ML16147A185

Seabrook Station, Revision 17 to Updated Final Safety Analysis Report, Chapter 3, Appendix 3D - Procedure for Calculating Elasto-Plastically Designed Pipe Whip Restraint Loads by Energy Balance Method, Appendix 3F - Verification of Computer

ML16147A185
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SEABROOKUPDATEDFSARAPPENDIX3DPROCEDUREFORCALCULATINGELASTO-PLASTICALLYDESIGNEDPIPEWHIPRESTRAINTLOADSBYENERGYBALANCEMETHODTheinformationcontainedinthisappendixwasnotrevised,buthasbeenextractedfromtheoriginalFSARandisprovidedforhistoricalinformation.

SB1&2FSARAmendment56NovemberlQHSAsimplifiedmathematicalmodelasonthenextpagecanbeusedforelascic-plasticdesignofpiperestraints.Anenergybalanceapproachhasbeenusedtoformulatethecalculationsfordeterminingtheplasticdeformationintherestraints.Inapplyingtheplasticdeformationdesignforrestraints,theregulatoryguidesrequirethateitheroneofthefollowingupperbounddesignlimitsformetallicductilematerialsbemet..(3)50%oftheminimumultimateuniformstrain(thestrainatthemaximumstressofanengineeringstress-straincurvebasedonactualmaterialtestsfortherestraint),'or(b)50%0:thepercentelongationasspecifiedinanapplicableASHE.ASTH,etc.Code,specification,orstandardwhendemonstratedtobelessthan50%oftheminimumultimateuniformstrainbasedonrepresentativetestresults.3D-l S1&2FSARSimolifiedapproachforelasto-?lastici\mendnlent5GNovember19R5Iftherestraintistogointotheplasticregion,thentherestraintdeflection,dcax*consistofanela3ticandaportionassho.wnbelov.(Figure1.0)RestraintDeflectionFigure1.0-IdealizedRestrain:where,deRestraintelasticdeflectionatyieldstressdmaxMaximumallowablerestraintdeflectionRpMaximumrestraintresistanceRp=kedekeRestraintelasticstructuralstiffnessIf'F'denotestheappliedforcingFunction(i.e.*aloadincaseofapipebreak)and'h'denotesthegapthepipingandtherestraint,anenergybalancerelationforthiscasegives)(see2.0).-Rp(dcax-de)23D-2 SB1&2FSARAmendment56November1985Ca)BeforeImpacth(b)AfterImpactFigure2.0EnergybalanceAnalvsisHodelRearranging,(Ro-F)2TIlerefore,dmax=122Fh.;.Rpde2(Rp-F)(1)Theaboveformulationcanbefurthersinlplif:edin2Fhismuchlarg-:rth2nTherefore,assuming.Rpde<<2FhEquation(1)gives,dmax:(Rp-F)(2)AfterdeterminingCmax.eitherbyequation(1)orequation(2)above(asapplicable),theresultingstraininthemembershouldbecalculated3ndshouldbecheckedagainstthecriteriagiveinpage1.Foruniaxialmembers,thestraineistakentobeequaltoLyhereListheoriginallengthoftherestraintmember.3D-3 SB1&2FSARPages4and5DeletedinAmendment56Amendment56November1985 SEABROOKUPDATEDFSARAPPENDIX3EPROCEDUREFORCALCULATINGELASTO-PLASTICALLYDESIGNEDPIPEWHIPRESTRAINTLOADSBYEQUIVALENTSTATICANALYSISMETHODTheinformationcontainedinthisappendixwasnotrevised,buthasbeenextractedfromtheoriginalFSARandisprovidedforhistoricalinformation.

