iiiios5

ISETJournalofEarthquakeTechnology,PaperNo.
469,Vol.
43,No.
1-2,March-June21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">06,pp.
31-4826thISETAnnualLectureSEISMICEVALUATIONANDRETROFITTINGOFBUILDINGSANDSTRUCTURESN.
LakshmananStructuralEngineeringResearchCentreCSIRCampus,TaramaniChennai–61f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0113ABSTRACTRecentearthquakesintheIndiansubcontinenthaveledtoanincreaseintheseismiczoningfactorovermanypartsofthecountry.
Also,ductilityhasbecomeanissueforallthosebuildingsthatweredesignedanddetailedusingearlierversionsofthecodes.
Undersuchcircumstances,seismicqualificationofexistingbuildingshasbecomeextremelyimportant.
Seismicqualificationeventuallyleadstoretrofittingofthedeficientstructures.
PushoveranalysisandevaluationofperformanceofbuildingusingCapacitySpectrumApproachorDisplacementCoefficientMethodareincreasinglyusedforthispurpose.
ThereisaneedtolookatcertainimportantissuesforincorporationintheIndiancodesbeforeuniformityofapproachcanbeachieved.
This,inturn,needsanin-depthunderstandingonwhathasgoneintoATC-41f20;BACKGROUND-COLOR:#4ae2f7">0(ATC,1996)orFEMA-356(FEMA,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0),andmakingappropriatemodificationstosuittheIndianconditions.
Itisnecessarythatthedebateonthisisstartedandcompletedearlytoachievethedesiredresults.
Pre-disasterpreparednessstrategiesleadtorepair/retrofittingofthereinforcedconcretestructuresforensuringsatisfactoryperformanceduringearthquakes.
Repairscanleadtoincreasedstiffness,strength,andfailure-deformation.
Thereisaneedtoquantifytheperformanceofthestructureaftertherepairshavebeencarriedout.
Performancefactorshavebeensuggestedforsuchquantification.
Theseareadequateincertaincasesbutmaynotbetotallysatisfactoryinothers.
Alarge-scaleexperimentalprogrammeundertakenatSERChasshownthatifthereareinherentweaknessesinthedetailingoftheoriginalstructure,itmaynotbepossibletoimprovetheperformancetothedesiredlevels.
Inthesecases,theperformancefactorsmaydependonthestateofdeformationconsideredforevaluationandmaynotbeunique.
Thereisaneedtoaddressthisissue,sothatsuitabilityofrepairmeasurescanbesatisfactorilyevaluated.
KEYWORDS:SeismicQualification,Retrofitting,PerformanceFactorsINTRODUCTIONConcretehasbeenthemostpreferredconstructionmaterialofthetwentiethcentury,andunlessanewmaterialwithspectacularcharacteristicsisinvented,itappearspoisedtoremainthiswayforanothercentury.
Thisisnottosuggestthattherehasbeennoprogressonconcreteandconcretetechnologyovertheyears.
Overthelast51f20;BACKGROUND-COLOR:#4ae2f7">0years,thestrengthsofvarioustypesofconcretehaveincreasedfromthelowlevelsof15-21f20;BACKGROUND-COLOR:#4ae2f7">0MPatovaluesintherangeof41f20;BACKGROUND-COLOR:#4ae2f7">0-71f20;BACKGROUND-COLOR:#4ae2f7">0MPa.
Strength-baseddesignsareslowlygivingwaytoperformance-baseddesignswherestrengthisonlyoneofthecriteriatobesatisfied.
Thereisanincreasedattentionbeingpaidtolifepredictionandmaintenancescheduling.
Finiteelementsoftwareisextensivelyusedindesignofficesfortheanalysisanddesignofconcretestructures.
Itmaybeworthwhileatthisstagetoexactlycalibratethestatusofpresentdayanalysisanddesignviz.
,the"realisticestimates"onloadeffectsanddeformations.
Consider,forexample,thedesignofamulti-storeyedframedstructure.
Theloadcasestobeconsideredarethedeadload,liveload,windload,seismicload,andtheircombinations.
Theinputdatathatisnormallyfedintothecomputersoftwareincludesmodulusofelasticity,Poisson'sratio,densityofconcrete,areasandmomentsofinertiaofallstructuralelements,basicwindspeed,zoningfactorforseismicloading,andsoon.
Thenonegoesontodefinetheloadcombinationstoobtaintheworstloadeffects.
Generallythegrosssectionpropertiesareused,andelastic32SeismicEvaluationandRetrofittingofBuildingsandStructuresanalysisisperformed.
Thedesignisbasedonthelimitstatephilosophy.
Sotheelasticloadeffectsthatareobtainedaremultipliedbytheloadfactorstoobtainthecapacityrequirements.
Theoryofplasticityisthenusedtoproportionthecross-sectionsformomentsandaxialforces.
Linearvariationofstrainisassumedacrossthecross-sections,equilibriumequationsforaxialforcesandmomentsarewrittendown,andareaofthesteelreinforcementrequirediscomputed.
WhatisdoneforthedesignforshearThisismoreorlessbasedontheempiricalequationsderivedfromthetestresults.
Thecontributionofconcreteisderivedbasedonthestrengthofconcreteandpercentageofthetensilereinforcement.
Thecontributionduetotheweb-steelisbasedona451f20;BACKGROUND-COLOR:#4ae2f7">0crack,thougheveryonerealizesthattheshearcracksseldomoccuratthisangle,dependonthe/MVdratio,andevenshowchangewiththeloading.
Thedesignisthenclaimedtobebasedonthelimitstatedesignphilosophycoveringlimitstatesofserviceabilityandcollapse.
ThelimitstateofserviceabilityisdeemedtobesatisfiedifalltherecommendationsgiveninIS:456-21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0(BIS,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0)regardingthedetailingaresatisfied.
Presentlyearthquake-resistantdesignisbeingdiscussedinmanyforums.
IfoneadoptstheprovisionsofIS:13921f20;BACKGROUND-COLOR:#4ae2f7">0-1993(BIS,1993),theresponsereductionfactoris5.
