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{{Adams
| number = ML18025A667
| issue date = 12/30/1977
| title = Susquehanna Units 1 and 2 - Final Report on Shear Studs
| author name = Gore A
| author affiliation = Bechtel Power Corp
| addressee name = 
| addressee affiliation = NRC/NRR
| docket = 05000387, 05000388
| license number = NPF-014, NPF-022
| contact person = 
| document type = Report, Technical
| page count = 179
}}

=Text=
{{#Wiki_filter:FINALREPORTSHEARSTUDSFORSUSQUEHANNA STEAHELECTRICSTATIONUNITS1AND2Preparedby:AravindS.GoreCheckedby:GirishH.ShahApprovedby:M.J.LidlBECHTELPOWERCORPORATION SanFrancisco, California December30,1977(P-85a)
IgV1 TABLEOFCONTENTSSectionTitlePage'1.0Purpose2.0ShearConnectors

===3.0Background===

==4.0 Description==
ofDeficiencies

==5.0 Immediate==
Corrective Action6.0AnalysisofSafetyImplications

==7.0 Technical==
Evaluation ofDeficiencies

==8.0 Corrective==
Actions269.0~Conclusion31APPENDICES Statistical Analysisand-Evaluation ofFieldTestDataFieldTestDataReducedFieldDataDRepairProcedures EandFReportby"Fngineering DecisionAnalysisCompany"(P-Sea>
1.0PURPOSEr.Thepurposeofthisreportistoprovidefinaldataandin-formation asrequiredby10CFR50.55 (e)(3)subsecuent tothenotification ofareportable deficiency.
'Thesubjectdeficiency isassociated withtheinstallation andinspec-tionofsteelshearconnectors inthereinforced concretecomposite floors.2.0SHEARCONNECTORS Shearconnectors, usedonthisproject,areround,headedsteelstuds,commercially manufactured.
Aftertheerectionoffloorbeamsandtheplacement ofthemetaldecking,studsareattachedtothetopflangeofstructural steelfloorbeams,byresistance, weldingusingasemi-automatic process.Thestudsarethenembeddedinsubsequently placedconcreteandprovideashearconnection betweentheconcreteslabsandstructural steelframingtodevelopacomposite floorsystem.Materials, i'nstallatio'n, welding,inspection andtestingofthestudsisinaccordance withProjectSpecification 8856-C-19,"Installation ofShearConnectors,"
andAmericanWeld-ingSocietyCodeAWSDl.l-75.Thespecification requiresabendtesttobeperformed onthefirsttwostudsweldedtoeachstructural steelmember.'fterthecompletion ofstudinstallation onanybeam,theweldbetweenthestudand 1
structural steelisrequiredtobeinspected visuallyandtestedbyselectively bendingthestudstoaminimumangleof30degreesfromthevertical.
Suchbendingdoesnotaf-fectthefunctioning ofthestudasashearanchor.Composite construction hasbeenusedinthefollowing structures:
CategoryIl.ReactorBuildingUnits1and2,2.ControlBuilding3.DieselGenerator BuildingNon-Category I1.TurbineBuildingUnits1and22.RadwasteBuilding3.Circulating WaterPumphouse Inspection ofstudsinallCategoryIstructures istherespon-sibilityofQualityControl(QC)personnel andtheQualityCon-trolprogramprovidesthetechnical directions andmeansofdocu-mentation ofinspection andtestingactivities.
ForNon-Category Istructures, thisfunctionisperformed byFieldEngineering; ahowever,documentation isnotarequirement.

==3.0 BACKGROUND==
Subsequent toQCfinalpre-concrete inspection andacceptance onMay21,1977forconcreteplacement 183-S-02(Area33atElevation 719'-1"intheReactorBuildingUnit2)Pennsylvania Power&LightCompanyQualityAssurance (PLNQA)personnel found(P-85a) somestuds,whichdidnotmeetspecification requirements.
Itwasalsoobservedthattheinspection requirements werenotcompletely met.Twootherareaswereinprogressatthistime(Placement 714-S-03, Area21,E)evation 771'-0"intheControlBuildingand201-S-02, Area28,Elevation 749'-1"intheReactorBuildingUnit1).QCperformed anotherinspection ofallstudsfortheseplacements.
Oncompletion oftherequiredrepair/rework, QCacceptedtheseplacement areasonMay26,1977.Subsequently, onthesamedate,PLNQAagainfoundafewmorenonconforming studsfortheseplacements.
AstopworkreportwasissuedonMay27,1977precluding anyconcreteplacement intheabovenotedareas.4.0DESCRIPTION OFDEFICIENCIES 4.1Construction personnel failedtorepair,testorreplacethedefective studsasrequiredbythespecification.
-4.2QCpersonnel failedtoinspectandcarryouttheassignedresponsibilities asdefinedinthequalitycontrolinstructions (QCI)forstudweldinspection.
Thefollowing specifics arecited:a.Responsible QCengineering personnel intheweldingdiscipline signedinspection records(P-Sea) 
'i signifying that100%inspection hadbeen.per-formed.However,theinspections asdefinedbytheprogramwerenotcompletely performed.
b.Responsible.QC supervision personnel atthejobsitefailedtoprovideadequate, definitive directions totheresponsible
.QCengineering personnel intheweldingdiscipline andfailedtodetectthelackofacceptable performance oftheQCengineering personnel.

==5.0 IMMEDIATE==
CORRECTIVE ACTION5.1Placements Identified inMCAR-1.18 Nonconformance reports(NCR's)wereissuedagainstthestudsfoundtobeinnoncompliance withspecified requirements forconcreteplacements 183-S-02, 201-S-02and714-S-03.
TheseNCR'swereevaluated anddisposi-tionprovidedtoeither"rework"or"useasis"de-pendinguponengineering evaluation.
Inaddition, QualityAssurance issueda-Management Corrective ActionReport(MCAR-1.18) onMay26,1977andaStopWorkReportonMay27;1977.Thesereportsprecluded furtherembedment ofshearstudspendingcompletereinspection ofstudsintheseplacements toassureconformance tospecification anddesigndrawingrequirements.
Acompletereinspection ofthethreeconcreteplacement (P-85a) areaswi.thinthescopeoftheSCARwascarriedout.Thereinspection wasaccomplished inaccordance withaspecially preparedprogram,containing severalpro-visionstomaximizetheeffectiveness oftheinspec-tionandtovirtually eliminate anyinspection error.Thespecialprovisions includedthefollowing:
a.Adetailedtrainingprogramspecifically ad-dressingtheuniqueaspectsofthespecialinspection andthefundamental requirements forstudinspection wasconducted.
Specialemphasiswasplacedontherecentproblemsrelatedtothestuds.b.Eachstudtobeinspected wasuniquelyidenti-fiedbynumber,providing traceability totheinspection recordfortheparticular stud.c.As-builtdrawingsweremadeidenti,fying thelocationofeverystudbyproviding thedirection sequenceofthestudnumbers.d.Aseparatechecklistwascompleted andsignedforeachparticular stud.e.Eachindividual studreceiveda"generalsound-nesstest,"consisting ofstrikingthestudusingaheavyhammer.Studsfailingthesoundness testwerereplacedwithnewstuds.(P-85a) f.Eachinspection foreachindividual studwasdoc-umented,andtheresulting inspection recordswereindependently reviewedforcompleteness andaccept-ability.g.NCR'swerewrittenidentifying nonconforming condi-tionsandweredispositioned'providing alternates ofrepairandretestorreplacement therebyallowingthefieldengineerparticipating inthereinspec-tiontoprovidedirection forimmediate replace-ementorrepairasnecessary.
Eachoccurrence wasdocumented.
Allrequiredrepairwasaccomplished withacceptable results.Resultsoftheaboveinspection activities havebeenproperlyrecordedanddocumented.
5.2FieldTestData5.2.1Duringthisperiod,studinstallation inprogressinotherareas,wasalsostopped.Theseareasincluded:
a.ReactorBuilding:
Placement 202-S-Ol, area27;199-S-01, area25;202-S-02, area29,allatEle-vation749'-1"inUnit1.Placement 182-S-Ol, area32;184-S-01, area34atElevation 719'-1"inUnit2.(P-85a) b.ControlBuildingPlacement 714-S-03,'rea 21c.Therewerealsosomestudsexposedinacon-struction openinginapreviously pouredslabintheDieselGenerator Building.
Allstudsintheaboveareaswerethoroughly inspected byQCusingthesameinspection criteriaasdescribed inSection5.1.5.2.2FieldEngineering alsoperformed athoroughinspection ofallexposedstudsinstalled priortoMay1977intheTurbineBuildingandCircu-latingHaterPumphouse.
5.2.3FortheRadwasteBuilding, civilconstruction wascompleted priortoMay1977.Thus,noexposedstudswereavailable forinspection.
5.3Aboveinspection resultsofSection5.2identified asfieldtestdatainthefollowing
: sections, arethebasisforstatistical evaluation.
Itmustbenot'edherethatfor.thethreeareasnoted.inSection5.1,1.Somestudswereinstalled afterthebottomre-inforcing steelwasplaced,thusmakingthestudinstall'ation difficult.
(P-85a>
2.Somestudswereweldeddirectlythroughdecking.Thus,thestudinstallation intheseareascannotbeconsi-deredas,representative.
Additionally, thestudsintheseareasweresubjected tomanyinspections, therefore, theinspection resultscannotbeusedasareliablesampledata.Basedontheseconsiderations, thisdatawasex-cludedinthestatistical analysis.

==6.0 ANALYSISOFSAFETYIMPLICATIONS==
Thestudinstallation isgroupedintovariouscategories notedbelow-toprovideabaseforanalyzing thesafetyimplications andperforming technical evaluation.
6.1StudsembeddedintheconcretepriortoMay1977.6.1.1Asthesestuds,areembedded, theyarenotac-cessibletodetermine thequalityofthestudinstallation.
Untilthediscovery oftheproblem,therehadbeennomajorchangeeitherintheinspection andtestingcriteriaorinthemethodofstudinstallation.
Thusthefieldtestdata,ob-tainedasdescribed insection5.0,canbeconsidered astrulyrepresentative ofthepastwork.Atcertainlocations, thedataindicates abnormally highstudfailurerates,whichdeservespecialattention.
H(P-8Sa) 

6.1.2Astatistical evaluation ofthefieldtestda-tahasbeenperformed forthepurposeofes-tablishing thefailurerateandprojecting at90%confidence levelthenumberofreliablestudsthatareconsidered effective intheexisting, installed beams.Thestatistical projection ofthenumberofreliablestuds,togetherwiththecalculated minimumnumberofstudsrequiredforeachbeam,arethebasisforverifying theadequacyofthecom-positestructural system.6.1.3Basedontheforegoing generalcriteriathefollowing twocategories areestablished:
6.1.3.1Forareas-whichexhibitacceptable studfailurerates,thetestdataonweldedstudsindicates thateitheroneofthefollowing conditions ismet:a)Studfailureratesfallwithinacceptable industrypracticesoasnottojeopardize thestruc-turalrequirements.
b)Theprojected numberofreliablestudsexceedstheactualminimum(P-85a) requiredaccording tostructural designcalculation.
Consequently, intheseareasthestructural integrity hasnotbeencompromised, andthestructural sys-temisinfullconformance withthebasicdesigncriteriaandthebasesoftheSafetyAnalysisReport.TheTurbineBuilding, Unit1and2,ControlBuilding, Circulating WaterPumphouse, RadwasteBuildingandDieselGenerator Buildingbelongtothiscategory.
6.1.3.2.Inareasassociated withhighfail-urerates,therearesomebeamsforwhichtheprojected numberofreli-ablestudsisinsufficient withre-specttotheminimumrequiredbystructural design.,Thiscondition hasthe,following implications:
Thedesignrequirements statedintheSafetyAnalysisReportarenotmetcompletely duetothepotential stud(P-S5a) 

deficiency.
Repairworkmustbeun-dertakentocorrectthedefective installations andassurethattherearenostructural systemswhichdonotmeetthedesignbases.TheReactorBuildingUnit1and2fallinthiscategory.
6.2StudsNotEmbeodedinConcreteattheTimeoftheReporteoProem.Intheseareas,deficient studsaretraceable tospecificconstruction and/orinspection practices, whichhavebeenpositively ioentified.
Thestudsintheseareashavebeeninspected understricten-forcement oftherevisedinsoection procedures andrepairedorreplacedasreauired.
Newstudswerealsoinspected tothefullinspection reauirements.
Thisprovidesadeauateassurance regarding theaualityofthestudinstallation intheseareas.70TECHNICAL EVALUATION OFDEFICIENCIES 7.1GeneralImpactoftheabovenoteddeficiencies rendersthestructural adeauacyofthestudsinstalled indeter-minateintheabsenceoftechnical evaluation.
Reme-dialmeasurestakenandtobetakentopreventtherecurrence aredescribed insection3.0and8.0.(P-S3a> 

