欧标 EC4 教程05.docx

欧标 EC4 教程05.docx

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欧标EC4教程05

StructuralSteelworkEurocodesDevelopmentof

ATrans-NationalApproach2

Course:

Eurocode4

Lecture5:

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