1f20;BACKGROUND-COLOR:#4ae2f7">0andfornormalframesitis3.
1f20;BACKGROUND-COLOR:#4ae2f7">0.
Thishasdirectimpactonthedesignforces.
Themethodofanalysisanddesignasdescribedaboveisthemostsophisticatedprocedureadoptedinthedesignoffices.
Thisisthepresentstatus,irrespectiveofwhattheinconsistenciesareinelasticanalysis,plasticdesignformomentsandaxialforces,andempiricalapproachfordesignforshear,bond,etc.
Itisextremelyimportanttorealizethatthevaluesobtainedintheanalysisareatbestgoodindicatorsfortheexpresspurposeof"design".
Themostessentialpart,andoftentheneglectedpart,istheproperguidancetoaidengineersinmakingthebestuseoftheresultsavailableandinprovidingthereinforcementadequately.
Itmustberealizedatthisstagethatwhenoneattemptstocarryouttheseismicevaluationofabuilding,strictlyspeaking,thecodalprovisionsatthetimeofconstruction,ageofthestructure,constructionpracticesetc.
,allbecomeimportant.
Itmustalsoberealizedthatifoneiswaitingforanexactmethodologyandrulesfortheseismicevaluation,onemayhavetowaitforafewmoreyears,ifnotdecades.
Presently,therearetwononlinearstaticanalysisproceduresavailable,onetermedastheDisplacementCoefficientMethod(DCM)includedintheFEMA-356document(FEMA,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0),andtheothertermedastheCapacitySpectrumMethod(CSM)includedintheATC-41f20;BACKGROUND-COLOR:#4ae2f7">0document(ATC,1996).
Bothofthesemethodsdependonthelateralload-deformationvariationobtainedbyusingthenonlinearstaticanalysisunderthegravityloadingandidealizedlateralloadingduetotheseismicaction.
Thisanalysisisgenerallycalledasthepushoveranalysis.
PUSHOVERANALYSISPushoveranalysisisanonlinearstaticanalysisforareinforcedconcrete(RC)framedstructuresubjectedtolateralloading.
Thegravityloadsareapplied,andthenlateralloadingisapplied–firstinX-directionstartingattheendofthegravitypush,andnextinY-directionagainstartingattheendofthegravitypush(Vallesetal.
,1996;CSI,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0).

Theconceptofplastichingeisextremelyimportantinthenonlinearanalysis.
Whileaconcreteelementundergoeslargedeformationsinthepost-yieldstage,itisassumedthatallthedeformationtakesplaceatapointcalled"plastichinge",whichhasapproximatelyalengthoftheorderoftheeffectivedepth(alsocalledasplastichingelength,dl).
Therotationcapacityθofaplastichingeistakenas()yudlφφ.
Asimilarapproachcanbeusedforobtainingtherotationcapacityofcolumnsunderaxialforceandbendingmomentintwodirections.
Similarplastichingeswithlimitcapacitiesondeformationcanbedefinedforallsixdegreesoffreedom,namely,axialforce,transverseshearforcesinX-andY-directions,momentsaboutY-andZ-axes,andtorsion(momentaboutX-axis).
Moredetailsonevaluationofductility,energyabsorption,damagemodeling,anddetailingareavailableelsewhere(Lakshmanan,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">03a,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">05a).
AtypicalresponseataplastichingemaybeasshowninFigure1.
Here,PointAistheorigin;Bisthepointofyielding;BCrepresentsthestrain-hardeningregion;Cisthepointcorrespondingtothemaximumforce;andDEisthepost-failurecapacityregion.
Ontheframestructure,theanalystidentifiesthepossiblelocationsforplastichingeformationfromhisexperience.
Mathematically,nonlinearstaticanalysisdoesnotleadtoauniquesolution.
Smallchangesinpropertiesorsequenceofloadingcanleadtolargevariationsinthenonlinearresponse.
ISETJournalofEarthquakeTechnology,March-June21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0633Fig.
1Idealisedforce-deformationcurveThepushoveranalysismaybecarriedoutusingforcecontrolordeformationcontrol.
Inthefirstoption,thestructureissubjectedtoanincrementaldistributionoflateralforce,andincrementaldisplacementsarecalculated.
Inthesecondoption,thestructureissubjectedtoadeformationprofile,andlateralforcesneededtogeneratethosedisplacementsarecomputed.
Sincethedeformationprofileisunknown,thefirstoptioniscommonlyused.
Forthedisplacementcontroltheuserspecifiesthetargetmaximumdisplacementatacontrolpoint.
Incertainsoftwares,displacementcontrolisnotthesameasapplyingdisplacementloadingonthestructure;displacementcontrolissimplyusedtomeasurethedisplacementthatresultsfromtheappliedloadsandtoadjustthemagnitudeoftheloadinginanattempttoreachcertainmeasureddisplacementvalue.
Theso-calleddisplacementcontrolinthiscaseisessentiallyamodifiedformoftheforcecontrol.
Theforcecontrolstrategycanhavefollowingoptions:(i)uniformdistribution,(ii)triangulardistribution,(iii)generalisedpowerdistribution,and(iv)modaladaptivedistributionwithsingleormultiplemodeparticipation.
Theresultsofthepushoveranalysiscarriedoutonatypicalreinforcedconcreteframe,whoseisometricviewisgiveninFigure2,areshowninFigure3.
IDEALIZEDSYSTEMPARAMETERSThemultilinearforce-displacementcurveobtainedafterthepushoveranalysisisidealizedasbilinearcurve,asshowninFigure4,withapositiveornegativepost-yieldslope.
Fig.
2Isometricviewofthebuilding34SeismicEvaluationandRetrofittingofBuildingsandStructuresPushalongtheX-directionPushalongtheY-directionFig.
3Basereaction(kN)versusmonitoreddisplacement(m)Firstletusconsidertheequivalentlinearizationmethod,whichisthebasisfortheCapacitySpectrumMethod.
