ML18025A667

Susquehanna Units 1 and 2 - Final Report on Shear Studs

ML18025A667
Person / Time
Site:	Susquehanna
Issue date:	12/30/1977
From:	Gore A Bechtel Power Corp
To:	Office of Nuclear Reactor Regulation
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Download: ML18025A667 (179)

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FINALREPORTSHEARSTUDSFORSUSQUEHANNASTEAHELECTRICSTATIONUNITS1AND2Preparedby:AravindS.GoreCheckedby:GirishH.ShahApprovedby:M.J.LidlBECHTELPOWERCORPORATIONSanFrancisco,CaliforniaDecember30,1977(P-85a)

IgV1 TABLEOFCONTENTSSectionTitlePage'1.0Purpose2.0ShearConnectors3.0Background4.0DescriptionofDeficiencies5.0ImmediateCorrectiveAction6.0AnalysisofSafetyImplications7.0TechnicalEvaluationofDeficiencies8.0CorrectiveActions269.0~Conclusion31APPENDICESStatisticalAnalysisand-EvaluationofFieldTestDataFieldTestDataReducedFieldDataDRepairProceduresEandFReportby"FngineeringDecisionAnalysisCompany"(P-Sea>

1.0PURPOSEr.Thepurposeofthisreportistoprovidefinaldataandin-formationasrequiredby10CFR50.55(e)(3)subsecuenttothenotificationofareportabledeficiency.'Thesubjectdeficiencyisassociatedwiththeinstallationandinspec-tionofsteelshearconnectorsinthereinforcedconcretecompositefloors.2.0SHEARCONNECTORSShearconnectors,usedonthisproject,areround,headedsteelstuds,commerciallymanufactured.Aftertheerectionoffloorbeamsandtheplacementofthemetaldecking,studsareattachedtothetopflangeofstructuralsteelfloorbeams,byresistance,weldingusingasemi-automaticprocess.Thestudsarethenembeddedinsubsequentlyplacedconcreteandprovideashearconnectionbetweentheconcreteslabsandstructuralsteelframingtodevelopacompositefloorsystem.Materials,i'nstallatio'n,welding,inspectionandtestingofthestudsisinaccordancewithProjectSpecification8856-C-19,"InstallationofShearConnectors,"andAmericanWeld-ingSocietyCodeAWSDl.l-75.Thespecificationrequiresabendtesttobeperformedonthefirsttwostudsweldedtoeachstructuralsteelmember.'fterthecompletionofstudinstallationonanybeam,theweldbetweenthestudand 1

structuralsteelisrequiredtobeinspectedvisuallyandtestedbyselectivelybendingthestudstoaminimumangleof30degreesfromthevertical.Suchbendingdoesnotaf-fectthefunctioningofthestudasashearanchor.Compositeconstructionhasbeenusedinthefollowingstructures:CategoryIl.ReactorBuildingUnits1and2,2.ControlBuilding3.DieselGeneratorBuildingNon-CategoryI1.TurbineBuildingUnits1and22.RadwasteBuilding3.CirculatingWaterPumphouseInspectionofstudsinallCategoryIstructuresistherespon-sibilityofQualityControl(QC)personnelandtheQualityCon-trolprogramprovidesthetechnicaldirectionsandmeansofdocu-mentationofinspectionandtestingactivities.ForNon-CategoryIstructures,thisfunctionisperformedbyFieldEngineering;ahowever,documentationisnotarequirement.3.0BACKGROUNDSubsequenttoQCfinalpre-concreteinspectionandacceptanceonMay21,1977forconcreteplacement183-S-02(Area33atElevation719'-1"intheReactorBuildingUnit2)PennsylvaniaPower&LightCompanyQualityAssurance(PLNQA)personnelfound(P-85a) somestuds,whichdidnotmeetspecificationrequirements.Itwasalsoobservedthattheinspectionrequirementswerenotcompletelymet.Twootherareaswereinprogressatthistime(Placement714-S-03,Area21,E)evation771'-0"intheControlBuildingand201-S-02,Area28,Elevation749'-1"intheReactorBuildingUnit1).QCperformedanotherinspectionofallstudsfortheseplacements.Oncompletionoftherequiredrepair/rework,QCacceptedtheseplacementareasonMay26,1977.Subsequently,onthesamedate,PLNQAagainfoundafewmorenonconformingstudsfortheseplacements.AstopworkreportwasissuedonMay27,1977precludinganyconcreteplacementintheabovenotedareas.4.0DESCRIPTIONOFDEFICIENCIES4.1Constructionpersonnelfailedtorepair,testorreplacethedefectivestudsasrequiredbythespecification.-4.2QCpersonnelfailedtoinspectandcarryouttheassignedresponsibilitiesasdefinedinthequalitycontrolinstructions(QCI)forstudweldinspection.Thefollowingspecificsarecited:a.ResponsibleQCengineeringpersonnelintheweldingdisciplinesignedinspectionrecords(P-Sea)

'i signifyingthat100%inspectionhadbeen.per-formed.However,theinspectionsasdefinedbytheprogramwerenotcompletelyperformed.b.Responsible.QCsupervisionpersonnelatthejobsitefailedtoprovideadequate,definitivedirectionstotheresponsible.QCengineeringpersonnelintheweldingdisciplineandfailedtodetectthelackofacceptableperformanceoftheQCengineeringpersonnel.5.0IMMEDIATECORRECTIVEACTION5.1PlacementsIdentifiedinMCAR-1.18Nonconformancereports(NCR's)wereissuedagainstthestudsfoundtobeinnoncompliancewithspecifiedrequirementsforconcreteplacements183-S-02,201-S-02and714-S-03.TheseNCR'swereevaluatedanddisposi-tionprovidedtoeither"rework"or"useasis"de-pendinguponengineeringevaluation.Inaddition,QualityAssuranceissueda-ManagementCorrectiveActionReport(MCAR-1.18)onMay26,1977andaStopWorkReportonMay27;1977.Thesereportsprecludedfurtherembedmentofshearstudspendingcompletereinspectionofstudsintheseplacementstoassureconformancetospecificationanddesigndrawingrequirements.Acompletereinspectionofthethreeconcreteplacement(P-85a) areaswi.thinthescopeoftheSCARwascarriedout.Thereinspectionwasaccomplishedinaccordancewithaspeciallypreparedprogram,containingseveralpro-visionstomaximizetheeffectivenessoftheinspec-tionandtovirtuallyeliminateanyinspectionerror.Thespecialprovisionsincludedthefollowing:a.Adetailedtrainingprogramspecificallyad-dressingtheuniqueaspectsofthespecialinspectionandthefundamentalrequirementsforstudinspectionwasconducted.Specialemphasiswasplacedontherecentproblemsrelatedtothestuds.b.Eachstudtobeinspectedwasuniquelyidenti-fiedbynumber,providingtraceabilitytotheinspectionrecordfortheparticularstud.c.As-builtdrawingsweremadeidenti,fyingthelocationofeverystudbyprovidingthedirectionsequenceofthestudnumbers.d.Aseparatechecklistwascompletedandsignedforeachparticularstud.e.Eachindividualstudreceiveda"generalsound-nesstest,"consistingofstrikingthestudusingaheavyhammer.Studsfailingthesoundnesstestwerereplacedwithnewstuds.(P-85a) f.Eachinspectionforeachindividualstudwasdoc-umented,andtheresultinginspectionrecordswereindependentlyreviewedforcompletenessandaccept-ability.g.NCR'swerewrittenidentifyingnonconformingcondi-tionsandweredispositioned'providingalternatesofrepairandretestorreplacementtherebyallowingthefieldengineerparticipatinginthereinspec-tiontoprovidedirectionforimmediatereplace-ementorrepairasnecessary.Eachoccurrencewasdocumented.Allrequiredrepairwasaccomplishedwithacceptableresults.Resultsoftheaboveinspectionactivitieshavebeenproperlyrecordedanddocumented.5.2FieldTestData5.2.1Duringthisperiod,studinstallationinprogressinotherareas,wasalsostopped.Theseareasincluded:a.ReactorBuilding:Placement202-S-Ol,area27;199-S-01,area25;202-S-02,area29,allatEle-vation749'-1"inUnit1.Placement182-S-Ol,area32;184-S-01,area34atElevation719'-1"inUnit2.(P-85a) b.ControlBuildingPlacement714-S-03,'rea21c.Therewerealsosomestudsexposedinacon-structionopeninginapreviouslypouredslabintheDieselGeneratorBuilding.AllstudsintheaboveareaswerethoroughlyinspectedbyQCusingthesameinspectioncriteriaasdescribedinSection5.1.5.2.2FieldEngineeringalsoperformedathoroughinspectionofallexposedstudsinstalledpriortoMay1977intheTurbineBuildingandCircu-latingHaterPumphouse.5.2.3FortheRadwasteBuilding,civilconstructionwascompletedpriortoMay1977.Thus,noexposedstudswereavailableforinspection.5.3AboveinspectionresultsofSection5.2identifiedasfieldtestdatainthefollowingsections,arethebasisforstatisticalevaluation.Itmustbenot'edherethatfor.thethreeareasnoted.inSection5.1,1.Somestudswereinstalledafterthebottomre-inforcingsteelwasplaced,thusmakingthestudinstall'ationdifficult.(P-85a>

2.Somestudswereweldeddirectlythroughdecking.Thus,thestudinstallationintheseareascannotbeconsi-deredas,representative.Additionally,thestudsintheseareasweresubjectedtomanyinspections,therefore,theinspectionresultscannotbeusedasareliablesampledata.Basedontheseconsiderations,thisdatawasex-cludedinthestatisticalanalysis.6.0ANALYSISOFSAFETYIMPLICATIONSThestudinstallationisgroupedintovariouscategoriesnotedbelow-toprovideabaseforanalyzingthesafetyimplicationsandperformingtechnicalevaluation.6.1StudsembeddedintheconcretepriortoMay1977.6.1.1Asthesestuds,areembedded,theyarenotac-cessibletodeterminethequalityofthestudinstallation.Untilthediscoveryoftheproblem,therehadbeennomajorchangeeitherintheinspectionandtestingcriteriaorinthemethodofstudinstallation.Thusthefieldtestdata,ob-tainedasdescribedinsection5.0,canbeconsideredastrulyrepresentativeofthepastwork.Atcertainlocations,thedataindicatesabnormallyhighstudfailurerates,whichdeservespecialattention.H(P-8Sa)

6.1.2Astatisticalevaluationofthefieldtestda-tahasbeenperformedforthepurposeofes-tablishingthefailurerateandprojectingat90%confidencelevelthenumberofreliablestudsthatareconsideredeffectiveintheexisting,installedbeams.Thestatisticalprojectionofthenumberofreliablestuds,togetherwiththecalculatedminimumnumberofstudsrequiredforeachbeam,arethebasisforverifyingtheadequacyofthecom-positestructuralsystem.6.1.3Basedontheforegoinggeneralcriteriathefollowingtwocategoriesareestablished:6.1.3.1Forareas-whichexhibitacceptablestudfailurerates,thetestdataonweldedstudsindicatesthateitheroneofthefollowingconditionsismet:a)Studfailureratesfallwithinacceptableindustrypracticesoasnottojeopardizethestruc-turalrequirements.b)Theprojectednumberofreliablestudsexceedstheactualminimum(P-85a) requiredaccordingtostructuraldesigncalculation.Consequently,intheseareasthestructuralintegrityhasnotbeencompromised,andthestructuralsys-temisinfullconformancewiththebasicdesigncriteriaandthebasesoftheSafetyAnalysisReport.TheTurbineBuilding,Unit1and2,ControlBuilding,CirculatingWaterPumphouse,RadwasteBuildingandDieselGeneratorBuildingbelongtothiscategory.6.1.3.2.Inareasassociatedwithhighfail-urerates,therearesomebeamsforwhichtheprojectednumberofreli-ablestudsisinsufficientwithre-specttotheminimumrequiredbystructuraldesign.,Thisconditionhasthe,followingimplications:ThedesignrequirementsstatedintheSafetyAnalysisReportarenotmetcompletelyduetothepotentialstud(P-S5a)

deficiency.Repairworkmustbeun-dertakentocorrectthedefectiveinstallationsandassurethattherearenostructuralsystemswhichdonotmeetthedesignbases.TheReactorBuildingUnit1and2fallinthiscategory.6.2StudsNotEmbeodedinConcreteattheTimeoftheReporteoProem.Intheseareas,deficientstudsaretraceabletospecificconstructionand/orinspectionpractices,whichhavebeenpositivelyioentified.Thestudsintheseareashavebeeninspectedunderstricten-forcementoftherevisedinsoectionproceduresandrepairedorreplacedasreauired.Newstudswerealsoinspectedtothefullinspectionreauirements.Thisprovidesadeauateassuranceregardingtheaualityofthestudinstallationintheseareas.70TECHNICALEVALUATIONOFDEFICIENCIES7.1GeneralImpactoftheabovenoteddeficienciesrendersthestructuraladeauacyofthestudsinstalledindeter-minateintheabsenceoftechnicalevaluation.Reme-dialmeasurestakenandtobetakentopreventtherecurrencearedescribedinsection3.0and8.0.(P-S3a>

Therefore,thetechnicalevaluationinthissectionislimitedtothestudsembeddedintheconcreteslabspriortoNay1977.Theapproachusedforthisevaluationisasfollows:a.Evaluatethedesigncriteriaandtheoreticalconsi-derations,assumptions,associatedresearchandtesting,whicharethebasisforthedesignre-quirementsintheAISCspecification.Baseduponthisevaluation,reassessand/orrevisetheoriginaldesignandcomputethenumberofstudsrequired,whichnotonlysatisfystrengthrequire-mentsbutalsomeetthespecificationrequirements.b.Analyzethefieldtestdatastatisticallytoarriveatasuccessrateatacertainconfidencelevelforeachbuilding.Baseduponthisanalysiscomputethenumberofre-liablestudsoneverybeam.c.Designshearconnectors.d.Identifythosebeamswherethenumberofstudsre-quiredislargerthanthereliablestuds.7.2DesignCriteriaandStructuralDesignofCompositeConstruction 0

