Lecture 15.docx

Lecture 15.docx

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Lecture15

StructuralSteelworkEurocodesDevelopmentof

ATrans-nationalApproach

Course:

Eurocode3

Module5:

Structuraljoints

Lecture15:

Generalitiesaboutstructuraljoints

Summary:

∙Traditionallystructuraljointsareconsideredasrigidorpinned.

∙Anintermediatebehaviourmaybeconsidered:

jointsarethensaid“semi-rigid”.

∙Theconceptofsemi-rigidityisintroduced.

∙Themeritsofthisconceptarediscussed.

∙Aparallelbetweenmembersectionsandjointsinthesemi-rigidapproachisthenestablished.

∙Inastructuralframe,fourtypesofjointconfigurationshavetobedistinguished:

beam-tocolumnjoints,beamsplices,columnsplicesandcolumnbases

Thewordsjointsandconnectionshavetobeclearlydifferentiated.

Foreachtypeofjointconfiguration,thepossiblesourcesofdeformabilityarespecified.

∙Stiffness,strengthandductilityclassesofstructuraljointsareintroduced.

∙Theprocessofjointmodellingforstructuralframeanalysisisdescribed.

Pre-requisites:

Basicknowledgeaboutframeanalysisanddesign.

NotesforTutors:

Thismaterialcomprisesone90minuteslecture.

Objectives:

Thestudentshould:

∙Knowthatjointsmaybeconsideredaspinned,semi-rigidorrigid.

∙Knowhowtoprofitfromthenewsemi-rigidconcept

∙Understandphysicallyhowstructuraljointsbehaveanddeform.

∙Beabletoclassifyjoints

∙Beabletoselecttheappropriatejointmodelforframeanalysis

References:

∙RevisedAnnexJofEurocode3,"JointsinBuildingFrames",Amendment2toENV1993-1-1,1998

∙Framedesignincludingjointbehaviour.User’smanualpublishedbytheEuropeanUnion,ReportEUR18563EN,OfficeforOfficialPublications,Luxembourg,1998（ISBN92-828-4904-X）

Contents

1.Aconsistentapproachforstructuraljoints

2.Themeritsoftheconsistentapproachforstructuraljoints

3.Aparallelbetweenmembersectionsandjoints

4.Definitionsofjointconfiguration,jointandconnection

5.Sourcesofjointdeformability

5.1.Beam-to-columnjoints

5.2.Beamsplicesandcolumnsplices

5.3.Beam-to-beamjoints

5.4.Columnbases

6.Jointclassification

6.1.General

6.2.Stiffnessclassification

6.3.Strengthclassification

6.4.Boundariesforclassification

6.5.Ductilityclasses

7.Jointmodelling

7.1.General

7.2.Modellingandsourcesofjointdeformability

7.3.SimplifiedmodellingaccordingtoEurocode3

7.4.Concentrationofthejointdeformability

1.Aconsistentapproachforstructuraljoints

Therotationalbehaviourofactualjointsiswellrecognisedasbeingoftenintermediatebetweenthetwoextremesituations,i.e.rigidorpinned.

Laterinthislecture,thedifferencebetweenjointsandconnectionswillbeintroduced.Forthetimebeing,examplesofjointsbetweenonebeamandonecolumnonlywillbeused.

Considernowthebendingmomentsandtherelatedrotationsatajoint（Figure1）:

（a）Rigidjoint（b）Pinnedjoint（c）Semi-rigidjoint

Figure1Classificationofjointsaccordingtostiffness

Whenallthedifferentpartsinthejointaresufficientlystiff（i.e.ideallyinfinitelystiff）,thejointisrigid,andthereisnodifferencebetweentherespectiverotationsattheendsofthemembersconnectedatthisjoint（Figure1.a）.Thejointexperiencesasingleglobalrigid-bodyrotationwhichisthenodalrotationinthecommonlyusedanalysismethodsforframedstructures.

Shouldthejointbewithoutanystiffness,thenthebeamwillbehavejustassimplysupportedwhateverthebehaviouroftheotherconnectedmember（s）（Figure1.b）.Thisisapinnedjoint.

Forintermediatecases（nonzeroandnoninfinitestiffness）,thetransmittedmomentwillresultintherebeingadifferencebetweentheabsoluterotationsofthetwoconnectedmembers（Figure1.c）.Thejointissemi-rigidinthesecases.

Thesimplestmeansforrepresentingtheconceptisarotational（spiral）springbetweentheendsofthetwoconnectedmembers.TherotationalstiffnessSofthisspringistheparameterthatlinksthetransmittedmomentMjtotherelativerotation,whichisthedifferencebetweentheabsoluterotationsofthetwoconnectedmembers.

WhenthisrotationalstiffnessSiszero,orwhenitisrelativelysmall,thejointfallsbackintothepinnedjointclass.Incontrast,whentherotationalstiffnessSisinfinite,orwhenitisrelativelyhigh,thejointfallsintotherigidjointclass.Inalltheintermediatecases,thejointbelongstothesemi-rigidjointclass.

Forsemi-rigidjointstheloadswillresultinbothabendingmomentMjandarelativerotationbetweentheconnectedmembers.Themomentandtherelativerotationarerelatedthroughaconstitutivelawwhichdependsonthejointproperties.ThisisillustratedinFigure2,where,forthesakeofsimplicity,theglobalanalysisisassumedtobeperformedwithlinearelasticassumptions.