Themaximumresponseoftheequivalentsystemiscomputedusing22eqeqeqeqeqeqgxxxxξωω++=(1)whereeqξandeqωarerespectivelytheviscousdampingratioandnaturalcircularfrequencyoftheequivalentlinearsystem.
Forabilinearsystem,thetimeperiodeqToftheequivalentsystemascomparedto1f20;BACKGROUND-COLOR:#4ae2f7">0ToftheoriginalsystemisgivenbyISETJournalofEarthquakeTechnology,March-June21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">06351f20;BACKGROUND-COLOR:#4ae2f7">0(1)eqTTαα=+(2)whereistheductilityratio,andαistheratioofthepositivepost-yieldstiffnesstotheoriginalstiffness.
Theequivalentdampingisgivenby()()1f20;BACKGROUND-COLOR:#4ae2f7">02112eqαξξπαα=++(3)Foranelasto-plasticsystem,eqoTT=(4)and1f20;BACKGROUND-COLOR:#4ae2f7">0211eqξξπ=+(5)Fig.
5Idealizedforce-displacementcurvesUsingTakedahystereticmodel(Takedaetal.
,1971f20;BACKGROUND-COLOR:#4ae2f7">0)andexperimentalinvestigationsonmodelreinforcedconcreteframes,anempiricalequationforequivalentdampingwasgivenbyGulkanandSozen(1974):1f20;BACKGROUND-COLOR:#4ae2f7">011f20;BACKGROUND-COLOR:#4ae2f7">0.
21eqξξ=+(6)Kowalskyetal.
(1994)usedthesecantstiffnessatmaximumdeformationfordefiningtheperiodtogetherwithhystereticmodelgivenbyTakedaetal.
(1971f20;BACKGROUND-COLOR:#4ae2f7">0)andanunloadingstiffnessfactorof1f20;BACKGROUND-COLOR:#4ae2f7">0.
5:36SeismicEvaluationandRetrofittingofBuildingsandStructures1f20;BACKGROUND-COLOR:#4ae2f7">0111neqαξξαπ=++(7)wherenisequaltozeroforsteelstructuresand1f20;BACKGROUND-COLOR:#4ae2f7">0.
5forconcretestructures.
Foranelasto-plasticsystem,1f20;BACKGROUND-COLOR:#4ae2f7">0111eqξξπ=+(8)InATC-41f20;BACKGROUND-COLOR:#4ae2f7">0(ATC,1996),eqξ,giveninEquation(3),isusedwiththeprovisothathoeqχξξξ+=(9)wherehξislimitedto45%.
Further,χisequalto1.
1f20;BACKGROUND-COLOR:#4ae2f7">0forhξ=16.
25%and1f20;BACKGROUND-COLOR:#4ae2f7">0.
77forhξ=45%withlinearinterpolationforotherdampingvalues,incaseofstructureshavingstableandfullhystereticbehaviour.
χisequalto1f20;BACKGROUND-COLOR:#4ae2f7">0.
67forhξ=25%forreasonablywell-behavedsystems,andisequalto1f20;BACKGROUND-COLOR:#4ae2f7">0.
33forsystemswithpoorhystereticbehaviour.
IntheDisplacementCoefficientMethodpioneeredbyVeletsosandNewmark(1961f20;BACKGROUND-COLOR:#4ae2f7">0),andNewmarkandHall(1982),thedisplacementmodificationfactorisshowntodependonthespectralregioninwhichtheperiodofvibrationofthesingle-degree-of-freedom(SDOF)systemislocated:()''(1/33sec)(1f20;BACKGROUND-COLOR:#4ae2f7">0.
125sec)2121(1f20;BACKGROUND-COLOR:#4ae2f7">0.
57sec)1.
1f20;BACKGROUND-COLOR:#4ae2f7">0aabbcccccCTTTTTTTTTTTTTTTβ=(11f20;BACKGROUND-COLOR:#4ae2f7">0)where()'21/ccTT=andlog(/)/2log(/).
abaTTTTβ=Miranda(21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01)hasrecentlysuggestedthat'112111TCe=+(11)where'1f20;BACKGROUND-COLOR:#4ae2f7">0.
8.
=Morerecently,Ruiz-GarcíaandMiranda(21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">03),andChopraandChintanapakdee(21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">03)haveproposedexpressionsforRCandCbasedonextensiveinvestigationsoffielddataandbyusingregressionanalyses.
DISPLACEMENTCOEFFICIENTMETHODThegeneralizedtargetdisplacementgiveninFEMA-356(FEMA,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0)includes,inadditiontothemodificationfactor1Cfortheinelasticresponse,modificationfactor1f20;BACKGROUND-COLOR:#4ae2f7">0CtorelatespectraldisplacementoftheSDOFsystemtotheroofdisplacementofthemulti-degree-of-freedom(MDOF)system,modificationfactor2Cforthedegradedhystereticperformance,andmodificationfactor3CforP-effectinasysteminwhichthepost-yieldstiffnessisnegative.
Ingeneral,thetargetdisplacementisgivenas21f20;BACKGROUND-COLOR:#4ae2f7">012324taTCCCCSδπ=(12)ISETJournalofEarthquakeTechnology,March-June21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0637WhileCandRC(whicharethecounterpartsof1C)havebeendiscussedindetail,theotherfactorsarealsounderscrutiny(Comartin,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">02).
CAPACITYSPECTRUMAPPROACHThespectralcoefficientgiveninIS:1893-21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">02(BIS,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">02)ismultipliedbythezoningfactorZtoobtaintheplotofspectralaccelerationversustimeperiod.
TheAccelerationDisplacementResponseSpectrum(ADRS),alsocalleddemandspectrum,isobtainedbyplottingaSversusdSwhere()()221/4/daSTZSgπ=.
Thecapacityspectrumisderivedfromtheinelasticshear-roofdisplacementcurveusing(){}1//aSVWgα=(13)androof,1/dRSPF=(14)where1αand1,RPFarethemodalmasscoefficientandmodalparticipationfactor,respectively,forthefirstmode.
