- I7.9-RotatIoncapacItyofplastIc hIngesandallowabledegree ofmomentredIstrIbutIon by R.Eligehausen P.Langer UniversitatStuttgart Stuttgart,January12,1987 - !7.10-1Introduction AccordingtoMe78themaximummomentsofcontinousbeams calculatedaccordingtothetheoryofelasticitycanbere-distributedwithoutcheckoftheductilityrequirements,if theconditionofequilibriumisfulfilledandifthere-ductionisnotlessthangivenbyeqn .(1) betanC12toC35 betonC40toC50 d=0.44+1.25x/d~ 0 . 75 6 =0.56+1 . 25x/d~ 0 . 75 (1) Eqn.(1)isvalidf o rbeamswithaslendernesslId~ 20.It wasdeducedbyMacchi/1/,usingtheallowableplasticrotation capacityaccordingtoMe78,Fig.8. 2 . Thestructuralanalysiscanalsobeperformedbynon-linear methods.Inthiscaseit mustbeverified,thatthenecessary plasticrotationisnotlargerthantheallowablevalueaccording toFig.8.2ofMC78. ThisfigurewasproposedbySiviero12/ .Heplottedtherotation capacitymeasuredinabout350testsonbeamsperformedapproxi-matelybetween1960and1970asafunctionoftheratioxld (Fig.1).Theallowableplasticrotation- showninFig.1as dottedline- wasevaluatedbyastatisticalanalysisofthedata andshallrepresentthe5%-fractileofthetestresults.The rotationcapacityincreasessignificantlywithdecreasingratiox/d. Thisindicatesthatinthetestsveryductilebarswereused. InTable1somecharacteristicvaluesofthetestsevaluatedby Sivieroaresummarised .Itcanbeseenthattheusedreinforcing steelhadaratherlargerelationshiprupturestrength ~ to c yieldstressf(ft / f~ 1.4to1.8).Thecorrespondingunit yy~elongationAGmusthavebeenratherlargeaswell(AG >10\). - I7.11-Furthermoreinmanytestsbarswithratherpoorbondbehavior (smoothbarsordeformedbarswitharelatedribarealess thanrequiredbyMe7mwereused.Inaddition,theheightof thetestspecimenswasrelativelysmall.Allthesefactors increasetherotationcapacity. InFig.2thestress-strainrelationshipofreinforcingbars usedtodayinGermanyareshown.Thesecurveswerefoundby evaluatingalargenumberofqualitycontroltestsfromseveral steelmills/16/.Theupperandlowerlinesareapproximate limitsofthescatterexpectedinpractice.Itcanbeseenthat modernreinforcingsteelislessductilethanthesteelemployed inthetests.Thisisespeciallytrueforcold-workedbarsand forweldedwiremeshproducedfromcoldworkedwires.Further-moremoderndeformedbarshaveaverygoodbondbehavior.Also theheightofrealbeamswilloftenbelargerthantheheight ofthetestbeams. ForthesereasonstheplasticrotationcapacitygiveninMe78 maynotalwaysbereachedwhenusingmodern- especiallycold-worked- reinforcement.ThisisindicatedinFig.3whichshows therotationcapacity(elasticandplasticcomponents)ofbeams ontwosupportsreinforcedwithcold-workeddeformedbarsasa functionofthepercentageofreinforcement~ =As/b'daccording totests/17/andcalculation(seeSection2). Thetypicallyroof-shapedcurvehasamaximumrotationcapacity atacriticalpercentageofreinforcement~ c r i t ~ c r i t depends onthedimensionsofthesection,thematerialbehaviorandthe confinement.Inthepresentcase~ c r i t amountstoabout0.42%. For~ ~ ~ c r i t thebeamfailsduetoruptureofthereinforcement, i.e.theductilityofthereinforcingbarsisfullyutilized. - I7 . 