GeneralAcommonapproachinthedesignofstructuralfloorsystemsistodevelopcompositeactionbetweenthesteelframingbeamsandtherein-forcedconcreteslabs.Thecompositeactionaffordsaflexuralsystemsuperiortothebeamorslabactionaloneandgenerallyresultsincostsavingsintheoveralldesign.Compositeactionisachievedbyprovidingshearconnec-torsweldedtothetopsideofthebeamandembeddedintheconcrete.Theseshearconnec-torscanalsobeusedto-improvetheanchorageofsteelframingintoconcreteslabstopermitthetransferofhorizontalloadsfromthefram-ingtotheslabdiaphragmandtoincorporatetheslabinresistingheavyloadssuspendedfromthebeams.7.2.2DesignCriteriaandTheoreticalConsiderationsSection1.11of'SpecificationforDesignFabri-cationandErectionofSteelforBuildings'SixthEdition)adoptedbyAmericaninstituteofSteelConstructionin1969andsubsequentthreesupplementsarethebasesforstructuraldesign.Thenewrevisionofthespecificationisdueforpublicationinearly1978.Revisedsection(P-85b) 1.11to.beincorporatedintheforthcomingedi-tionispublishedin"InrycoCompositeBeamDesignManual,21-12"byInrycoInc.inJuly1977.Thisrevisionisessentiallybaseduponthepaper"CompositeBeamswithFormedSteelDeck,"byGrant,FisherandSlutter,inAESCEngineeringJournal,Volume14,FirstQuarter1977.Promthereviewofthedevelopmentofthissec-tion,itisevidentthatthedesigncriteriaisstillinthedevelopmentalstage,andisbeingmodifiedcontinuouslytoreflectthelateststateoftheart.Themajorityoftheresearchandtestingdonetodatepertainstocompositebeamswiththinslabs.Intheassociatedtheoreticalconsidera-tions,theultimatemomentcapacityof,thetconcretesectionisdisregarded.Thus,thecontributionoftheinternalcoupleproducedbyshearconnectionbecomesverysignificantincomputingtheultimatestructuralcapacityandthefactorofsafety.Forreinforcedthickslabs,however,theultimatemomentcapacityoftheconcretesectionbecomessodominant thatthesignificanceoftheshearconnectionisgreatlyreduced.Thus,thedesignbaseduponthespecificationresultsinahighre-servecapacityforcompositebeamswiththickslabs.TheAISCspecification,however,.hasnotrecognizedthisphenomenon.The-AISCSpecificationanditssupplementsde-finetheallowablehorizontalshearloadsforstudsandalsoprescribeanalyticalproceduresforevaluatingincompletecompositeactionbyequation(l.ll-l)asfollows:Sff=S+Vh(S~-S)VIiWhere:Vhthelesserofthehorizontalshearassociated.witheithertheconcreteorthesteelsectionV11theshearvaluepermittedbythe"number,ofconnectorsprovided,re-levantforincompletecompositeactionSssectionmodulusofthesteelbeamreferredtoitsbottomflangesectionmodulusofthetransformedcompositesection(ful1)referredtoitsbottomflangeeffectivesectionmodulusoftheincompletecompositesection(P-85b)

Theequationisbasedonearlyresearch,anditrepresentsalinearvariationofSffwitheffrespecttoV'h.RecentresearchrecognizedbytheAISCindic-atesthatthefunctionalrelationshipdescribedaboveismoreaccuratelyexpressedbyintroduc-ingasquarerootexpressionfortheshearra-tioinequation(l.ll-l).Thismodificationrepresentsarefinementontheanalyticaltech-niquefortheevaluationofincomplete.compo-siteaction,anditresultsinasubstantiallyhighercapacitythanthatallowedbythepre-vious,extremelyconservativelinearexpres-sion.Thisproposedexpressionoffersalib-eralizedanalysisreflectingthecurrentthink-ing,butitprudentlyaffordssomeconservatismwithrespecttotheresearchfindings.Thespecificationalsoprescribesaminimumof25%ofcompleteshearconnectiontobedevel-opedbythestuds.Thislowerlimit,however,isarbitraryandisnotnecessarilybaseduponthetheory.Znfact,testresultsdescribedintheabovereferencedpaperindicatethatthetestbeamswithwideslabsandlessthan25%ofcompleteshearconnectionperformed0 satisfactorilywithanadequatefactorofsafety.Thus,thetestprovesthatthepercentageshearconnectionisnotneces-sarilyafunctionofthecapacityofthecompositebeamoritsfactorofsafety.DetaileddiscussiononthissubjectcanbefoundintheabovenotedpaperbyGrant,FisherandSlutterandalsoinAppendix"E".Asasummaryitisconcludedthat:1.TheanalyticalapproachperthepresentAISCspecification,althoughreasonableforbeamswiththinslabs,=isaverycon-servativemethodforthecompositebeamswiththickslabs.2.Thedesignbaseduponthespecificationusingrevised1.11-1equationandassum-ing25%completeshearconnectionwillstillprovideadequatemarginofsafetyandconservatism.7.2.3StructuralDesignInthecurrentstructuraldesign,theweldedstudswereprovidedinthemajorityofthebeamstodevelopcompleteaction,andthe(P-85b) steelbeamsectionsweredesignedaccordingtothearbitraryoverallfloorloadsprescribedforthevariousareas.However,inviewofthepotentialproblemwiththeweldedstuds,thestructuraldesignwasreassessedwiththeintentionofrelievingthestudreouirementswithoutviolatingthebasicoesigncriteria.Thefirststepinthereassessmentwastore-viewtheloadingassociatedwitheachofthefloorbeams.Thiswasachievedbyconsideringactualloaddistributionsobtainedfromtheeouipmentandflooroccupancieswhichatthisdatehavebeenestablishedmoredefinitelythanatthetimeofinitialdesign.Anotheraspectoftheloadrefinementconsistedofamoredetailedanalvsisofthetributaryareasforeachbeambyrecognizingactualloaddis-tributionsoerivedfromtheone-wayandtwo-wayflexuralactionofthecorrespondingcon-creteslabs.Thesecondstepinthereassessmentwastore-finetheoesignbycomputingtheeffectivesec-tionmodulusaccordingtothelatestanalytical(0criteria,i.e.,theAISCapprovedexpression-ls-

withthesouareroot.Thisanalyticalrefine-mentallowedforarevisedhighercapacityforsectionsinwhichtheprojectednumberofreli-ablestuasdidnotpermitcompletecompositeaction.Theaboveanalyticalfeatureswereusedprudently,andtheminimumnumberofstudsreouiredperbeamwasjudiciouslyselectedbythecriteriadescribedinSection7.4.7.3Outline-ofStatisticalAnalysisandEvaluation:Thissectionprovidesabriefdescriptionofthesta-tisticalapproachusedintheprojectionofthereli-abilityofstudsinstalledtodate.AmoredetailedcoverageofthestatisticalanalysisusedforthisreportisprovidedinAppendixA.Anotherstatisticalanalysisusingdifferentmethodwasperformedindepen-dently,whichgaveessentiallysamebasicresults(ReferAppendixF).Theinitialphaseofthestatisticalanalysiswastosegregatethefieldtestdataintohomogeneousgroupsjudgedtobestatisticallycompatible.ThisjuogementwasbasedonChi-sauaretestonsimilaritiesofthestudfailureratesandtheirdistributionpatterns.Thefirstlevelofsegregationestablishedwasaccord-ingtothevariousbuildingswithintheplant.Eachstructurewasthusrecognizedasaseparategroupwithitsown-characteristicsamplingandcorresponoingsta-.tisticalprojections.

Thesecondphaseofthestatisticalevaluationconsistedofdeterminingthereliablestudsforeachoftheestablishedgroups.Thesepro-jectionsarebasedonthefailureratesde-rivedfromfieldtestdata.Theirdevelopmenttakesintoaccountthenumberofstudstestedwithrespecttothetotalnumberinstalled,andrecognizesthatthereliabilityofthestudsmustnotbeonanindividualbasis,butwithdueregardtostudgroupingsderivedfromtherequirednumberofstudsperbeam.The,ana-lyticalbasesofthestatisticalprojectionsareder:ivedfromtherequirednumberofstudsperbeamandarebasedonthehyperbinominaldistributions,withoutresortingtoempiricalidealizations.Thefundamentalassumptionisthatthefieldsamplesareunbiasedandapplic-ableto,thebalanceofthecorrespondingstudgroup.Thisassumptionisjustifiedsincetheexposedareaswherethesamplingwasobtainedcameintoexistencerandomly,andduetorea-sonswhichareunrelatedtothestudweldingandQCinspection.ThequalityofthestudJwelding.intheseexposedareaswerenotin-fluencedbyandareindependentofthelo-cationoftheseareas.'P-85b)

Theconfidencelevelofthestatisticalprojec-tionofreliablestudswassetat90%.Thislevelofconfidenceisconsistentwiththecri-tieriausedbygoverningorganizationsin-volvedinthepreparationofcodesofpractice.Additionally,baseduponengineeringjudgement,theprobabilityofexceedingthedesignliveloadisextremelylow.7.4DesignofShearConnectors7.4.1GeneralTheshearconnectorsusedinallinstanceswereweldedheadedstuds,andar'edesignedtobein-stalledbyusingasemi-automaticweldingpro-,cess.7.4.2DesignCriteriaa.AsdiscussedinSection7.2.2,partialcompositeaction(V'h)waslimitedto25%.b.Thelatestexpression(squareroot)wasusedforcomputingtheeffectivesectionmodulusunderincompletecompositeactionandthecorrespondingstudrequirement.c.P'resentAESCcodedoesnotaddresstheef-feetofgroupingofstudsinarib.Latest researchandproposedrevisiontothespec-ificationrequiresthatiftherearemorethanthreestudsinarib,thecumulativeallowablecapacitymust'becomputedbyusingthereductionfactor(Equations1.11-8and1.11-9).Thestudrequirement,whichismorestringentbaseduponthenewcode,hasbeenused.7.4.3.Followingtheabovedesigncriteria,thenum-berofstudsdictatedbytherevisedstruc-turaldesigncalculations,basedonreassessedloadinganalysis,werecomputed.7.5ConservativeFeaturesNotResortedtointheDesignThisisacommentaryonsomefeaturesthatwouldin-creasethemarginofsafetyofthedesign.1.Basedonengineeringjudgement,theallowableloadsstudscouldbeincreasedinproportiontothesquarerootoftheconcretecompressivestrengthf'c.Znthecurrentdesign,theallowablestud,loadsbasedonf'4000psi,accordingtotheAISCSpecifica-tionhavebeenusedactualf'hichiscwithouttakingcreditforthecloseto5000psi.(P-85b) 2.Inthebasicdesigncriteria,liveloadsareas-sumedtobeactingovertheentirefloorarea.However,underactualoperatingconditions,thisishighlyunlikelytooccur.Thus,thereductionthatmaybeachievedbyconsideringactualliveloadsisnotusedinthereviseddesign.3.ForcomputingN2,(Equation1.11-7),theunderly-ingassumptionisthatthehorizontalshearisre-sistedbyonlythosestudswithintheshearspan.Inreality,becauseofthelongitudinalbottomreinforcingsteel,thehorizontalshearwillbetransferredtoadjoiningstuds,althoughthisphenomenonisnotrecognizedbyAISC.Thus,thecomputedN2baseduponpresentdesignwillresultinanevenhigherfactorofsafety.7.6DiscussiononRadwasteBuildingTheRadwasteBuildingwascompletedpriortoMay1977.Asnostudswereexposedatthetimetheproblemwasdiscovered,actualtestdatacouldnotbeobtainedonthesamebasisasitwascollectedforotherstruc-tures.Fortheslabat715'-0"elevation,thereissomerecordavailableonthevisualinspectionandtestingactivitiesperformedbyFieldEngineeringcol-lectivelyonareabasisinsteadofindividualbeam(P-85b) basis.Additionally,therearenosoundnesstestre-sultsavailablefortheseareas.Therecordincludingbendtestresultsonthestudsfailingvisualexamina-tionisshowninthefollowingTable.TABLElAreaNo.ofTotalNo.beamsstudsStudsfailingStudsfailingvisualexam-bendtestination272322352,4901841694110315881771375761141,0958512729591280175959InterviewswiththeresponsibleFieldEngineerandthewelderprovidedfollowinginformation.I,1.Studsfailingvisualorbendtestwerenotinasingleclusterbutwerespreadovertheentireareawithoutanydefinitepattern.(P-85b)-

2.Thewelderwhodidthemajorityofthestudweld-ingonthisbuilding,workedpreviouslyontheCirculatingWaterPumphouse,andispresentlyworkingontheDieselGeneratorBuildingfromtheverybeginning.ItisnotedthatthefieldtestdatafortheabovetwobuildingindicateOSfail-urerate,whichisareflectionontheworkmanshipofthe.welder.3.Asamatterofroutine,ithasbeenthepolicyoftheweldertoreplacethestud,whenitwouldgiveunsatisfactorysoundoftheshot.4.Additionally,althoughnotrequiredbythespeci-fication,thewelderhasbeenbendtestingthelasttwostudsoneverybeam.Basedupontheengineeringjudgementandtheevalua-tionofaboverecordandinformation,thepotentialfailurerateontheexistingstudinstallationwouldbeextremely'low.Inaddition,presentstructuraldesignisbaseduponcompletecompositeaction;there-fore,theadditional'factor.ofsafetyisinherentlybuiltintothedesign.Thus,withadeauateassurance,itisconcludedthatthepresentstudinstallationmeetsthedesign,criteria.(P-85b)

7.7Conclusions7.7.1ThedesignofcompositebeamswiththickslabsperpresentAISCspecificationisextremelyconservative.7.7.2=Allexistingbeamswhendesignedbaseduponthebasictheoryandcomputednumberofreli-ablestuds,haveadequatemarginofsafetywithoutperformingany.repairormodifica-tion.Thisdesign,however,doesnotsatisfytherequirementofthespecificationforall*beams.7.7.3Inordertomeetthespecificationrequire-mentsasnotedintheSafetyAnalysisReport,thosebeamswherethenumberofstudsrequiredperreviseddesignissmallerthanthenumberofcomputedreliablestuds,willberepaired.7.7.4Usingtheabovecriteria,itisobservedthatafewbeamsintheReactor'Buildingrequirerepair.Thesebeamsareidentified,andtheassociatedrepairmethodsaredescribedinAppendixD.8.0CORRECTIVEACTIONCorrectiveactionaregroupedinthreecategories.Eachcategoryandcorrespondingactionsaredescribedbelow.(P-85b) 8.1CategoryIThiscategorydescribesthosestudsalreadyembeddedinconcretepriortodiscoveryofthisprobleminMay1977.Toevaluatetheimpactofthedeficienciesonthe.adequacyofthestructuralmembers,fielddatawasobtained,analyzedandevaluated.Baseduponthisevaluation,thenumberofprojectedreliablestudswascomputedforeachbeamandcomparedwiththe-numberofstudsrequiredbaseduponreassessmentofthedesigncriteria:Wherevertherevisedstudrequirementisfoundtobegreaterthantheprojec-tedreliablestuds,thesebeamswillberepaired,asdescribedinAppendix'D'RepairProcedures",.Oncompletionoftherequiredrepair,theexistingstructuralmembers,willsatisfythedesignrequire-ments.8.2CategoryZIThiscategorydescribesthestudsineightplacementsinControlandReactorBuildings,whentheproblemwasdiscovered(SeeSection3.'0and5.0).Studsintheseplacementshavebeenextensivelyin-spe'cted,examinedandtestedasdescribedinSection5.0,thusprovidingadequateassurancethatthesestuds(P-95a}