Therefore, thetechnical evaluation inthissectionislimitedtothestudsembeddedintheconcreteslabspriortoNay1977.Theapproachusedforthisevaluation isasfollows:a.Evaluatethedesigncriteriaandtheoretical consi-derations, assumptions, associated researchandtesting,whicharethebasisforthedesignre-quirements intheAISCspecification.
Baseduponthisevaluation, reassessand/orrevisetheoriginaldesignandcomputethenumberofstudsrequired, whichnotonlysatisfystrengthrequire-mentsbutalsomeetthespecification requirements.
b.Analyzethefieldtestdatastatistically toarriveatasuccessrateatacertainconfidence levelforeachbuilding.
Baseduponthisanalysiscomputethenumberofre-liablestudsoneverybeam.c.Designshearconnectors.
d.Identifythosebeamswherethenumberofstudsre-quiredislargerthanthereliablestuds.7.2DesignCriteriaandStructural DesignofComposite Construction 0
GeneralAcommonapproachinthedesignofstructural floorsystemsistodevelopcomposite actionbetweenthesteelframingbeamsandtherein-forcedconcreteslabs.Thecomposite actionaffordsaflexuralsystemsuperiortothebeamorslabactionaloneandgenerally resultsincostsavingsintheoveralldesign.Composite actionisachievedbyproviding shearconnec-torsweldedtothetopsideofthebeamandembeddedintheconcrete.
Theseshearconnec-torscanalsobeusedto-improvetheanchorage ofsteelframingintoconcreteslabstopermitthetransferofhorizontal loadsfromthefram-ingtotheslabdiaphragm andtoincorporate theslabinresisting heavyloadssuspended fromthebeams.7.2.2DesignCriteriaandTheoretical Considerations Section1.11of'Specification forDesignFabri-cationandErectionofSteelforBuildings'Sixth Edition)adoptedbyAmericaninstitute ofSteelConstruction in1969andsubsequent threesupplements arethebasesforstructural design.Thenewrevisionofthespecification isdueforpublication inearly1978.Revisedsection(P-85b) 1.11to.beincorporated intheforthcoming edi-tionispublished in"InrycoComposite BeamDesignManual,21-12"byInrycoInc.inJuly1977.Thisrevisionisessentially baseduponthepaper"Composite BeamswithFormedSteelDeck,"byGrant,FisherandSlutter,inAESCEngineering Journal,Volume14,FirstQuarter1977.Promthereviewofthedevelopment ofthissec-tion,itisevidentthatthedesigncriteriaisstillinthedevelopmental stage,andisbeingmodifiedcontinuously toreflectthelateststateoftheart.Themajorityoftheresearchandtestingdonetodatepertainstocomposite beamswiththinslabs.Intheassociated theoretical considera-tions,theultimatemomentcapacityof,thetconcretesectionisdisregarded.
Thus,thecontribution oftheinternalcoupleproducedbyshearconnection becomesverysignificant incomputing theultimatestructural capacityandthefactorofsafety.Forreinforced thickslabs,however,theultimatemomentcapacityoftheconcretesectionbecomessodominant thatthesignificance oftheshearconnection isgreatlyreduced.Thus,thedesignbaseduponthespecification resultsinahighre-servecapacityforcomposite beamswiththickslabs.TheAISCspecification, however,.has notrecognized thisphenomenon.
The-AISCSpecification anditssupplements de-finetheallowable horizontal shearloadsforstudsandalsoprescribe analytical procedures forevaluating incomplete composite actionbyequation(l.ll-l)asfollows:Sff=S+Vh(S~-S)VIiWhere:Vhthelesserofthehorizontal shearassociated.
witheithertheconcreteorthesteelsectionV11theshearvaluepermitted bythe"number,ofconnectors
: provided, re-levantforincomplete composite actionSssectionmodulusofthesteelbeamreferredtoitsbottomflangesectionmodulusofthetransformed composite section(ful1)referredtoitsbottomflangeeffective sectionmodulusoftheincomplete composite section(P-85b)
Theequationisbasedonearlyresearch, anditrepresents alinearvariation ofSffwitheffrespecttoV'h.Recentresearchrecognized bytheAISCindic-atesthatthefunctional relationship described aboveismoreaccurately expressed byintroduc-ingasquarerootexpression fortheshearra-tioinequation(l.ll-l).
Thismodification represents arefinement ontheanalytical tech-niquefortheevaluation ofincomplete.
compo-siteaction,anditresultsinasubstantially highercapacitythanthatallowedbythepre-vious,extremely conservative linearexpres-sion.Thisproposedexpression offersalib-eralizedanalysisreflecting thecurrentthink-ing,butitprudently affordssomeconservatism withrespecttotheresearchfindings.
Thespecification alsoprescribes aminimumof25%ofcompleteshearconnection tobedevel-opedbythestuds.Thislowerlimit,however,isarbitrary andisnotnecessarily baseduponthetheory.Znfact,testresultsdescribed intheabovereferenced paperindicatethatthetestbeamswithwideslabsandlessthan25%ofcompleteshearconnection performed 0
satisfactorily withanadequatefactorofsafety.Thus,thetestprovesthatthepercentage shearconnection isnotneces-sarilyafunctionofthecapacityofthecomposite beamoritsfactorofsafety.Detaileddiscussion onthissubjectcanbefoundintheabovenotedpaperbyGrant,FisherandSlutterandalsoinAppendix"E".Asasummaryitisconcluded that:1.Theanalytical approachperthepresentAISCspecification, althoughreasonable forbeamswiththinslabs,=isaverycon-servative methodforthecomposite beamswiththickslabs.2.Thedesignbaseduponthespecification usingrevised1.11-1equationandassum-ing25%completeshearconnection willstillprovideadequatemarginofsafetyandconservatism.
7.2.3Structural DesignInthecurrentstructural design,theweldedstudswereprovidedinthemajorityofthebeamstodevelopcompleteaction,andthe(P-85b) steelbeamsectionsweredesignedaccording tothearbitrary overallfloorloadsprescribed forthevariousareas.However,inviewofthepotential problemwiththeweldedstuds,thestructural designwasreassessed withtheintention ofrelieving thestudreouirements withoutviolating thebasicoesigncriteria.
Thefirststepinthereassessment wastore-viewtheloadingassociated witheachofthefloorbeams.Thiswasachievedbyconsidering actualloaddistributions obtainedfromtheeouipment andflooroccupancies whichatthisdatehavebeenestablished moredefinitely thanatthetimeofinitialdesign.Anotheraspectoftheloadrefinement consisted ofamoredetailedanalvsisofthetributary areasforeachbeambyrecognizing actualloaddis-tributions oerivedfromtheone-wayandtwo-wayflexuralactionofthecorresponding con-creteslabs.Thesecondstepinthereassessment wastore-finetheoesignbycomputing theeffective sec-tionmodulusaccording tothelatestanalytical (0criteria, i.e.,theAISCapprovedexpression
-ls- 

withthesouareroot.Thisanalytical refine-mentallowedforarevisedhighercapacityforsectionsinwhichtheprojected numberofreli-ablestuasdidnotpermitcompletecomposite action.Theaboveanalytical featureswereusedprudently, andtheminimumnumberofstudsreouiredperbeamwasjudiciously selectedbythecriteriadescribed inSection7.4.7.3Outline-ofStatistical AnalysisandEvaluation:
Thissectionprovidesabriefdescription ofthesta-tisticalapproachusedintheprojection ofthereli-abilityofstudsinstalled todate.Amoredetailedcoverageofthestatistical analysisusedforthisreportisprovidedinAppendixA.Anotherstatistical analysisusingdifferent methodwasperformed indepen-dently,whichgaveessentially samebasicresults(ReferAppendixF).Theinitialphaseofthestatistical analysiswastosegregate thefieldtestdataintohomogeneous groupsjudgedtobestatistically compatible.
Thisjuogement wasbasedonChi-sauare testonsimilarities ofthestudfailureratesandtheirdistribution patterns.
Thefirstlevelofsegregation established wasaccord-ingtothevariousbuildings withintheplant.Eachstructure wasthusrecognized asaseparategroupwithitsown-characteristic samplingandcorresponoing sta-.tisticalprojections. 

Thesecondphaseofthestatistical evaluation consisted ofdetermining thereliablestudsforeachoftheestablished groups.Thesepro-jectionsarebasedonthefailureratesde-rivedfromfieldtestdata.Theirdevelopment takesintoaccountthenumberofstudstestedwithrespecttothetotalnumberinstalled, andrecognizes thatthereliability ofthestudsmustnotbeonanindividual basis,butwithdueregardtostudgroupings derivedfromtherequirednumberofstudsperbeam.The,ana-lyticalbasesofthestatistical projections areder:ivedfromtherequirednumberofstudsperbeamandarebasedonthehyperbinominal distributions, withoutresorting toempirical idealizations.
Thefundamental assumption isthatthefieldsamplesareunbiasedandapplic-ableto,thebalanceofthecorresponding studgroup.Thisassumption isjustified sincetheexposedareaswherethesamplingwasobtainedcameintoexistence
: randomly, andduetorea-sonswhichareunrelated tothestudweldingandQCinspection.
ThequalityofthestudJwelding.intheseexposedareaswerenotin-fluencedbyandareindependent ofthelo-cationoftheseareas.'P-85b)
Theconfidence levelofthestatistical projec-tionofreliablestudswassetat90%.Thislevelofconfidence isconsistent withthecri-tieriausedbygoverning organizations in-volvedinthepreparation ofcodesofpractice.
Additionally, baseduponengineering judgement, theprobability ofexceeding thedesignliveloadisextremely low.7.4DesignofShearConnectors 7.4.1GeneralTheshearconnectors usedinallinstances wereweldedheadedstuds,andar'edesignedtobein-stalledbyusingasemi-automatic weldingpro-,cess.7.4.2DesignCriteriaa.Asdiscussed inSection7.2.2,partialcomposite action(V'h)waslimitedto25%.b.Thelatestexpression (squareroot)wasusedforcomputing theeffective sectionmodulusunderincomplete composite actionandthecorresponding studrequirement.
c.P'resentAESCcodedoesnotaddresstheef-feetofgroupingofstudsinarib.Latest researchandproposedrevisiontothespec-ification requiresthatiftherearemorethanthreestudsinarib,thecumulative allowable capacitymust'becomputedbyusingthereduction factor(Equations 1.11-8and1.11-9).Thestudrequirement, whichismorestringent baseduponthenewcode,hasbeenused.7.4.3.Following theabovedesigncriteria, thenum-berofstudsdictatedbytherevisedstruc-turaldesigncalculations, basedonreassessed loadinganalysis, werecomputed.
7.5Conservative FeaturesNotResortedtointheDesignThisisacommentary onsomefeaturesthatwouldin-creasethemarginofsafetyofthedesign.1.Basedonengineering judgement, theallowable loadsstudscouldbeincreased inproportion tothesquarerootoftheconcretecompressive strengthf'c.Znthecurrentdesign,theallowable stud,loadsbasedonf'4000psi,according totheAISCSpecifica-tionhavebeenusedactualf'hichiscwithouttakingcreditforthecloseto5000psi.(P-85b) 2.Inthebasicdesigncriteria, liveloadsareas-sumedtobeactingovertheentirefloorarea.However,underactualoperating conditions, thisishighlyunlikelytooccur.Thus,thereduction thatmaybeachievedbyconsidering actualliveloadsisnotusedinthereviseddesign.3.Forcomputing N2,(Equation 1.11-7),theunderly-ingassumption isthatthehorizontal shearisre-sistedbyonlythosestudswithintheshearspan.Inreality,becauseofthelongitudinal bottomreinforcing steel,thehorizontal shearwillbetransferred toadjoining studs,althoughthisphenomenon isnotrecognized byAISC.Thus,thecomputedN2baseduponpresentdesignwillresultinanevenhigherfactorofsafety.7.6Discussion onRadwasteBuildingTheRadwasteBuildingwascompleted priortoMay1977.Asnostudswereexposedatthetimetheproblemwasdiscovered, actualtestdatacouldnotbeobtainedonthesamebasisasitwascollected forotherstruc-tures.Fortheslabat715'-0"elevation, thereissomerecordavailable onthevisualinspection andtestingactivities performed byFieldEngineering col-lectively onareabasisinsteadofindividual beam(P-85b) basis.Additionally, therearenosoundness testre-sultsavailable fortheseareas.Therecordincluding bendtestresultsonthestudsfailingvisualexamina-tionisshowninthefollowing Table.TABLElAreaNo.ofTotalNo.beamsstudsStudsfailingStudsfailingvisualexam-bendtestination272322352,4901841694110315881771375761141,0958512729591280175959Interviews withtheresponsible FieldEngineerandthewelderprovidedfollowing information.
I,1.Studsfailingvisualorbendtestwerenotinasingleclusterbutwerespreadovertheentireareawithoutanydefinitepattern.(P-85b)-
2.Thewelderwhodidthemajorityofthestudweld-ingonthisbuilding, workedpreviously ontheCirculating WaterPumphouse, andispresently workingontheDieselGenerator Buildingfromtheverybeginning.
ItisnotedthatthefieldtestdatafortheabovetwobuildingindicateOSfail-urerate,whichisareflection ontheworkmanship ofthe.welder.3.Asamatterofroutine,ithasbeenthepolicyoftheweldertoreplacethestud,whenitwouldgiveunsatisfactory soundoftheshot.4.Additionally, althoughnotrequiredbythespeci-fication, thewelderhasbeenbendtestingthelasttwostudsoneverybeam.Basedupontheengineering judgement andtheevalua-tionofaboverecordandinformation, thepotential failurerateontheexistingstudinstallation wouldbeextremely'low.
Inaddition, presentstructural designisbaseduponcompletecomposite action;there-fore,theadditional'factor.
ofsafetyisinherently builtintothedesign.Thus,withadeauateassurance, itisconcluded thatthepresentstudinstallation meetsthedesign,criteria.
(P-85b) 