12-Therotationcapacitydecreasesrapidlywithdecreasingper-centageofreinforcement,becauseonlyfewcracksareformed andthecontributionofconcretebetweencracksissignificant. For thefailureofthebeamisduetocrushingofthe concreteinthecompressionzone.Thesteelstrainsaresmaller thanthevalueswhichcanbesustainedbythebars . Thesetestsdemonstratethatforsmallpercentagesofreinforce-menttherotationcapacityofplastichingesisgovernedbythe ductilityofthereinforcement. Theanalyticalmodelsofplastichingesproposedsofarte.g./19,19/ : predictthebehaviorofthesehingesqualitativelyrat,er ever,thequantitativeagreementbetweentestresultsandcalcu-lationisnottoowell.Thereforeananalyticalmodelforplastic hingeswasdevelopedwhichisbasedontheworkin/18,19/.Inthe followingonlyabriefdescriptionofthestudyisgiven,for detailssee/20/ . 2AnalyticalModel Basedonthegivendimensionsofthecrosssection(concreteand reinforcement)andtheassumedstress-strainrelationshipsof steelandconcrete,themoment-curvaturerelationshiporthe tensileforce-curvaturerelationship,respectively,arecalcu-lated(Fig .4b),assumingplainesectionsremainplaine.Thedis-tributionofmomentsalongthebeamiscalculatedtakinginto accountthewidthoftheloadingplate.Theloadisincreased untiltheultimatemomentpreviouslycalculatedisreached.In staticallyindeterminatestructuresanstaticallydeterminate beamwithalengthequaltothedistancebetweentwoadjacent pointsofzeromomentiscut oftherealsystem.Ifshear cracksmustbeexpected,theshiftingofthetensileforce comparedtotheM/z-line(M= Moment,Z= leverarm)(trussana-logy)1stakenintoaccountanangleoftheinclined compressionstrutsaccordingtoRef./18/.Fromthetensileforce distributionandthetensileforce-curvaturerelationship thecurvatureinthecracksisreached(Fig.4a).Thecrack distanceiscalculatedaccordingto/21 / . Thecontributionofconcretebetweencracksiscalculatedfor everybeamsectionbetweentwocrac'ksbymeansofaniterative solutionofthedifferentialequationofbond,usingamodified versionoftheprogramdescribedinRef ./22/.OnthebaSisof thecalculatedsteelstraindistribution,thedistributionof curvaturebetweenthecracksisderivedbyusingthedistance ofthetensilereinforcementtotheneutralaxis(Fig.4a). Integrationofthesecurvaturesoverthebeamlengthyields therotationcapacityofthebeam.Theplasticrotationisde-finedasthedifferencebetweentherotationatultimateload andataloadcausingyieldingofthereinforcementatthe pointofmaximummoment(seeFig.4a). Themathematicalmodelcanonlyyieldreliableresultsifthe behaviourofthematerialisdescribedveryaccurately.Therefore thestress-strainrelationshipofthereinforcingsteelisdes-cribedbyapolygon(withupto30paints,whichallowsavery closerepresentationoftherealbehaviour(Flg.5.Thestress-strainrelationshipoftheconcreteisformulatedasproposedin Ref ./23/.Thismodelwhichconsistsofaparabolaandatrilinear continuation(Fig.6)takesintoaccounttheinfluencesofconfine-mentbystirrupsonthp.strength01andcorrespondingstrainfl,the descendingbranchofthestress-strainrelationship(defined by~ 1 / E 2 andoJ/EJ)andontheresidualstrength~ 4 Thevalues forthesecharacteristicparametersarechosenaccordingto Ref./23/fortheproblemonhand.Thebondbehaviorisdes-cribedbythebondstress-sliprelationshipsshowninFig.7 whicharebasedonthemodelproposedinRef./24/takinginto