(-willperformsatisfactorilyunderdesignloads.There-fore,nofurthercorrectiveactionisdeemednecessary.8.3CategoryI1IThiscategorybelongstopresentstudinstallationsincethediscoveryoftheproblem.Sincecompletionofabovenotedeightplacementsthefollowingspecificcorrectiveactionshavebeeninstitutedatthesite.8.3.1CorrectiveActionsbyQualityControl.a.TheQCweldingdisciplinehasbeenre-lievedoftheresponsibilityforin-spection"ofthestuds,exceptthosein-stalledduringprefabricationofembeds.TheQCcivildisciplinehasbeendirectedtoassumethisresponsibility.Thisac-tionresultsinthefollowingupgradingoftheinspectionprogram:i.Theinspectionofstudsisnowmorecloselyintegratedwithotherrelat-edpr'eplacementinspections,suchasembeds,reinforcingsteel,conduit,etc.ii.Additionofthe'General'SoundnessTest'P-95a) iii.TheamountofQCengineeringmanpowerwhichmaybefocuseduponstudin-spectionisnowincreased.1v~Inspectionmaynowmoreoftenbecar-riedoutwhilestudinstallationis,beingperformed,andwhilecraftper-sonnelarepresenttoperformimme-diatereworkorrepairifnecessary.v.Studinspectionmaynownormallybecompletedbeforethestudsarevisual-ly,obscuredby,otherinstalleditems,suchascurtainsofreinforcingsteel.b.Theinspectionplanforstudinspectionhasbeenreviewedandstrengthenedinthefol-lowingspecificareas:Markingtophysicallyidentifybothacceptableandunacceptablestudshasbeenclearlydefinedinthein-spectionplan.ii.Verificationofproperstudweldingcablelength(i.e.,lessthan100feet)hasbeenadded.8.3.2CorrectiveActionsbyFieldEngineering.a.Aspecialtrainingsessiononstudinstal-lationdatedJune10,1977wasconducted

atthejobsiteforQC,EngineeringandSu-pervisiontoguaranteeimprovedqualityofinstallation.b.Infutureplacements,installationofrein-forcingsteelorothermaterialswhichwouldinterferewithinstallationorinspec-tionofshearstudswillbewithhelduntiltheshearstud.installationintheareaiscompleted.c.AtrainingsessionwasheldonJune26,1977forallironworkersinvolvedwithstudinstallation.Emphasiswasplacedonthecraftsman'sprimaryresponsibilityforcorrectinstallationofshearstuds.Thecompleteinstallationsequenceofstudswasalsoreviewedindepth.d.AvendorrepresentativefortheweldingequipmentwasbroughtonsiteJune22,1977.Duringthisvisitequipmentset-tings,maintenanceandtroubleshootingwerereviewedwiththeironworkersandsuperintendents.e.Equipmentmaintenanceprogramhasbeenrevisedandre-organizedincludinga(P-95a) largerinventoryofsparepartsbeingmaintainedonsite.f.Allrectifiersinthefieldarereturnedtothemanufactureronarotationalbasistoensuretheyareperformingcorrectly.

9.0CONCLUSION

9.1Inmostoftheareas,theprojectednumberreliablestudsarenotonlysufficienttoperformstructuralfunctionbutalsomeetthespecification.9.2Althoughallprojectedreliablestudsareadequatetosatisfythestructuralrequirement,therearesomebeamsatafewelevationsintheReactorBuildingwhichdonotconformtospecificationrequirementsinitsentirety.Thus,thesedeficiencieswillbecor-rectedbyrepairsperformedontheexistinginstalla-tion.9.3Oncompletionoftherequiredrepair,thestructuralanalysisanddesignwillsatisfy.strengthandcoderequirementsandwillalsoassurethattheexistinginstallationwillconformtothedesigncriteriaandbasesofSafetyAnalysisReport.(P-95a)

APPENDIXATOFINALREPORTONSHEARSTUDSSTATISTICALANALYSISANDEVALUATIONOFFIELDTESTDATA(P-74b)

STATISTICALANALYSISANDEVALUATIONOFFIELDTESTDATA1.0OBJECTIVEToanalyzethetestdataineachbeamcompletedpriortoNay1977andtodetermine,t.hestatisticalbasisforesti-matingthetotalnumberofooodstudsthatcanbereliedupon.2.0FIELDTESTDATA2.1GeneralInthefourthweekofMay1977,whentheproblemwasdiscovered,thereweremanyareaswherethestudin-stallationwascompletedandalsothestudswereaccessible.Thesestudsweresubjectedtoathoroughinspectionandtestingasshownbelowintheflowchart.Inadditiontovisualexaminationandselec-tivebendtestingasperthespecificationreguire-menteverystudreceived'generalsoundnesstest'.CompletefieldtestdataandthereducedfieldtestdatausedforstatisticalanalysisisprovioedinAppendixBandCrespectively.2.2DEFINITIONS:l.SoundnessTest:Oncompletionofstudwelding,thestudisstruckwithaheavyhammer.Ifit.givesacleanringingsound,thestudisconsi-deredacceptable.Otherwiseitisreplacedwithanewstud.(P-74a) 2.VisualExamination:Aftercompletionof'thesoundnesstest,eachstudisexaminedvisually'oinsurethatthereisfilletweldallaroundth'eperipheryofthestud.lftherearenovoids,thestudisconsideredpassingthevisualexamina-tion.:3.BendTest:Studsfailingvisualexamination.arebent15.awayfromthevoidintheweldwithre-.,specttothe-verticalaxis.lfthestuddoesnot'developcracksattherootorseparatesfromthebeams,itisconsideredacceptable.Thisisthe.mostsevereand,reliabletest.2.3FLO!0CHARTStudstestedinabeamStudspassingsoundnesstestPs.StudsfailingsoundnesstestFsStudspassingvisualexaminationStudsfailingvisua3examinationStudsbendtestedFvlStudswhichwererepairedFv2PassbendtestPlFailbendtestPassbendtestP2FailBendtestF2.-Rote:P2andF2areassumednumbers.Seesection2.6.3;3forclarification.(P-74a) 2.4Notations:2X=Chi-squareN=Numberofbeamstestedineachbuilding.T=Totalstudstestedinabeam.Ps=Studspassing-soundnesstest.Fs=Studsfailingsoundnesstest.Pv=Studspassingvisualexamination.Fv=Studsfailingvisualexamination.Fvl=Studsfailingvisualexamination,whichwerebendtested.Fv2Studsfailingvisualexamination,whichwerere-pairedpriortobendtest.Pl=Studs(Fvl)passingbendtest.Fl=Studs(Fvl)failingbendtest.P2=Studs(Fv2)passingbendtest(assumed).F2=Studs(Fv2)failingbendtest(assumed).P=GoodstudsPv+Pl+P2F=BadstudsFs+Fl+F2(P-74a) 2.5SummaryofFieldTestDataTable1StructureNumberofbeamsTotalstudstested/examinedReactorBuildingControlBuildingTurbineBuilding17113091764831CirculatingHaterpumphouseDieselGeneratorBuilding1072.6DiscussiononFieldTestData2.6.1Studsfailingsoundnesstest(Fs)Thesoundnesstestindicatesthequalityoftheweldbetweenastudandstructuralsteelbutitmaynotbefoolproof.Thatis,itisverylikelythatsomeofthestudsfailingthistestmaybegoodfromastruc-turalstrengthpointofview.Sincetheexactreliabilityofthesoundnesstestisnotknown,allstudsfailingthesoundnesstestareconsideredtobebadstuds,toinsureconservative'estimates.(P-74a) 2.6.2Stuospassingvisualexamination.(Pv)Studmanufacturershaveindicatedthatirre-spectiveofthemethodoftesting,theoverallfailurerateisobservedtobeabout2%undernormalworkingconditions.Baseduponthisfact,inagivenpopulationofstuds(T),ifthestudsfailingvisualandsoundnesstest(Fs+Fv)areremoved,the'uccessratefortheremainingsample(Pv)canreasonablybeconsideredtobe100%.Arecentbendtestconductedonrandomlypickedpopulationof543studs,whichhadpassedbothvisualandsoundnesstestgave3.005successrate.Thus,theseresultsalsoreinforcethevalidityoftheaboveassumption.2.6.3Studsfailingvisualexamination(Fv)Forthiscategory,thespecificationprovidesanoptiontothefieldeithertoperformabendtestortorepair.Fieldtestindicateshthatallstudswerenotnecessarilysubjectedtobendtest.Thetestwasperformedon(Case1)all,(Case2)one,(Case3)someor(Case4)noneofthsstudsonabeam.Reasonsforei-therincludingorexcludingthestudstobesubjectedtobendtestwasbaseduponanyone

ofthefollowing:constructionschedule,ac-cessibilityy,inadeauateroomforreplacementincaseofafailureandarbitrarydecisionbythefield.Thus,forcase2,3and4toincludethestudsrepaired(FV2)'orstatis-ticalanalysis,followingcriteriahasbeenused.2.6.3.1'Case1:Pv=FV1FV2=0Asthebendtestisperformedonallstudsfailingvisual(Fv),thetestdataisused'asis'.2.6.3.2Case2:Fvl=1Fv2=Fv-1Inthiscase,onlyonestudwassub-jectedtobendtest,thusitsresultscannotbeappliedinameaningfulwaytootherstuds.Therefore,beamsamplescontainingthiscombinationareomittedfromthetotalsample.2.6.3.3Case3:FvlQ'Fv2=FV--FV1Forthereasonsstatedabove,selec-tionofthestudstobebendtested(P-74a) wasarbitrarythereforethefailurerateasobservedforFV1canreason-ablybeassumedtobesameforFV2.2.6.3.4.Case4:Fvl=0Fv=Fv2AsnobendtestdataisavailableforFvl,beamsamplescontainingthiscombinationwereexcludedfromthetotalsample.2.7Basedupontheabovecriteria,failurerateforeach"beamiscalculatedasnotedbelow.Failurerate=Fs+Fl+F2~Totastu<utsT)whereGoodstuds=Pv+Pl+P2andBadstuds=Fs+Fl+F23.0ANALYSISOFFIELDTESTDATA3.1AlthoughtheFieldtestdataisavailableforfivebuildings,thedataforonlythreebuildingswithhigherfailureratesisconsideredhereforstatis-ticalanalysis.Thereasonforthisis,thefailurerateforCirculatingWaterPumphouseandDieselGen-eratorBuildingis0%.FortheReactor,ControlandTurbinebuildings,inatotalsampleof72beams,7967studsweretested.Fol-lowingthecriteriadescribedinsections2.6.3and 2.7,7427passedand540failedforanoverallsuccessrateof93.22%.Itwouldbeattractivetotreatthisdataasasingleaggregatesamplesincethatwouldyieldthegreatestprecisionoftheestimateofthesuccessrateparameterp.However,differentfailurerateshavebeenobservedindifferentbuildingssothatfailureparametersmaydifferfrombuildingtobuilding.Statisticaltestswereusedtodeterminewhetherthisinfactdidoccur.3.2Constructionofvariousbuildingsisdoneontheareaconcept,i.e.aseparategroupofFieldEngineers,Superintendentsandworkersareassignedtoandre-sponsiblefortheconstructionofthatparticularbuilding.Thus,eventhoughthegoverningspecifica-tionisthesameforallbuildings,workmanshipandaualitymayvarywithinreasonablelimitsfrombuild-ingtobuilding.Testresultsfortheabovethreebuildingsaresum-marizedasbelow.Table2BuildingStudspassedStudsfailed%FailurerateReactorControlTurbine4970163382440213177..487.420.84Total74275406.78Fromtheabovetablethereisanoticeableamountof variationinthefailurerate.Theprimaryquestionisifthesearevariationstobeobservedinanyrandompro-cess(e.g.,10tossesofthesamefaircoinmayyield7headsinonesequenceand4intheother).ltmustbeemphasizedherethatallknownparametersaffectingthefailureratearethesamefortheentirestudweldingoperationinanybuilding.Ifthedifferentratescanbeshowntoliewithintherealmofprobabilistic'noise,'henallindividualtestsmaybepooledtogetherintoanaggregatesampleand6.78%asthefailurerate.However,ifthiscannotbeshown,thenthedatamustberegardedasseparatesubsamplesandanallowancemadeforthelowerprecisionwhichresults.Thesub-sequentsectiononthehyperbinomialdistributionde-scribeshowthefinalrecommendationsincorporatethislossinprecisiontoassurearigorousandcon-servativeanalysis.Thekeyanalyticquestioniswhetherornottheunderly-ingpass/failprobabilityisthesameforabovethreebuildings.Theprincipalstatisticaltooltobeusedis2.theXtestofhomogeneity.Ifthestudsinallthreebuildingshadacommonfailurerateof6.78%,(i.e.ifhomogeneityisnullhypothesis),theexpectednumberof"passes"intheReactor.Buildingwouldhavebeen5008with1644and775expectedintheControlandTurbineBuildingsrespectively.Similarly,(P-74a) theexpectednumberoffailureswouldhavebeen364,120and56.TheXteststatisticisbaseduponthedifferencesbe-tweenall6observedandexpectedvalues.Xtest=(4970-5008)+(1633-1644)+(824-775)+(402-364)+(131-120)+(7-56)=51.31*ThisteststatisticisapproximatelydistributedasanXrandomvariablewith2degreesoffreedom[1]for"whichthereisonly0.5%chanceofexceeding10.6.Sincetheteststatisticissomuchgreaterthanthisvalue,theconclusionisthatthesampleunderconsi-derationisnon-homogeneous.Thus,eachbuildingmustbeconsideredasanindividualsubsample.3.3Evenaftertheneedtoanalyzethedatabuildingbybuildingisestablished,themajorconcernistheadequacyofcollectionofstudsoneachindividualbeamorgirder,fordeterminingeffectivenessofcompositeaction.Therefore,itisnecessarytoconsiderthefielddataforeachbeamasanindividualsample.*TisvaueiersromteexactXvalue.Theapparentdifference2isduetoroundingofftheexpectedvaluestointegersfornarrativepurpose.Theexactvalueswereusedinreachingalldataclusteringdecisions.[1]A.M.MoodandF.A.Graybill,IntroductiontoTheoryofStatistics.McGrawHill(1963)p.318.

