鋼橋EUROCODE教學(xué)講解課件

同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong01.ClassificationofcrosssectionsClass1cross-sections歐洲的鋼結(jié)構(gòu)規(guī)范適用于所有鋼結(jié)構(gòu)Canformaplastichingewiththerotationcapacityrequiredfromplasticanalysiswithouteductionoftheresistance.Class2cross-sectionsCandeveloptheirplasticmomentresistance,buthavelimitedrotationcapacitybecauseoflocalbuckling.Class3cross-sectionsThestressintheextremecompressionfibreofthesteelmemberassuminganelasticdistributionofstressescanreachtheyieldstrength邊緣受壓應(yīng)變可以達(dá)到屈服應(yīng)力Localbucklingisliabletopreventdevelopmentoftheplasticmomentresistance.Class4cross-sectionsLocalbucklingwilloccurbeforetheattainmentofyieldstressinoneormorepartsofthecross-section.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong11.Classificationofcrosssections1.2.3表示截面分類。該圖的大致意思就是對于某一類截面，某一特定的應(yīng)力分布情況，寬厚比或長細(xì)比要滿足的要求同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong21.Classificationofcrosssections自由邊，即無支撐的邊緣同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong31.ClassificationofcrosssectionsTubular表示圓管截面。對于圓管截面，滿足d/t的條件之后，無需布置加勁肋同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong42.Shearlaginmemberdesign2.1Generalshearlag表示剪力滯Shearlaginflangesmaybeneglectedifb0

<Le/50

b0istakenastheflangeoutstandorhalfthewidthofaninternalelementLeisthelengthbetweenpointsofzerobendingmomentIfb0

≥Le/50theeffectsduetoshearlaginflangesshouldbeconsidered

Atserviceability

andfatiguelimitstateverifications,aneffectiveswidthmaybeused.

Atultimatelimitstateverifications,aneffectivearea

maybeused.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong52.Shearlaginmemberdesign2.2Shearlaginglobalanalysis

(calculationofinternalforcesandmoments,asimpleruletotakeshearlagintoaccountintheglobalanalysisofamulti-spanI-orbox-girder.)Theeffectivesflangewidth(oneachsideofthemainweb)isassumedtobeuniformoverthelengthofeachspan.Foreachspanofthegirder,thiseffectivesflangewidthbeffshouldbetakenasthelesserofthefullwidthb0(oneachsideofthemainweb)andL/8,whereListhespanofthegirder.Incaseofacantilevergirder,Lisequaltotwicethedistancefromthesupporttotheendofthecantilever.ThesameeffectiveswidthappliesforcalculatingtheinternalforcesandmomentsatSLSandatULS.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong62.Shearlaginmemberdesign2.3Elasticshearlaginsectionanalysis

(calculationofstressesatserviceabilityandfatiguelimitstates)beff=bb0Fig.2.5:Definitionofnotations(b0,Asl)同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong72.Shearlaginmemberdesign同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong82.Shearlaginmemberdesign同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong92.Shearlaginmemberdesign要記得大致趨勢Fig.2.8:Influenceoftheflangestiffeningratioontheelasticeffectiveswidth同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong102.ShearlaginmemberdesignFig.2.8:Influenceoftheflangestiffeningratioontheelasticeffectiveswidth同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong112.Shearlaginmemberdesign四次曲線同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong122.Shearlaginmemberdesign2.4Elasto-plasticshearlaginsectionanalysis(calculationofstressesatultimatelimitstate(ULS))UsetheSLSelasticshearlag(conservativeapproachwhichdoesnotconsidertheelasto-plasticredistributionatall),Usetheelastic-plasticshearlageffectsallowingforlimitedplasticstrainsAeff

=bkAc,eff

≥b

Ac,eff

bandkaretakenfromTable3.1.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong131.Shearlaginmemberdesign

彈塑性分析的剪力滯導(dǎo)致的有效寬度大，負(fù)彎矩區(qū)折減多

Fig.2.10:Influenceoftheconsideredlimitstateandofthebendingzoneontheeffectiveswidth(forthecase0=1)同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong142.Shearlaginmemberdesign2.5CombinedeffectsofshearlagandofplatebucklingatULSAeff

=bult

Ac,eff

Ac,eff

istheeffectivepareaofthecompressionflangeduetoplatebuckling

bult

istheeffectiveswidthfactorfortheeffectofshearlagattheultimatelimitstate,whichmaybetakenasbdeterminedfromTable3.1witha0replacedby同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong152.Shearlaginmemberdesign2.6ShearlaginflangesintensionTheexpressionsabovemayalsobeappliedforflangesintensioninwhichcaseAc,effshouldbereplacedbythegrossareaofthetensionflange.Aeff