7.7Conclusions 7.7.1Thedesignofcomposite beamswiththickslabsperpresentAISCspecification isextremely conservative.
7.7.2=Allexistingbeamswhendesignedbaseduponthebasictheoryandcomputednumberofreli-ablestuds,haveadequatemarginofsafetywithoutperforming any.repairormodifica-tion.Thisdesign,however,doesnotsatisfytherequirement ofthespecification forall*beams.7.7.3Inordertomeetthespecification require-mentsasnotedintheSafetyAnalysisReport,thosebeamswherethenumberofstudsrequiredperreviseddesignissmallerthanthenumberofcomputedreliablestuds,willberepaired.
7.7.4Usingtheabovecriteria, itisobservedthatafewbeamsintheReactor'Building requirerepair.Thesebeamsareidentified, andtheassociated repairmethodsaredescribed inAppendixD.8.0CORRECTIVE ACTIONCorrective actionaregroupedinthreecategories.
Eachcategoryandcorresponding actionsaredescribed below.(P-85b) 8.1CategoryIThiscategorydescribes thosestudsalreadyembeddedinconcretepriortodiscovery ofthisprobleminMay1977.Toevaluatetheimpactofthedeficiencies onthe.adequacyofthestructural members,fielddatawasobtained, analyzedandevaluated.
Baseduponthisevaluation, thenumberofprojected reliablestudswascomputedforeachbeamandcomparedwiththe-numberofstudsrequiredbaseduponreassessment ofthedesigncriteria:
Wherevertherevisedstudrequirement isfoundtobegreaterthantheprojec-tedreliablestuds,thesebeamswillberepaired, asdescribed inAppendix'D'Repair Procedures",.
Oncompletion oftherequiredrepair,theexistingstructural members,willsatisfythedesignrequire-ments.8.2CategoryZIThiscategorydescribes thestudsineightplacements inControlandReactorBuildings, whentheproblemwasdiscovered (SeeSection3.'0and5.0).Studsintheseplacements havebeenextensively in-spe'cted, examinedandtestedasdescribed inSection5.0,thusproviding adequateassurance thatthesestuds(P-95a} 
(-willperformsatisfactorily underdesignloads.There-fore,nofurthercorrective actionisdeemednecessary.
8.3CategoryI1IThiscategorybelongstopresentstudinstallation sincethediscovery oftheproblem.Sincecompletion ofabovenotedeightplacements thefollowing specificcorrective actionshavebeeninstituted atthesite.8.3.1Corrective ActionsbyQualityControl.a.TheQCweldingdiscipline hasbeenre-lievedoftheresponsibility forin-spection" ofthestuds,exceptthosein-stalledduringprefabrication ofembeds.TheQCcivildiscipline hasbeendirectedtoassumethisresponsibility.
Thisac-tionresultsinthefollowing upgrading oftheinspection program:i.Theinspection ofstudsisnowmorecloselyintegrated withotherrelat-edpr'eplacement inspections, suchasembeds,reinforcing steel,conduit,etc.ii.Additionofthe'General'Soundness Test'P-95a) iii.TheamountofQCengineering manpowerwhichmaybefocuseduponstudin-spectionisnowincreased.
1v~Inspection maynowmoreoftenbecar-riedoutwhilestudinstallation is,beingperformed, andwhilecraftper-sonnelarepresenttoperformimme-diatereworkorrepairifnecessary.
v.Studinspection maynownormallybecompleted beforethestudsarevisual-ly,obscuredby,otherinstalled items,suchascurtainsofreinforcing steel.b.Theinspection planforstudinspection hasbeenreviewedandstrengthened inthefol-lowingspecificareas:Markingtophysically identifybothacceptable andunacceptable studshasbeenclearlydefinedinthein-spectionplan.ii.Verification ofproperstudweldingcablelength(i.e.,lessthan100feet)hasbeenadded.8.3.2Corrective ActionsbyFieldEngineering.
a.Aspecialtrainingsessiononstudinstal-lationdatedJune10,1977wasconducted 

atthejobsiteforQC,Engineering andSu-pervision toguarantee improvedqualityofinstallation.
b.Infutureplacements, installation ofrein-forcingsteelorothermaterials whichwouldinterfere withinstallation orinspec-tionofshearstudswillbewithhelduntiltheshearstud.installation intheareaiscompleted.c.AtrainingsessionwasheldonJune26,1977forallironworkers involvedwithstudinstallation.
Emphasiswasplacedonthecraftsman's primaryresponsibility forcorrectinstallation ofshearstuds.Thecompleteinstallation sequenceofstudswasalsoreviewedindepth.d.Avendorrepresentative fortheweldingequipment wasbroughtonsiteJune22,1977.Duringthisvisitequipment set-tings,maintenance andtroubleshootingwerereviewedwiththeironworkers andsuperintendents.
e.Equipment maintenance programhasbeenrevisedandre-organized including a(P-95a) largerinventory ofsparepartsbeingmaintained onsite.f.Allrectifiers inthefieldarereturnedtothemanufacturer onarotational basistoensuretheyareperforming correctly.

==9.0CONCLUSION==

9.1Inmostoftheareas,theprojected numberreliablestudsarenotonlysufficient toperformstructural functionbutalsomeetthespecification.
9.2Althoughallprojected reliablestudsareadequatetosatisfythestructural requirement, therearesomebeamsatafewelevations intheReactorBuildingwhichdonotconformtospecification requirements initsentirety.
Thus,thesedeficiencies willbecor-rectedbyrepairsperformed ontheexistinginstalla-tion.9.3Oncompletion oftherequiredrepair,thestructural analysisanddesignwillsatisfy.strengthandcoderequirements andwillalsoassurethattheexistinginstallation willconformtothedesigncriteriaandbasesofSafetyAnalysisReport.(P-95a)
APPENDIXATOFINALREPORTONSHEARSTUDSSTATISTICAL ANALYSISANDEVALUATION OFFIELDTESTDATA(P-74b)
STATISTICAL ANALYSISANDEVALUATION OFFIELDTESTDATA1.0OBJECTIVE Toanalyzethetestdataineachbeamcompleted priortoNay1977andtodetermine,t.he statistical basisforesti-matingthetotalnumberofooodstudsthatcanbereliedupon.2.0FIELDTESTDATA2.1GeneralInthefourthweekofMay1977,whentheproblemwasdiscovered, thereweremanyareaswherethestudin-stallation wascompleted andalsothestudswereaccessible.
Thesestudsweresubjected toathoroughinspection andtestingasshownbelowintheflowchart.Inadditiontovisualexamination andselec-tivebendtestingasperthespecification reguire-menteverystudreceived'generalsoundness test'.Completefieldtestdataandthereducedfieldtestdatausedforstatistical analysisisprovioedinAppendixBandCrespectively.
2.2DEFINITIONS:
l.Soundness Test:Oncompletion ofstudwelding,thestudisstruckwithaheavyhammer.Ifit.givesacleanringingsound,thestudisconsi-deredacceptable.
Otherwise itisreplacedwithanewstud.(P-74a) 2.VisualExamination:
Aftercompletion of'thesoundness test,eachstudisexaminedvisually'oinsurethatthereisfilletweldallaroundth'eperiphery ofthestud.lftherearenovoids,thestudisconsidered passingthevisualexamina-tion.:3.BendTest:Studsfailingvisualexamination.
arebent15.awayfromthevoidintheweldwithre-.,specttothe-verticalaxis.lfthestuddoesnot'developcracksattherootorseparates fromthebeams,itisconsidered acceptable.
Thisisthe.mostsevereand,reliabletest.2.3FLO!0CHARTStudstestedinabeamStudspassingsoundness testPs.Studsfailingsoundness testFsStudspassingvisualexamination Studsfailingvisua3examination StudsbendtestedFvlStudswhichwererepairedFv2PassbendtestPlFailbendtestPassbendtestP2FailBendtestF2.-Rote:P2andF2areassumednumbers.Seesection2.6.3;3forclarification.
(P-74a) 2.4Notations:
2X=Chi-square N=Numberofbeamstestedineachbuilding.
T=Totalstudstestedinabeam.Ps=Studspassing-soundness test.Fs=Studsfailingsoundness test.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) 2.5SummaryofFieldTestDataTable1Structure NumberofbeamsTotalstudstested/examined ReactorBuildingControlBuildingTurbineBuilding17113091764831Circulating Haterpumphouse DieselGenerator Building1072.6Discussion onFieldTestData2.6.1Studsfailingsoundness test(Fs)Thesoundness testindicates thequalityoftheweldbetweenastudandstructural steelbutitmaynotbefoolproof.
Thatis,itisverylikelythatsomeofthestudsfailingthistestmaybegoodfromastruc-turalstrengthpointofview.Sincetheexactreliability ofthesoundness testisnotknown,allstudsfailingthesoundness testareconsidered tobebadstuds,toinsureconservative
'estimates.
(P-74a) 2.6.2Stuospassingvisualexamination.
(Pv)Studmanufacturers haveindicated thatirre-spectiveofthemethodoftesting,theoverallfailurerateisobservedtobeabout2%undernormalworkingconditions.
Baseduponthisfact,inagivenpopulation ofstuds(T),ifthestudsfailingvisualandsoundness test(Fs+Fv)areremoved,the'uccess ratefortheremaining sample(Pv)canreasonably beconsidered tobe100%.Arecentbendtestconducted onrandomlypickedpopulation of543studs,whichhadpassedbothvisualandsoundness testgave3.005successrate.Thus,theseresultsalsoreinforce thevalidityoftheaboveassumption.
2.6.3Studsfailingvisualexamination (Fv)Forthiscategory, thespecification providesanoptiontothefieldeithertoperformabendtestortorepair.Fieldtestindicates hthatallstudswerenotnecessarily subjected tobendtest.Thetestwasperformed on(Case1)all,(Case2)one,(Case3)someor(Case4)noneofthsstudsonabeam.Reasonsforei-therincluding orexcluding thestudstobesubjected tobendtestwasbaseduponanyone 