accountthetestresultsgiveninRef./25/.Fig.7isvalidfor aconcretecompressionstrengthfc=30N/mm2Forothervalues offthebondstress- sliprelationshipsarevariedaccording c toRef./24/. I7.14-Tocheckthevalidityoftheassumptions,thepredictedres-ponseofbeamswascomparedwithavailabletestresults.In Fig.8thecalculatedandmeasureddistributionoftheresidual steelelongationafterunloadingfrommaximumloadisplotted. Notethatintheexperiment(Ref./17/)thecrackspacingvaries, whileinthecalculationaconstantvaluewasassumed.Fig.9 showsthepredictedrotationcapacityof70beamsasafunction ofthemeasuredvalue.Thedatapointsscatteraroundthe45-degreelineforperfectagreement.Thecoefficientofvariation isonly17\.InFig.3thepredictedandmeasuredrotation capacitiesofotherwiseidenticalbeamsareplottedasafunction ofthepercentageofreinforcement.Thetypicalbehaviorfound inthetestsiscapturedquitewellbythecalculation. Fromthesefiguresitcanbeconcludedthattheproposedanaly-ticalmodelissufficientlyforpractical3ParameterStudies 3.1Influenceofstress-strainrelationshipofsteel Fig.10showsschematicallytheinfluenceofthestressstrain curveontherotationcapacityofasinglespanreinforcedconcrete beamloadedinmidspan(Fig.lOa). InFig.lOb,whichshowsthemomentdistributionalongthebeam, theinfluenceoftheratioft/fyontherotationcapacityisin-vestigated.Itisassumedthatthestrengthofthesteelandthe unitelongationareconstant.Undertheseconditionsthemaximum sectioncurvatureandtheultimatemomentarealmostconstant. Theplasticrotationcapacityisapproximatelyproportionalto thelengthoftheplasticzone.Becausethislengthincreaseswith increasingratioft/fy'therotationcapacityalsoincreasescon-siderablywithincreasingratioft/fy. - I7.15-InFig.IOc,whichshowsthedistributionofsectioncurvature alongthebeamlength,aconstantratioft/fy'butdifferent valuesfortheunitelongationareassumed.Inthiscasethe lengthoftheplasticzoneisalmostconstant.However,with increasingunitelongationthemaximumsectioncurvaturein-creases,resultinginincreasingrotationcapacity. ThereinforcementpercentageofthebeaminvestigatedinFig.10 isrelativelysmallandthereforethebeamwillfailbyrupture ofthesteel.Forhigherreinforcementratiosleadingtoaconcrete failuretherotationcapacitywillalsoincreasewithin-creasingratioft/fy'butwillalmostbeindependentofthe unitelongation. Inpracticeforacertaintypeofreinforcement(e.g.coldworked bars)theunitelongationtncreaseswithincreasingratioft/fy (compareFig.2).ThecombinedeffectisinvestigatedinFig.11 usingthesamebeamasinFig.10.Plottedistheplasticrotation capacityasafunctionoftheshapeofthestress-straindiagram. Theassumedstress-strainrelationships(Fig.lla)coverapproxi-matelytherangevalidfor (nofailureinthewelds). weldedwirefabricproducedinGermany Theplastic beamreinforcedwiththemoreductile largerthanforsteel3(Fig.lIb). rotationcapacity steel1isabout3 ofthe times Fromthisfigurethesignificantinfluenceofthebondbetween barsandconcreteontheplasticrotationcanalsobeseen.While thedottedlineisvalidfortheso-callednakedstate(nobond betweencracks),thefulllinetakestheinfluenceofbond(tension stiffeningduetocontributionofconcretebetweencracks)into