Table1givestypicalvaluesof1αand1,RPFforrectangularbuildingswithuniformmassandstraightlinemodeshape.
Table1:EffectiveMassCoefficient1αandModalParticipationFactor1,RPFforRoofNumberofStoreys1α1,RPF11.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">021f20;BACKGROUND-COLOR:#4ae2f7">0.
91f20;BACKGROUND-COLOR:#4ae2f7">01.
21f20;BACKGROUND-COLOR:#4ae2f7">031f20;BACKGROUND-COLOR:#4ae2f7">0.
861.
31f20;BACKGROUND-COLOR:#4ae2f7">051f20;BACKGROUND-COLOR:#4ae2f7">0.
821.
3511f20;BACKGROUND-COLOR:#4ae2f7">0≥1f20;BACKGROUND-COLOR:#4ae2f7">0.
781.
41f20;BACKGROUND-COLOR:#4ae2f7">0BasedonthemultiplyingfactorsgiveninIS:1893-21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">02(BIS,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">02)forobtainingseismicresponseaccelerationcoefficients,thevariationsof/aSgwithdSforvariousdampingratioscanbeplotted(Figure5).
PerformancepointwillbeapointonthecapacityspectrumwhereeqTandeqξwouldbesatisfied.
Tosatisfythelife-safetyrequirement,theroofdisplacementshouldbelessthan1.
2%ofheightforordinaryframesand2%forspecialmoment-resistingframes.
Life-safetyrequirementcanbeconsideredascorrespondingtothedesignbasisearthquake.
Forcollapseprevention,theperformancepointshouldexist.
Inanycase,thetotaldriftshouldnotexceed1f20;BACKGROUND-COLOR:#4ae2f7">0.
33/VP,whereVisthebaseshearandPisthegravityloadforcollapseprevention.
Also,inadegradingnonlinearresponse,thelimitofdegradationonstrengthascomparedtothepeakvalueis21f20;BACKGROUND-COLOR:#4ae2f7">0%.
Theabovediscussionclearlyrevealsthatpushoveranalysisneedstobeusedwithlotofcautionandexpertjudgment.
Infact,itcouldbecomeadangeroustoolinthehandsofpractitionerswhohavelittleexposuretononlinear/dynamicbehaviourofconcretestructures.
VULNERABILITYINDEXThevulnerabilityindexisameasureofthedamageinabuildingobtainedfromthepushoveranalysis.
Itisdefinedasascaledlinearcombination(weightedaverage)ofperformancemeasuresofthehingesinthecomponents,andiscalculatedfromtheperformancelevelsofthecomponentsattheperformancepointoratthepointofterminationofthepushoveranalysis(Lakshmanan,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">05b).
Ithasbeenmentionedearlierthattheload-deformationcurveforaparticularhingeisassumedtobepiecewiselinear(Figure1).
Theplasticplateau(B-C)intheload-deformationcurveissubdividedintotheperformanceranges,namely,B-IO,IO-LS,LS-CP,CP-C,D-E,and>E.
Afterthepushoveranalysis,performancerangesofthehingesformedinthecomponentcanbenotedfromthedeformedshapeoutput.
Thenumberofhingesformedinthebeamsandcolumnsforeach38SeismicEvaluationandRetrofittingofBuildingsandStructuresperformancerangeareavailablefromtheoutput.
A'weightagefactor'(ix)isassignedtoeachperformancerange.
TheproposedvaluesofixaregiveninTable2.
Ascolumnsaremoreimportantthanbeamsintheglobalsafetyofabuilding,an'importancefactor'of1.
5isadditionallyassignedforcolumns.
ThebuildingvulnerabilityindexbldgVIisaccordinglygivenbythefollowingweightedaverage:bldg1.
5chiiiichiiNxNxVINN+=+∑∑∑∑(15)Here,ciNandhiNarethenumbersofhingesincolumnsandbeams,respectively,fortheithperformancerange.
Thesummationsignisintendedtocovertheperformanceranges,i=1,2,…6.
Fig.
5DemandandcapacityspectraTable2:WeightageFactorsforPerformanceRangeSerialNumberPerformanceRange(i)WeightageFactor(ix)11f20;BACKGROUND-COLOR:#4ae2f7">02B-IO1f20;BACKGROUND-COLOR:#4ae2f7">0.
1253IO-LS1f20;BACKGROUND-COLOR:#4ae2f7">0.
3754LS-CP1f20;BACKGROUND-COLOR:#4ae2f7">0.
6255CP-C1f20;BACKGROUND-COLOR:#4ae2f7">0.
8756C-D,D-E,and>E1.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0bldgVIisameasureoftheoverallvulnerabilityofthebuilding.
AhighvalueofbldgVIreflectspoorperformanceofthebuildingcomponents(i.
e.
,highrisk)asobtainedfromthepushoveranalysis.
However,thisindexmaynotreflectasoftstoreymechanism,inwhichaperformancepointmaynotbeachieved.
Table3givesthevulnerabilityindexofatypicalframedbuildinganalysedusingthepushoveranalysis.
ThedamageindexforX-pushiscomputedas1f20;BACKGROUND-COLOR:#4ae2f7">0.
34andY-pushas1f20;BACKGROUND-COLOR:#4ae2f7">0.
41.
AstoreyvulnerabilityindexstoreyVIcanbedefinedtoquantifythepossibilityofasoft/weakstoreywiththeformationofflexuralhinges.
ForeachstoreystoreyVIisdefinedasstoreyciiciNxVIN=∑∑(16)ISETJournalofEarthquakeTechnology,March-June21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0639whereciNisthenumberofcolumnhingesinthestoreyunderinvestigationforaparticularperformancerange.
Inagivenbuilding,thepresenceofsoft/weakstoreyisreflectedbyarelativelyhighvalueofstoreyVIforthatstorey,inrelationtotheotherstoreys.
Iftheanalysisisterminatedduetotheformationofshearhinges,thentheabovedefinitionisnotapplicable.