=max{bult

A,bkA,b

A}

bandkaretakenfromTable3.1.bult

istheeffectiveswidthfactorfortheeffectofshearlagattheultimatelimitstate,whichmaybetakenasbdeterminedfromTable3.1witha0replacedby同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong163.Platebucklingeffectsduetodirectstresses3.1PlatebucklingFig.2.12:Post-criticalresponseofslenderplatesincompression同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong173.Platebucklingeffectsduetodirectstresses3.2BucklingbehaviourofplatesincompressionPlate-likebucklingbehaviourColumn-likebucklingbehaviourFig.2.19:Plate-likeandcolumn-likebehaviourofplatesincompression同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong183.Platebucklingeffectsduetodirectstresses3.2BucklingbehaviourofplatesincompressionColumn-likebucklingbehaviourForshorterplateswithlowaspectratios=a/b,

the"two-dimensional"plate-likebehaviourhaschangedinto"one-dimensional"column-likebehaviourthatdoesnotpossessanypostcriticalresistance,seeFig.2.19.意思是屈曲之后不再有承載力Forunstiffenedpanelsthisoccursataspectratio=a/bwellbelow1.0,Forlongitudinallystiffenedpanelswithpronouncedorthotropicpropertiessuchbehaviourmaystartatlargeraspectratios1.0(Fig.2.19c)).InEN1993-1-5platesincolumn-likebucklingaretreatedasunsupportedalongthelongitudinaledges.Thereforeitisevidentthatcriticalstressesforplate-likebucklingarealwayslargerthancriticalstressesforcolumn-likebuckling.Ultimateresistanceofshorterplatesdependsonbothtypesofbuckling,plate-likeaswellascolumn-like,andasuitableinterpolationbetweenbothtypesofbehaviourwasintroducedinEN1993-1-5designprocedures同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong193.Platebucklingeffectsduetodirectstresses正應(yīng)力3.4SimplifiedmethodsinpracticaldesignEffectivewidthmethodorreducedcross-sectionmethodReducedstressmethod.Fig.2.13:Basicideasofreducedcross-sectionmethodandreducedstressmethod同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong204.Effectivewidthmethod4.1RequirementsoftheeffectivewidthmethodtobeappliedThepanelsandthesub-panelsarerectangularornearlyrectangularwithflangesdeviatingfromthehorizontallinenotmorethan10°Thepanelsmaybeunstiffenedorstiffenedwithlongitudinalortransversestiffenersorinbothdirections.Unstiffenedopeningsandcut-outsshouldbesmall,withdiametersnotexceeding0.05b,wherebisthewidthoftheplateelement.Properlystiffenedholesmaybelarger,butEN1993-1-5doesnotprovideanydesignrules(seeforthedocumentsonlargewebopenings).Membersareofuniformcross-sections.Whenthethicknessofthepanelisnotconstant,thentheequivalentthicknessmaybetakenequaltothesmallestone.Flangeinducedwebbucklingispreventedbyselectingappropriatewebslenderness.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong214.Effectivewidthmethod4.2PrinciplesofeffectivewidthcalculationTheeffectivepwidthsofeachplateelementincompressionarecalculatedindependently.Basedontheseeffectivepwidthseffectivecross-sectionareaAeff,effectivesecondmomentofinertiaIeff

andeffectivesectionmodulusWeff

arecalculated(Fig.2.14,Fig.2.15,Fig.2.16).ForcompressionelementstheeffectivewidthsaredeterminedbytakingintoaccountcombinedeffectofshearlagandplatebucklingFortensionelementseffectiveswidthscomeonlyfromshearlageffects.Theeffectivecross-sectionisthentreatedasanequivalentClass3cross-section,assuminglinearelasticstrainandstressdistributionoverthereducedcross-section.Theultimateresistanceisreachedwiththeonsetofyieldinginthemostcompressedfibre.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong224.Effectivewidthmethod4.3Effectivecross-sectionFig.2.14:Effectivecross-section同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong234.Effectivewidthmethod4.3Effectivecross-sectionFig.2.15:Class4cross-sectionsinpurecompression同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong244.Effectivewidthmethod4.3Effectivecross-sectionFig.2.16:Class4cross-sectioninpurebending同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong254.Effectivewidthmethod4.3Effectivecross-sectionInnon-symmetricalcross-sectionssubjectedtoaxialforceNedTheshifteNoccurs(ofthecentroidG′oftheeffectiveareaAeffrelativetothecentreofgravityofthegrosscross-sectionG,seeFig.2.15).ThisshiftresultsinanadditionalbendingmomentM=eNNEdthatshouldbetakenintoaccountinthecross-sectionverificationShifteM(seeFig.2.16)ofthecentreofgravityduetopurebendingisnotincludedinthecalculationofM,evenifthecross-sectionissubjectedtothecombinationofaxialforceandbendingmoment.IfaxialforceandbendingmomentactsimultaneouslyThecalculationofeffectivepwidthsmaybebasedontheresultingstressdistribution.EN1993-1-5allowsasimplifiedapproachwhereAeff