account.Underotherwiseconstantconditions,theplasticro-tationcapacityisreducedtoabout40%duetobondcompared tothe"nakedstate".Theinfluenceofthebondissmallerfor - I7.16-higherpercentagesofreinforcement,butstillsignificant. Thiscanbee xplainedbythefact,thatforsteelstrains smalldifferencesinforcescausedbythebondaction resultinlargechangesofsteelstrain.Theinfluenceof bondisespeciallypronouncedforsteelwithalowratio ft/fy. Theimpo rtanceofthesteelbehavioronther o tationcapacity hasalsobee npointedoutin/ 18,19/. InFig.12theplasticrotationcapacityaccordingtoCEBis comparedwiththetheoreticalvaluesusingtwodifferenttypes ofreinforcement:heattreatedbarsandweldedwiremeshproduced fromcold-workedTheaverage relatlonshios giveninFig.2(heattreatedsteelft/fy=1,18,eg =8\, weldedwiremesh:ft/fy=1,06,tg=3 wereassumed .The calculatedvaluesarevalidforthefollowingparameters: - Reinforcedconcretebeamorslab(h=30cm,l/h=6)with tensionandshearreinforcement,butwithoutcompressionre-inforcement .Itwasassumed,thatsufficientshearreinforce-mentwasprovidedtopreventashearfailure. - ConcretestrengthC40.Aparabolic-rectangularstress-strain diagramaccordingtoCEB,butwithamaximumstrainof5\0 wasassumed . - Bondbehavioraccordingto/24/,however,thebondstrengthwas reducedtoSO\ofthevaluesgivenin/24/tomodelthe situationoverthesupport(badbondcondition). ""' Itcanbeseenthatforheattreatedsteelandvaluesx/d> O.15 thecalculatedplasticrotationcapacitiesagreefairlywellwith ---theCEB-curveihowever,forvaluesx / dLO.IS,thecalculated valuesdecreaseduetoruptureofthesteel.Forweldedwiremesh thecalculatedrotationcapacitiesaresmalleroverthefull rangeofx/dthantheCEBcurve.Thisiscausedbythesmallratio ft/fyandthesmallunitelongationoftheemployedreinforcement. -17.17-InFig_12,theresultsofthreetestsonslabsreinforced withweldedwiremesh/26/areplottedaswell.Thetest resultsagreeratherwellwiththetheoreticalvalues. 3.2Beamorslabslenderness Ifthespaniskeptconstant,theslendernessincreaseswith decreasingheight.Becausethemaximumsectioncurvaturein-creaseswithdecreasingheight,therotationcapacityofthe specimenincreaseswithdecreasingheightorincreasingslender-ness,respectively(Fig.13). Whenincreasingthespan(heightconstant),thelengthofthe plasticzoneincreases(Fig.14)andthereforetheplastic rotationcapacityincreasesaswell(Fig.15).Whendoubling theslenderness,therotationcapacityincreasesapproximately by50%. In1171theinfluenceofthebeamslendernessontherotation capacitywasinvestigatedinexperimentsbyvaryingthespan. TheresultsareplottedinFig.16.Theplasticrotationin-creaseswithincreasingslenderness.However,theincreaseis lessthanshowninFig.15.Thismightbeduetothedifferent reinforcementemployed:Thecalculationisvalidforwelded wiremesh(ft/fy =1.06),whileinthetestsratherductile bars wereused. 4ProposalfortherevisionoftheCEB-FIPModelCode AsshowninSection3,theplastiCrotationcapacityissig-nificantlyinfluencedbythestress-strainrelationshipof thetensionreinforcement.Whiletheallowableplasticrotation giveninMC78isvalidonlyforratherductilesteel,the rotationcapacitymaybemuchlessforlessductilereinforce-ment.Totakethisinfluenceintoaccount,itisproposedto classifythereinforcementasfollows: -17.18-