3.4Baseduponabovediscussionandcriteria,thebeamdataforeachbuildingisanalyzed.3.4.1ReactorBuildingUnits1and2AlthoughthefollowingdiscussionpertainstotheReactorBuilding,itisalsoapplicabletootherbuildingsexceptasnotedotherwise..Forasampleof44beams,thedatacanbegroupedasfollows:NumberofbeamsFailurerate20to38$15to20%10to15%205to10%0to5%Itisevidentfromtheabovegrouping,thatforthemajorityofthebeams,thefailureraterangesfrom0to108.WhentheXtestwasperformedonthesam-2pieof44beams,thesamplewasfoundtobenon-homo-geneous.Notwithstandingthatthemethodofstudin-stallation,thegoverningspecification,workmanship,constructionsequence,andallotherknown'variablesweresame,thewidevariationinthefailureratecannotbeexplained.Despitetestingthesamplewithvariouspermutationsandcombinations,noreasonwasfoundwhich-couldbeattributedforthisoccurrence.(P-74a)-ll-Inlightofthissituation,itwasdecidedtotestthetruncatedsamplei.e,disregardingthebeamsam-plesstartingwiththelowestfailurerates,fores-tablishinghomogeneity.Afterseveraliterations,asampleof6beamswith,failureraterangingfrom19.05%to38.36%wasfoundtobehomogeneous.Thistruncatedsamplewith390'passes'nd146'failures'aveoverallfailurerateof27.2%.Withtheabovediscussion,itmustbeemphasizedherethatusingthishigherfailurerateisindeedanextremelyconservativeassumption,andcanbeapplied,withahighconfidencelevel,inprojecting'good'tudsintheareaswherethestudshavealreadybeenembeddedintheconcrete.3.4.2ControlBuildingThedataisavailablefor11beamswith1764studstested.Thefailurerateforthebeamsrangedfrom3.53to25.93%.Itwasalsoob-servedthatonlyonebeamhasunusuallyhighfailurerate.When,thetotalsamplewastest-edforhomogeneity,thesamplewasfound'tobenon-homogeneous.However,thesampleex-cludingthebeamwiththehighestfailureratewasfoundtobehomogeneous.Inlightofthisfact,itcanbeconcludedthatthedataforthisparticularbeamwiththehighestfailurerateisastraysample.However,forcomputing(P-74a) vtheoverallfailurerate,'hisbeamisin-cluded.3.4.3TurbineBuildingAvailabledataisfor17beamswith831studstested.Outofthistotal,824passedand7failedgivingaveragefailurerateof0.84%.Itisobservedthat15beamsoutof17beams,have0%failurerate.Thesampleconsisting\ofremainingtwobeamswasfoundtobehomo-geneous.Thusthefailurerateof4.14%forthesetwobeamshasbeenusedforallthebeamsinTurbineBuildingwhichagainisaconservativeapproach.3.4.4CirculatingWaterPumphouseAtthetime,whentheproblemwasdiscovered,onlytwobeamswithatotalof107studswereexposed.Outofthistotal,onlyonestudfailedvisualexaminationbutthestudpassedthesubsequentbendtest.Thus,theobservedfailurerateis0%.3.4.5Diesel-GeneratorBuildingForty-fourstudsonabeaminaconstructionopeningwereexposed.Allthestudsweretestedwithnofailure,thusgivingafailurerateof0%.(P-74a) 3.5SummaryBuildingStudsPassedStudsfailedFailurerateReactorControl390164214612127.2%6.85%Turbine16274e14%Aboveinformationwasusedasinputsintothehyper-binomialdistributiontoestablishprobabilisticchar-acteristicsofbeamsandgirdersforeachbuildingasdescribedinthesubsequentsection.4.0HYPERBINOMIALDISTRIBUTIONTheresultsoftheaboveanalysisestablishestheappropri-atehomogeneousgroupingsoftestdataforqualitycharac-teristicsofindividualstuds.Thisanalysisproceedsbyrecallingthehyperbinomialdis-tribution.()Themotivationisasfollows.First,ifthesuccessparameter,p,wereknownprecisely.thenthetotalnumberofgoodstuds(k)inacollectionofhwouldvaryaccordingtoabinomialdistribution:PtkofhIp)kp,1pForexample,ifp=6andh=5,thenthenumericalvalues'oftheresultingmassfunctionwouldbe:H.RaiffaandR.Schlaifer,AppliedStatisticalDecisionTheoryHarvardUniversityPress(1961).p.237(P-74b)

No.GoodStuds=kpkof5;p=.6012345.010.077.230.346.259.07800However,ifpisnotknownbutmustbeestimated,thensuchabinomialdistributionassumesmoreprecisionthanactuallyexistsandmakesthingsappearbetterthantheyare.Forex-ample,ifnstudshavebeentestedandonlyrpassed,thentheparameterpitselfhasaprobabilitydistribution,f()(n+1)!r(1)r!(n-r)!for0<p<1~lthefamiliarbetadistribution().Thus,whiletheexpectedvalueofpisr/n,othervaluesofpbetween0and1mayalsohavegeneratedthesample,andthesecannotbeignoredinanysubsequentinferences.Toobtaintheprobabilityofkgoodstudsinabeamofhwhenrofnsimilarstudshavepassedthestriketest,theuncondi-tionaldistributionmavbefoundby:1~P[kofh;rofn]=P[kofh)p)f(p;r,n)dp01h!k1h-k(n+1)!rn-r!p0al,-,,....,.,~,........,...,yofStatistics,McGraw-Hill(1963)p.129ff.(P-74b)

Collectingconstants:h!(n+1)!k!(h-k)!r!(n-r)!k+r(1p)n+h-r-kdpperformingtheintegration,h!(n+1)!(k+r)!(n+h-r-.k)!!hk)!r!nr)!n+h+1)!andrearrangingtermsincombinationalnotationyieldsthehyperbinomialdistribution:P[kofh;rofn]r+kn+h-r.-krh-kn+h+1fork=0,...,handr<nTogainasenseoftheeffectofthisdistribution,supposethat1Sstudshavebeentestedand9havepassed.Theesti-matedvalueofpis9/15(i.e.,still.6)asbefore.However,repeatedevaluationsoftheaboveexpressionyieldsthefol-lowingdistribution:No.GoodStuds(k)012345pk;9of15.023.103.227.303.246.098MRoNotethatthisdistributionismorediffusethanthesimplebinomial;i.e.thetailsofthedistributionare,-"fatter"andlessprobabilitymassisconcentratedaroundthecentralvalue.Theimportofthisisthatwheninfe'rencesaremadeabouttheadequacy(orinadequacy)ofstudsonbeamsorgird-ers,amorestringent,conservativesetofstandardsareap-pliedthanwouldresultfromthesimple(andinappropriate)(P-74b)

binomialdistribution.Thevaluesofnandrareontheorderof20studstoseveralhundredinsomeinstances.Thus,theevaluationofalltheappropriatemassandcumulativedistributionsisalaboriousandcomputationallydemandingtask.Accordingly,acomputerprogramwasdevelopedtoassistinthesestudies.Thepro-gramlistingaccompaniesthisappendix.Theprogramcontainscommentstomakeitself-documenting.Statements20,30,and40areusedtosettheparametersofthedistribution.Thetwokeyideasare:i)allprobabilitiesarecarriedinlogarithmicform.-untilthefinalprintouttoguardagainstround-offerrorandassuretherequisitelevelofaccuracy.ii)eachvalueofthemassfunctionisrelatedtothepreviousone,sothatoncep(0ofh;rofn)isfound,theothervaluesmaybecalculatedrecursive-ly.Thisreducesthenumberoffactorialevaluationsand.aidsthecomputationalefficiencyofthetotalprogram.Executionofthecomputerprogramyieldsthedensityandtheprobabilityfunctionsderivedfromagivensetoffieldtestdataforagiventotalofstudsgroupedaccordingtothenum-berofstudsperbeam.Nextthisoutputisreducedtoobtaintheprobabilityofexceedingtheprescribeddesigncriteriaasafunctionofthenumberofreliablestudswhichexistorwhich(P-74b) aretobeprovidedinagivenbeam.Fromthisinformation,'heprojectednumberofreliablestudsforagivenbeamisderivedobservingthestipulated90%confidencelevel.Acknowledgement:TheforegoingappendixwaspreparedunderthedirectionofDr.CarlW.Hamilton,AssociateProfessorofQuantitativeBusinessAnalysis,University'ofSouthernCalifornia.Dr'.Hamiltonwasengagedasaconsultantforstatisticalstudies.(P-74b)

~~(ySTUDS>t~PROGFWtLISTINGFORTHEHYPERBINOMIALPROBABILITYDISTRIBVTIOh~ao20304045506070901101401501601701SO190200210220230240250260270280500510520530540550DIHP[300]H=5R=9N=15REH~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~REHFINDP(0)FORTHESTARTINGPOINTREMSETTHENILfERATORFACTORSh'1]~h+H-RN[2]-N+1REM.SETTHEDENOMINATORFACTORSD[1]=N-RD[2]=h+H+1h'l=D1=0FORJ=lTO2FN'[j]COSUB500N1~Nl+FaNEXTJFORJ~aTO2F=D[J]GOSUB500Dl=Dl+FlNEXTJP[1]=Na-DaGOTO600RH1~~~~~o~~~~o~~~~~~oooo~'o~~~~o~~~o~oo~~~oREHSUBROUTINETOGETF1=LOG(F()F1~0IFF>lTHEN550RETURNFORZ~2TOF~~ooo~o~~~~560Fl=F1+IOG(Z)570NEXTZ590RETURN(~595.6006106156206256306406506606706806907007107207309000I~~~~~~~~~~~~~~o~~~~o~~~~~~~~~~~o~~~~o~~REtREHCOMPUTEP(1),P(2),....,ETC.FORK~2TOH+1x=k-aP[K]=P[1'-1]+LOG(R+X)-I.OG(N+H-R-X+1)P[K]=P[K]-LOG(X)+LOG(H-X+1)NEXTKREHCHANGEI-OCSTOPROBABILITIESFORK=1TOH+1P[K]-EXP(P[K])NEXTKREHPRINTTHERESULTSC=OFORK=1TOK+1C=C+r[K]PRINT1'-l,p[K]+NEXTI'~~~~~~~~~~

APPENDIXBTOFINALREPORTONSHEARSTUDSFIELDTESTDATA 1.inspectionresultsnotedasFieldTestDataonthefol-lowingpages,pertaintotheexposedstudsinstalledpriortoHay19772.Fortheexplanationofthetermsandexpressionsused,refertoAppendix"A".

Cr:IFIELDTESTDATAFORREACIORBLDG.41Placement:202-S-01Area:29Elev.749'-1"SampleBeamStudNo.No.InstalledStudsFailingSoundnessTestStudsFailingVisualExam.WithBendTestResultsFailingTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarks1688Case1178627Case3188816Case18634Case1208815Case3218613Case2228847Case42386Case424108635Case48330Case426128032Case4271321337Case328149018Case3291513210Case3~~86ai I

FIELDTESTDATAFORREACIORBLDG.41Placement:199-S-01Area:25Elev.749'-1"SampleNo.BeamStudNo.Installed\StudsFailingSoundnessTestStudsFailingVisualExam.KithBendTestResultsFallngTotalBendTestStudsFailingVisualExam.ButRepairedRemarksFSFl450188Case43915Case421Case42610Case4CO,50301622Case4Case44831Case417216105Case4187612Case410197616Case42076Case412217627Case42276Case114~30123Case4(r86a)

I~It 1FIELDTESTDATAFORREACIORBLDG.41Placement:199-S-OlArea:25Elev.749'-1SampleBeamStudNo.No.InstalledStudsFailingSoundnessTestFSStudsFailingVisualExam.KithBendTestResultsFaizngTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarks153116529Case4(P-86a)

CFIEKZ)TESTDATAFORREACTORBLOG.41r"Placement:r202-S-01Area:29Elev.749'-1"SampleBeamStudNo.No.InstalledStudsFailingSoundnessTestFSStudsFailingVisualExam.WithBendTestResultsFallngTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarksFV2301662160Case131173220Case43218711102Case3331917762Case1342014919Case1C352186,14Case136228423Case437239616Case1382410635Case439'270022-Case44026340Case22717Case4422810141.Case3r4329105018Case4<P-86a>

,~F1ELDTESTDATAFORREACTORBLDG.41Placement:202-S-02Area:29Elev.749'-1"SampleBeamStudNo.No.InstalledStudsFailingSoundnessTestFSStudsFailingVisualExam.WithBendTestResultsFaxxngTotalBendTestFV1FlStudsFailingVisualExam.ButRepairedRemarks44309639Case43188Case13213015Case447331302424Case3 fIlie ceFIELDTESTDATAFORREACTORBLDG.41Placement:202-S-01Area:27Elev.749'-1"SampleBeamStudNo.No.InstalledStudsFailingSoundnessTestFSStudsFailingVisualExam.WithBendTestResultsFanxngTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarks48114Case413Case4503413Case310Case15276.66Case4ce-Case3542746720Case318Case35718Case3104430Case145184Case159124814Case3601342Case4(0611421Case1(P-86a)

(FIELDTESTDATAFORREACTORBLDG.ClPlacement:202-S-OlArea:27Elev.749'-1"SampleBeamStudNo.No.InstalledStudsFailingSoundnessTestFSStudsFailingVisualExam.WithBendTestResultsFaxzngTotalBendTestFV1FlStudsFailingVisualExam.ButRepairedRemarks621722319Case16319382212Case1 (FIELDTESTDATAFORR-WCIORBLDG.42Placement:l82-S-01Area:32Elev.719'-1"SarrnleBeamStudNo.No.InstalledStudsFailingSoundnessTestStudsFailingVisualExam.WithBendTestResultsFal1ngTotalBendTestStudsFailingVisualExam.ButReoairedRemarksFSFV1Fl646621Case4657023Case2666229Case4676236Case4686218Case4i69122Case470Case47116Case4728721Case473105019Case4743212Case41224131Case2761320410Case377'419853Case4 lf/

'FIELDTESTDATAFOR1HACTORBLDG.02Placement:182-S-01Area:32Elev.719'-1"SannleBeamStudNo.No.InstalledStudsFailingSoundnessTestFSStudsFailingVisualExam.WithBendTestResultsFanzngTotalBendTestStudsFailingVisualExam.ButRepairedRemarks78307Case179203619Case48021Case4812268Case482237622Case4(832915Case4<r86a)

