Nonlinear-Models-of-Reinforced-and-Post-tensioned-

ElectronicJournalofStructuralEngineering,2(2001)2001EJSEInternational.Allrightsreserved.Website::[e-mail]16Jul2001;revised8Sep2001;accepted12Sep2001.ABSTRACTCommercialfiniteelementsoftwaregenerallyincludesdedicatednumericalmodelsforthenonlinearresponseofconcreteunderloading.Thesemodelsusuallyincludeasmearedcrackanalogytoaccountfortherelativelypoortensilestrengthofconcrete,aplasticityalgorithmtofacilitateconcretecrushingincompressionregionsandamethodofspecifyingtheamount,thedistributionandtheorientationofanyinternalreinforcement.ThenumericalmodeladoptedbyANSYSisdiscussedinthispaper.Appropriatenumericalmodellingstrategiesarerecommendedandcomparisonswithexperimentalload-deflectionresponsesarediscussedforordinaryreinforcedconcretebeamsandpost-tensionedconcreteT-beams.KEYWORDSConcrete;post-tensioning;finiteelementmodelling.1.Introduction:theANSYSreinforcedconcretemodelTheimplementationofnonlinearmateriallawsinfiniteelementanalysiscodesisgenerallytackledbythesoftwaredevelopmentindustryinoneoftwoways.Inthefirstinstancethematerialbehaviourisprogrammedindependentlyoftheelementstowhichitmaybespecified.Usingthisapproachthechoiceofelementforaparticularphysicalsystemisnotlimitedandbestpracticemodellingtechniquescanbeusedinidentifyinganappropriateelementtypetowhichany,ofarange,ofnonlinearmaterialpropertiesareassigned.Thisisthemostversatileapproachanddoesnotlimittheanalysttospecificelementtypesinconfiguringtheproblemofinterest.Notwithstandingthishowevercertainsoftwaredevelopersprovidespecificspecialisednonlinearmaterialcapabilitiesonlywithdedicatedelementtypes.ANSYS[1]providesadedicatedthree-dimensionaleightnodedsolidisoparametricelement,Solid65,tomodelthenonlinearresponseofbrittlematerialsbasedonaconstitutivemodelforthetriaxialbehaviourofconcreteafterWilliamsandWarnke[2].Theelementincludesasmearedcrackanalogyforcrackingintensionzonesandaplasticityalgorithmtoaccountforthepossibilityofconcretecrushingincompressionzones.Eachelementhaseightintegrationpointsatwhichcrackingandcrushingchecksareperformed.Theelementbehavesinalinearelasticmanneruntileitherofthespecifiedtensileorcompressivestrengthsareexceeded.Crackingorcrushingofanelementisinitiatedonceoneoftheelementprincipalstresses,atanelementintegrationpoint,exceedsthetensileorcompressivestrengthoftheconcrete.Crackedorcrushedregions,asopposedtodiscretecracks,arethenformedperpendiculartotherelevantprincipalstressdirectionwithstressesbeingredistributedlocally.Theelementisthusnonlinearandrequiresaniterativesolver.Inthenumericalroutinestheformationofacrackisachievedbythemodificationofthestress-strainrelationshipsoftheelementtointroduceaplaneofweaknessintherequisiteprincipalstressdirection.TheamountofsheartransferacrossacrackcanbevariedbetweenfullsheartransferandnosheartransferElectronicJournalofStructuralEngineering,2(2001)2001EJSEInternational.Allrightsreserved.Website:3.0mlongOrdinarilyReinforcedConcreteBeamsAcrosssectionthroughthe3.0mlongbeams,Figure1,illustratestheinternalreinforcement.Three12mmdiametersteelbarswereincludedinthetensionzonewithtwo12mmsteelbarsascompressionsteel.Tenshearlinks,formedfrom6mmmildsteelbars,wereprovidedat125mmcentresforshearreinforcementintheshearspans.Twobeamsweretestedeachofwhichweresimplysupportedwithaclearspanof2.8mandloadedsymmetricallyandmonotonically,underdisplacementcontrol,infourpointbending,withpointloads0.3meithersideofthemid-spanlocation,tofailure.Cylindersplitting[3]andcrushingtests[4]oncoredsamplesofthebeams,inaccordancewiththeBritishStandards,wereundertakentoidentifytheuni-axialtensileandcompressivestrengthsoftheconcrete,(ft=5.1N/mm2andfc=69.0N/mm2respectively),andtheYoung’sModulusoftheconcrete[5],(39,200N/mm2),fori