Type1,fst/fyt1.10 E;;6\ g Type2,1.05:!:fst/fyt20). Thepossibledegreeofmomentredistributioncrisgivenby eqn.(5). :>0,44+1,25 0,70forcontinousbeamsandbraced framesreinforcedwithsteel type1 0,85forcontinousbeamsandbraced(5) framesreinforcedwithsteel type2 0,90forswayframes Eqn.(5)isvalidforconcreteC12toC35.It mustbechecked, whetheritsvaliditycanbeextendedto50. AccordingtoaproposalofCom.VII,theconditionsgivenin eqns.(2)and(3)shallalsobeappliedtoprestressingsteel. Ingeneral,theductilityofprestressingsteelisratherlow andthereforethissteelwouldoftenbeclassifiedastype2. Inthiscasethepossibledegreeofmomentredistributionof prestressedbeamswi 11be1 imi tedtoJ-?: 0,85. - I7.20-Itseemsreasonabletolimitthepossibledegreeofmomentre-distributionalsobyFig.17bwheninthestaticanalysisof linearelementsthetheoryofplasticityisused. Intheregionofsplicesbyoverlapping,bymechanicalde-vices,orbyweldingthesteelstrainsarerathersmall.Further-morethestrengthandtheductilityofthebarsmightbere-ducedbywelding.Thereforeitisproposedthatsplicingofthe reinforcementisnotallowedintheregionswhereplastichinges areanticipatedintheanalysis. Becausethetypeofsteelhasasignificantinfluenceonthe allowabledegreeofmomentredistribution,itmustbepossible todistinguishtype1andtype2steelclearlyandeasilyon site,forinstancebydifferentribpatterns. 5Openproblems Inthefollowingsomeproblemswhichshouldbeinvestigatedbya commonresearcharelisted: alTheinvestigationsdescribedinSection3arevalidforrein-forcedconcrete.Inprestressedconcretecrackingmightoccurat ratherahighfractionoftheultimateload.Furthermorethe employedprestressingsteelmightberatherbrittle.!'herefore it mustbecheckedwhetherFig.17bcanalsobeappliedto prestressedconcrete. blFig.17aisvalidforspecimenwithnooronlynominalconfine-mentoftheconcreteinthecompressionzone.Withincreasing degreeofconfinementbycloselyspacedstirrupstherotation capacitycanbeimprovedconsiderably,providedatsufficiently highpercentagesofreinforcementthefailureiscausedbya failureofthecompressedconcrete.Itshouldbecheckedhow thisSignificantinfluencecanbetakenintoaccountinthe codeprovisions. -17.21-c}InFig.17aitisassumedthatfailureiscausedby bendingandnotbyshearforces.In127,28 /thei n-fluenceoftheshearforceontherotationcapacityof plastichingeswasstudied.Itwasshownthatincases wheretheshearstrengthwasbasedonthestrengthofthe shearreinforcementandaconcretecontribution,inaccordanc e withDutchprovision,therotationcapacitywasrathe rsmall, becausethe"bending"failureoccurredsoonaftertheyield stressofthemainreinforcementwasreached.Similarre-sultswerefoundin129/whentheshearfailureoccurre dbe-forereachingthefullbendingstrength.Itmustbechecked, whethertheprovisionsgivenintheModelCodefordimension-ingtheshearreinforcementaresuitabletoensureasuffi-cientlyhighshearstrengthtodeve lopthefullbending capacityofthebeam. d)Intheultimatelimitstatetheforcescausedbyimposed deformationsarereducedtoalmostzero.However,theim-poseddeformationsconcentrateintheplastichingeand reducetheplasticrotation forredistribution ofmomentscausedbyloads.Thereforeithastobeclari-fiedhowtheeffectofimposeddeformationsontheinelastic behaviorofstructuresshallbetakenintoaccountinthe analysis. e)Plastichingescanoccuronly,iftheamountoftensilerein-forcementislargeenoughtoavoidabrittlefailureafter cracking.ItshouldbecheckedwhetherthevaluegiveninMC78 =0.15%)issufficienttoguaranteetheassumedplastiC rotations. f)Experimentalandanalyticalinvestigationsdonesofarare