FIELDTESTDATAFORREACK)RBLDG.g2Placement:184-S-OlArea:34Elev.719'-1"SamoleBeamStudNo.No.InstalledStudsFailingSoundnessTestFSStudsFailingVisualExam.WithBendTestResultsFanxngTotalBendTestFVlFlStudsFailingVisualExam.ButReoairedRemarksFV284681616Case3856819Case2866825Case3876831Case388(089767620Case2Case4906817Case4917223Case2926523Case493266113Case3941212532Case49513166Case19615Case197160.26Case4 I~rFIELDTESTDATAFORREACIORBLDG.42Placement:184-S-01Area:34Elev.719'-1"SampleBeamStudNo..No.InstalledStudsFailingSoundnessTestStudsFailingVisualExam.WithBendTestResultsFaizngTotalBendTestStudsFailingVisual'xam.ButRepairedRemarks981776FSFVlFl0010Case499181531564Case41001971Case11012070Case3102217014Case3~103104222372269110Case2Case41057020Case2106257027Case4.107266908'ase410827732328Case1109282563713105Case3110298613Case3(.312451289Case4(Z86a>

FIELDTESTDATAFORCONTROLBUILDINGPlacement:714-S-03Area:21SampleNo.StudsFailingBeamStudSoundnessNo.InstalledTestFSStudsFailingVisualExam.With'BendTestResultsFaizngTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarks7,-891031704.16742025A54204210141101381351690217472415142238342913201319Case3Case3Case3Case3Case3Case3Case3Case3Case3Case3Case1(~(P-86b)

(~~FIELDTESTDATAFORIURBQKBLDG.41Placement:-Area:16Elev.729'-0"SanpleBeamNo.No.StudsFailingStudSoundnessInstalledTestFSStudsFailingVisualExam.NithBendTestResults,FanzngTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarks8,010.121315161791013141516171864321002424124804645484240960105'00Case1Case1Case1Case1Case1Case1Case1Case1Case1Case1.Case1Case1Case1Case1Case1Case1Case1<0(P-86b)

~~

FIELDTESTDATASweeNo.StudsFailingBeam,StudSoundnessNo.InstalledTestStudsFailingVisualExam.WithBendTestResultsFanxngTotalBendTestStudsFailingVisualExam.ButReoairedRemarksCirculatingWaterPumphouse153FSFlCase1540Case1DieselGeneratorBuildingqe44Case1(P-86b)

APPENDIXCTOFINALREPORTONSHEARSTUDSREDUCEDFIELDTESTDATA(P-74b)

SUMMARYOFREDUCEDFIELDDATAStructureSample-Nos.TotalStUdSTotalPassTotalFailReactorBuildingUnits1and24453724970402TurbineBuildingUnits1and217831824ControlBuilding17641633131CirculatingWaterPumphouse107107DieselGeneratorBuilding4444Note:FortheexplanationoftermsandexpressionsusedonthisandthefollowingpagesrefertoAppendix"A".(P-86b)

REDUCEDFIELDDATAFORSTATISTICALANALYSISBuilding:ReactorBuildingStudsfailingvisualwithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestSampleTotalNo.StudsStudsFail-Studsing.PassingTotalSoundnessVisualPassFailPassFailbendbendTotalAssumedAssumed(Pv+Pl(Fs+FltesttestPassFail+P2)+F2)RemarksFSPVFV1PlFlFV2P2F213761688178618881986208827213'8902913230620706758685217468114462127163437181619191327361300208130"0700315912321103070867781'9791211842129059(P-86b)

REDUCEDFIELDDATAFORSTATISTICALANALYSISBuilding:ReactorBuildingStudsfailingvisualvithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestSampleTotalNo.StudsStudsFail-StudsingPassingTotalSoundnessVisualPassFailPassFailbendbendTotalAssumedAssumed(Pv+Pl(Fs+FltesttestPassFail+P2)+F2)Remarks32711331773414935863796421014588471305034511053157542745171798179201013913614164124131667PVFVl55352ill62130.19PlFlFV2P25111021005319900000201000042420310000ll5252152015F27047164'314908249061001880119ll304100151620371(P-86b)

II~~'

REDUCEDFIELDDATAFORSTATISTICALANALYSISBuilding:ReactorBuildingStudsfailingvisualwithbendtestresultsStudsfag.ingvisualbutrepairedpriortobendtestSampleTotalNo.StudsStudsFail-StudsingPassingTotalSoundnessVisualPassFailPassFailbendbendTotalAssumedAssumed(Pv+Pl(Fs+FltesttestPassFail+P2)+F2)Remarks5557565757445845594861216222363.38762047830784688668FS1230232614125151783053494221633PVFVl38183818Pl1210FlFV2P2610810219144140'33751910120101100001601616802525F20~PF50748933ll37846217420023251319773052662662(P-86b) tI REDUCEDFIELDDATAFORSTATISTICALANALYSISBuilding:ReactorBuildingStudsfailingvisualwithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestPassFailPassFailbendbendTotalAssumedAssumed(Pv+Pl(Fs+FltesttestPassFail+P2)+F2)StudsFail--StudsSampleTotalingPassingTotalNo.StudsSoundnessVisualRemarks8768932669516696441007110170102701087310925611086FS233712136675247221014542281335PVFVl3521384PlFlFV2P2340313101131138000000003740141422131235012110596F2P0680255110155ll044006743601006550452892094716719(P-86b)

If REDUCEDFIELDDATAFORSTATISTICALANALXSISBuilding:TurbineBuildingStudsfailingvisualwithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestStudsFail-StudsPassFailPassFailSampleTotali.ngPassingTotalbendbendTotalAssumedAssumed(Pv+Pl(Fs+FlNo.StudsSoundnessVisualtesttestPassFail+P2)+F2)RemarksFSPlFlFV2P211826433643251006247248.1249801046ll451248185631.92232010979464310-001806403603201000240240118080046044048 REDUCEDFIELDDATAFORSTATISTICALANALYSISBuilding:TurbineBuildingStudsfailingvisualwithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestStudsFail-StudsSampleTotalingPassingNo.StudsSoundnessVisualTFSPVPassFailPassFailTotalbendbendTotalAssumedAssumed(Pv+Pl(Fs+Fl.testtestPassFail+P2)+F2)RemarksFVlPlFlFV2P2F2'F131415421640179637360424096(P-86b)

REDUCEDFIELDDATAFORSTATISTICALANALYSISBuilding:ControlBuildingSampleTotalNo.StudsStudsfailingvisualwithbendtestresultsStudsFail-StudsPassFailingPassingTotal.bendbendSoundnessVisualtesttestStudsfailingvisualbutrepairedpriortobendtestPassFailTotalAssumedAssumed(Pv+Pl(Fs+FlPassFail+P2)+F2)Remarks1'6921743170416752026547204821091411013811135FSPV12614712912615337149170115116121FVlPlFlFV2241861992734277202923134132198015ll4141402122175153827llllP22115158161164154187131513401912001331231221413101513F2PF(P-86b)

I REDUCEDFIELDDATAFORSTATISTICALANALYSISStudsfailingvisualwithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestSampleTotalNo.StudsStudsFail-StudsingPassingSoundnessVisualFSPVPassFailPassFailTotalbendbendTotalAssumedAssumed(Pv+Pl(Fs+FltesttestPassFail+P2)+F2)PlFlFV2P2F2PFRemarksCirculatingWaterPumphouse53545353000053DieselGeneratorBuilding144440044(P-86b)

APPENDIXDTOFINALREPORTONSHEARSTUDSREPAIRPROCEDURES l4 REPAIRPROCEDURES1.0GeneralAsnotedinsection7.6ofthefinalreport,somebeamsintheReactorBuildinghavebeenidentified,wheresomerestitutionofstudsisnecessary.Thesebeamsaremarkedontheplans(Seefigures1thru5).2e0RepairHethodsandDesignCriteriaFollowingrepairmethodsareproposedtoachievethere-quiredrestitution.2.1Thefirstmethodistoprovideahorizontalshearkeywithintheridgewhenthemetaldeckispro-videdoverandacrossthesteelbeams.Theshearkeyiswellanchoredtothetopflangebyafric-tiontypebolt.Positiveengaoementandthecon-tactatthekey-deckingisattainedbythebond-ingpropertiesoftheepoxyagent,andatthedecking-slabinterfaceisdevelopedby.thecon-creteengagementintothecorrugationofthedeck-ing.Seefigure6fordetails.2.2Thesecondapproachistoprovideathrough-boltwheretheoeckingcorruoationsareparalleltothesteelbeams.Thebasicconcepthereistodevelopafrictiontypeconnectionbetween.beamandslabthroughthepre-tensioned,highstrengthbolt.The(P-74b)

'I4If groutingoftheboltinthedrilledho1eandthefrictionconnectionrenderthedetaileffectivebyminimizingthetendencyofinitialslip.Seefig-ure7fordetails.2.3Xnsomeinstances,whenthedeckingisparalleltothebeamandtheabovemethodcannotbeusedbe-causeofembeddedconduitsinthes1ab,itispro-posedtodesignthesteelbeamasanon-compositesectionandreinforcetheexistingbeamtoprovidethereauiredsectionmodulus.Theactualdetailsofreinforcementwillbedesignedonacasebycasebasisdependingontheexistingconditionsatthetimeofrepair.

021.0'azQnSJ-0g~IId4~'1.2Qyo~S114AIIS~4S~111NI4t441CNOICSItSfIffPIp4Jd~tIIA(")SSP414d:rddSOPIoh/2;JXC'-2Ia~reVJ144dlfffd4Jf111114OO'SP4$a)j0I141AASSCANI/fdfSPACA+SSS4141141(fflt)I0QeNOTE:Beamstoberepairedarcmarkedthus.~~~~~wav~444hkuNO4Wk)dfoaf'ahPOIAASACAIf4IfffffASSA+CCSANSIAtffQg2gi~ANISC.SCfP~SICAAVCV1114:t2'J"C~jPJ-.4O'ASCIAOSISQll/Of4414411dffCOOCfff14'442oVvP444r."./'fv"*'@'V>vhrPS~w4ISII~IASVINS'JttfVC'4144'lljj'JII~SI'll",4411~tvI4".iI)0OSCfNOISJCftf1)NIICfICCIÃAIC'thft4f4IRLVAtACICAINNlVfCACfhhCCAN44OhhLCCI(rStructuralSteelFraming,PlanEl.670'-0"ReactorBuildingUnit1FigurelJ4lSII;tvdtlfvfOPA)g]414...);lIl<O.lhtf(">Il.4fw.f~~Sf'A)I~4ftJluPQgI~.4vCASfl41AhfON'Ifvvlvff2ffSllSPdCSOI21Sl4IVI'JdNI114Sdffr22SIC114JCC~f>144CIVslid(SOP44fICPSAAIICC.CCSICPwld)J'2I141Qd>COAppendixD 11501150cf>c>tttcii4>CVcIQOI,srcivotrgrift)S:rdt>>5>VSOrt>TCtldwOrd<<d>Vo>>lwTSOltftttSCCWotdO>OMV~fo.0tIlCfsj1'oL.g,Beamstoberepairedaremarkedthus>OOC~tt1tistwortrSO~IrVtt>>Olt~Ttiitttut~Cco>ftvotcot.crit~doSfCCwoCVGI1IIfvtrtcrofts,f'o>rood@~~tuGt>ff>COCC.GSCYO~qlsdA5>Oo>c~ic>I>5SCC>TS>CCIcnlt~i~V-*w>>ol>v~GCsdaiSftd>OC411rS!s>OcolocdClttVO>ftOt/V>WCCCtofftlfCW>CftffIWSff0>>C4>ff4A~-ttioftO,~..jw55Q4,ir.64.wtiTtt>OO.c,~Tft4>5>VCS1dtt>S>O'S>0IIBttWOV>GCII;jJcr>!G,g(~I4YJTSGCOG50ids>0Su>>)GtCVGCCC8CottotOlidsfccw>IcotStructuralSteelFramcingPlanatEl.670'-0"ReacterIIuildingVni2Figure2AppendixDraS-tc>Su>c0iolOi'olf>atCGOtd0C>IDIO.

n<<IIII/.rC-<I>/.IlS<./~IIt/S.l>10Qt>1jStgktsS0Wf/'>0co4~W~II.1gCCAC/S>hfaI.S<<d$(CSr)C.o.l,stt0)I~fr>/~J'I~fltss':c0fl!III<</>sI1>/IllaIfp'sdf-i!qWISS4/S(/d7t'l~It"I0~lt'o~I'0IUOTB:Beamstoberepairedaremarkedthusf~~wm~~~wltsAh/h1COCA'rtfPO,/rI'I~'4LCahdtI//N.1>,l)l/drIIII>A>Cf<<<<Drls<<<<<<>hfItv<<>15/It>httdh./<SStructuralSteelFramingPlanEl.683'-0"ReactorBuildingUnit1~'t.I~fI~,hIrr~lr/ICrh0rsent~lt//t<<I'lt.)~-'l<<0'[I~Ilgr0dOIhI.'N}raFigure3AppendixD

0r.atlarac~riec/e4vrI~14cg4$IPH4-Iwt~l411P.44~IS}=-1-""$JCcvtOPIII4'4WLL4c0o~ioNOTE:Beamstoberepairedarentarkedthus0ra/CJCt/I/IAIIttalentttltHYtl/I/rett1Sct/c4DIrtcd/~/o~kII/II~C,Rt~++@tet~'tCC~)toestepsIi$5afIC/C4$Q~d,4,4'ct4'/>hhIIM4'~44~i'll,,I4h1I~~'I)NŽ~rtlgI'44}r/r/Itltttyr'Iclitct-t'I}4'44'}ct>StructuralSteelFramingPlanEl.683'-0"ReactorBuildingUnit2Figure4AppendixDL4/404444

etr0270702170I/fe'50'rh57/b65I474d@.P//tritI4'0/453'IOt9:Ctrrt4no'r0~~I'II~~C.I~ttIIIC4/ttWIWIItt'OIII-9~p/d.ed.e-0b0)fW'I+I~ICCkrtt/I.irI.tt7-e'-0)7r440I3WtrrW/05-fl-~9Ie4.44IP</ceo<OLctrrI<.t.ttI00.<Ir'.t.tthen'4h440Irttktea.<rw~~CIIIIOI47~ttt/W0<7to)7t.'I99t)/Iog7I?WdrdlQtt<OCr-I;'~'%.,:,i-4'-dtUtt,gt-g3IttkI44'2W~kr60I/0'o,~'~Att2IIrt/.Isete'llihhhII~p"iJ~IOCAO1OXOIOVtttoIIhh5:o'/0~~IOO,II0(/0IIh7I7/00Cltl<rrICCAr/0rdirpocrktctrppokr244Itdtt*DWCL4'JOI~ITk44rdrt<tttt)I.at.oIII0arett4ktt<twhItltt1ekkIVOIC2I/+Irreet:97IWtkIIIElWttrd4II--iQSi4'I,?o-70.2Ittt55<7797WttrdotorIttt7~'=te2'f6297WtkredtthlO..o!ttk6IWr7etit/Cr1<IIl--t/ItnorttIl~<<I)too4->>~w>5~too4W~~rrd~lttrdhetk/90/to~t'1dioretPittI<IICOIII0Iro4~Crt44fkt4Wtk.dt~4tt4ro44I04~rtkde5474ddtOOI62cd4'kt.~~enIttT"0o00k7444r4J[i'4ttre/0b7/tttr/4)~644~t-z-Beamstobcrepairedarcmarkedthus.~~~m~~StructuralSteelFramingPlanEl,.7lglReactorBuildingUnit1Figure5AppendixD