ofthefollowing:
construction
: schedule, ac-cessibilityy, inadeauate roomforreplacement incaseofafailureandarbitrary decisionbythefield.Thus,forcase2,3and4toincludethestudsrepaired(FV2)'orstatis-ticalanalysis, following criteriahasbeenused.2.6.3.1'Case1:Pv=FV1FV2=0Asthebendtestisperformed onallstudsfailingvisual(Fv),thetestdataisused'asis'.2.6.3.2Case2:Fvl=1Fv2=Fv-1Inthiscase,onlyonestudwassub-jectedtobendtest,thusitsresultscannotbeappliedinameaningful waytootherstuds.Therefore, beamsamplescontaining thiscombination areomittedfromthetotalsample.2.6.3.3Case3:FvlQ'Fv2=FV--FV1Forthereasonsstatedabove,selec-tionofthestudstobebendtested(P-74a) wasarbitrary therefore thefailurerateasobservedforFV1canreason-ablybeassumedtobesameforFV2.2.6.3.4.Case4:Fvl=0Fv=Fv2Asnobendtestdataisavailable forFvl,beamsamplescontaining thiscombination wereexcludedfromthetotalsample.2.7Basedupontheabovecriteria, failurerateforeach"beamiscalculated asnotedbelow.Failurerate=Fs+Fl+F2~Totastu<utsT)whereGoodstuds=Pv+Pl+P2andBadstuds=Fs+Fl+F23.0ANALYSISOFFIELDTESTDATA3.1AlthoughtheFieldtestdataisavailable forfivebuildings, thedataforonlythreebuildings withhigherfailureratesisconsidered hereforstatis-ticalanalysis.
Thereasonforthisis,thefailurerateforCirculating WaterPumphouse andDieselGen-eratorBuildingis0%.FortheReactor,ControlandTurbinebuildings, inatotalsampleof72beams,7967studsweretested.Fol-lowingthecriteriadescribed insections2.6.3and 2.7,7427passedand540failedforanoverallsuccessrateof93.22%.Itwouldbeattractive totreatthisdataasasingleaggregate samplesincethatwouldyieldthegreatestprecision oftheestimateofthesuccessrateparameter p.However,different failurerateshavebeenobservedindifferent buildings sothatfailureparameters maydifferfrombuildingtobuilding.
Statistical testswereusedtodetermine whetherthisinfactdidoccur.3.2Construction ofvariousbuildings isdoneontheareaconcept,i.e.aseparategroupofFieldEngineers, Superintendents andworkersareassignedtoandre-sponsible fortheconstruction ofthatparticular building.
Thus,eventhoughthegoverning specifica-tionisthesameforallbuildings, workmanship andaualitymayvarywithinreasonable limitsfrombuild-ingtobuilding.
Testresultsfortheabovethreebuildings aresum-marizedasbelow.Table2BuildingStudspassedStudsfailed%FailurerateReactorControlTurbine4970163382440213177..487.420.84Total74275406.78Fromtheabovetablethereisanoticeable amountof variation inthefailurerate.Theprimaryquestionisifthesearevariations tobeobservedinanyrandompro-cess(e.g.,10tossesofthesamefaircoinmayyield7headsinonesequenceand4intheother).ltmustbeemphasized herethatallknownparameters affecting thefailureratearethesamefortheentirestudweldingoperation inanybuilding.
Ifthedifferent ratescanbeshowntoliewithintherealmofprobabilistic
'noise,'hen allindividual testsmaybepooledtogetherintoanaggregate sampleand6.78%asthefailurerate.However,ifthiscannotbeshown,thenthedatamustberegardedasseparatesubsamples andanallowance madeforthelowerprecision whichresults.Thesub-sequentsectiononthehyperbinomial distribution de-scribeshowthefinalrecommendations incorporate thislossinprecision toassurearigorousandcon-servative analysis.
Thekeyanalyticquestioniswhetherornottheunderly-ingpass/fail probability isthesameforabovethreebuildings.
Theprincipal statistical tooltobeusedis2.theXtestofhomogeneity.
Ifthestudsinallthreebuildings hadacommonfailurerateof6.78%,(i.e.ifhomogeneity isnullhypothesis),
theexpectednumberof"passes"intheReactor.Building wouldhavebeen5008with1644and775expectedintheControlandTurbineBuildings respectively.
Similarly, (P-74a) theexpectednumberoffailureswouldhavebeen364,120and56.TheXteststatistic isbaseduponthedifferences be-tweenall6observedandexpectedvalues.Xtest=(4970-5008)
+(1633-1644)
+(824-775)
+(402-364)
+(131-120)
+(7-56)=51.31*Thisteststatistic isapproximately distributed asanXrandomvariablewith2degreesoffreedom[1]for"whichthereisonly0.5%chanceofexceeding 10.6.Sincetheteststatistic issomuchgreaterthanthisvalue,theconclusion isthatthesampleunderconsi-derationisnon-homogeneous.
Thus,eachbuildingmustbeconsidered asanindividual subsample.
3.3Evenaftertheneedtoanalyzethedatabuildingbybuildingisestablished, themajorconcernistheadequacyofcollection ofstudsoneachindividual beamorgirder,fordetermining effectiveness ofcomposite action.Therefore, itisnecessary toconsiderthefielddataforeachbeamasanindividual sample.*TisvaueiersromteexactXvalue.Theapparentdifference 2isduetoroundingofftheexpectedvaluestointegersfornarrative purpose.Theexactvalueswereusedinreachingalldataclustering decisions.
[1]A.M.MoodandF.A.Graybill, Introduction toTheoryofStatistics.
McGrawHill(1963)p.318.
3.4Baseduponabovediscussion andcriteria, thebeamdataforeachbuildingisanalyzed.
3.4.1ReactorBuildingUnits1and2Althoughthefollowing discussion pertainstotheReactorBuilding, itisalsoapplicable tootherbuildings exceptasnotedotherwise..
Forasampleof44beams,thedatacanbegroupedasfollows:NumberofbeamsFailurerate20to38$15to20%10to15%205to10%0to5%Itisevidentfromtheabovegrouping, thatforthemajorityofthebeams,thefailureraterangesfrom0to108.WhentheXtestwasperformed onthesam-2pieof44beams,thesamplewasfoundtobenon-homo-geneous.Notwithstanding thatthemethodofstudin-stallation, thegoverning specification, workmanship, construction
: sequence, andallotherknown'variables weresame,thewidevariation inthefailureratecannotbeexplained.
Despitetestingthesamplewithvariouspermutations andcombinations, noreasonwasfoundwhich-could beattributed forthisoccurrence.
(P-74a)-ll-Inlightofthissituation, itwasdecidedtotestthetruncated samplei.e,disregarding thebeamsam-plesstartingwiththelowestfailurerates,fores-tablishing homogeneity.
Afterseveraliterations, asampleof6beamswith,failureraterangingfrom19.05%to38.36%wasfoundtobehomogeneous.
Thistruncated samplewith390'passes'nd 146'failures'ave overallfailurerateof27.2%.Withtheabovediscussion, itmustbeemphasized herethatusingthishigherfailurerateisindeedanextremely conservative assumption, andcanbeapplied,withahighconfidence level,inprojecting
'good'tuds intheareaswherethestudshavealreadybeenembeddedintheconcrete.
3.4.2ControlBuildingThedataisavailable for11beamswith1764studstested.Thefailurerateforthebeamsrangedfrom3.53to25.93%.Itwasalsoob-servedthatonlyonebeamhasunusually highfailurerate.When,thetotalsamplewastest-edforhomogeneity, thesamplewasfound'tobenon-homogeneous.
However,thesampleex-cludingthebeamwiththehighestfailureratewasfoundtobehomogeneous.
Inlightofthisfact,itcanbeconcluded thatthedataforthisparticular beamwiththehighestfailurerateisastraysample.However,forcomputing (P-74a) vtheoverallfailurerate,'his beamisin-cluded.3.4.3TurbineBuildingAvailable dataisfor17beamswith831studstested.Outofthistotal,824passedand7failedgivingaveragefailurerateof0.84%.Itisobservedthat15beamsoutof17beams,have0%failurerate.Thesampleconsisting
\ofremaining twobeamswasfoundtobehomo-geneous.Thusthefailurerateof4.14%forthesetwobeamshasbeenusedforallthebeamsinTurbineBuildingwhichagainisaconservative approach.
3.4.4Circulating WaterPumphouse Atthetime,whentheproblemwasdiscovered, onlytwobeamswithatotalof107studswereexposed.Outofthistotal,onlyonestudfailedvisualexamination butthestudpassedthesubsequent bendtest.Thus,theobservedfailurerateis0%.3.4.5Diesel-Generator BuildingForty-four studsonabeaminaconstruction openingwereexposed.Allthestudsweretestedwithnofailure,thusgivingafailurerateof0%.(P-74a) 3.5SummaryBuildingStudsPassedStudsfailedFailurerateReactorControl390164214612127.2%6.85%Turbine16274e14%Aboveinformation wasusedasinputsintothehyper-binomialdistribution toestablish probabilistic char-acteristics ofbeamsandgirdersforeachbuildingasdescribed inthesubsequent section.4.0HYPERBINOMIAL DISTRIBUTION Theresultsoftheaboveanalysisestablishes theappropri-atehomogeneous groupings oftestdataforqualitycharac-teristics ofindividual studs.Thisanalysisproceedsbyrecalling thehyperbinomial dis-tribution.(
)Themotivation isasfollows.First,ifthesuccessparameter, p,wereknownprecisely.
thenthetotalnumberofgoodstuds(k)inacollection ofhwouldvaryaccording toabinomialdistribution:
PtkofhIp)kp,1pForexample,ifp=6andh=5,thenthenumerical values'oftheresulting massfunctionwouldbe:H.RaiffaandR.Schlaifer, AppliedStatistical DecisionTheoryHarvardUniversity Press(1961).p.237(P-74b)
No.GoodStuds=kpkof5;p=.6012345.010.077.230.346.259.07800However,ifpisnotknownbutmustbeestimated, thensuchabinomialdistribution assumesmoreprecision thanactuallyexistsandmakesthingsappearbetterthantheyare.Forex-ample,ifnstudshavebeentestedandonlyrpassed,thentheparameter pitselfhasaprobability distribution, f()(n+1)!r(1)r!(n-r)!for0<p<1~lthefamiliarbetadistribution(
).Thus,whiletheexpectedvalueofpisr/n,othervaluesofpbetween0and1mayalsohavegenerated thesample,andthesecannotbeignoredinanysubsequent inferences.
Toobtaintheprobability ofkgoodstudsinabeamofhwhenrofnsimilarstudshavepassedthestriketest,theuncondi-tionaldistribution mavbefoundby:1~P[kofh;rofn]=P[kofh)p)f(p;r,n)dp01h!k1h-k(n+1)!rn-r!p0al,-,,....,.,
~,........,...,y ofStatistics, McGraw-Hill (1963)p.129ff.(P-74b)
Collecting constants:
h!(n+1)!k!(h-k)!r!(n-r)!k+r(1p)n+h-r-kdpperforming theintegration, h!(n+1)!(k+r)!(n+h-r-.k)
!!hk)!r!nr)!n+h+1)!andrearranging termsincombinational notationyieldsthehyperbinomial distribution:
P[kofh;rofn]r+kn+h-r.-krh-kn+h+1fork=0,...,handr<nTogainasenseoftheeffectofthisdistribution, supposethat1Sstudshavebeentestedand9havepassed.Theesti-matedvalueofpis9/15(i.e.,still.6)asbefore.However,repeatedevaluations oftheaboveexpression yieldsthefol-lowingdistribution:
No.GoodStuds(k)012345pk;9of15.023.103.227.303.246.098MRoNotethatthisdistribution ismorediffusethanthesimplebinomial; i.e.thetailsofthedistribution are,-"fatter" andlessprobability massisconcentrated aroundthecentralvalue.Theimportofthisisthatwheninfe'rences aremadeabouttheadequacy(orinadequacy) ofstudsonbeamsorgird-ers,amorestringent, conservative setofstandards areap-pliedthanwouldresultfromthesimple(andinappropriate)
(P-74b) 