iscalculatedonlyforstressescomingfrompurecompressionandWeff

onlyforstressescomingfrompurebending.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong264.Effectivewidthmethod4.4EffectivepwidthsbyiterativeprocedureGenerallythecalculationofeffectivepwidthsrequiresiterativeprocedureshowninFig.2.17thatendswhenthedifferencesbetweentwostepsaresufficientlysmall.Fig.2.17:Determinationofeffectivepareabyiterativeprocedure同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong274.Effectivewidthmethod4.4EffectivepwidthsbyiterativeprocedureIterativeprocedureThefirstiterationstartswiththestressdistributiononthegrosscross-sectionAG1.TheeffectiveareafortheseconditerationAeff2iscalculatedfromthisstressdistributionTheeffectiveareaforthethirditerationAeff3fromthestressesonAeff2.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong284.Effectivewidthmethod4.4EffectivepwidthsbyiterativeprocedureForI-sectionandboxcross-sectioninbendingEN1993-1-5allowsasimplifiedapproachthatendsintwosteps.Inthefirststepeffectivepwidthsinflanges(ifany)aredeterminedfromthestressdistributiononthegrosscross-section.Inthesecondstepthestressesaredeterminedonthecross-sectioncomposedoftheeffectivepareaofthecompressedflangesandthegrossareasofthewebandthetensionalflanges.Theeffectivepwidthinthewebiscalculatedbasedonthesestresses.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong294.Effectivewidthmethod4.4EffectivepwidthsbyiterativeprocedureWhendifferentstagesofconstructionhavetobeconsidered,whichisanormalcaseinthedesignofcompositebridges,thefollowingsimplifiedapproachproposedinaNotetoclause4.4(2)ofEN1993-1-5maybeused:inallrelevantconstructionstages(e.g.concretingoftheslab,normaluseofabridge)thestressesshouldbecalculatedonthegrosscross-sectionofthewebandeffectivecross-sectionoftheflanges(platebucklingand/orshearlag),whenrelevantthestressesfromdifferentconstructionstagesaresummedupandusedtodetermineasingleeffectivecross-sectionofthewebthatisusedforallconstructionstagesfinally,thestressesforindividualconstructionstagesarecalculatedoncorrespondingeffectivecross-sectionsandsummeduptogetthefinalcumulativestresses同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong30

4.Effectivewidthmethod

類似于混合梁的意思，指材料不同，無論橫橋向還是縱橋向4.5HybridgirdersFig.2.18:Assumedstressdistributioninahybridgirderwithh=460N/mm2/235N/mm2=1.96同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong314.Plate-likebuckling4.5HybridgirdersRequirementstoutilizethefullstrengthoftheflangesapartialplasticredistributionofstressesisallowedintheweb(seeFig.2.18)toassuresomeminimumductilityrequirementsintheweb,theeffectivepareaofthewebshouldbedeterminedbasedontheflangeyieldstrengthfyfandnotonthewebyieldstrengthfywtolimitthepartialplasticstressdistributionintheweb,fortheflangetowebyieldstrengthratiofhthefollowingupperlimitisrecommended:WhencalculatingthelocationofthecentreofgravityofeffectivepareaG',linearstressdistributioninthewebmaybeassumed,neglectingthelimitationofthewebstress.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong325.Plate-likebuckling5.1UnstiffenedplatesTheeffectivepwidthsbefforeffectiveareasAc,effoftheslenderplateelementsincompressionareobtainedwiththehelpoftheplatebucklingreductionfactor

=loc

同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong335.Plate-likebuckling5.1UnstiffenedplatesplatebucklingreductionfactorFig.2.20:Examplesofinternalandoutstandplateelementsofcrosssectionsinternalcompressionplateelements:同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong345.Plate-likebuckling5.1Unstiffenedplatesplatebucklingreductionfactorinternalcompressionplateelements

whereistheratioofstressesatbothedgesoftheplatewiththemaximumcompressionstressinthedenominatoroutstandcompressionplateelements同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong355.Plate-likebuckling5.1UnstiffenedplatesRelativeplateslendernesselasticcriticalplatebucklingstress

b istheappropriateplatewidthtistheplatethicknessE iselasticmodulusofsteel(E=210000N/mm2)ν isthePoissoncoefficientofsteel(ν=0.3)k