Inverted3"metaldeckingNo~-shrinkhighstrengthepoxygrout3"longsteelblock(AS2".2-441)we&atarredinholefor3/4"PA-325ric~antyoebolt.l/oversizedhole.TopflangeofsteelbeamQCtvIU)0lAQHaroenedp]ate~asher*Naninaloeckin"dim~~sionspmmanufacture'scatalogR"?PZBPFKEDJRE-YiETHOD'2'IGUK6APP~IX'D'P-74b)

't Non-shrinkhighstrengthgrout5llp4-1/2"Px1/2"hardenedplatewashereachside.~tg~rC'.0880steelbeamorplategirder1-1/2"gthreadedrodwithonenutoheachendASTNA-325torquedforfric-tionconnection.1/16"oversizedholeinplatewashersandthetopflange.3/8"oversizeholeinconcreteslab.Notes:1.Priortodrillingcheckholelocationasfollows:-withrebardetector,ascertainthattoplayerorreinforcementandanyembedsareclearofhole.2.Preferredlocationisatvalleyofdeckingcorrugations.Donotlocatethrusidesofdecking.REPAIRPROCEDURE-S<ETHOD'1'IGURE7APPENDIX'D'P-74b)

APPENDIXEFINALREPORTONSHEARSTUDSBASICTHEORYOFCOMPOSITEBEAMCONSTRUCTIONENGINEERINGDECISIONANALYSISCOMPANY BASICTHEORYOFCOYiPOSITEBEANCONSTRUCTIONSUSQUEHANNASTEANELECTRICSTATIONpreparedforBECHTELPO'HERCORPORATIONSanFrancisco,California21Decemberl977LE<L7ENGII4EERINGD-CISIONANA'SISCOMPANY.INC.480CALIFORNIAAVESUITF3012400MICHELSONDRIVESURNITZSTRASSE34G TABLEOFCONTENTSPaoeSYNOPSIS.1.INTRODUCTION.2.GENERALTHEORYANDACOMPARISONWITHTHEAISCTheoryandVerification.3.COYiPAR'SONWITHAISCSPECIFICATIONS;Ana1ysisofCompositeBeams......;-.Ana1ysisofProjectBeam14.....OtherAISCProvisions.~oo~~~~e~1-1SrECIFICATIONS..2-12-13-13-23-43-44.RECOt"ENOATIONSANDCONCLUSIONS................4-1REFERENCES twSYNOPSISThis'reportpresentsageneralultimatestrengththeoryforcompositebeamsthatfitsthetypefoundintheSusquehannaSteamElectricStation(SSES)andmoreconventionalconstruction.TheconstructionoftheSSESemployscompositebeams.havingheavy,thickreinforcedconcreteslabspouredonaformedsteeldeckwhichinturnissupportedbythegenerallyunshoredsteelbeams.Incontrast,theconstructioninordinarybuild-ingsemploy>athinlightweightfloorslabwithaformedsteeldecksup-portedondeepbutlightsteelrolledsections.Anextensivestudyofthe.experimentaldatauponwhichtheAISCspecifi-.cationsarebasedwasmadesincetheprojectbeamsareverydifferentfromthoseforwhichtheAISCspecificationsaremeanttoapply.Itis,shownthattheAISCspecificationsaregrosslyconservative.Avalidultimatestrengthprocedurewhichfitstheexperimentaldataandthepro-jectbeamsisderivedbasedonrecognizedconcepts.Thestudycloseswithrecommendationsforuse-inevaluatingthe,projectbeams.

1-1l.INTRODUCTIONThisreportispreparedinaccordancewithBechtelContractNo.7PE-TSA-11andinaccordancewithmeetingsbetween8echtelPowerCor-porationandEngineeringDecisionAnalysisCompany,Inc.(EDAC).Thisreportisconcernedwitha,studyofthebasictheoryofcompositebeamconstructionandtherelationshiptothespecificationsoftheAmericanInstituteofSteelConstruction.ThefocusisonthetypeofcompositeconstructionemployedintheSSES.Chapter2ofthisreportisconcernedwiththegeneraltheoryofcom-positebeamconstructionandtheverificationofthattheory.Chapter3focusesonthesuitabilityoftheAISCspecificationsforcompositecon-structionwithbeamsofthetypeemployedintheSSESdesign.Theexper-imentaldatauponwhichtheAISCspecificationsarebasedinvolveathinconcre'teslabpouredonaformedsteeldeckwithshearstudsconnectingtheconcreteslabtoasteelbeam.Inlaboratorytests,therewassuf-ficientslippagebetweentheslabandthesteelbeamforallstudsintheshearspantobedeveloped,andfailurewasassociatedwithconcretefailureinvolvingpulloutofthestudsfromtheslabandthedevelopmentofayieldhingeinthesteelbeam.Thebendingstrengtho,theslabbyitselfonthespanofthesteelbeamswasverysmall,sothatthestrengthofthecompositebeamwasthesumofthestrengthofthesteelbeamandthestudconnectionintermsoultimatebendingmovement.Inallcases,thedeadloadwasverysmallcomparedtotheult'imateload.

1-2Thebeamsemployedintheprojectdiffergreatlyfromthetestbeamsinthattheslabthicknessisofthesameorderasthatofthesteelbeam.Theslabisheavilyreinforced.Thedeadloadisnotsmallcomparedtotheliveloadandthesteelbeamsaregenerallyunshoredwnentheslabisplacedsothatthesteelbeamsupportsallofthedeadloadwhilecompos-itebehaviorispresentunderliveload.AnalysespresentedinChapter2disclosethattheAISCspecificationsmustbemodifiedtofitbeamsofthetypeofinterestinthisstudy.Ageneral,methodofanalysisanddesignispresentedinChapter3whichfitstheexperimentaldata,isconsistentwiththeliterature,andpro-videsarelationshipbetwentheAISCspecificationsandconstructionofthetypeemployedintheproject.Finally,Chapter4presentsrecommendationsandconclusions.

2-12.GENERALTHEORYOFCOMPOSITEBEAMCONSTRUCTIONANDVERIFICATIONOFTHETHEORYThischapterisconcernedwithadevelopmentofageneralstrengththeoryandverificationofthattheorybycomparisonwithexperimentalresultsoftestsofcompositebeamsemployingaformedsteeldeck.TheprovenanalyticalmethodologyisthencomparedwiththeAISCspecificationsinChapter3.-AmethodologyforanalysisofthecompositebeamsintheSSESisalsopresentedinChapter3.THEORYThediscussionthatfollowsisbasedontheworkofGrant,Fisher,andSlutter(Ref.1).Themethodologyisbasedontheultimatestrengthofthecompositebeam.Sufficientslippageisassumedtotakeplaceattheslabbeaminterfacetoassumethateachshearstudintheshearspancar-riesthesameloading.TheAISCspecificationsassumethatitispossibletorelatetheultimatebendingstrengthofthecompositesectioninwhichthesteelbeamdevel-opsayieldhingetoanelasticstressanalysisatthesamesectionusingtransformedsectiontechniquesfocusedontheunitstressinthebottomtensionflangeofthesteelbeam.Theassumptionisalsomadethattheeffectivesectionmodulusofthecompositesectionisalinearfunctionoftheratioofthecapacityoftheshearstudsintheshearspantothetheoreticallimitofthiscapacity.

'I~00 2-2ExaminationoftheexperimentaldatauponwhichtheAISCspecificationsarebaseddisclosesthatthecompositebeamsthathavebeentestedfitaparticulartypeofbuildingconstruction,thatinvolvingathinconcretefloorslab,andlightbutdeepsteelbeams.Thelargestslabthicknessin74testswas9in.witha3inribheightmakinga6in.netslabthickness.Thebeamspanwas34.9ft.Yiorethanhalfoftheslabswereconstructedoflightweightconcrete.Thebendingstrengthoftheslabwasneglectedintheanalysis.Theslabwaseffectivelyconsideredtobea'purelycompressionmemberwiththecomprhssive,orcelocatedatthecenterofgravityoftheconcretesectionneglectingtheribconcrete.Thesingleelasticdeformationrequirementisthatthecurvatureofthenetconcreteslabbethesameasthatofthesteelbeams.Ifbothslabandbeamareelastic,theliveloadcarriedbytheslabandbeamispro-portionaltotheirstiffnesses(EI).Thelargestratioofslabtobeamstiffnessintheexperimentaldatais0.15,thatforthe17Lehightestranoesfrom0.009to0.021,andGrant,Fisher,andSluttersaythatthisratioisgenerallylessthan0.05.Withprojectbeam14,thisratiois2.07.~Grant,Fisher,andSlutter(Ref.1)statethattheratioofthesectionmodulusofthetransformedsectiontothatofthesteelbeamsisapproxi-mately1.5forcompositebeamscomnonlyusedinbuildingconstruction.Thisraiois2.9forprojectbeam14.HThegeneraltheoryforultimatestrengthofacompositebeamisshowninFigure2-1.TheequilibriumconditionisshowninFigure2-Iband2-1c.Withtheexperimentalbeams,theslabswereveryflexiblecomparedtothe~steelsection.InFigure2-1c,abendingmomemtisshownto.existattheslabtosteelbeaminterface.Thisbendinomomentislargecomparedtothatfromloaddistributioninallexperimentaltests.Mithverythin 2-3slabs,itisreasonabletoassumethatthecompressiveforceintheslabactsatthecentero,gravityofthenetconcretesection(seeGrant,Fisher,and.Slutter)(Fig.2-lc).Thetensileforceonthesteelsectionactstoreducetheplasticmomentcapacity(Fig.2-ld).Intheanalysisoftheexperimentaltestsmadein.thisstudy,itwasassumedthatthewebandflanoesofthesteelrolledsectioniereofconstantthicknessasgiveninAISChandbook.Withthickslabsitisnecessarytomodifythetheorytoaccountfortheultimatestrengthcharacristicsoftheslab(Fig.2-2).Equation4resultsandthisrelationshipwerecheckedbycomparisonwiththeexperi-mentaldata.Theanalysisshowedthatthemeanratioofexperimentaltocalculatedstrengthwas1.000(0.9997)withastandarddeviationof0.081forthe74testbeamsandthedatahadarangeof0.835to1.1884.Theratioofobserved-to-calculatedcapacityisplottedinthehistogramofFigure2-3andthesamedataareplottedonno'rmalprobabilitypaperinFigure2-4.Thefittoastraightlineisexcellentsothattheobservedvariabilitycanbeassumedtobethesumofrandomvariationsnooneofwhichisdominant.The.standarddeviationisequaltothecoefficientofvariationwiththesedatasincethemeanisunity.Thecoefficientofvariationisofthesameorderasthatfoundintheyieldpointofsteelrolledsectionsofnominallyident'icalmaterial.TheanalyticalcomparisonisalsoshowninFigure2-5inwhichtheratioofexperimental-to-calcuatedstrengthisplottedagainsttheratioofshearstudcapacityprovidedtomaximumshearstudcapacity.Itappearsreasonabletostatethatthereliabilityofthetheoryisnotafunctionoftheshearstuddesignlevel.Thatis,thedesignwithaY'h/Vhof0.25isfullyasreliableasthatwitharatioofunity.

t 2-4DlHcSl~s~eirw~PCStagJ~'Srec.lSec&anHp5<ppork8b~5leclckomLIhC.9.CO~C.-DFCQOI75~IIC'S~t-'(g+h)P~rop;S>IiI~Compr.oFYPFkyejSfCCIin7erSI'an0I'P?ezsimLo&0<5/ud~of'kcIFIGURE2-1COMPOSITEBEAMRELATIONSHIPS 2-5IV'h='.zs7u.bArFy)~C=~rFf<t"-Ar~gra.SlabCona'I'ho~V'kl+~~sC22.2g>+8<+y'h(2+t-~)(3)V'/7.a=-O.ZSFcbYh~=o,F5Ki5cf-h)js+4,-gpfyQp(fP)(l-)gv'hv'h~zv~.JS(l.7)(ocdFyCs)FIGURE2-2CO'",POSITEBAMULTIMATESTRNGTHRELATIO"'SHIPS 2-6/5Exrgi~e~&lCC!PoCI~'a6o:Cc/cu/afedCA,~<<i'yon=l.go,5ja~+orr/Strich~=4.08'jGUpE2-3HjSTOGRA!~jOfEXpERj~,ENTALTOCAlCULATEDULTjl'tATESTRENGTH 2-7'tttSWtt%tlSSC>SCCSSC4%1$t1CdCCCICCSC1)~II~'1e/4Iee\'eIee-.1Ch'1eeeI---.-:-e11~I~.:1".te.'I~...e'i,l~"f"f".I~.e.1]1).~.;f,.)"If,I+1~':fHt>rt~l00;f'-:f':;:1'I~'I'.l,:;cr!r~zrrr~~~~eIepeggVCl~ePI~~~~&~~r~i/'e~ee~Is.f--.)..~l-~".eA.erClllL5CJCCS1t1lt0S4SCQtC410ttttttttltt.lffB0~arlrgFIGURE2-4PLOTOFRATIOOFEXPERIYIENTALCAPACITYTOCALCULATEOCAPACITYONNORl'IALPROBABILITYPAPER Z-8/.2Z~x.Cap.Ca/C.Cu/d0,9s=o.oI/X'xO.gx.Lchij/jTnU~0/herTisfsP.6FIGURE2-5PLOTSHO'r'ING2EROCORRELATIONOFSTRENGTHRATIOVITHV'hlyn