Table3:VulnerabilityIndexBasedonPushoverSerialNumberDirectionElementWeight,iWCoefficient,iCNumberofHingesiiiWCNBeam1.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0.
1251f20;BACKGROUND-COLOR:#4ae2f7">0.
3751f20;BACKGROUND-COLOR:#4ae2f7">0.
6253162682839.
3811f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0.
51f20;BACKGROUND-COLOR:#4ae2f7">023.
751XColumn1.
51f20;BACKGROUND-COLOR:#4ae2f7">0.
1251f20;BACKGROUND-COLOR:#4ae2f7">0.
3751f20;BACKGROUND-COLOR:#4ae2f7">0.
6251.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">031f20;BACKGROUND-COLOR:#4ae2f7">0129243256.
44164.
2541f20;BACKGROUND-COLOR:#4ae2f7">0.
313.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0Beam1.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0.
1251f20;BACKGROUND-COLOR:#4ae2f7">0.
3751f20;BACKGROUND-COLOR:#4ae2f7">0.
6251.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0877121f20;BACKGROUND-COLOR:#4ae2f7">03111f20;BACKGROUND-COLOR:#4ae2f7">0.
8826.
63126.
881.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">02YColumn1.
51f20;BACKGROUND-COLOR:#4ae2f7">0.
1251f20;BACKGROUND-COLOR:#4ae2f7">0.
3751f20;BACKGROUND-COLOR:#4ae2f7">0.
6259727118.
1915.
191f20;BACKGROUND-COLOR:#4ae2f7">0.
94DAMAGEINDICESANDDAMAGEMODELLINGEventhoughtheperformance-basedevaluationapproachperseisbasedondamageclassification,itisclearlyevidentthatdamageindicesareusedonlyforthequantificationoftheconclusionofananalysis.
Damageindicesarenotusedtoinfluencethewaystructuralresponseevolves.
Theresponseofadamagedsystemnotonlydependsontheprevioushistorybutalsoontherateatwhichdamageaccumulates.
Asystemwithsameinitialconditionscanreachfailureatdifferentstagesduetocharacteristicsoftheearthquakeanddamageaccumulatedovertheresponsetime.
Theresponse-baseddamageindicesareductilityratio/uyδδ,inter-storeydriftasapercentageofstoreyheight,sloperatiodefinedbytheratiooftheslopeofloadingbranchtotheslopeofunloadingbranch,stiffnessratiodefinedastheratioofinitialstiffnesstothesecantstiffnessatthemaximumdisplacement,maximumpermanentdrift,andsoon.
Allthesefailtorecognisethecyclicnatureofresponse.
Cumulativedamagelawbasedonlow-cyclefatigueleadstoanexpressionfordamageas(Cosenzaetal.
,1993)111bniiuD==∑(17)wherebtypicallyvariesfrom1.
5to1.
8.
ThemostpopularParkandAngmodelisacombinedmodelbasedondeformationandaccumulateddamage:cstyuDdEFβδ=+∫(18)Thebasicassumptionintheabovedamagemodelisthatthedamageduetoresponseandthedamageduetocumulativeenergycanbesuperposedlinearly,andβistobeobtainedthroughlaboratorytestsorfielddata.
WilliamsonandKaewkulchai(21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">03)havesuggested:41f20;BACKGROUND-COLOR:#4ae2f7">0SeismicEvaluationandRetrofittingofBuildingsandStructures()()DUWαδβδ=+(19)whereαandβareconstants;()δUisafunctionofmaximumdeformation;and()Wδisafunctionoftheaccumulatedplasticenergy.
αandβcanbeadjustedtoaccountfordifferentratesofdamageleadingtoavarietyofresponsemodels.
AnothervariationoftheParkandAngruleisgivenbyLowesetal.
(21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">04):()432max1~αααα+=uiEEdD(21f20;BACKGROUND-COLOR:#4ae2f7">0)where()max,min,maxmaxminmax,iiffddddede=and.
iEdE=∫Oftenthemonotonictestresultsshowthatthestrengthiscappedandisfollowedbyanegativetangentstiffness.
Ingeneral,cyclicresponseindicatesthatthestrengthdecreaseswithnumberandamplitudeofcyclesevenifthedisplacementassociatedwiththepeakstrengthisnotreached.
Strengthdeteriorationoccursatafasterrateinthepost-cappingregion,andtheunloadingstiffnessmayalsodeteriorate.
Also,itispossiblethatthereloadingstiffnessmaydeteriorateatafasterrate.
AholisticdamagemodelindividuallyaccountingforallthesehasbeenproposedbyIbarraetal.
(21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">05).
SEISMICSTRENGTHENINGRepairandretrofittingofconcretestructureshavebeenattractingtheattentionofresearchersoverthelasttwodecades.
Variousrepair/retrofitoptionsavailabletodayincludecrackinjection,shortcreting,steeljacketing,steelplatebonding,CFRP/GFRPjacketing,RCjacketing,additionofnewstructuralelements(braces,walls,etc.
),incorporationofpassiveenergydissipationdevices,andprovisionofbaseisolation.
Retrofittingcanbeatthesystemleveloratthelocallevel.
Introductionofadditionalshearwalls,braces,baseisolationetc.
,toenhancetheperformanceofastructurebelongstotheformercategory,whilerepairofabeamorcolumnelementusingvariousjacketingtechniques,suchasjacketingusingmicro-concrete,steel,carbonfibrereinforcedplastics(CFRP),andglassfibrereinforcedplastics(GFRP),essentiallyfallsunderthecategoryoflocalretrofitting.
Repairandretrofittechniquescanbeusedforenhancingthestiffness,strength,and/orductility.
Ingeneral,repairtechniquesmayaffectmorethanoneoftheaboveparameters.
StudieshavebeenconductedatStructuralEngineeringResearchCentre(SERC),Chennaionbeams,columns,andbeam-columnjointstoevaluatetheperformanceofbondedsteelplatejacketingandFRPwrappingtechniquesusingCFRPandGFRP(Lakshmananetal.