validfornormalstrengthconcrete50).Thevalidityof theproposalshastobecheckedforhighstrengthconcrete (C60-C90). - I7.22-6Summary Accordingtoexperimentalandanalyticalstudies,theshape ofthestress-straincurveintheinelasticrangehasasig-nificantinfluenceontherotationcapacityofplastichinges. TheplasticrotationcapacitygiveninMe78,Fig.8.2,1s validonlyforratherductilesteelwhichwasused1nthetests evaluatedin/2/.Theductilityofmoderncold-workedrein-forcingsteelmayherathersmall,resultinginlowvaluesfor theplasticrotationcapacity.Thereforeit1sproposedto classifyreinforcingsteelintwogroups: Type1:Steelwithhighductility Type2:Steelwithreducedductility Theconditionsfortheclassificationaregivenineqns.(2)and (3)ofthereport. Whilefortype1steeltheplasticrotationcapacitygivenin Me78,Fig.8.2,canbeusedwithsomesmallmodificationsfor lowvaluesx/d(lowpercentagesofreinforcement),anewcurve givingsmallerplasticrotationcapacitiesisproposedfor type2steel.Dependingonthetypeofsteelusedinastructure, themaximumdegreeofmomentredistributionislimitedto [;:>0,70 d:>0,85 steeltype1 steeltype2 Figures8.3and8.4ofMe78givethepossibledegreeofmoment redistributionasafunctionoftheratiox/d.Theseequations arevalidonlyiftheslendernessissmallerthanlId=20. Becausetherotationcapacityincreaseswithincreasingslender-ness,itisproposedtodropthislimitation. - I1.23-Intheregionofsplicesbyoverlapping,mechanicaldevices orwelding,theaveragesteelstrainsarerathersmall(often belowtheyieldstrain).Thereforeit1sproposedthatsplicing ofthereinforcementbyanytypeofspliceisnotallowedin theregionwheretheformationofplastichingesisanticipated intheanalysis. Becauseofitsimportancefortheplasticrotationcapacityand thepossibledegreeofmomentredistribution,it mustbepossible todistinguishthetypeofsteel(type1ortype2)clearlyand easilyonsite,e.g.bydifferentribpatterns. InSection5ofthereportsomeopenproblemsarelisted. - I7.24-References /1/Macchi,G.:DuctilityConditionforSimplifiedDesign withoutCheckofDuctility.CEBBulletind'Information No.lOS,P ~ r l s 1976 /2/Slviero,E.:RotationCapacityofMonodimensionalMembers inStructuralConcrete.CEBBulletind'InformatlcnNo.105, 1976 / 3 /CEB-Bulletind'InformationNo.30,1969 /4/Burnett,E.F.P . :Trenberth.R.J.:TheInfluenceofthe ColumnLoadontheReinforcedConcreteBeam- Column Connection,JournalA.C.l.,Vol .69,No.2,Feb .1972 /S/Lenkei,P.:LocalandOverallSpecificInelasticRotation CapacitiesinReinforcedConcreteBeams.Scientific PublicationNo.79,HungarianInstituteforBuildingScience (ETI),Budapest,1974 /6/Rao,P.S.:DieGrundlagenzurBerechnungderbelstatisch unbestimmtenStahlbetonkonstruktlonen1mplastlschenBereich auftretendenUmlagerungenderSchnittkrafte.Heft177der SchriftenreihedesDAfStb,1966 /7/Yamada,M.:DrehfahigkeitplastischerGelenkeimStahlbeton-bau.BetonundStahlbetonbau53,Heft4,1958 /8/Burns,N.M.;Siess,C.P.:PlasticHinginginReinforced Concrete.A.S.C.E.StructuralDivision,Oct.1966 /9/Corley,G.:RotationalCapacityofReinforcedConcreteBeams. PortlandCementAssociation,Bulletin0101,Skokie,1965 - I7.25-/10/Mattock,A.H.:RotationalCapacityofHingingRegionsin ReinforcedConcreteBeams.PortlandCementAssociation, Bulletin0101.Skokie.1965 /11/Meschkat,R. :RotationalCapacityofReinforcedConcrete BeamsUnderVariousLoadingConditions.M.Se.Thesis, UniversityofCalgary,March1969 /12/Tadros,G.S.:PlasticRotationsofReinforcedConcrete MembersSubjectedtoBending,AxialLoadandShear. Ph.D.Thesis,UniversityofCalgary,May1970 /13/Yamashiro,R.;Siess,C.P.:MomentRotationCharacteristics ofReinforcedConcreteMembersSubjectedtoBending,Shear andAxialLoad.CivilEngineeringStudies,Structural ResearchSeriesNo.260,UniversityofIllinois,Dec.1962 /14/Thomas,K.;Sozen,M.A.:AStudyoftheInelasticRotation MechanismofReinforcedConcreteConnections.CivilEngi-neeringStudies,StructuralResearchSeriesNo.301, UniversityofIllinois,Aug .1965 /15/Nawy,E.G.;Danesi,R.F.:Grosko,J.J.:RectangularSpiral BindersEffectonPlasticHingeRotation.JournalACI, Vol.65,No.12,1968 /16/Eligehausen,R.;Langer,P.;Kreller,H.:Anwendungstech-nischeUntersuchungenanBetonstahl.BerichtzumEGKS Forschungsvorhaben,TeilIB,VereinDeutscherEisenhlitten-leute,Dlisseldorf,1984 /17/Eifler,H.iPlauk,G.:DrehfahigkeitplastischerGelenkein biegebeanspruchtenStahlbetonkonstruktionen.Berichtder BundesanstaltflirMaterialprlifung(BAM)zurnForschungsvor-habenBAM:Vh221.2.221,Berlin,1974 ' - I7.26-/18/Dilger,W.:VeranderlichkeitderBlege- undSchubtrag-fahigkeitbelStahlbetontragwerkenundihrEinfluBauf SchnittkraftverteilungundTraglastbeistatischunbe-stirnmterLagerung.PublicationNo.179ofDeutscher AusschuBfilrStahlbeton,VerlagWilhelmErnst&Sohn, Berlin,1966 /19/Bachmann,H.:ZurplastizitatstheoretischenBerechnung statischunbetimmterStahlbetonbalken.Dissertation, EldgenossischeTechnischeHochschule,ZUrich,1967 /20/Langer,P.:Verdrehfahigkeitplastlz1erterTraqwerks-bereiche1mStahlbetonbau.Dissertation at~ h Unive::-si,ty ofStuttgart(1npreparation) /21/Martin,H.;SchieGl,P.;Schwarzkopf,M.:Ableltungeines allgemelngliltigenBerechnungsverfahrensfUrRi6breiten ausLastbeanspruchungaufderGrundlagevontheoretischen ErkenntnissenundVersuchsergebnissen.Schriftenreihe "Stra6enbauundStra6enverkehrstechnik",Bundesanstalt fUrStra6enwesen,HeftNr.257,Kcln,1978 /22/Ciampi,V.iEligehausen,R.;Bertero,V.V.:Popov,E.P.: AnalyticalModelforConcreteAnchoragesofReinforcing BarsUnderGeneralizedExcitations.EarthquakeEngineering ResearchCenter,ReportNo.UCB/EERC82/23,Universityof California,Berkeley,1982 /23/Sheikh,S.A.;Uzumeri,S.M. :AnalyticalModelforConcrete ConfinementinTiedColumns.ASCEJournaloftheStuctural Division,Vol.108,No.ST12,Dec.1982 /24/Eligehausen,R.;Popov,E.P.;Bertero,V.V.:LocalBond Stress-SlipRelationshipofDeformedBarsUnderGeneralized Excitations.EarthquakeEngineeringResearehCenter,Report No.UCB/EERC83/23,UniversityofCalifornia,Berkeley,1983 - I7.27-/25/Eifler,H.:BerichttiberVorversuchefurdieErmittlung desWerkstoff- undVerbundverhaltens1mBereichplastl-scherGelenkevonStahlhetonplattenbeistatischerBe-lastung.BundesanstaltflirMaterlalprlifung(BAM), Az.2.2/119311.Berlin.1969 /261Eibl,J.,Curbach,M.,Stempniewski,L.:Moglicheplasti-scheRotationbeiPlatten1mHochbau.Reportofthe InstitutfUrMassivbauundBaustofftechnologle,University ofKarlsruhe,Nov.1986 /27/CURrapport108"PlastischeScharniere".Reportofthe CUR-VBCommissionA24,Sept.1982 /28/Gijsbers,F.:Rotationsfahigkeit,in:Heron,Vol.21,1976, No.2,"Betonforschungunterwegs" /29/Michalka,C.:ZurRotationsfahigkeitvonplastischen GelenkeninStahlbetontragernmitSchubbewehrung. DissertationattheUniversityofStuttgart,Feb.1986 Year Author 1960-CEB 1965 1971 Burnett 1965 Lenkei 1966 Rao 1958 Yamada 1962 Burns-Siess 1954 Mc-Collister Ref. /3/ /4/ /5/ /6/ 17/ /8/ in /Il/ /9/ Height d mm 180-280 220 280 370 200-250 250-450 250 130-760 Slenderness l/d 10-13 6-11 10 4-10 4 8-14 ftlfy MS CWS 1.8 1.5 1. 4 5 HT 1.5 Us '\ 0.4 -6.8 1.2 -2.4 0.2 -2.4 Us '\ 0.0 -1.7 0.2 1966 1965 1969 1970 1962 1965 1968 Corley Mattock Meschkat /10/ 250-510 /11/ 280 11 6-14 6-22 6-13 1.7 1.7 1.5 1. 36 0.9 -2.6 1.1 -2.0 0.6 -5.1 1.1 -2.9 0.7 -2.9 1.2 0.0 -1.0 0.0 -2.0 0.0 -4.0 0.1 -1.5 0.2 -0.4 0.15 Tadros /12/ Yamashiro-Siess /13/ Thomas-Sozen /14/ Nawy /15/ 270 6-12 1.5 2.2 2.2 250 14 1.6 0.7 -3.3 0.7 -3.3 reinforced with strands with ft/fy = 1584/1825 N/mm' tests with normal force,