,.-,~,JCOMPARISONOFTHEORYMITHAISCSPECIFICATIONS3-1The1969EditionoftheAISCspecificationsemploystherelationshipshowninFigure3-1forelastic'designbasedonultimatestrengthproper-'ies.Thecriteriaisthetensilestressinthebottomflangeofthesteelbeam(0.66Fy}andtheeffectivesectionmodulusforelasticdesignis.equaltoasimplelinearfunctionofthesectionmodulusoftherolledsteelsection,thetransformedsectionmodulusreferredtothebottomflange,andtheratioofactualshearstudcapacitytothemaximumshear1studcapacity.ThetrueeffectivesectionmodulusforpseudoelasticdesignisgivenbyEquation5(Fig.1-2)inwhichtheloadfactoris1.7andtheallowableunitstressis0.66Fy.ThetruesectionmodulusforeachoftheexperimentalbeasmusingthecalculatedultimatestrengthbyEquation4ofChapter2isplottedinFigure3-1againsttheeffectivesectionmodulusdefinedbytheAISCspecifications.TheplotshowsthattheAISCrelationshipisconserva-tivelybiasedbyapproximately30percent'asedonameanvaluefunc-tion.However,approximately50percentofthebeamshavecapacitiessmallerthanthatdefinedbythemeanvaluefunction.ThevariabilityofthedataaboutthemeanvaluefunctionappearstobeindependentofthesectionmodulusandindependentofY'h/Vh.TheAISCrelationshipapprox-imatesalowerboundonstrengthforsectionmodulusuptoapproximately'0to100in.~ThevariabilityshowninFigure3-1isconsistentwiththatoftheplas-ticdesignmethodologyforstructuralsteelbeamssothatitdoesnot 3~2appearreasonabletorequiretheconservatismforcompositebeamswithasectionmoduluslargerthanapproximately100in.~Theprojectbeamsofinteresthaveverylargesectionmodulus,oftheorderof1200in.sThereisastrongtrendfortheshearstudconnectiontoshowadecreaseinvariabiltywithincreaseinthenumberofstudsowingtothelowcor-relationbetweenindividualstudstrengths.Hostudiesweremadeoftheexperimentaldatawithrespecttostudpro-perties.ANALYSISOFCOMPOSITEBEAMSStrictelasticanalysisofacompositebeamcannotaccountfortheunde-finedslippageontheslabtosteelbeaminterfacesothatitisneces-sarytoemploypseudoelasticprocedureswhichfundamentallyarebasedonultimatestrengthproperties.Thusthisdiscussionwillfocusontheanalysisbasedonultimatestrength,Figure3-2.Equation4ofChapter2definestheultimatemomentcapacityofacompos-itesectionforcombineddeadandliveload.Atultimate,thebeamdevelopsayieldhinge,thereinforcedconcreteslabisatitsultimatecapacity,andtheV'hforcehasitslargestpossiblemomentarmconsis-tentwiththestrainconditionsinthesteelbeamandtheslab.Withthreeinterrelatedsourcesofstrength,itispossibleforanyonesourcetodevelopthenecessarycapacity,,anycombinationoftwosouces,orallthreesourcestogether.Ingeneral,thedesignwillnotbebal-ancedsothatatleastonesourceneednotbefullydeveloped.Theanal-ysisthatfollowsconsidersfirstthesteelbeamtoitsplasticlimit,thenaddsthereinforcedconcreteslabtoitsultimate,andthenaddsas 3-3manyshearconnectorsasnecessarytosatisfytheloadingcriteriawhileaccountingfortheinfluenceofthetensiononthesteelbeamandforthecompressionintheslab.Fromthestandpointofultimateload,itmakesnodifferencewhetherthesteelbeamisshoredorunshoredatthetimetheconcretefortheslabisplaced.Thisistrueregardlessofthestressconditioninthesteelbeamunderdeadloadaloneasaconsequenceofredistributionofloadingamongthethreeresistingsystemspriortoultimate.Theultimatestrengthisindependentofthepathemployedtoattaintheultimatestrainconditi'ons.Thesameisnottruewithregardtodeflectionsandrigidity.Ifboththesteelbeamandtheslabdeformelasticallywhileslippageisallowedatthestudline,therequirementofidenticalcurvatureallowsthecal-culationoftheloadcarriedbytheslabandthesteelbeam.Ifnoshearstudsareprovided,thedeflectionisthatofthesteelbeamundertheloadingsupportedbythesteelbeam(withproperaccountingforthedeadloaddeflection).Mithshearstuds,theelasticstressconditionsare-undefinedsincetheslippageconditionsattheshearstudsareunde-fined.However,ifthedeadload(concreteslabandsteelbeam)unitstressesinthebottomflangeofthesteelbeamreachtheyieldpointunderthisloading,thecompositebeamwillshowdegradingrigiditywiththeapplicationoffurtherloadingalthoughtheultimatecapacityofthecompositesectionisunchanged.Apseudoelasticanalysisofthecomposite-sectionisshowninFigure3-2.Awidevarietyofsuchempiricalproceduresarepossible.

Cif~,3-4ANAlYSISOFPROJECTBEAN14Projectbeam14isanalyzedinFigure3-3bothonanultimatestrengthandapseudoelasticanalysisconcept.Fromthestandpointofultimatestrength,itisseenthattheslabandsteelbeamwithoutcompositeactioncansupply93percentoftherequiredmomentcapacity.Atrialstudcapacity(intheshear.span)of200kipswasassumed.Thestrengthexceededtherequiredcapacitywithonlyninestudsneededwhen46.5areprovidedand42areeffectiveatanormal2percentlevel.SeeEDACReport249.03,"StudiesofShearStudAdequacy-.SusquehannaSteamElec-tricStation,"fordevelopmentoftheequivalencerelationship.~'pseudoelasticanalysisofprojectbeam14isalsoshowninFigure3-3.Theanalysisbeginsbyassumingthattherearenoshearstudsandchecksfordesignadequacyassumingthatthesteelbeamsupportsallthedeadloadanditsproportionoftheliveload.Itisfoundthatthestiffslabisnotadequatelyreinforcedtosupportitsportionofthe-liveloadwhilethesteelbeamunitstressesarelessthanallowable.Theelasticslabcapacityplusthesteelbeamcapacityis92percentofthatneeded(neglectingelasticstrainrequirements).AtrialV'hof200kips(elastic)producedasatisfactorycapacitywiththesteelsectionnotusedtocapacityora-V'hof100kipswassatisfactorywiththesteelatelasticcapacity.Therequirednumberofstudswasninewith100kipstudloadsand18with200kipstudloads.OTHERAISCPROVISIONSTheAISCspecificationscontainalimitationonthetransformedsectionmoduluswhichisafunctionofthe.ratio-ofdeadtoliveloadbendingmoment(Equ.1.11-2)andstudlayoutrelationship(11.1-6).Thereappearstobenojustificationfortheequationinvolvingthelivetodeadloadbendingmomentratio.Fromthestandpointofultimatestrength,thestrainconditionatultimatestrengthisindependentofthe

3-5ratiooflive-to-deadload.Eveniftheunitstressesinthebottomflangeofthesteelbeamareatfullyieldunderthedeadload(un-shored),theultimatemomentcapacityofthecompositesectionisun-changed.Thedeadloadiscons~deredthesameastheliveloadinthestrengthcalculation.Mithunitstressesunderdeadloadlimitedto0.66.Fy,thereappearstobenojustificationforthespecification.ltwasnotpossibletodeterminethebasisoftherequirements.Thesecondrequirementdealingwiththelayoutofshearstudsintheshearspanproblemcannotbejustifiedonthebasisofultimat'estrengthconsiderations.TheLehightestsinvolvedafour-pointloadingwithone-quarteroftheloadingappliedatapoint19to22percentofthespanfromtheendsupports.AvarietyofshearstudarrangementswereexaminedintheLehightestsrangingfromproportioningthelayoutinaccordwiththerelativeshearinthespantoauniformlayoutindepedentoftheshearinthecompositebeam.Statisticalanalysisofthedatarelatingtheexperimentaltocal-culatedstrength(notconsideringstudlayout)asafunctionofthestudsintheregionofmaximumsheartothetotalnumberofstudsshowedthatstrengthisuncorrelatedwithlayout(Fig.3-4).Unless,otherevidenceexiststoverifyAISCEquation1.11.-6(p.5-35),therelationshipisnotvalid.Theresultoftheapplicationoftheequationistoincreasetheproportionofstudsintheportionofthebeamhavingthelargestshearandmoreorlessreflectsanalysisanddesignproceduresbasedonanas-sumedelasticbehaviorofthestuds-1 3-67hisRepaint/.ooQP0UpA/SCSqff=Ss~-Qp~-Ss)YAVAgy~k/+60x/op/5o5'e/C'Attic)-i'n~'zooFIGURE3-1PLOTOFTRUEEFFECTIYESECTIONNODULUSTOTHATBYAISCSPECIFICATIONS I1 3-7/41A/'/8/5-'L7/P///7ESi/'-Eh/bT//'.7(hey>HHg)=f7~+c/.7')+/.7McDLons&Iplo~e-Cnsz2=Q7Hp+I.7'.-(Hs-Ag))7~u-/Vs+~cC+szW:hgV,(I'h+obenrni~i~u~)P>o~/VowenfCc~t~aeifp:a.V'h-d~(4-Ztp-)F~s=~D~~$L-Vjdj/(d-fF)6.V'h~8wCol-~<Z)Fpcl'-2dn'-('p-~)~Prt~lcnS/cnCVpProc'en'ure-CuseZICc/Iculofe'<g=I-7<+oPM3a~d~~-MpWoC0.16+yS2.~Check,~~~I>Z+McZXSO,Vh=u3.IfVhIsceeded,P.+SainteVolumes'ofp"h0>.Coypu*'PAL(h'ofeg~z~5~I>)PJCr~pscfeWc,e.CI.k=~~r/>>/7//c<see/-/c<-[a'<erht//h)/'h)jVh/2or~u=Ies+Ac+.VAgo'//~p-g,+(x'-h)g/V'h)72Vhc~F1GURE3-2ULTIYiATESTRENGTHANALYSIS

3-8ANALYS'/5':ULg/MAiw57R+A67&~Cd/iflnued)CessZ..V/yOL've/~c/'andep~o~rbib<<d~~cordi~9oE'i.lwn~Ys(s:E~zsiic(ps~~~o)CAs-~=Vh=0Ll~eloam's/obancl'.anpro/or6'onol*E3cod'oa@~oSkc/8c,a~.Pfc>(P~Z/fgpDf+1//I">4kel/ur'cledbp/./pHCzI7JCheckdopacrh'es:ahg:Z.L(+,+~so~ol~)Shd/=3L+LI(Pr4Porflon)CAsz-W-YhgODL4s/cc'.l,gljpSPec/on@'oncrek'cpodrono/9oEZu.Concrete:Check<ciME'Pm>do~5ke/'hccEp7>p5zz~,O'erF>Sc.Cow~+legureah(l)Co~c~.-Vh=t--Z(z)Si'eel:R>m~~F=0>~~isfCa~if=<>(Ccrc+Uljgn"Rk)goopy+ffAorc'her&cap4kcIIQfearcol/v(n+i@1CRiada)FIGURE3-2continued)ULTIMATESTREt>GTHANALYSIS 3-9Ah'I-.'L)'5I~PZOJd=C7'-"dqff6+)re@z.zs.g3--3'r).stuc/s/n9rovers3/5/mspd..rroc++55-+S'/VHStn5heor'nHD=255,2.(/s=7.i~)~c=/27P./"(f=37.Ag>c=F'$'/ZS/3'/~c=>~"Ar"(ACZ)FcZc-=z.o9AZsgc'bcb76.S"F>--wok5CP9e/Z"~2/.5oI~Z91Z"Spy/.IBS')~O'.D9/2)53'C'iS/205=e/+"2-"/8'S~2'/75/GOfy~SpQi'h=2358S)'cc/t//,=czezc.~g/5s=I./ordc)~gcPus~218HCA/SC8/3,9)Qrc=-'(J(-)8+s=@755gsPu=2'3.8$'sf~dULd//3AiS'/p&'65//'/V/n/'rrdurr)numberpi/sleddsneeded.Pf).7(go/.h'-26ob.4+VsSV3sX-Vh-"0C<oSgvds7dssdrd)spxo~<6<~/9'375/5/hd/zGobGsp/zCsosfZ:ZCOC.C-Zg'q35dr)pprcv.6'rrckdVhfVc/7enslonCe/.=~~(d'-2'/.-)Fy~(o.CSCXZ2.//S)CSo)=13'C.5/7'hmZggCucb0kPly=cc/c.-<<pdg(c/'-dp')Hs~(/5/.09/)g//3s)(s'o)(261'z-I./95)(/z)=/57/,co*sla'35sia(55)(l)j-1l-57li3-7i3iss(1--jj=5+Vhc(Z)(liPC2'/Zdc++S+Ny/+54+/$2/-W7'ISO=ZCP.Gp24O&.tpo'hc.875dci&nd'ecIPcl=-=S'S(YC.5~vp+aid)Zoo23.<S(535ZPfkchm~/g'%)FIGURE3-3EXAMPLE:ANALYSISOFPROJECTBEAM14

g<ALY5/SPRoJCTBERN~>+(Canflnved)EL<5Tl<-CFbeudo)CAszI':Vh=o=?ZAN27o:SleekPil~/~lZ.of*dPfgi=-(/277.I)=d'4+5lvz.ofiVsg=-L'/?7F.l)='//S6"'Og'~<Cn~='OZ.C+ASS'2=4GRg"/S3XZ~~~+P.'6$F<S=JVOC.S"95C+cz==NZ46/.7o.CCF>$=(in;So~CjgSZ/58K3-/+oCyPPPrtP'$~~.,0:90.+COoycraI2'W3'ry'fFCd/5->CSqgC3'ryVh=ZooE/ps&a'~uiv'.=(2g2OQ)=+00vV72~gdP5+4+Cdh)(I-~)J/gpssq<=pf(~~)V/I-Vi,IH(El.)=-H'g(V<7)=7517/I4~++h(EL)9Hz<=/'/Egg)/277./1ok.(Doesno/crscs/cr/4ccpacr~g)/XV'h./oo"H>CeZ)=-=3l'~"r+cFeG.C't'<$+HrgCc,L)=1/F~<o4AnApprvi'mA'on51'odspA&p'=(0.J'o9)C/s.3)=lJ.4d/svudzdu"/7Aecdca'~n8/oo0/-'~eckJoE(0FIGURE3-3continuedEXAMPLE:ANALYSISOFPROJECTBEAM14 PPpl.2Rg5+dsSh:orSpun~C)/,0fSfogc=OOOE8cSPSgQo~~Fik)+~<~f0.6Z~bro]V'z07FIGURE3-4PLOTSHORINGlACKOFCORRELATIONOFULTIMATESTRNGTHMITHVARIATIONINSTUDPLACEt'ENTPATTERN 4.RECOi"8ENDATIONSANDCONCLUSIONSThetwobasicconclusionsofthestudyare,first,anadequateultimatestrengththeoryexistsforevaluatingcompositebeams,andsecond,theAISCspecificationsforcompositebeamsreflectaspecifictypeofdesignratherthanageneral-methodologyandthusshouldonly,beappliedtothinslabscombinedwithdeepsteelbeams.Itisshowninthereportthatthick-slabcompositebeamsofthetypeemployedintheprojectareapproximately30percentstrongerthanthestrengthbyAISCspecifica-tions.Theinfluenceofthoformedsteeldeckappearstobeadequatelycoveredbyexistingrelationships.

i'.0REFERENCESR-11.Grant,J.A.,Fisher,J.M.,andSlutter,R.G.,"CompositeBeamswithFormedSteelDeck,"EngineeringJournalAISC,Firstquarter1977.2."hanualofSteelConstruction,"AISC,SeventhEditionandSupplements3.Benjamin,J.R.andCornell,C.A.,Probabi-lity,Statistics,andDecisionforCivilEngineers,McGraw>Iooompany,nc.,I0.