,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">04;SERC,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">04a,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">04b,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">04C).
Fig.
6ComputationofequivalentelasticforcesforductilestructuresDuctility-baseddesignconceptsuseequivalenceoffailuredeformation(Figure6(a))orequivalenceoffailureenergy(Figure6(b))betweentheelasticandelasto-plasticsystems,ormodificationstodampingfactorbasedontheductilityratio.
Thesethreeapproacheshavebeenusedforacomparativeevaluationoftheperformanceofjacketedspecimenviz.
,conventionalspecimen.
ISETJournalofEarthquakeTechnology,March-June21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0641Theequivalentelasticforces1ePand2eParecomputedusing1/212yeyAPPd=(21)2eyuPPyδδ=(22)Henceitisfeltthattoevaluatetheeffectivenessofanyrepairmeasure,thefollowingeffectivenessfactorsmaybeused.
Thesameproceduremaybeadoptedforevaluatingnewmaterialsagainstconventionalreinforcedconcrete.
Theeffectivenessfactorsmaybedefinedas()111(retrofit)controleePFP=(23)and()222(retrofit)controleePFP=(24)IS:1893-21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">02(BIS,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">02)givesthemultiplyingfactorsforobtainingseismicforcesincaseofdifferentdampingfactors(Table3ofIS:1893-21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">02).
Basedonthese,theefficiency,particularlyofaductility-basedrepairstrategy,canbeevaluatedascom3repairmFm=(25)wherecommisthemultiplyingfactorfordampingintheoriginalstructure,andrepairmisthemultiplyingfactorfordampingintherepairedstructure.
Theaboveperformancefactorshavebeendiscussedinanumberofpublications(Lakshmanan,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">03b,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">05c,21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">05d).
BEAMSWITHBONDEDLAMINATESTESTEDUNDERPUREFLEXURETable4showstypicaldetailsofRCbeamstestedwithbondedlaminates.
Moredetailsonthesizeofspecimen,testprocedureetc.
,areavailableinLakshmanan(21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">06).
Atypicalload-deflectiondiagramofCFRP-bondedspecimenisshowninFigure7.
TypicalfailuresofjacketedbeamsareshowninFigure8.
TheperformancefactorsforthebeamstestedaregiveninTable5.
Table4:DetailsofRCBeamsSerialNumberBeamNumberBeamDetailsTypesofWrappingNumberofLayers1S1Control--2S2RetrofittedCFRPSingleLayer(Parallel)3S3RetrofittedCFRPSingleLayer(Perpendicular)4S4RetrofittedCFRPDoubleLayer(OneParallelandOnePerpendicular)5S5RetrofittedCFRPDoubleLayer(BothLayersParallel)6S6RetrofittedCFRPSingleLayer(Continuous)7S7RetrofittedCFRPSingleLayer(TwoOverlaps)8S8RetrofittedCFRPDoubleLayer9S9RetrofittedCFRPDoubleLayer42SeismicEvaluationandRetrofittingofBuildingsandStructures11f20;BACKGROUND-COLOR:#4ae2f7">0S11f20;BACKGROUND-COLOR:#4ae2f7">0RetrofittedSteelPlate-11S11RetrofittedSteelPlate-12S12RetrofittedSteelPlate-Fig.
7Load-deflectiondiagramofCFRP-bondedbeamsCFRPspecimenGFRPspecimenBondedsteelplateFig.
8TypicalfailuresinbondedbeamsISETJournalofEarthquakeTechnology,March-June21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0643Table5:PerformanceandMultiplicationFactorsoftheRetrofittedRCBeamsSerialNumberBeamNumber1eP(kN)2eP(kN)1F2Fξ(%)3F1S1166.
8181f20;BACKGROUND-COLOR:#4ae2f7">0.
41.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">01.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">07.
931.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">02S2259.
1f20;BACKGROUND-COLOR:#4ae2f7">031f20;BACKGROUND-COLOR:#4ae2f7">02.
71.
551.
6811.
141.
123S3162.
2172.
31f20;BACKGROUND-COLOR:#4ae2f7">0.
971f20;BACKGROUND-COLOR:#4ae2f7">0.
967.
61f20;BACKGROUND-COLOR:#4ae2f7">01.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">04S421f20;BACKGROUND-COLOR:#4ae2f7">06.
3223.
31.
241.
249.
351.
1f20;BACKGROUND-COLOR:#4ae2f7">045S5266.
1f20;BACKGROUND-COLOR:#4ae2f7">031f20;BACKGROUND-COLOR:#4ae2f7">08.
11.
591.
7111.
231.
136S6222.
7275.
1f20;BACKGROUND-COLOR:#4ae2f7">01.
341.
5211f20;BACKGROUND-COLOR:#4ae2f7">0.
61f20;BACKGROUND-COLOR:#4ae2f7">01.
11f20;BACKGROUND-COLOR:#4ae2f7">07S7263.
2327.
71.
581.
8211.
561.
138S8276.
2311.
71.
661.
7311.
291.
139S9325.
7428.
61.
952.
3812.
871.
1811f20;BACKGROUND-COLOR:#4ae2f7">0S11f20;BACKGROUND-COLOR:#4ae2f7">0311.
3499.
21.
872.
7713.
541.
1911S11297.
2434.
91.
782.
4112.
941.
1812S12394.
1f20;BACKGROUND-COLOR:#4ae2f7">0749.
22.
364.
1515.
1f20;BACKGROUND-COLOR:#4ae2f7">091.
24BEAM-COLUMNJOINTSAnumberofbeam-columnjointshavebeentestedusingtheCFRPandGFRPwrappings.
Aschematicdiagramofloadingonabeam-columnjointisshowninFigure9,andthereinforcementdetailsaregiveninFigure11f20;BACKGROUND-COLOR:#4ae2f7">0.
Theload-deflectiondiagramsofvariousbeam-columnjointstestedareshowninFigures11and12.