I} Test-specimen with region of constant moment Table 1: Main parameters of the tests evaluated by Siviero Remarks MS=Mlld Steel CWS= COld-Worked Steel 11 11 11

Steel H ..... tv ex> 0,20 0,15 c: 0 -+-Cj 0,10 -+-0

u -+-VI Cj

0. 0,05 o - I7.29- I .. ..

0. , .. ,. o. R. ...

.. Ul' M.", ,,-" .. ... "... ,....... ....e. '1 L .. I' , .u. g= 5Yo o123456 35 30 . c o20 -o -o ~u -:;10 -0. bl0 strainEs [%] {JPI[rod10-3] 1\ lj-\ IJ= 0,3% \lid= 6 \ wi thout bond '< I ~, ' ... )tn withbond ~)tm -c: 30 -.E o ::;20 -." d 0.10 - I7 . 38-\ l,t.l.d acc.CEB ......r--. .... ":>. cold'itorkfd:--II ----.testresult according/ 26 / o o0.10.20.30.40.5 relative depthof neutral axis x/d Fig_12:PlasticrotationcapacityaccordingtoCEBand analyticalmodelfordifferenttypesofrein-forcement -40 o o i\

/9

....

-- -----= 135270405 beamheight 540 (mm] Fig.13:Influenceofbeamheightonrotationcapacity 200

E Z 160 .x

120 X -L .... 80 c:: QJ E 40 0 E 0 0 a) .150 .120 L - QJ '-.E.060 Cl > '-a030 b) o o I I - I7.39- ._-, , =12I =3 , , , , , , .J.- 810-43240 beamlength[mm) I =12 II "I !!' "I .L41=3

",' " .' .... _----. ------_. ---_ ... ---- " +- 810-43240 beamlength[mm) Fig.14:Distributionofmomentandsectioncurvaturealong beamfordifferentslendernessratioslid - I7.40-20 weldedwiremesh .., , 15 RuIRe::1,06AG= 3% "C e -\l=0,50 % c:- 10 '" :J; '" ... .... '" E QJ = 0,75% ... .c .... 5VI '" a. -150 -,0 0 = 2,0% 03691215 slendernesslId Fig.15:Plasticrotationcapacityasafunctionofthe slendernesslIdaccordingtocalculation Fig.16: 120 coldworkedbars

.., , 0 -. "C -e '" -0-

-0----

... c:a 0 QJ = O, B2 40 .c .... VI

.E 0_0- -0--... -0--- ____ ______ o3691215 slendernesslId Rotat i oncapacityasafunctionofthebeam slendernessl/daccordingtotests/17/ = totalrotationcapacity =plasticrotationcapaci ty a) -17.41-0,030177r-,.-,--,--,--.,....----, "act. (EB stee I 1 c0,020o c: - ., E o., e0,015 u ..... c: .,

IIIE EO, 0 10::>;+-,.L-II------''d-Q.E c: 0,005 o ..... c g.!!:!0,80 ._u _.--E o0,10,20,30,40,5 re lotive depth of neutralaxis x/d 0102030405 I ,steel 2 / V v ,steel 1 /

::JQJ b)0,60 Fig.17:Proposalfortheallowableplasticrotation capacityandtheallowabledegreeofmoment redistribution - I7.42-CHAPTER7 Thetextinthefollowingchaptershouldbeconsideredas: ~ x t asText-proposalText-proposalText-proposalMeme inMC78fromConunissionfranreporterfromMCR:; * CHAPTER8 Thetextinthefollowingchaptershouldbeconsideredas: TextasText-proposalText-proposalText-proposalMeme inMC78fromCommissionfranreporterfromMCR:; * CHAPTER9 Thetextinthefollowingchaptershouldbeconsideredas: TextasText-proposalText-proposalText-proposalMemo inIIC78fromCommissionfranreporterfromMCR:; * CHAPTER - 7.1-7IIDETERMINATIONOFTHELOADEFFECTSII ThereV1S10nofthischapterisforeseen afterthediscussionofchapters8and heldatthePlenarySessioninTreviso. byPCII 9tobe