binomialdistribution.
Thevaluesofnandrareontheorderof20studstoseveralhundredinsomeinstances.
Thus,theevaluation ofalltheappropriate massandcumulative distributions isalaborious andcomputationally demanding task.Accordingly, acomputerprogramwasdeveloped toassistinthesestudies.Thepro-gramlistingaccompanies thisappendix.
Theprogramcontainscommentstomakeitself-documenting.
Statements 20,30,and40areusedtosettheparameters ofthedistribution.
Thetwokeyideasare:i)allprobabilities arecarriedinlogarithmic form.-untilthefinalprintouttoguardagainstround-off errorandassuretherequisite levelofaccuracy.
ii)eachvalueofthemassfunctionisrelatedtothepreviousone,sothatoncep(0ofh;rofn)isfound,theothervaluesmaybecalculated recursive-ly.Thisreducesthenumberoffactorial evaluations and.aidsthecomputational efficiency ofthetotalprogram.Execution ofthecomputerprogramyieldsthedensityandtheprobability functions derivedfromagivensetoffieldtestdataforagiventotalofstudsgroupedaccording tothenum-berofstudsperbeam.Nextthisoutputisreducedtoobtaintheprobability ofexceeding theprescribed designcriteriaasafunctionofthenumberofreliablestudswhichexistorwhich(P-74b) aretobeprovidedinagivenbeam.Fromthisinformation,
'heprojected numberofreliablestudsforagivenbeamisderivedobserving thestipulated 90%confidence level.Acknowledgement:
Theforegoing appendixwaspreparedunderthedirection ofDr.CarlW.Hamilton, Associate Professor ofQuantitative BusinessAnalysis, University
'ofSouthernCalifornia.
Dr'.Hamiltonwasengagedasaconsultant forstatistical studies.(P-74b) 
~~(ySTUDS>t~PROGFWtLISTINGFORTHEHYPERBINOMIAL PROBABILITY DISTRIBVTIOh~
ao20304045506070901101401501601701SO190200210220230240250260270280500510520530540550DIHP[300]H=5R=9N=15REH~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~REHFINDP(0)FORTHESTARTINGPOINTREMSETTHENILfERATOR FACTORSh'1]~h+H-RN[2]-N+1REM.SETTHEDENOMINATOR FACTORSD[1]=N-RD[2]=h+H+1 h'l=D1=0FORJ=lTO2FN'[j]COSUB500N1~Nl+FaNEXTJFORJ~aTO2F=D[J]GOSUB500Dl=Dl+FlNEXTJP[1]=Na-Da GOTO600RH1~~~~~o~~~~o~~~~~~oooo~'o~~~~o~~~o~oo~~~oREHSUBROUTINE TOGETF1=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-OCSTOPROBABILITIES FORK=1TOH+1P[K]-EXP(P[K])
NEXTKREHPRINTTHERESULTSC=OFORK=1TOK+1C=C+r[K]PRINT1'-l,p[K]
+NEXTI'~~~~~~~~~~
APPENDIXBTOFINALREPORTONSHEARSTUDSFIELDTESTDATA 1.inspection resultsnotedasFieldTestDataonthefol-lowingpages,pertaintotheexposedstudsinstalled priortoHay19772.Fortheexplanation ofthetermsandexpressions used,refertoAppendix"A".
Cr:IFIELDTESTDATAFORREACIORBLDG.41Placement:
202-S-01Area:29Elev.749'-1"SampleBeamStudNo.No.Installed StudsFailingSoundness TestStudsFailingVisualExam.WithBendTestResultsFailingTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarks1688Case1178627Case3188816Case18634Case1208815Case3218613Case2228847Case42386Case424108635Case48330Case426128032Case4271321337Case328149018Case3291513210Case3~~86ai I
FIELDTESTDATAFORREACIORBLDG.41Placement:
199-S-01Area:25Elev.749'-1"SampleNo.BeamStudNo.Installed
\StudsFailingSoundness TestStudsFailingVisualExam.KithBendTestResultsFallngTotalBendTestStudsFailingVisualExam.ButRepairedRemarksFSFl450188Case43915Case421Case42610Case4CO,50301622Case4Case44831Case417216105Case4187612Case410197616Case42076Case412217627Case42276Case114~30123Case4(r86a)
I~It 1FIELDTESTDATAFORREACIORBLDG.41Placement:
199-S-OlArea:25Elev.749'-1SampleBeamStudNo.No.Installed StudsFailingSoundness TestFSStudsFailingVisualExam.KithBendTestResultsFaizngTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarks153116529Case4(P-86a)
CFIEKZ)TESTDATAFORREACTORBLOG.41r"Placement:
r202-S-01Area:29Elev.749'-1"SampleBeamStudNo.No.Installed StudsFailingSoundness TestFSStudsFailingVisualExam.WithBendTestResultsFallngTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarksFV2301662160Case131173220Case43218711102Case3331917762Case1342014919Case1C352186,14Case136228423Case437239616Case1382410635Case439'270022-Case44026340Case22717Case4422810141.Case3r4329105018Case4<P-86a> 
,~F1ELDTESTDATAFORREACTORBLDG.41Placement:
202-S-02Area:29Elev.749'-1"SampleBeamStudNo.No.Installed StudsFailingSoundness TestFSStudsFailingVisualExam.WithBendTestResultsFaxxngTotalBendTestFV1FlStudsFailingVisualExam.ButRepairedRemarks44309639Case43188Case13213015Case447331302424Case3 fIlie ceFIELDTESTDATAFORREACTORBLDG.41Placement:
202-S-01Area:27Elev.749'-1"SampleBeamStudNo.No.Installed StudsFailingSoundness TestFSStudsFailingVisualExam.WithBendTestResultsFanxngTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarks48114Case413Case4503413Case310Case15276.66Case4ce-Case3542746720Case318Case35718Case3104430Case145184Case159124814Case3601342Case4(0611421Case1(P-86a) 
(FIELDTESTDATAFORREACTORBLDG.ClPlacement:
202-S-OlArea:27Elev.749'-1"SampleBeamStudNo.No.Installed StudsFailingSoundness TestFSStudsFailingVisualExam.WithBendTestResultsFaxzngTotalBendTestFV1FlStudsFailingVisualExam.ButRepairedRemarks621722319Case16319382212Case1 (FIELDTESTDATAFORR-WCIORBLDG.42Placement:
l82-S-01Area:32Elev.719'-1"SarrnleBeamStudNo.No.Installed StudsFailingSoundness TestStudsFailingVisualExam.WithBendTestResultsFal1ngTotalBendTestStudsFailingVisualExam.ButReoairedRemarksFSFV1Fl646621Case4657023Case2666229Case4676236Case4686218Case4i69122Case470Case47116Case4728721Case473105019Case4743212Case41224131Case2761320410Case377'419853Case4 lf/ 
'FIELDTESTDATAFOR1HACTORBLDG.02Placement:
182-S-01Area:32Elev.719'-1"SannleBeamStudNo.No.Installed StudsFailingSoundness TestFSStudsFailingVisualExam.WithBendTestResultsFanzngTotalBendTestStudsFailingVisualExam.ButRepairedRemarks78307Case179203619Case48021Case4812268Case482237622Case4(832915Case4<r86a)
FIELDTESTDATAFORREACK)RBLDG.g2Placement:
184-S-OlArea:34Elev.719'-1"SamoleBeamStudNo.No.Installed StudsFailingSoundness TestFSStudsFailingVisualExam.WithBendTestResultsFanxngTotalBendTestFVlFlStudsFailingVisualExam.ButReoairedRemarksFV284681616Case3856819Case2866825Case3876831Case388(089767620Case2Case4906817Case4917223Case2926523Case493266113Case3941212532Case49513166Case19615Case197160.26Case4 I~rFIELDTESTDATAFORREACIORBLDG.42Placement:
184-S-01Area:34Elev.719'-1"SampleBeamStudNo..No.Installed StudsFailingSoundness TestStudsFailingVisualExam.WithBendTestResultsFaizngTotalBendTestStudsFailingVisual'xam.ButRepairedRemarks981776FSFVlFl0010Case499181531564Case41001971Case11012070Case3102217014Case3~103104222372269110Case2Case41057020Case2106257027Case4.107266908'ase410827732328Case1109282563713105Case3110298613Case3(.312451289Case4(Z86a>
FIELDTESTDATAFORCONTROLBUILDINGPlacement:
714-S-03Area:21SampleNo.StudsFailingBeamStudSoundness No.Installed TestFSStudsFailingVisualExam.With'Bend TestResultsFaizngTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarks7,-891031704.16742025A54204210141101381351690217472415142238342913201319Case3Case3Case3Case3Case3Case3Case3Case3Case3Case3Case1(~(P-86b) 
(~~FIELDTESTDATAFORIURBQKBLDG.41Placement:
-Area:16Elev.729'-0"SanpleBeamNo.No.StudsFailingStudSoundness Installed TestFSStudsFailingVisualExam.NithBendTestResults,FanzngTotalBendTestFlStudsFailingVisualExam.ButRepairedRemarks8,010.121315161791013141516171864321002424124804645484240960105'00Case1Case1Case1Case1Case1Case1Case1Case1Case1Case1.Case1Case1Case1Case1Case1Case1Case1<0(P-86b) 
~~
FIELDTESTDATASweeNo.StudsFailingBeam,StudSoundness No.Installed TestStudsFailingVisualExam.WithBendTestResultsFanxngTotalBendTestStudsFailingVisualExam.ButReoairedRemarksCirculating WaterPumphouse 153FSFlCase1540Case1DieselGenerator Buildingqe44Case1(P-86b)
APPENDIXCTOFINALREPORTONSHEARSTUDSREDUCEDFIELDTESTDATA(P-74b)
SUMMARYOFREDUCEDFIELDDATAStructure Sample-Nos.TotalStUdSTotalPassTotalFailReactorBuildingUnits1and24453724970402TurbineBuildingUnits1and217831824ControlBuilding17641633131Circulating WaterPumphouse 107107DieselGenerator Building4444Note:Fortheexplanation oftermsandexpressions usedonthisandthefollowing pagesrefertoAppendix"A".(P-86b)
REDUCEDFIELDDATAFORSTATISTICAL ANALYSISBuilding:ReactorBuildingStudsfailingvisualwithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestSampleTotalNo.StudsStudsFail-Studsing.PassingTotalSoundness VisualPassFailPassFailbendbendTotalAssumedAssumed(Pv+Pl(Fs+FltesttestPassFail+P2)+F2)RemarksFSPVFV1PlFlFV2P2F213761688178618881986208827213'8902913230620706758685217468114462127163437181619191327361300208130"0700315912321103070867781'9791211842129059(P-86b)
REDUCEDFIELDDATAFORSTATISTICAL ANALYSISBuilding:
ReactorBuildingStudsfailingvisualvithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestSampleTotalNo.StudsStudsFail-StudsingPassingTotalSoundness VisualPassFailPassFailbendbendTotalAssumedAssumed(Pv+Pl(Fs+FltesttestPassFail+P2)+F2)Remarks32711331773414935863796421014588471305034511053157542745171798179201013913614164124131667PVFVl55352ill62130.19PlFlFV2P25111021005319900000201000042420310000ll5252152015F27047164'314908249061001880119ll304100151620371(P-86b)
II~~'
REDUCEDFIELDDATAFORSTATISTICAL ANALYSISBuilding:ReactorBuildingStudsfailingvisualwithbendtestresultsStudsfag.ingvisualbutrepairedpriortobendtestSampleTotalNo.StudsStudsFail-StudsingPassingTotalSoundness VisualPassFailPassFailbendbendTotalAssumedAssumed(Pv+Pl(Fs+FltesttestPassFail+P2)+F2)Remarks5557565757445845594861216222363.38762047830784688668FS1230232614125151783053494221633PVFVl38183818Pl1210FlFV2P2610810219144140'33751910120101100001601616802525F20~PF50748933ll37846217420023251319773052662662(P-86b) tI REDUCEDFIELDDATAFORSTATISTICAL ANALYSISBuilding:
ReactorBuildingStudsfailingvisualwithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestPassFailPassFailbendbendTotalAssumedAssumed(Pv+Pl(Fs+FltesttestPassFail+P2)+F2)StudsFail--StudsSampleTotalingPassingTotalNo.StudsSoundness VisualRemarks8768932669516696441007110170102701087310925611086FS233712136675247221014542281335PVFVl3521384PlFlFV2P2340313101131138000000003740141422131235012110596F2P0680255110155ll044006743601006550452892094716719(P-86b)
If REDUCEDFIELDDATAFORSTATISTICAL ANALXSISBuilding:
TurbineBuildingStudsfailingvisualwithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestStudsFail-StudsPassFailPassFailSampleTotali.ngPassingTotalbendbendTotalAssumedAssumed(Pv+Pl(Fs+FlNo.StudsSoundness VisualtesttestPassFail+P2)+F2)RemarksFSPlFlFV2P211826433643251006247248.1249801046ll451248185631.92232010979464310-001806403603201000240240118080046044048 REDUCEDFIELDDATAFORSTATISTICAL ANALYSISBuilding:TurbineBuildingStudsfailingvisualwithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestStudsFail-StudsSampleTotalingPassingNo.StudsSoundness VisualTFSPVPassFailPassFailTotalbendbendTotalAssumedAssumed(Pv+Pl(Fs+Fl.testtestPassFail+P2)+F2)RemarksFVlPlFlFV2P2F2'F131415421640179637360424096(P-86b) 