Figure13showsthefailureofatypicalbeam-columnjointstrengthenedwiththeCFRPwrap.
Thedetailsofthebeam-columnjointstestedaregiveninTable6.
Fig.
9Schematicdiagramofloadingonabeam-columnjointFig.
11f20;BACKGROUND-COLOR:#4ae2f7">0Reinforcementdetailsofabeam-columnjoint44SeismicEvaluationandRetrofittingofBuildingsandStructuresLoad-deflectionplotforbeam-columnjoint1f20;BACKGROUND-COLOR:#4ae2f7">011f20;BACKGROUND-COLOR:#4ae2f7">021f20;BACKGROUND-COLOR:#4ae2f7">031f20;BACKGROUND-COLOR:#4ae2f7">041f20;BACKGROUND-COLOR:#4ae2f7">051f20;BACKGROUND-COLOR:#4ae2f7">061f20;BACKGROUND-COLOR:#4ae2f7">071f20;BACKGROUND-COLOR:#4ae2f7">081f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">011f20;BACKGROUND-COLOR:#4ae2f7">021f20;BACKGROUND-COLOR:#4ae2f7">031f20;BACKGROUND-COLOR:#4ae2f7">041f20;BACKGROUND-COLOR:#4ae2f7">051f20;BACKGROUND-COLOR:#4ae2f7">061f20;BACKGROUND-COLOR:#4ae2f7">071f20;BACKGROUND-COLOR:#4ae2f7">081f20;BACKGROUND-COLOR:#4ae2f7">091f20;BACKGROUND-COLOR:#4ae2f7">011f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0Deflection(mm)Load(kN)BCJ-2-16-CFRP-1LBCJ-2-16-2L-GFRPBCJ-2-16-1L-GFRPBCJ-2-16-2L-CFRPBCJ-2-16-CONTROLFig.
11Load-deflectiondiagramofbeam-columnjointsLoad-deflectionplotforbeam-columnjoint1f20;BACKGROUND-COLOR:#4ae2f7">021f20;BACKGROUND-COLOR:#4ae2f7">041f20;BACKGROUND-COLOR:#4ae2f7">061f20;BACKGROUND-COLOR:#4ae2f7">081f20;BACKGROUND-COLOR:#4ae2f7">011f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0121f20;BACKGROUND-COLOR:#4ae2f7">0141f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">011f20;BACKGROUND-COLOR:#4ae2f7">021f20;BACKGROUND-COLOR:#4ae2f7">031f20;BACKGROUND-COLOR:#4ae2f7">041f20;BACKGROUND-COLOR:#4ae2f7">051f20;BACKGROUND-COLOR:#4ae2f7">061f20;BACKGROUND-COLOR:#4ae2f7">071f20;BACKGROUND-COLOR:#4ae2f7">081f20;BACKGROUND-COLOR:#4ae2f7">091f20;BACKGROUND-COLOR:#4ae2f7">011f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0Deflection(mm)Load(kN)BCJ-3-16-21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0(c)BCJ-3-16-11f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0(c)BCJ-2-16-2L-GFRPBCJ-2-16-2L-CFRPBCJ-3-16-LacingFig.
12Load-deflectiondiagramofbeam-columnjointsFig.
13Typicalfailureofbeam-columnjointwithCFRPISETJournalofEarthquakeTechnology,March-June21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0645Table6:DetailsoftheReinforcedConcreteBeam-ColumnJointSpecimensSpecimenIDStrengtheningMethodSpacingofStirrupsintheColumnBCJC1ControlSpecimen21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0mmc/c(with3#16mmBarsasTensionReinforcementintheBeam)BCJC2ControlSpecimen21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0mmc/c(with2#16mmBarsasTensionReinforcementintheBeam)BCJR1CFRP(SingleLayer)BCJR2CFRP(DoubleLayer)BCJR3GFRP(SingleLayer)BCJR4GFRP(DoubleLayer)21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0mmc/c(with2#16mmBarsasTensionReinforcementintheBeam)BCJR5CFRP(DoubleLayer)21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0mmc/c(with3#16mmBarsasTensionReinforcementintheBeam)BCJR6MicroconcretewithLacing21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0mmc/c(with3#16mmBarsasTensionReinforcementintheBeam)Theload-deformationcharacteristicsclearlyrevealthatthereisnosignificantimprovementtostiffnessbecauseofGFRPorCFRPwrappings;itisfeasibletoenhancethecapacityofthebeam-columnjointbyGFRPorCFRPwrappings;thepost-peakresponseofcontrol,aswellasstrengthenedbeams,showahighrateofload-dropwhichisnearlyconstantinallthebeam-columnjointstested;GFRPgivesbetteroverallperformanceascomparedtoCFRP;itgiveshigherstrength,andtheloaddeflectioncurveenvelopstheloaddeflectioncurveofCFRPatallstages.
1.
Procedure-1Ascanbeseenfromtheload-deformationbehaviourofthebeam-columnjointstested,thereisasignificantloaddropinthepost-peakloadbehaviour,possiblyduetoaninherentdetailingdeficiencyinthebeam-columnjunction.
Allrepairmeasurescarriedoutcouldnotrectifythisinherentweakness,thoughtheyhaveregisteredhigherloadanddeformationlevels.
Asafirstapproximation,themaximumpermissibleloaddrophasbeenassumedas25%andananalyticalmodelinghasbeendone.
WithreferencetoFigure14,PointCischosensuchthatithasavalueofloadequalto1f20;BACKGROUND-COLOR:#4ae2f7">0.
75Pmax(atPointB).
Disdeflectioncorrespondingtotheaboveload.
Fig.
14Idealisedload-deformationdiagramofbeam-columnjointApproximatingareaundertheexperimentalload-deflectioncurveABCDbytheareaundertheidealizedcurveAB'C'D,weobtain46SeismicEvaluationandRetrofittingofBuildingsandStructures/2eLuLLAPPδδ=(26)Substituting()11/,LLPPδδ=thisbecomes()211//2eLuLAPPPδδ=(27)SinceeA,uδ,1δ,and1Pareknown,LPcanbeobtained.
