslationalongitsmovingsurfaceandrotationaboutjointA i e onerollersupportreducesonedegreeoffreedomandisequivalenttoonerestraint n 2 ThehingedsupportcanrestrictthetranslationofjointAinverticarandhorizontaldirectionsbutcannotpreventtherotationaboutjointA i e onehingedsupportreducestwodegreesoffreedoman
14、disequivalenttotworestraints RestrictinverticalandhorizontaldirectionsandtherotationaboutAthreerestraints 2 Connectingrestraintsbetweenrigidbodieswewillpaymoreattentiontoconnectingrestraintsbetweentworigidbodies Onerigidbodyhasthreedegreesoffreedomandtwoindependentrigidbodieshavesixdegreesoffreedomi
15、naplanarcoordinatesystem whenconnectingthemtogether theirdegreesoffreedomwouldbereduced Nowwewilldiscusstheequivalentrestraintsofafewkindsofcommonlyusedconnections n 1 n 0 Link thetwoindependentrigidbodiesABandDChavethreerelativedegreesoffreedomwithrespecttoeachother whentheyareconnectedbylinkEFwhic
16、hisabarwithhingesatitsends therelativebetweenthetworigidbodiesinthedirectionofthelinkisrestricted i e oneofthedegreeoffreedombetweenthemisremoved Therefore onelinkisequivalenttoonerestraint SimplehingeOnlyonerelativedegreeoffreedomBetweenthemisexisted i e therelativerotationaboutA there onesimplehinge 2restraint SimplerigidjointThereexistnorelativedegreeoffreedomBetweenthemintheplane threeofdegreeSo onesimplerigidjoint 3restraints Bysimilaranalysis ahingeconnectingthreerigidbodiesmakesthesystemr