REDUCEDFIELDDATAFORSTATISTICAL ANALYSISBuilding:
ControlBuildingSampleTotalNo.StudsStudsfailingvisualwithbendtestresultsStudsFail-StudsPassFailingPassingTotal.bendbendSoundness VisualtesttestStudsfailingvisualbutrepairedpriortobendtestPassFailTotalAssumedAssumed(Pv+Pl(Fs+FlPassFail+P2)+F2)Remarks1'6921743170416752026547204821091411013811135FSPV12614712912615337149170115116121FVlPlFlFV2241861992734277202923134132198015ll4141402122175153827llllP22115158161164154187131513401912001331231221413101513F2PF(P-86b)
I REDUCEDFIELDDATAFORSTATISTICAL ANALYSISStudsfailingvisualwithbendtestresultsStudsfailingvisualbutrepairedpriortobendtestSampleTotalNo.StudsStudsFail-StudsingPassingSoundness VisualFSPVPassFailPassFailTotalbendbendTotalAssumedAssumed(Pv+Pl(Fs+FltesttestPassFail+P2)+F2)PlFlFV2P2F2PFRemarksCirculating WaterPumphouse 53545353000053DieselGenerator Building144440044(P-86b)
APPENDIXDTOFINALREPORTONSHEARSTUDSREPAIRPROCEDURES l4 REPAIRPROCEDURES 1.0GeneralAsnotedinsection7.6ofthefinalreport,somebeamsintheReactorBuildinghavebeenidentified, wheresomerestitution ofstudsisnecessary.
Thesebeamsaremarkedontheplans(Seefigures1thru5).2e0RepairHethodsandDesignCriteriaFollowing repairmethodsareproposedtoachievethere-quiredrestitution.
2.1Thefirstmethodistoprovideahorizontal shearkeywithintheridgewhenthemetaldeckispro-videdoverandacrossthesteelbeams.Theshearkeyiswellanchoredtothetopflangebyafric-tiontypebolt.Positiveengaoement andthecon-tactatthekey-decking isattainedbythebond-ingproperties oftheepoxyagent,andatthedecking-slab interface isdeveloped by.thecon-creteengagement intothecorrugation ofthedeck-ing.Seefigure6fordetails.2.2Thesecondapproachistoprovideathrough-bolt wheretheoeckingcorruoations areparalleltothesteelbeams.Thebasicconcepthereistodevelopafrictiontypeconnection between.beamandslabthroughthepre-tensioned, highstrengthbolt.The(P-74b) 
'I4If groutingoftheboltinthedrilledho1eandthefrictionconnection renderthedetaileffective byminimizing thetendencyofinitialslip.Seefig-ure7fordetails.2.3Xnsomeinstances, whenthedeckingisparalleltothebeamandtheabovemethodcannotbeusedbe-causeofembeddedconduitsinthes1ab,itispro-posedtodesignthesteelbeamasanon-composite sectionandreinforce theexistingbeamtoprovidethereauiredsectionmodulus.Theactualdetailsofreinforcement willbedesignedonacasebycasebasisdepending ontheexistingconditions atthetimeofrepair.
021.0'azQnSJ-0g~IId4~'1.2Qyo~S114AIIS~4S~111NI4t441CNOICSItSfIffPIp4Jd~tIIA(")SSP414d:rddSOPIoh/2;JXC'-2Ia~reVJ144dlfffd4Jf111114OO'SP4$a)j0I141AASSCANI/
fdfSPACA+
SSS4141141(fflt)I0QeNOTE:Beamstoberepairedarcmarkedthus.~~~~~wav~444hkuNO4Wk)dfoaf'ahPOIAASACA If4IfffffASSA+CCSANSIAtffQg2gi~ANISC.SCf P~SICAAVCV1114:t2'J"C~jPJ-.4O'ASCIAOSISQll
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>vhrPS~w4ISII~IASVINS'JttfVC'4144'lljj'JII~SI'll",4411~tvI4".iI)0OSCfNOISJCftf1)NIICfICCI&#xc3;AIC'thft4f4IRLVAtACICAINNlVfCACfhhCCAN44OhhLCCI(rStructural SteelFraming,PlanEl.670'-0"ReactorBuildingUnit1FigurelJ4lSII;tvdtlfvfOPA) g]414...);lIl<O.lhtf(">Il.4fw.f~~Sf'A)I~4ftJluPQgI~.4vCASfl41AhfON'Ifvvlvff2ffSllSPdCSOI21Sl4IVI'JdNI114Sdffr22SIC114JCC~f>144CIVslid(SOP44fICPSAAII CC.CCSICPwld)
J'2I141Qd>COAppendixD 11501150cf>c>tttcii4>CVcIQOI,srcivotrgrift)S:rdt>>5>VSOrt>TCtldwOrd<<d>Vo>>lwTSOltftttSCCWotdO>OMV~fo.0tIlCfsj1'oL.g,Beamstoberepairedaremarkedthus>OOC~tt1tistwortrSO~IrVtt>>Olt~Ttiitttut~Cco>ftvotcot.crit~doSfCCwoCVGI1IIfvtrtcrofts, f'o>rood@~~tuGt>ff>COCC.GSCYO~qlsdA5>Oo>c~ic>I>5SCC>TS>CCIcnlt~i~V-*w>>ol>v~GCsdaiSftd>OC411 rS!s>OcolocdClttVO>ftOt/V>WCCCtofftlfCW>CftffIWSff0>>C4>ff4A~-ttioftO,~..jw55Q4,ir.64.wtiTtt>OO.c,~Tft4>5>VCS1dtt>S>O'S>0 IIBttWOV>GCII;jJcr>''!G,g(~I4YJTSGCOG50ids>0 Su>>)GtCVGCCC8CottotOlidsfccw>IcotStructural SteelFramcingPlanatEl.670'-0"ReacterIIuilding Vni2Figure2AppendixDraS-tc>Su>c0iolOi'olf>at CGOtd0C>IDIO.
n<<IIII/.rC-<<I/.It>I>/.IlS<./~IIt/S.l>10Qt>1jStgktsS0Wf/'>0co4~W~II.1gCCAC/S>hfaI.S<<d$(CSr)C.o.l,stt0)I~fr>/~J'I~f''ltss':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<<<<<<>hf Itv<<>15/It>httdh./<<s/lS'1hfdl)v'ol/I'/I 5'sr>SStructural SteelFramingPlanEl.683'-0"ReactorBuildingUnit1~'t.I~fI~,hIrr~lr/ICrh 0rsent~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/IAIItt alentttltHYtl/I/rett 1Sct/c4DIrtcd/~/o~kII/II~C,Rt~++@tet~'tCC~)toestepsIi$5afIC/C4$Q~d,4,4'ct4'/>hhIIM4'~44~i'll,,I4h1I~~'I)N&#x17d;~rtlgI'44}r/r/Itltttyr'Iclitct-t'I}4'44'}ct>Structural SteelFramingPlanEl.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.tt hen'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~IOCAO1OXO IOVtttoIIhh5:o'/0~~IOO,II0(/0IIh7I7/00Cltl<rrICCAr/0rdirpocrkt ctrppokr244Itdtt*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/9 0/to~t'1dioretPittI<IICOIII0Iro4~Crt44fkt4Wtk.dt~4tt4ro44I04~rtkde5474ddtOOI62cd4'kt.~~enIttT"0o00k7444r4J[i'4ttre/0b7/tttr/4)~644~t-z-Beamstobcrepairedarcmarkedthus.~~~m~~Structural SteelFramingPlanEl,.7lglReactorBuildingUnit1Figure5AppendixD 

Inverted3"metaldeckingNo~-shrink highstrengthepoxygrout3"longsteelblock(AS2".2-441)we&atarredinholefor3/4"PA-325ric~antyoebolt.l/oversized hole.TopflangeofsteelbeamQCtvIU)0lAQHaroenedp]ate~asher*Naninaloeckin"dim~~sions pmmanufacture
'scatalogR"?PZBPFKEDJRE-YiETHOD'2'IGUK6APP~IX'D'P-74b) 
't Non-shrink highstrengthgrout5llp4-1/2"Px1/2"hardenedplatewashereachside.~tg~rC'.0880steelbeamorplategirder1-1/2"gthreadedrodwithonenutoheachendASTNA-325torquedforfric-tionconnection.
1/16"oversized holeinplatewashersandthetopflange.3/8"oversizeholeinconcreteslab.Notes:1.Priortodrillingcheckholelocationasfollows:-withrebardetector, ascertain thattoplayerorreinforcement andanyembedsareclearofhole.2.Preferred locationisatvalleyofdeckingcorrugations.
Donotlocatethrusidesofdecking.REPAIRPROCEDURE
-S<ETHOD'1'IGURE7APPENDIX'D'P-74b) 

APPENDIXEFINALREPORTONSHEARSTUDSBASICTHEORYOFCOMPOSITE BEAMCONSTRUCTION ENGINEERING DECISIONANALYSISCOMPANY BASICTHEORYOFCOYiPOSITE BEANCONSTRUCTION SUSQUEHANNA STEANELECTRICSTATIONpreparedforBECHTELPO'HERCORPORATION SanFrancisco, California 21Decemberl977LE<L7ENGII4EERING D-CISIONANA'SISCOMPANY.INC.480CALIFORNIA AVESUITF3012400MICHELSON DRIVESURNITZSTRASSE 34G TABLEOFCONTENTSPaoeSYNOPSIS.
1.INTRODUCTION.
2.GENERALTHEORYANDACOMPARISON WITHTHEAISCTheoryandVerification
.3.COYiPAR'SON WITHAISCSPECIFICATIONS; Ana1ysisofComposite Beams......;-.Ana1ysisofProjectBeam14.....OtherAISCProvisions
.~oo~~~~e~1-1SrECIFICATIONS..
2-12-13-13-23-43-44.RECOt"ENOATIONS ANDCONCLUSIONS
................4-1REFERENCES twSYNOPSISThis'report presentsageneralultimatestrengththeoryforcomposite beamsthatfitsthetypefoundintheSusquehanna SteamElectricStation(SSES)andmoreconventional construction.
Theconstruction oftheSSESemployscomposite beams.havingheavy,thickreinforced concreteslabspouredonaformedsteeldeckwhichinturnissupported bythegenerally unshoredsteelbeams.Incontrast, theconstruction inordinarybuild-ingsemploy>athinlightweight floorslabwithaformedsteeldecksup-portedondeepbutlightsteelrolledsections.
Anextensive studyofthe.experimental datauponwhichtheAISCspecifi-.cationsarebasedwasmadesincetheprojectbeamsareverydifferent fromthoseforwhichtheAISCspecifications aremeanttoapply.Itis,shownthattheAISCspecifications aregrosslyconservative.
Avalidultimatestrengthprocedure whichfitstheexperimental dataandthepro-jectbeamsisderivedbasedonrecognized concepts.Thestudycloseswithrecommendations foruse-inevaluating the,projectbeams.
1-1l.INTRODUCTION Thisreportispreparedinaccordance withBechtelContractNo.7PE-TSA-11 andinaccordance withmeetingsbetween8echtelPowerCor-porationandEngineering DecisionAnalysisCompany,Inc.(EDAC).Thisreportisconcerned witha,studyofthebasictheoryofcomposite beamconstruction andtherelationship tothespecifications oftheAmericanInstitute ofSteelConstruction.
Thefocusisonthetypeofcomposite construction employedintheSSES.Chapter2ofthisreportisconcerned withthegeneraltheoryofcom-positebeamconstruction andtheverification ofthattheory.Chapter3focusesonthesuitability oftheAISCspecifications forcomposite con-struction withbeamsofthetypeemployedintheSSESdesign.Theexper-imentaldatauponwhichtheAISCspecifications arebasedinvolveathinconcre'te slabpouredonaformedsteeldeckwithshearstudsconnecting theconcreteslabtoasteelbeam.Inlaboratory tests,therewassuf-ficientslippagebetweentheslabandthesteelbeamforallstudsintheshearspantobedeveloped, andfailurewasassociated withconcretefailureinvolving pulloutofthestudsfromtheslabandthedevelopment ofayieldhingeinthesteelbeam.Thebendingstrengtho,theslabbyitselfonthespanofthesteelbeamswasverysmall,sothatthestrengthofthecomposite beamwasthesumofthestrengthofthesteelbeamandthestudconnection intermsoultimatebendingmovement.
Inallcases,thedeadloadwasverysmallcomparedtotheult'imate load.
1-2Thebeamsemployedintheprojectdiffergreatlyfromthetestbeamsinthattheslabthickness isofthesameorderasthatofthesteelbeam.Theslabisheavilyreinforced.
Thedeadloadisnotsmallcomparedtotheliveloadandthesteelbeamsaregenerally unshoredwnentheslabisplacedsothatthesteelbeamsupportsallofthedeadloadwhilecompos-itebehaviorispresentunderliveload.Analysespresented inChapter2disclosethattheAISCspecifications mustbemodifiedtofitbeamsofthetypeofinterestinthisstudy.Ageneral,methodofanalysisanddesignispresented inChapter3whichfitstheexperimental data,isconsistent withtheliterature, andpro-videsarelationship betwentheAISCspecifications andconstruction ofthetypeemployedintheproject.Finally,Chapter4presentsrecommendations andconclusions.
2-12.GENERALTHEORYOFCOMPOSITE BEAMCONSTRUCTION ANDVERIFICATION OFTHETHEORYThischapterisconcerned withadevelopment ofageneralstrengththeoryandverification ofthattheorybycomparison withexperimental resultsoftestsofcomposite beamsemploying aformedsteeldeck.Theprovenanalytical methodology isthencomparedwiththeAISCspecifications inChapter3.-Amethodology foranalysisofthecomposite beamsintheSSESisalsopresented inChapter3.THEORYThediscussion thatfollowsisbasedontheworkofGrant,Fisher,andSlutter(Ref.1).Themethodology isbasedontheultimatestrengthofthecomposite beam.Sufficient slippageisassumedtotakeplaceattheslabbeaminterface toassumethateachshearstudintheshearspancar-riesthesameloading.TheAISCspecifications assumethatitispossibletorelatetheultimatebendingstrengthofthecomposite sectioninwhichthesteelbeamdevel-opsayieldhingetoanelasticstressanalysisatthesamesectionusingtransformed sectiontechniques focusedontheunitstressinthebottomtensionflangeofthesteelbeam.Theassumption isalsomadethattheeffective sectionmodulusofthecomposite sectionisalinearfunctionoftheratioofthecapacityoftheshearstudsintheshearspantothetheoretical limitofthiscapacity. 
'I~00 2-2Examination oftheexperimental datauponwhichtheAISCspecifications arebaseddiscloses thatthecomposite beamsthathavebeentestedfitaparticular typeofbuildingconstruction, thatinvolving athinconcretefloorslab,andlightbutdeepsteelbeams.Thelargestslabthickness in74testswas9in.witha3inribheightmakinga6in.netslabthickness.
Thebeamspanwas34.9ft.Yiorethanhalfoftheslabswereconstructed oflightweight concrete.
Thebendingstrengthoftheslabwasneglected intheanalysis.
Theslabwaseffectively considered tobea'purelycompression memberwiththecomprhssive
,orcelocatedatthecenterofgravityoftheconcretesectionneglecting theribconcrete.
Thesingleelasticdeformation requirement isthatthecurvature ofthenetconcreteslabbethesameasthatofthesteelbeams.Ifbothslabandbeamareelastic,theliveloadcarriedbytheslabandbeamispro-portional totheirstiffnesses (EI).Thelargestratioofslabtobeamstiffness intheexperimental datais0.15,thatforthe17Lehightestranoesfrom0.009to0.021,andGrant,Fisher,andSluttersaythatthisratioisgenerally lessthan0.05.Withprojectbeam14,thisratiois2.07.~Grant,Fisher,andSlutter(Ref.1)statethattheratioofthesectionmodulusofthetransformed sectiontothatofthesteelbeamsisapproxi-mately1.5forcomposite beamscomnonlyusedinbuildingconstruction.
Thisraiois2.9forprojectbeam14.HThegeneraltheoryforultimatestrengthofacomposite beamisshowninFigure2-1.Theequilibrium condition isshowninFigure2-Iband2-1c.Withtheexperimental beams,theslabswereveryflexiblecomparedtothe~steelsection.InFigure2-1c,abendingmomemtisshownto.existattheslabtosteelbeaminterface.
Thisbendinomomentislargecomparedtothatfromloaddistribution inallexperimental tests.Mithverythin 2-3slabs,itisreasonable toassumethatthecompressive forceintheslabactsatthecentero,gravityofthenetconcretesection(seeGrant,Fisher,and.Slutter)
(Fig.2-lc).Thetensileforceonthesteelsectionactstoreducetheplasticmomentcapacity(Fig.2-ld).Intheanalysisoftheexperimental testsmadein.thisstudy,itwasassumedthatthewebandflanoesofthesteelrolledsectioniereofconstantthickness asgiveninAISChandbook.
Withthickslabsitisnecessary tomodifythetheorytoaccountfortheultimatestrengthcharacristicsoftheslab(Fig.2-2).Equation4resultsandthisrelationship werecheckedbycomparison withtheexperi-mentaldata.Theanalysisshowedthatthemeanratioofexperimental tocalculated strengthwas1.000(0.9997)withastandarddeviation of0.081forthe74testbeamsandthedatahadarangeof0.835to1.1884.Theratioofobserved-to-calculated capacityisplottedinthehistogram ofFigure2-3andthesamedataareplottedonno'rmalprobability paperinFigure2-4.Thefittoastraightlineisexcellent sothattheobservedvariability canbeassumedtobethesumofrandomvariations nooneofwhichisdominant.
The.standarddeviation isequaltothecoefficient ofvariation withthesedatasincethemeanisunity.Thecoefficient ofvariationisofthesameorderasthatfoundintheyieldpointofsteelrolledsectionsofnominally ident'ical material.
Theanalytical comparison isalsoshowninFigure2-5inwhichtheratioofexperimental-to-calcuated strengthisplottedagainsttheratioofshearstudcapacityprovidedtomaximumshearstudcapacity.
Itappearsreasonable tostatethatthereliability ofthetheoryisnotafunctionoftheshearstuddesignlevel.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'kcIFIGURE2-1COMPOSITE BEAMRELATIONSHIPS 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'",POSITE BAMULTIMATESTRNGTHRELATIO"'SHIPS 2-6/5Exrgi~e~&lCC!PoCI~'a6 o:Cc/cu/afedCA,~<<i'yon=
l.go,5ja~+orr/Strich~=4.08'jGUpE2-3HjSTOGRA!~j OfEXpERj~,ENTALTOCAlCULATED ULTjl'tATE STRENGTH 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~arlrgFIGURE2-4PLOTOFRATIOOFEXPERIYIENTALCAPACITYTOCALCULATEO CAPACITYONNORl'IALPROBABILITY PAPER Z-8/.2Z~x.Cap.Ca/C.Cu/d0,9s=o.oI/X'xO.gx.Lchij/j TnU~0/herTisfsP.6FIGURE2-5PLOTSHO'r'ING 2EROCORRELATION OFSTRENGTHRATIOVITHV'hlyn 
,.-,~,JCOMPARISON OFTHEORYMITHAISCSPECIFICATIONS 3-1The1969EditionoftheAISCspecifications employstherelationship showninFigure3-1forelastic'designbasedonultimatestrengthproper-'ies.
Thecriteriaisthetensilestressinthebottomflangeofthesteelbeam(0.66Fy}andtheeffective sectionmodulusforelasticdesignis.equaltoasimplelinearfunctionofthesectionmodulusoftherolledsteelsection,thetransformed sectionmodulusreferredtothebottomflange,andtheratioofactualshearstudcapacitytothemaximumshear1studcapacity.
Thetrueeffective sectionmodulusforpseudoelasticdesignisgivenbyEquation5(Fig.1-2)inwhichtheloadfactoris1.7andtheallowable unitstressis0.66Fy.Thetruesectionmodulusforeachoftheexperimental beasmusingthecalculated ultimatestrengthbyEquation4ofChapter2isplottedinFigure3-1againsttheeffective sectionmodulusdefinedbytheAISCspecifications.
TheplotshowsthattheAISCrelationship isconserva-tivelybiasedbyapproximately 30percent'ased onameanvaluefunc-tion.However,approximately 50percentofthebeamshavecapacities smallerthanthatdefinedbythemeanvaluefunction.
Thevariability ofthedataaboutthemeanvaluefunctionappearstobeindependent ofthesectionmodulusandindependent ofY'h/Vh.TheAISCrelationship approx-imatesalowerboundonstrengthforsectionmodulusuptoapproximately'0 to100in.~Thevariability showninFigure3-1isconsistent withthatoftheplas-ticdesignmethodology forstructural steelbeamssothatitdoesnot 3~2appearreasonable torequiretheconservatism forcomposite beamswithasectionmoduluslargerthanapproximately 100in.~Theprojectbeamsofinteresthaveverylargesectionmodulus,oftheorderof1200in.sThereisastrongtrendfortheshearstudconnection toshowadecreaseinvariabilty withincreaseinthenumberofstudsowingtothelowcor-relationbetweenindividual studstrengths.
Hostudiesweremadeoftheexperimental datawithrespecttostudpro-perties.ANALYSISOFCOMPOSITE BEAMSStrictelasticanalysisofacomposite beamcannotaccountfortheunde-finedslippageontheslabtosteelbeaminterface sothatitisneces-sarytoemploypseudoelasticprocedures whichfundamentally arebasedonultimatestrengthproperties.
Thusthisdiscussion willfocusontheanalysisbasedonultimatestrength, Figure3-2.Equation4ofChapter2definestheultimatemomentcapacityofacompos-itesectionforcombineddeadandliveload.Atultimate, thebeamdevelopsayieldhinge,thereinforced concreteslabisatitsultimatecapacity, andtheV'hforcehasitslargestpossiblemomentarmconsis-tentwiththestrainconditions inthesteelbeamandtheslab.Withthreeinterrelated sourcesofstrength, itispossibleforanyonesourcetodevelopthenecessary capacity,,any combination oftwosouces,orallthreesourcestogether.
Ingeneral,thedesignwillnotbebal-ancedsothatatleastonesourceneednotbefullydeveloped.
Theanal-ysisthatfollowsconsiders firstthesteelbeamtoitsplasticlimit,thenaddsthereinforced concreteslabtoitsultimate, andthenaddsas 3-3manyshearconnectors asnecessary tosatisfytheloadingcriteriawhileaccounting fortheinfluence ofthetensiononthesteelbeamandforthecompression intheslab.Fromthestandpoint ofultimateload,itmakesnodifference whetherthesteelbeamisshoredorunshoredatthetimetheconcretefortheslabisplaced.Thisistrueregardless ofthestresscondition inthesteelbeamunderdeadloadaloneasaconsequence ofredistribution ofloadingamongthethreeresisting systemspriortoultimate.
Theultimatestrengthisindependent ofthepathemployedtoattaintheultimatestrainconditi'ons.
Thesameisnottruewithregardtodeflections andrigidity.
Ifboththesteelbeamandtheslabdeformelastically whileslippageisallowedatthestudline,therequirement ofidentical curvature allowsthecal-culationoftheloadcarriedbytheslabandthesteelbeam.Ifnoshearstudsareprovided, thedeflection isthatofthesteelbeamundertheloadingsupported bythesteelbeam(withproperaccounting forthedeadloaddeflection).
Mithshearstuds,theelasticstressconditions are-undefined sincetheslippageconditions attheshearstudsareunde-fined.However,ifthedeadload(concrete slabandsteelbeam)unitstressesinthebottomflangeofthesteelbeamreachtheyieldpointunderthisloading,thecomposite beamwillshowdegrading rigiditywiththeapplication offurtherloadingalthoughtheultimatecapacityofthecomposite sectionisunchanged.
Apseudoelasticanalysisofthecomposite
-sectionisshowninFigure3-2.Awidevarietyofsuchempirical procedures arepossible. 