Correspondingtoa25%dropinLP,thedeformation*uδandeffectivearea*eAcanbecomputed.
UsingLP,Lδ,*uδand*eA,theperformancefactors1Fand2FarecomputedasgiveninTable7.
Table7:PerformanceFactorsforBeam-ColumnJointSpecimensBeamIDLP(kN),repaired,companionLLPPLδ(mm)uδ(mm)1eP(kN)1F2eP(kN)2FBCJC239.
31f20;BACKGROUND-COLOR:#4ae2f7">01.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">05.
51f20;BACKGROUND-COLOR:#4ae2f7">026.
85162.
871.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0191.
791.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0BCJR135.
511f20;BACKGROUND-COLOR:#4ae2f7">0.
91f20;BACKGROUND-COLOR:#4ae2f7">04.
4541f20;BACKGROUND-COLOR:#4ae2f7">0.
11215.
941.
33319.
931.
67BCJR251f20;BACKGROUND-COLOR:#4ae2f7">0.
1f20;BACKGROUND-COLOR:#4ae2f7">041.
276.
1536.
28227.
21f20;BACKGROUND-COLOR:#4ae2f7">01.
39295.
421.
54BCJR358.
221.
486.
8531.
69232.
731.
43269.
371.
41f20;BACKGROUND-COLOR:#4ae2f7">0BCJR461.
631.
577.
1539.
18272.
1f20;BACKGROUND-COLOR:#4ae2f7">031.
67337.
691.
76BCJC151f20;BACKGROUND-COLOR:#4ae2f7">0.
821.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">05.
4244.
19277.
1f20;BACKGROUND-COLOR:#4ae2f7">081.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0414.
281.
1f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0BCJR563.
251.
246.
2348.
19332.
551.
21f20;BACKGROUND-COLOR:#4ae2f7">0489.
431.
18BCJR696.
571.
91f20;BACKGROUND-COLOR:#4ae2f7">04.
3352.
52647.
1f20;BACKGROUND-COLOR:#4ae2f7">072.
341171f20;BACKGROUND-COLOR:#4ae2f7">0.
832.
83Fromtheabovetable,itisseenthattheperformancefactors1Fand2FareimprovedfortheRCbeam-columnjointspecimensprovidedwith2nos.
of16mmdiameterbarsandretrofittedwithcarbonaswellasglassfibrescomparedtothecontrolspecimens.
Theperformancefactors1Fand2FarealsoimprovedfortheRCbeam-columnjointsprovidedwith3nos.
of16mmdiameterbarsandretrofittedwithtwolayersofCFRPandmicroconcrete.
Further,thosearemuchhigherfortheRCbeam-columnjointspecimensretrofittedwithmicroconcreteandlacingcomparedtothespecimenswithFRPwrapping.
2.
Procedure-2Thebasichypothesismadebasedontheexperimentalresultsisthattherepairdoesnotaltertheslopeofthefallingbranch.
Also,thefailuredeflectioninallthesecaseshasbeenobservedtobebetween55to71f20;BACKGROUND-COLOR:#4ae2f7">0mm,andallowingforexperimentalscatter,thiscanbetakenasaconstantat61f20;BACKGROUND-COLOR:#4ae2f7">0mm.
Thiswouldstraightawayleadtothesamevaluefor2,ePand2Fwouldbeconstantat1.
1f20;BACKGROUND-COLOR:#4ae2f7">0.
Hence,forlong-periodstructureswithdroopingpost-peakresponsesandconstantfailuredeformations,therepairsareineffectiveunlessthestiffnesscanbesignificantlyaltered.
Thishasnothappenedinthesecases.
Thevalueof1ePcanbeshowntobe()121f20;BACKGROUND-COLOR:#4ae2f7">012eyeyAAPPδ=(28)whereeAistheareaoftheelasto-plasticsystem,and1f20;BACKGROUND-COLOR:#4ae2f7">0Aisthereductionduetothepost-peakresponse.
Thisleadstothevaluesof1Fequalto1.
1f20;BACKGROUND-COLOR:#4ae2f7">07,1.
16,1.
23,and1.
33fortheBeamsBCJR1toBCJR4,whicharesignificantlylowerthanthevaluesgiveninTable7.
Furtherstudiesare,however,neededforamorerealisticevaluation.
ISETJournalofEarthquakeTechnology,March-June21f20;BACKGROUND-COLOR:#4ae2f7">01f20;BACKGROUND-COLOR:#4ae2f7">0647CONCLUSIONSThispaperattemptstogathertheavailableinformationparticularlyonthenonlinearbehaviour,andthevariousapproachesavailabletoevaluatetheseismicsafetyofbuildings.
Itisemphasizedthattheexistingprocedureisgrosslyapproximate,andhenceimprovingsectionsoftheapproachtohighlevelsofaccuracywouldnotnecessarilyleadtoabetterresult.
TheneedofthepresenthouristoseewhatneedstobedoneintheIndiancontext.
Thebasicinputsareearthquakespectrum,nonlinearload-deformationbehaviourundermonotoniccyclicandrandomloadings,acceptablelevelsofdamageundervariousperformancelevelsetc.
,andthesehavealotofgreyareas.
Thereneedstobeawiderdiscussionamongtheresearcherstoevolveagoodstandardforusebytheprofession.
Theneedforevaluatingthevariousrepairstrategiesforuseintheimprovementoftheseismicperformanceofreinforcedconcretestructureshasbeenhighlighted.
Thebehaviourofrepairedbeamsandbeam-columnjointshasbeendiscussed.
Itisobservedthatinherentdeficienciesinthedetailingofthebeam-columnjointsgetreflectedevenafterrepair,thoughtheperformancefactorsindicatesignificantimprovement.
Thereisaneedtoevolvesuitableperformancefactorswhenthesystemshowsanegativestiffness.
Twoofthelogicalextensionsshowthattherepairwouldnotbeaseffectiveinthesecases.
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