APPENDIXFTOFINALREPORTONSHEAR.STUDSSTUDIESOFSHEARSTUDADEQUACYENGINEERINGDECISIONANALYSISCOMPANY(P-74b) 4 EDAC-249.03STUDJESOFSHEARSTUDADEQUACYSUSQUEHANNASTEAt~jELECTRICSTATIONpreparedforBECHTELPOWERCORPORATIONSanFrancisco,California21December1977L'!t:EK.".aENGINERINGDECISIONANALYSISCOMPANY,INC.460CALIFORNIA,AYE.~SUITE301PALOALTOCA'LIF.943062403L4ICHEI.SONDRIVEIRVIN"=.CALIF.92715BURNITZSTRASSE346FRANKFURT70.IV.GERMANY

~,TABLEOFCONTENTS~PaeSYNOPSIS.1.INTRODUCTION.2.STATISTICALANALYSISOFSHEARSTUDDATAAnalysisbyBeams.AnalysisbyStuds...........Interpretation..RECOt"'PENDATIONSANDCONCLUSIONS00~0~0~00~111~000~~t~0~01-100~~~~~000~21~0~~~00000~2-1~~000~~t~0~2-20000000~0t02~20000000~t00~3-1REFERENCES SYNOPSISUponinspectionattheSusquehannaSteamE'lectricStationconstructionsite,ahigherproportionofimproperlyweldedshear-studswasobservedthanisconsiderednormalincompositebeamconstruction.It-isnormal,.forapproximately2percentoftheshearstudstobeinadequately'eldedtothesteelbeam.Oftheshearstudstested,approximately9percentfailedtopassinspectiononanaverage.Aportionofthereinforcedconcretefloorslabwasinplaceatthetimeoftheinspectionandthequestionistodeterminewhetherornotmeasuresshouldbetakentoim-provetheshearconnectionbetweenthesteelrolledsectionandthecon-creteslabin.thatportionofthestructurewherethefloorslabhasbeenplaced,sincetheshearstudconnectionisuncertain.Theconstructionatthepowerplantemploysheavy,thickslabsonheavysteelrolledsections.Incontrast,thecommonconstructioninordinarybuildingsemploysathinlightweightfloorslabwithaformedsteeldeck(asslabforming)andthestructuralsteel.beam.'Aformedsteel.deckwasemployedintheprojectconstructionandthesteelbeamsweregenerallynotshoredwhentheslabconcretewasplaced;Thestatistical-analysisof'ataonshearstudpropertieswheretheycouldbetestedshowedthatthemeannumberofstudsnotpassinginspec-tioninanybeaminReactorBuildings1and2andtheControlBuildingwas9.2,percent,andthestandard-deviationofthismeasurewas6.4per-cent.Thedataforthethreestructuresweresosimilarthattheycouldbecombined.Incontrast,themeanpercentofstudsnotpassinginspec-tionwas0.42percentintheTurbineBuilding,sothattwodifferent conditionsexist.NodetailedanalyticalstudyappearstobenecessaryfortheTurbineBuilding.Atotalof13,904studswereexaminedinthefield,13,073forReactor,Buildings1and2andtheControlBuilding,and831intheTurbineBuild-ing.Themeanfailurerateofindividualstudsintheformergroupofstructuresisestimatedtobe0.0842andforthelatterstructureisestimatedtobe0.0084.Thereasonfortheneedtoestimatetheseratesarisesfromthefactthatmanystudswererepaireduponfailingtopassthevisualtest,whileonlyapproximately18percentofthosefailingthevisualtestactuallyfailedthebendingtest.Thesamplesizeisadequateforestimationandforecasting.Thestudycloseswithrecomnendationsforuseinevaluatingtheprojectbeams.

1-11.INTRODUCTIONThisreportispreparedinaccordancewithBechtelContractNo.7PE-TSA-11andinaccordancewith,meetingsbetweenBechtelPowerCorpor-ationandEngineeringDecisionAnalysisCompany,Inc(EDAC).Thisreportisconcernedwithastasticalstudyofshearstudadeouacyandrecormien-dationsforhandlingtheproblemsfromthestandpointofdesign.ceReferenceismadetotheBechtelPowerCorporationreport(Ref.1)of1?Dune1977forastatementoftheproblem.In.essence,ahigherfailurerate(soundnessandbendtest)ofshearstudsthanexpectedhasbeenobservedintheconstructionofsomeofthecompositebeamsintheSus-quehannaSteamElectricStationconstruction.Thequestioniswhetherornotthosebeamswhichhadtheirslabspouredpriortothisobservationareadequate.StudfailuredataanalysisandforecastproceduresarediscussedinChap-ter2using,twodifferenttypesofanalysis.Thefirst,typeofanalysisassumesthattheoccurrenceofinadquatestudsisbybeamswithindepend-encebetweenbeams.Thistypeofanalysisproducesafailurerateintermsofthepercentofstudsthataresatisfactoryand-unsatisfactoryinanygivenbeam.Thesecondtypeofanalysisassumesthattheoccurrenceofaninadeouatestudisanindependentchanceevent.Nosystematicphe-nomenaappeartoexistwhichmakesfailurestendtooccurtogether'onaparticularbeamorinareasofthestructure.Thetwostatisticalpro-ceduresyieldslightlydifferentforecastsofthenumberofadequatestudsinanybeam.Itwasnotfoundpossibletoconsiderpartialstrengthsofstudsinthestudyo~ingtoalackofdata.ceFinally,Chapter3presentsrecomnendationsandconclusions.

4 2-12.STATISTICALANAYSISOFSHEARSTUDOATATwodifferentanalysesofthesamedataarepresentedinthischapter.Tnthefirstanalysis,thedataareconsideredinabeam-by-beambasisassumingindependencebetweenbeamsbutnotnecessarilybtweenthestuds.inanyonebeam.Incontrast,thesecondtypeofanalysisassumesthateachindividualstudisindependentofallotherstuds.Thechaptercloseswithaninterpretationoftheresultsin=termsofequivalenceoftheportionoftheconstructionofconcernandnormalconditions.ANALYSISBYBEAMSThedatafallintofoursets,ReactorBuildings.1'and2,ControlBuild-ing,and,TurbineBuilding.Ineachset,thetotalnumberofinadequatestudswastakenasthesumofthosethatfailedthesoundness(hamerblow)test,plusthosethatfailedthevisualtestandthebendtest,'lusaportionofthosethatfailedthevisualtestandwererepairedwithoutfurthertesting.Thelatterportionwasassumedtohavethesame.proportionoffailuresasthosethatfailedthebendingtest'afterfail<<ingthevisualtest.Theresultsoftheanalysisare-giveninTable'-1.ItisseenthatalldataexceptfortheTurbine.Buildinghavesimi-larpropertiessothatthedataonbeamsforReactorBuildings1and2andControlBuildingwerecombinedintothefirstdataset.(Fig.2-1),withthatfromtheTurbineBuildingbeingtheseconddataset.Nodetailedanalysisoftheseconddatasetwasnecessaryowingtothelowinadequacyrate.

~,2~2Thedataofthefirstset-wereorderedandplottedonbothnormalandlognormalprobabilitypaper.Thefitofthedatatoastraightlinewasfaironnormalprobabilitypaper(Fig.2-2)andfaironlognormalproba-bilitypaper(Fig.2-3).Thisresultisreasonableconsideringthefactthatsomedependencyisapparentinthedataonanareabas~sthatcannotbequantifiedstatistically.Themedianofthelognormaldistributionwas7.5percentandthestandarddeviationwas0.626(log).ANALYSISBYSTUDSIfthesametreatmentofthedataisemployedonanindividualstudbasis,thefailurerateis0.0842forReactorBuildings1and2,andCon-trolBuil'ling.Ifeachstudamountstoanindependenttrial,theproba-,bilityofanycombinationoffailuresandsuccessescanbereadilycalcu-latedusingthebinominalprobabilitymodel.Ampledataexisttoallowthepointestimateofthefailureratetobeusedinthebinomialdistri-bution.Thusifabeamcontains100studs,themeannumberofunsatis-factorystudsis(100)(0.0842)=8.42studsorthemeannumberofsatis-factorystudsis100-8.42=91.58.Usingtheanalysisbybeams,thecorrespondingmeannumberofsatisfactorystudsis90.82.INTERPRETATIONThetwodifferentprobabilitymodelsyieldslightlydifferentresults,withthelognormalmodelbeingmoreconservativethanthebinominalmodel.Thatis,,thelognormalmodelproducesalargerprobabilityof'Ihighfailureratesthanwiththebinomialmodel.Fromapracticalstandpoint,however,thetwomodelsyieldverysimilarresults.Figure2-4providesausefulinterpretationofthestatisticalstudies.Thefigurewasconstructedbyassumingthatabeamcontained100studs,andinspectionhasshownthattheproportionofstudswhichdonotpassthebendingtestis5,8.42,orIOpercent(binomialbystuds)

~.~2~3or9.18percentbybeam(lognormal).Ifthe,apaccetablefailurerateis2cetthat100studspercent(ordinae),analysiscanbebasedontheconcepaareplacedwhenthedesignonlyneeds92.5(8.42percentcurve)studsinordertoachieveaneffectivemeanfailurerateof2percent.Thustoachieveaneffectivemeanfailureraeptof2ercent{acceptable)whentheactualrateislargerthanthisvalue,itisonlynecessarytoplaceadditionalstuds.Miththebinomialmodel,100studsinplaceatafailurerate-of8.42percentbecomesa2percentf'ailurerateusing92.5ofthe100inplacestuds.Thebeam(lognorma)y'l)analsisyields91of100studsinplaceassociatedwith2percentfailureailurerate.Thetwosolu-tionsareessentiayasllthtarnewiththelognormal(beam)analysisbeingveryconservative.Agamnamodelwasals'goinvestiatedwithresultsshown.Theconcept.ofequivalenceexpressedinFigur're2-4isusefulinanalysisanddesignsince-thecurvesrelate100stuspdataarticularfailureratetoareducednumberofstudsatanacceptableornormalfailurerate.TheaboveresultsagreewiththestudymadeybBechtelPowerCorporation{Ref.5)(AppendixA).

TABLE2-1DATAPARAMETERSBYBEAMSRBlSourceRB2Contro1CompositeSetTurbineBeams63481112217'IMeanPercent9.269.387.889.180.42StandardDeviationPercent6.55&.69.3.756.361.26CoefficientofVariation0.710.480.69InsufficientData

-<hC90Zo/0geon=v.iE/0ZORemend30FIGURE2-1HISTOGRAM>OFSENDTESTFAILURESINPERCENTOFSTUDSPROVIDEDIt(ABEAM ir 2-655.55tt5tWttSe0500'001000500..00105051100CdC)0050102ti-I~~CNCJ00C051000Zl00A0007000005$0555ttltkttLttCsrdih'CPrsko4'II~JFlGURE2-2PLOTOFBENDTESTFA1LURERATEONNORMALPROBABILITYPAPER I,I' iEV(2-7I~.'.',,~,20.2020~~waI~'..tt~'~'Il!;'l."'!iI:!I..!!!i'!:.!:I<,",.:~-'<!;!:i:!I<'i(,].i.a,~,;i~!$!;!<~~IJ<0"s.:.,;"tpcp.Ict,<cr~..<~c.<m<Ic<ri~strctstr.~....isc<yp.ae<rs'.'<..I<,~'aswK.::2I$icr4av~I~r~p~I~I~,pJrsrst~~ch~'~'It,ant~,ti,'tI'pJIt$42C~~",'IP'W',~t<,...,.t~rs0$.$.$CJIJ~rSJ'.CWSC<~~WCSCPP,0$,4,s.s~'i'-"Pc'$-'I"w"1<wi<-i'i<'i"tts'<ll'i'ii"i-i!!i::::i:l!Il:.::i:.:.:<!"i~.I!i<I!:!";!I!.ii!liI':!:$lsh'i:li!i.is<<i<.'!l<<'.'iii'!i::!!i:!!:!'::!i<<0~~I~2~'t"<~;t-.~~.I"atsr~~.~~~~~~I'~.:I'~~tP{rsI~C4<mcc/c7TI${'QIrpEy61%~gFIGURE2-3PLOTOFBENOTESTFAILURERATEOhLOGNORNALPROBABIL1TYPAPER ifltCf

~~~2-8/0EPPESA'nolgse(Zoynormal)'Rl8fo+amHnolysrs($a~mn)%/E'%%ang~lj'ufo'atpInIc5Si~8.92F0JOOo~5-oZggi'OP'urn$erg~<umPd/doormatOf/00SFadSTaiga/FlGURE2-4EUIVALENCEDIAGRAM 3-13.RECOt'~Pi"NDATIONSANDCONCLUSIONSAdetailedstatisticalanalysisofshearstudadequacydisclosedthattheoccurrenceofstudswhichfailtopassthesoundnessandbendtestfol-lowsrecognizedprobabilisticmodels.Detailedanalysesprovidedavalidbasisforforecastingstudadequacyonthebasisofequivalenceofthoseprovidedwiththosehavinga2percentinadequacyratebythesoundnessandbendtests.AslightlydifferentalternatetechniquewasusedbyBechtelPowerCorporation(Ref.5)withthesambasicresults.

REFERENCES

R-1REFERENCESl.BechtelPowerCorporation,"InterimReportonShearStudsforSusque-hannaSteamElectricStationUnits1and2,"17June1977.-2.Grant,J.A.,Fisher,J.h'.,andSlutter,R.G.,"CompositeBeamswithFormedSteelDeck,"EngineeringJournalAISC,Firstquarter1977.3."manualofSteelConstruction,"AISC,SeventhEdition4.Benjamin,J.-R.and,Cornell,C.A.,Probability,Statistics,andDecisionforCivilEngineers,NcGrawHi1]BookCompany,Inc.,1970.5.BechtelPowerCorporation,"FinalReportonShearStudsforSusque-hannaSteamElectricStationUnits1and2,"30December1977.

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