Cif~,3-4ANAlYSISOFPROJECTBEAN14Projectbeam14isanalyzedinFigure3-3bothonanultimatestrengthandapseudoelasticanalysisconcept.Fromthestandpoint ofultimatestrength, itisseenthattheslabandsteelbeamwithoutcomposite actioncansupply93percentoftherequiredmomentcapacity.
Atrialstudcapacity(intheshear.span)of200kipswasassumed.Thestrengthexceededtherequiredcapacitywithonlyninestudsneededwhen46.5areprovidedand42areeffective atanormal2percentlevel.SeeEDACReport249.03,"StudiesofShearStudAdequacy-.Susquehanna SteamElec-tricStation,"
fordevelopment oftheequivalence relationship.
~'pseudoelasticanalysisofprojectbeam14isalsoshowninFigure3-3.Theanalysisbeginsbyassumingthattherearenoshearstudsandchecksfordesignadequacyassumingthatthesteelbeamsupportsallthedeadloadanditsproportion oftheliveload.Itisfoundthatthestiffslabisnotadequately reinforced tosupportitsportionofthe-liveloadwhilethesteelbeamunitstressesarelessthanallowable.
Theelasticslabcapacityplusthesteelbeamcapacityis92percentofthatneeded(neglecting elasticstrainrequirements).
AtrialV'hof200kips(elastic) producedasatisfactory capacitywiththesteelsectionnotusedtocapacityora-V'hof100kipswassatisfactory withthesteelatelasticcapacity.
Therequirednumberofstudswasninewith100kipstudloadsand18with200kipstudloads.OTHERAISCPROVISIONS TheAISCspecifications containalimitation onthetransformed sectionmoduluswhichisafunctionofthe.ratio-ofdeadtoliveloadbendingmoment(Equ.1.11-2)andstudlayoutrelationship (11.1-6).
Thereappearstobenojustification fortheequationinvolving thelivetodeadloadbendingmomentratio.Fromthestandpoint ofultimatestrength, thestraincondition atultimatestrengthisindependent ofthe 

3-5ratiooflive-to-dead load.Eveniftheunitstressesinthebottomflangeofthesteelbeamareatfullyieldunderthedeadload(un-shored),theultimatemomentcapacityofthecomposite sectionisun-changed.Thedeadloadiscons~dered thesameastheliveloadinthestrengthcalculation.
Mithunitstressesunderdeadloadlimitedto0.66.Fy,thereappearstobenojustification forthespecification.
ltwasnotpossibletodetermine thebasisoftherequirements.
Thesecondrequirement dealingwiththelayoutofshearstudsintheshearspanproblemcannotbejustified onthebasisofultimat'e strengthconsiderations.
TheLehightestsinvolvedafour-point loadingwithone-quarter oftheloadingappliedatapoint19to22percentofthespanfromtheendsupports.
Avarietyofshearstudarrangements wereexaminedintheLehightestsrangingfromproportioning thelayoutinaccordwiththerelativeshearinthespantoauniformlayoutindepedent oftheshearinthecomposite beam.Statistical analysisofthedatarelatingtheexperimental tocal-culatedstrength(notconsidering studlayout)asafunctionofthestudsintheregionofmaximumsheartothetotalnumberofstudsshowedthatstrengthisuncorrelated withlayout(Fig.3-4).Unless,otherevidenceexiststoverifyAISCEquation1.11.-6(p.5-35),therelationship isnotvalid.Theresultoftheapplication oftheequationistoincreasetheproportion ofstudsintheportionofthebeamhavingthelargestshearandmoreorlessreflectsanalysisanddesignprocedures basedonanas-sumedelasticbehaviorofthestuds-1 3-67hisRepaint/.ooQP0UpA/SCSqff=Ss~-Qp~-Ss)YAVAgy~k/+60x/op/5o5'e/C'Attic)
-i'n~'zooFIGURE3-1PLOTOFTRUEEFFECTIYE SECTIONNODULUSTOTHATBYAISCSPECIFICATIONS 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'of p"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~F1GURE3-2ULTIYiATE STRENGTHANALYSIS 

