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ShearConnectorsandStructuralAnalysis
Summary:
∙Thelecturegivesinformationonhowtodeterminatetheinternalforcesinacompositestructureatultimateandserviceabilitylimitstates.
∙Particularconcernisgiventomomentredistributionaspectsresultingfromplasticity,cracking,creepandshrinkagephenomenainthecompositecross-section.
∙Theevaluationofthedeflectionunderserviceloadsisalsoaddressed,togetherwithconcretecrackingandvibrationsaspects.
Pre-requisites:
∙Basicknowledgeonframeanalysisaspects(elasticity,plasticity,firstandsecondordereffects,momentredistribution,etc)
∙ThepreliminaryreadingofSSEDTA1“Eurocode3”lecturen°
4onframeanalysisisrecommended.
NotesforTutors:
Thismaterialcomprisestwo60-minutelectures.
Objectives:
Thestudentshould:
∙Havesomeknowledgeabouttheneedforandtheperformancesoftraditionalshearstuds(resistance,ductility).
∙Beabletoselectandapplytheavailableanalysisproceduresforcompositeframes(elastic,plastic)atultimatelimitstates.
∙Havesufficientknowledgetochecktheresistance,thedisplacements,theconcretecrackingintheslabsandthevibrationsofcompositestructuresatserviceabilitylimitstates.
References:
∙ESDEPlecturesoncompositestructures(Volume10)
Contents:
1.Shearconnectors3
1.1General3
1.1.1Theforcesappliedtoconnectors3
1.1.2Basicformsofconnection7
1.1.3Classificationoftheconnectors7
1.2Designresistanceofcommonshearconnectors9
1.2.1Headedstudsinsolidconcreteslabs9
1.2.2Headedstudswithprofiledsteelsheeting10
1.2.3Weldedangleconnectors11
1.2.4Otherconnectors12
2.Globalanalysisofacompositestructure13
2.1Globalanalysisforultimatelimitstates13
2.1.1Rigid-plasticglobalanalysis14
2.1.2Elasticglobalanalysis16
2.2Globalanalysisforservicelimitstates18
2.2.1Globalanalysis18
2.2.2Calculationofdeflections19
2.2.3Concretecracking21
2.2.4Vibrations22
3.Concludingsummary23
1.Shearconnectors
1.1General
1.1.1Theforcesappliedtoconnectors
Consideracompositebeam.Ifthereisnomechanicalconnectionbetweentheconcreteslabandthesteelbeam(theeffectofnaturalbondisignored)thenthetwomaterialswillsliderelativetooneanotherandthebendingstressesinthesectionwillbeasshowninFigure1a.Clearly,iflongitudinalshearresistanceisprovidedbysomeformofconnectionsothatthestressesattheinterfaceofthetwomaterialsarecoincident,thenthebeamactsasafullycompositesection.Ifitisassumedthatthefullyconnectedcompositebeamactsinanelasticwaythentheshearflow,T(shearforceperunitlength),betweentheconcreteslabandthesteelsectionmaybecalculatedfrom:
Eq.1-1
where
:
6.7.1.1
(2)
V:
istheappliedverticalshearforceatthepointconsidered;
I:
isthesecondmomentofareaoftheequivalentsection(seeLecture3);
S:
isthefirstmomentofareaofeithertheequivalentconcreteslaborthesteelsectionabouttheelasticneutralaxis.
Figure1Strain,bendingandshearstressesfor
a)noconnectionandb)fullconnection
Figure1alsoshowstheelasticshearstressdevelopedinthesectionfortheconditionsofbothfullandzeroconnection.
Itcanbeseen,fromtheaboveequation,thatthelongitudinalshearforcesthatmustbecarriedbytheconnectionwillvarydependingupontheverticalshearpresent.ThesolidlineofFigure2ashowsthedistributionoflongitudinalshear,theconnectorforcealongtheinterfacebetweenthesteelsectionandtheslab,alongonehalfofasimplysupporteduniformlyloadedbeamthathasarigidfullconnection.Itmustberemembered,however,thatthisappliesonlywhenthebeamisassumedtobebehavinginanelasticmanner.Astheultimatemomentofresistanceisreached,thesteelsectionwillyieldortheconcreteslabwillcrushandaplastichingewillformatthecriticalsection.ThebendingstressesinthebeamareasshownbythedashedlinesofFigure1;
thedistributionoflongitudinalshearinthebeamalsochangesandtheconnectorsclosetothehingearesubjecttohigherloads.ThedashedlineinFigure2ashowsthedistributionofshearforceclosetothefullyplasticfailureload.
Figure2Connectorloadsforrigidandflexibleconnectors
Inpractice,connectorsareneverfullyrigid,andthereisalwayssomeslipbetweentheslabandthesteelsection.Theflexibilityoftheconnectorsallowsmoreductilityandavariationinthedistributionoflongitudinalshearbetweenslabandsteelsection.ThecorrespondinglongitudinalshearforcedistributionpresentinacompositebeamwithflexibleconnectionisshowninFigure