Attheglobalanalysisstage,theeffectofhavingsemi-rigidjointsinsteadofrigidorpinnedjointsistomodifynotonlythedisplacements,butalsothedistributionandmagnitudeoftheinternalforcesthroughoutthestructure.

Asanexample,thebendingmomentdiagramsinafixed-basesimpleportalframesubjectedtoauniformlydistributedloadaregiveninFigure3fortwosituations,wherethebeam-to-columnjointsarerespectivelyeitherpinnedorsemi-rigid.Thesamekindofconsiderationholdsfordeflections.

（a）Rigidjoint（b）Pinnedjoint（c）Semi-rigidjoint

（=0）（Mj=0）（Mjand0）

Figure2Modellingofjoints（caseofelasticglobalanalysis）

（a）Pinnedjoints（b）Semi-rigidjoints

Figure3Elasticdistributionofbendingmomentsinasimpleportalframe

2.Themeritsoftheconsistentapproachforstructuraljoints

BoththeEurocode3requirementsandthedesiretomodelthebehaviourofthestructureinamorerealisticwayleadstotheconsiderationofthesemi-rigidbehaviourwhennecessary.

ManydesignerswouldstopatthatbasicinterpretationofEurocode3andhencewouldbereluctanttoconfronttheimpliedadditionalcomputationaleffortinvolved.Obviouslyacrudewaytodealwiththisnewburdenwillbeforthemtodesignjointsthatwillactuallycontinuetobeclassifiedasbeingeitherpinnedorfullyrigid.Howeversuchpropertieswillhavetobeprovenattheendofthedesignprocessand,inaddition,suchjointswillcertainlybefoundtobeuneconomicalinanumberofsituations.

ItshouldbenotedthattheconceptofrigidandpinnedjointsstillexistsinEurocode3.Itisacceptedthatajointwhichisalmostrigid,oralmostpinned,maystillbeconsideredasbeingtrulyrigidortrulypinnedinthedesignprocess.Howtojudgewhetherajointcanbeconsideredasrigid,semi-rigidorpinneddependsonthecomparisonbetweenthejointstiffnessandthebeamstiffness,whichdependsonthesecondmomentofareaandlengthofthebeam.

Thedesignerisstronglyencouragedtogobeyondthis"allornothing"attitude.Actuallyitisimportanttoconsiderthebenefitstobegainedfromthesemi-rigidbehaviourofjoints.Thosebenefitscanbebroughtintwoways:

1.Thedesignerdecidestocontinuewiththepracticeofassuming-sometimeserroneously-thatjointsareeitherpinnedorfullyrigid.However,Eurocode3requiresthatproperconsiderationbegiventotheinfluencethattheactualbehaviourofthejointshasontheglobalbehaviourofthestructure,i.e.ontheprecisionwithwhichthedistributionofforcesandmomentsandthedisplacementshavebeendetermined.Thismaynotprovetobeeasywhenthejointsaredesignedatalatestageinthedesignprocesssincesomeiterationsbetweenglobalanalysisanddesigncheckingmayberequired.Nevertheless,thefollowingsituationscanbeforeseen:

∙Sothatajointcanbeassumedtoberigid,itiscommonpracticetointroducewebstiffenersinthecolumn.Eurocode3nowprovidesthemeanstocheckwhethersuchstiffenersarereallynecessaryforthejointtobebothrigidandhavesufficientresistance.Therearepracticalcaseswheretheyarenotneeded,thuspermittingtheadoptionofamoreeconomicaljointdesign.

∙Whenjointsassumedtobepinnedarelaterfoundtohavefairlysignificantstiffness（i.e.tobesemi-rigid）,thedesignermaybeinapositiontoreducebeamsizes.Thisissimplybecausethemomentscarriedbythejointsreducethespanmomentsinthebeams.

2.Thedesignerdecidestogiveconsideration,atthepreliminarydesignstage,notonlytothepropertiesofthemembersbutalsotothoseofthejoints.Itmaybeshownthatthisnewapproachisnotatallincompatiblewiththesometimescustomaryseparationofthedesigntasksbetweenthosewhohavetheresponsibilityforconceivingthestructureandcarryingouttheglobalanalysisandthosewhohavetheresponsibilityfordesigningthejoints.Indeed,bothtasksareveryoftenperformedbydifferentpeople,orindeed,bydifferentcompanies,dependingonnationalorlocalindustrialhabits.Adoptingthisnovelearlyconsiderationofjointsinthedesignprocessrequiresagoodunderstandingofthebalancebetween,ontheonehand,thecostsandthecomplexityofjointsand,ontheotherhand,theoptimisationofthestructuralbehaviourandperformancethroughthemoreaccurateconsiderationofjointbehaviourforthedesignasawhole.Twoexamplesaregiventoillustratethis:

∙Itwasmentionedpreviouslythatitispossibleinsomesituationstoeliminatecolumnwebstiffenersandthereforetoreducecosts.Despitethereductioninitsstiffnessand,possibly,initsstrength,thejointcanstillbeconsideredtoberigidandbefoundtohavesufficientstrength.Thisisshowntobepossibleforindustrialportalframeswithrafter-to-columnhaunchjoints,inparticular,butothercasescanbeenvisaged.