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/'hccE p7>p5zz~,O'erF>Sc.Cow~+legurea''h(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>GTH ANALYSIS 3-9Ah'I-.'L)'5 I~PZOJd=C7'-"dqff6+)re@z.zs.g''3--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/'rrdu rr)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(0FIGURE3-3continued EXAMPLE:ANALYSISOFPROJECTBEAM14 PPpl.2Rg5+dsSh:orSpun~C)/,0fSfogc=OOOE8cSPSgQo~~Fik)+~<~f0.6Z~bro]V'z07FIGURE3-4PLOTSHORINGlACKOFCORRELATION OFULTIMATESTRNGTHMITHVARIATION INSTUDPLACEt'ENT PATTERN 4.RECOi"8ENDATIONS ANDCONCLUSIONS Thetwobasicconclusions ofthestudyare,first,anadequateultimatestrengththeoryexistsforevaluating composite beams,andsecond,theAISCspecifications forcomposite beamsreflectaspecifictypeofdesignratherthanageneral-methodology andthusshouldonly,beappliedtothinslabscombinedwithdeepsteelbeams.Itisshowninthereportthatthick-slab composite beamsofthetypeemployedintheprojectareapproximately 30percentstrongerthanthestrengthbyAISCspecifica-tions.Theinfluence ofthoformedsteeldeckappearstobeadequately coveredbyexistingrelationships. 
''i'.0REFERENCES R-11.Grant,J.A.,Fisher,J.M.,andSlutter,R.G.,"Composite BeamswithFormedSteelDeck,"Engineering JournalAISC,Firstquarter1977.2."hanualofSteelConstruction,"
AISC,SeventhEditionandSupplements 3.Benjamin, J.R.andCornell,C.A.,Probabi-lity, Statistics, andDecisionforCivilEngineers, McGraw>Iooompany,nc.,I0.
APPENDIXFTOFINALREPORTONSHEAR.STUDSSTUDIESOFSHEARSTUDADEQUACYENGINEERING DECISIONANALYSISCOMPANY(P-74b) 4 EDAC-249.03 STUDJESOFSHEARSTUDADEQUACYSUSQUEHANNA STEAt~jELECTRICSTATIONpreparedforBECHTELPOWERCORPORATION SanFrancisco, California 21December1977L'!t:EK.".aENGINERINGDECISIONANALYSISCOMPANY,INC.460CALIFORNIA, AYE.~SUITE301PALOALTOCA'LIF.943062403L4ICHEI.SON DRIVEIRVIN"=.CALIF.92715BURNITZSTRASSE 346FRANKFURT 70.IV.GERMANY 
~,TABLEOFCONTENTS~PaeSYNOPSIS.
1.INTRODUCTION.
2.STATISTICAL ANALYSISOFSHEARSTUDDATAAnalysisbyBeams.AnalysisbyStuds...........Interpretation.
.RECOt"'PENDATIONS ANDCONCLUSIONS 00~0~0~00~111~000~~t~0~01-100~~~~~000~21~0~~~00000~2-1~~000~~t~0~2-20000000~0t02~20000000~t00~3-1REFERENCES SYNOPSISUponinspection attheSusquehanna SteamE'lectric Stationconstruction site,ahigherproportion ofimproperly weldedshear-studswasobservedthanisconsidered normalincomposite beamconstruction.
It-isnormal,.forapproximately 2percentoftheshearstudstobeinadequately'elded tothesteelbeam.Oftheshearstudstested,approximately 9percentfailedtopassinspection onanaverage.Aportionofthereinforced concretefloorslabwasinplaceatthetimeoftheinspection andthequestionistodetermine whetherornotmeasuresshouldbetakentoim-provetheshearconnection betweenthesteelrolledsectionandthecon-creteslabin.thatportionofthestructure wherethefloorslabhasbeenplaced,sincetheshearstudconnection isuncertain.
Theconstruction atthepowerplantemploysheavy,thickslabsonheavysteelrolledsections.
Incontrast, thecommonconstruction inordinarybuildings employsathinlightweight floorslabwithaformedsteeldeck(asslabforming)andthestructural steel.beam.'Aformedsteel.deckwasemployedintheprojectconstruction andthesteelbeamsweregenerally notshoredwhentheslabconcretewasplaced;Thestatistical
-analysis of'ataonshearstudproperties wheretheycouldbetestedshowedthatthemeannumberofstudsnotpassinginspec-tioninanybeaminReactorBuildings 1and2andtheControlBuildingwas9.2,percent,andthestandard-deviation ofthismeasurewas6.4per-cent.Thedataforthethreestructures weresosimilarthattheycouldbecombined.
Incontrast, themeanpercentofstudsnotpassinginspec-tionwas0.42percentintheTurbineBuilding, sothattwodifferent conditions exist.Nodetailedanalytical studyappearstobenecessary fortheTurbineBuilding.
Atotalof13,904studswereexaminedinthefield,13,073forReactor,Buildings 1and2andtheControlBuilding, and831intheTurbineBuild-ing.Themeanfailurerateofindividual studsintheformergroupofstructures isestimated tobe0.0842andforthelatterstructure isestimated tobe0.0084.Thereasonfortheneedtoestimatetheseratesarisesfromthefactthatmanystudswererepaireduponfailingtopassthevisualtest,whileonlyapproximately 18percentofthosefailingthevisualtestactuallyfailedthebendingtest.Thesamplesizeisadequateforestimation andforecasting.
Thestudycloseswithrecomnendations foruseinevaluating theprojectbeams.
1-11.INTRODUCTION Thisreportispreparedinaccordance withBechtelContractNo.7PE-TSA-11 andinaccordance with,meetingsbetweenBechtelPowerCorpor-ationandEngineering DecisionAnalysisCompany,Inc(EDAC).Thisreportisconcerned withastastical studyofshearstudadeouacyandrecormien-dationsforhandlingtheproblemsfromthestandpoint ofdesign.ceReference ismadetotheBechtelPowerCorporation report(Ref.1)of1?Dune1977forastatement oftheproblem.In.essence,ahigherfailurerate(soundness andbendtest)ofshearstudsthanexpectedhasbeenobservedintheconstruction ofsomeofthecomposite beamsintheSus-quehannaSteamElectricStationconstruction.
Thequestioniswhetherornotthosebeamswhichhadtheirslabspouredpriortothisobservation areadequate.
Studfailuredataanalysisandforecastprocedures arediscussed inChap-ter2using,twodifferent typesofanalysis.
Thefirst,typeofanalysisassumesthattheoccurrence ofinadquate studsisbybeamswithindepend-encebetweenbeams.Thistypeofanalysisproducesafailurerateintermsofthepercentofstudsthataresatisfactory and-unsatisfactory inanygivenbeam.Thesecondtypeofanalysisassumesthattheoccurrence ofaninadeouate studisanindependent chanceevent.Nosystematic phe-nomenaappeartoexistwhichmakesfailurestendtooccurtogether'on aparticular beamorinareasofthestructure.
Thetwostatistical pro-ceduresyieldslightlydifferent forecasts ofthenumberofadequatestudsinanybeam.Itwasnotfoundpossibletoconsiderpartialstrengths ofstudsinthestudyo~ingtoalackofdata.ceFinally,Chapter3presentsrecomnendations andconclusions.
4 2-12.STATISTICAL ANAYSISOFSHEARSTUDOATATwodifferent analysesofthesamedataarepresented inthischapter.Tnthefirstanalysis, thedataareconsidered inabeam-by-beam basisassumingindependence betweenbeamsbutnotnecessarily btweenthestuds.inanyonebeam.Incontrast, thesecondtypeofanalysisassumesthateachindividual studisindependent ofallotherstuds.Thechaptercloseswithaninterpretation oftheresultsin=termsofequivalence oftheportionoftheconstruction ofconcernandnormalconditions.
ANALYSISBYBEAMSThedatafallintofoursets,ReactorBuildings.
1'and2,ControlBuild-ing,and,Turbine Building.
Ineachset,thetotalnumberofinadequate studswastakenasthesumofthosethatfailedthesoundness (hamerblow)test,plusthosethatfailedthevisualtestandthebendtest,'lus aportionofthosethatfailedthevisualtestandwererepairedwithoutfurthertesting.Thelatterportionwasassumedtohavethesame.proportion offailuresasthosethatfailedthebendingtest'afterfail<<ingthevisualtest.Theresultsoftheanalysisare-giveninTable'-1.ItisseenthatalldataexceptfortheTurbine.Building havesimi-larproperties sothatthedataonbeamsforReactorBuildings 1and2andControlBuildingwerecombinedintothefirstdataset.(Fig.2-1),withthatfromtheTurbineBuildingbeingtheseconddataset.Nodetailedanalysisoftheseconddatasetwasnecessary owingtothelowinadequacy rate. 
~,2~2Thedataofthefirstset-wereorderedandplottedonbothnormalandlognormal probability paper.Thefitofthedatatoastraightlinewasfaironnormalprobability paper(Fig.2-2)andfaironlognormal proba-bilitypaper(Fig.2-3).Thisresultisreasonable considering thefactthatsomedependency isapparentinthedataonanareabas~sthatcannotbequantified statistically.
Themedianofthelognormal distribution was7.5percentandthestandarddeviation was0.626(log).ANALYSISBYSTUDSIfthesametreatment ofthedataisemployedonanindividual studbasis,thefailurerateis0.0842forReactorBuildings 1and2,andCon-trolBuil'ling.
Ifeachstudamountstoanindependent trial,theproba-,bilityofanycombination offailuresandsuccesses canbereadilycalcu-latedusingthebinominal probability model.Ampledataexisttoallowthepointestimateofthefailureratetobeusedinthebinomialdistri-bution.Thusifabeamcontains100studs,themeannumberofunsatis-factorystudsis(100)(0.0842)
=8.42studsorthemeannumberofsatis-factorystudsis100-8.42=91.58.Usingtheanalysisbybeams,thecorresponding meannumberofsatisfactory studsis90.82.INTERPRETATION Thetwodifferent probability modelsyieldslightlydifferent results,withthelognormal modelbeingmoreconservative thanthebinominal model.Thatis,,thelognormal modelproducesalargerprobability of'Ihighfailureratesthanwiththebinomialmodel.Fromapractical standpoint, however,thetwomodelsyieldverysimilarresults.Figure2-4providesausefulinterpretation ofthestatistical studies.Thefigurewasconstructed byassumingthatabeamcontained 100studs,andinspection hasshownthattheproportion ofstudswhichdonotpassthebendingtestis5,8.42,orIOpercent(binomial bystuds) 
~.~2~3or9.18percentbybeam(lognormal).
Ifthe,apaccetablefailurerateis2cetthat100studspercent(ordinae),analysiscanbebasedontheconcepaareplacedwhenthedesignonlyneeds92.5(8.42percentcurve)studsinordertoachieveaneffective meanfailurerateof2percent.Thustoachieveaneffective meanfailureraeptof2ercent{acceptable) whentheactualrateislargerthanthisvalue,itisonlynecessary toplaceadditional studs.Miththebinomialmodel,100studsinplaceatafailurerate-of8.42percentbecomesa2percentf'ailurerateusing92.5ofthe100inplacestuds.Thebeam(lognorma
)y'l)analsisyields91of100studsinplaceassociated with2percentfailureailurerate.Thetwosolu-tionsareessentiayasllthtarnewiththelognormal (beam)analysisbeingveryconservative.
Agamnamodelwasals'goinvestiatedwithresultsshown.Theconcept.ofequivalence expressed inFigur're2-4isusefulinanalysisanddesignsince-the curvesrelate100stuspdataarticular failureratetoareducednumberofstudsatanacceptabl eornormalfailurerate.TheaboveresultsagreewiththestudymadeybBechtelPowerCorporation
{Ref.5)(Appendix A).
TABLE2-1DATAPARAMETERS BYBEAMSRBlSourceRB2Contro1Composite SetTurbineBeams63481112217'IMeanPercent9.269.387.889.180.42StandardDeviation Percent6.55&.69.3.756.361.26Coefficient ofVariation 0.710.480.69Insufficient Data 
-<hC90Zo/0geon=v.iE/0ZORemend30FIGURE2-1HISTOGRAM>
OFSENDTESTFAILURESINPERCENTOFSTUDSPROVIDEDIt(ABEAM ir 2-655.55tt5tWttSe0500'001000500..00105051100CdC)0050102ti-I~~CNCJ00C051000Zl00A0007000005$0555ttltkttLttCsrdih'CPrsko4'II~J FlGURE2-2PLOTOFBENDTESTFA1LURERATEONNORMALPROBABILITY PAPER I,I' iEV(2-7I~.'.',,~,20.2020~~waI~'..tt~'~'I''l!;'l."'!iI:!I
..!!!i'!:.!:I<,",.:
~-'<!;!:i:!I<'i(,].i.a,
~,;i~!$!;!<~~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'i''i"i''-i!!i::::i:l!Il:.::i:.:.:<!"
i~.I!i<I!:!";!I!.ii!liI':!:$lsh'i:li!i.is<<i<.'!l<<'.'iii'!i::!!i:!!:!'::!i<<0~~I~2~'t"<~;t-.~~.I"atsr~~.~~~~~~I'~.:I'~~tP{rsI~C4<mcc/c7 TI${'QIrpEy61%~gFIGURE2-3PLOTOFBENOTESTFAILURERATEOhLOGNORNAL PROBABIL1TY PAPER ifltCf 
~~~2-8/0EPPESA'nolgse(Zoynormal)
'Rl8fo+amHnolysrs($a~mn)%/E'%%ang~lj'ufo'atp InIc5Si~8.92F0JOOo~5-oZggi'OP'urn$erg~<umPd/doormatOf/00SFadSTaiga/FlGURE2-4EUIVALENCEDIAGRAM 3-13.RECOt'~Pi" NDATIONSANDCONCLUSIONS Adetailedstatistical analysisofshearstudadequacydisclosed thattheoccurrence ofstudswhichfailtopassthesoundness andbendtestfol-lowsrecognized probabilistic models.Detailedanalysesprovidedavalidbasisforforecasting studadequacyonthebasisofequivalence ofthoseprovidedwiththosehavinga2percentinadequacy ratebythesoundness andbendtests.Aslightlydifferent alternate technique wasusedbyBechtelPowerCorporation (Ref.5)withthesambasicresults. 

REFERENCES 

R-1REFERENCES l.BechtelPowerCorporation, "InterimReportonShearStudsforSusque-hannaSteamElectricStationUnits1and2,"17June1977.-2.Grant,J.A.,Fisher,J.h'.,andSlutter,R.G.,"Composite BeamswithFormedSteelDeck,"Engineering JournalAISC,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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