istheplatebucklingcoefficient,dependantonthestressratio

andboundaryconditions(forplateswith

α=a/b1.0

kisgiveninTable2.2andTable2.3).Forplateswith<1.0andsubjectedtouniformcompression,k

isgivenas

同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong365.Plate-likebuckling5.1UnstiffenedplatesEffectivepwidthandplatebucklingcoefficient同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong375.Plate-likebuckling5.1UnstiffenedplatesEffectivepwidthandplatebucklingcoefficient同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong385.Plate-likebuckling5.1UnstiffenedplatesIfmaximumcompressivestresscom,Edislessthanfy,effectivecross-sectionislargerandthisbeneficialeffectmaybeaccountedforbyreducingrelativeplateslenderness.Thisprocedureisconservativeandrequiresaniterativecalculation.Analternativeandmoreaccurateprocedureforinternalcompressionelementsforoutstandcompressionelements

同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong395.Plate-likebuckling5.2LongitudinallystiffenedplatesPlate-likebucklingoflongitudinallystiffenedplatesmeansaglobalbucklingofthewholepanelcomposedofaplateandstiffeners(Fig.2.21).Fig.2.21:Plate-likebucklingofastiffenedplate同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong405.Plate-likebuckling5.2LongitudinallystiffenedplatesWhensub-panelsofwidthbi

areslenderandsubjectedtolocalbuckling,theinteractionoflocalandglobalplatebucklingshouldbeconsidered.Thisinteractionistakenintoaccountbymodifiedrelativeplateslenderness:Fig.2.22:Stiffenedplateunderuniformcompression

同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong415.Plate-likebuckling5.2LongitudinallystiffenedplatesWhentheplateisunderstressgradientFig.2.23:Stiffenedwebplateinbending

同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong425.Plate-likebuckling5.2LongitudinallystiffenedplatesWhentheplateisunderstressgradient,effectivepwidthsandcontributingwidthsofthegrossareaaredeterminedaccordingtoTable4.1andTable4.2.

同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong435.Plate-likebuckling5.2LongitudinallystiffenedplatesElasticcriticalstressofstiffenedplateswiththreeormoreequallyspacedstiffenerswithaspectratio

=

a/b

0.5.Isl isthesecondmomentofareaofthewholestiffenedplateIp=bt3/(12(1-p2))=bt3/10.92 isthesecondmomentareaoftheplateitselfAslisthesumofthegrossareasofindividuallongitudinalstiffenersApisthegrossareaoftheplate.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong445.Plate-likebuckling5.2LongitudinallystiffenedplatesElasticcriticalstressofstiffenedplateswithonestiffenerinthecompressionzoneFig.2.24:Webplatewithasinglestiffenerincompression同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong455.Plate-likebuckling5.2LongitudinallystiffenedplatesElasticcriticalstressofstiffenedplateswithtwostiffenersinthecompressionzoneFig.2.25:Modelwithtwolongitudinalstiffenersincompressionzone

同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong465.Plate-likebuckling5.2LongitudinallystiffenedplatesElasticcriticalstressofstiffenedplateswithtwostiffenersinthecompressionzoneAboveprocedureforonestiffenerisrepeatedthreetimesforeachofthestiffenersconsideringtheotherstiffenerasarigidsupporttoawebforafictivelumpedstiffenerdefinedasfollows:thecross-sectionpropertiesarethesumofthepropertiesofindividualstiffenersthelumpedstiffenerislocatedinthepointofapplicationofthestressresultantsactinginindividualstiffenersmaybecalculatedwithThesmallestofthethreeresultsforcr,pistakenintoaccount.同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong476.Column-likebuckling6.1UnstiffenedplatesTheplateisconsideredcompletelyunsupportedalongthelongitudinaledgesThecorrespondingcolumnreductionfactorcisobtainedfromofEN1993-1-1byselectingabucklingcurvea(=0.21)同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong486.Column-likebuckling6.2Longitudinallystiffenedplates加勁是縱向加勁肋Therelativecolumnslendernessforstiffenedplatesisdefinedas:Asl,1isthegrosscross-sectionalareaofthestiffenerandadjacentpartsoftheplateAsl,1,effistheeffectivepcross-sectionalareaofthestiffenerandadjacentpartsoftheplatewithdueallowanceforplatebucklingofsub-panels同濟(jì)大學(xué)吳沖

TongjiUniversity,WuChong496.Column-likebuckling6.2LongitudinallystiffenedplatesTheelasticcriticalcolumnbucklingstresscr,cisdeterminedasthebucklingstresscr.sl

ofasinglestiffenerclosesttothepaneledgehavingthehighestcompressionstress:Asl,1,Isl,1aretheareaandthesecondmomentofareaofthegrosscross-sectionofthestiffenerandtheadjacentpartsoftheplate