SB1&.2FSARAPPENDIX3EPROCEDUREFORCALCULATINGELASTICALLYDESIGNEDPIPEWHIPRESTRAINTLOADSBYEQUIVALENTSTATICANALYSISMETHODPREPAREDBY:REVIDVEDBY::1/.1.11}1F.JANMECHANICAL.'lliALYSIS11/29/77R.F.PERRY.{l.A..'IALYSISGROCP Inordertoevaluatetheresponseofanelasticallydesignedpipewhiptoapipebreakloadbyusingtheequivalentstaticanalysisapproach,theloadfactorassociatedwiththeapplicableforcingfunction'andtheclearance(gap)becweenthepipeandtherestrainthastobeAsimplifiedmathematicalmodelasshowntheoextpage,'beusedtothedynamicloadfactor.Sincethepipesizeeffectsarealreadybeing.reflectedinthemagnitudeofthepipebreakload,thepipesizealoneisnotconsideredagainasamodelparameter.Theloadfactor(DL'F)*thusdeterminedisusedtocalculatetherestraint:load(R)asfollows:R*aXDLF.-where:{1.26forsteam-saturatedwaterct.:2.0forsubcoolednon-flashingu.s.NRCStandardReviewPlan,3.6.2(III)(2)(c)(42]P*OperatingPressureA*PipeBreakAreaAseriesofcurvesfordeterminingtherestraintloadsforsteam-saturatedwaterorsteam-watermixturesaregiveninPages3-14. AS1J1PLEMODELFORLOADFACTORBysubstituting(3)into(2),wehaveF(h+d)=1/2{...L\d2dstJFdeSkF(h+d)1/2kd!From(1).k&..!....dst(1)(2)(3)FhF.\d--.----L.//#1//F/l/CD..CDOr,(d2dstJ-2(...!-\-2(-!:""\c0\dst')DLFd*-z:dstWhere,F*AppliedLoad(PipeRuptureLoad)dstcRestraintdeflectionforstaticallyappliedFd*Maximumrestraintdeflectionh-Gapsizek*RestraintstiffnessDLFCDynamicloadfactor )*I*,*'1C*,***,.,i,.I*,"1rf2.J*,*.,*t10'P-AINLBS.=O.f200INCHESFORELRSTIlPIPEWHIPRES(Applicablenlytowaerorrmixtures,21.26))**.7.tleT FORElRSTIPIPERESRRINTS.(ApplicableInlytosteam1saturatedYaerorsteam-watr1.26)GRP=0.2500INCHESJ'.,*,.'1rf*,""'1rJINLBS.**"'1cJP*AJ*,*,.'1ct 2**4I*,*'10'.:'c'."*'1O*INLBS.GRP=0.5000INCHESJ***,..04P*RFORELASTl'PIPEWHIP(Applicablenlyto.steamr!saturatedwaerorsteam-watr*1.26).)*I*"'1I.10= GRP=0.7500lNCHESFORELASTIPIPEWHIPRESRAINTS.(Applicablenlytosteam*saturated.waerorsteam-watrmixtures,a*1.26)J4I*,,'10'2.J*"*,.'1rtINLBS.J***.,.'1O*P*R CURVESFORPI?EWHIPRESRRtNTS.(Applicable6nlytostearn'saturatedwater,orsteam-W8lrr*1.26)-7-*,*"',rjINLBS.=1.0000INCHES)***,."0'P*R:*I*,*'1cr CUFORPIPE(Applicabletosteam+saturatedwaerorsteam-wat'rmixtures,l-1.26)4*,.,.'1rJINLBS.=1.2500INCHES ICCU.YESFOR1PIWHIPRESINTS.Itosteacsaturatedwaterorsteam-walermixtures,*1.26)GRP=1.5000INCHESJ4J,*"'1O*P*)*I*1,'iltINLBS.J***,1'1O*)4,.,tllC ,I,4,4,*to',*&47.'I05INlBS.GRP=1.7500INCHES,*I*,8'1O*P*APARAMETRICCUVESFORELASTIPIPEWHIPRESRRINTS.(Applicablenlytosteamwaerorsteam-watrmixtures,Q1.26),4,*,*t0'10'I.,0It#I"')N"0enCD,...CDlI)*trlN'b(1)cD,...CDV)f'I")*UUP'S/IN.100000enQ),...10000(,,()V).000*f'I')2000Nb 58le81O*INLBS.GRP=2.0000INCHES,Ie7,*J0'P*APRRRHETR1CCUV£SFORELRSTIPIPERES(Applicableonlytosteamsaturatedwaerorsteam-waer=1.26)J*I*,.e0'I.-1",Npo.0enCDt-aoV)*C'I")Nb(7)CDr-CD\f)I{..,'NI{I'S/IN.100000N(J)(D-Jz"benr-CDV)fI")NbmCDf"-lOCCD&I).0.."10, 0'GAP=2.5000INCHESCUYESFORELASTIPIPEWHIPRESRAINTS.(Applicablenlytosteamsaturatedwalerorsteam-watre1.26)J4**,**IJ,*,i*O*S4i87*I06IP*AINLBS.I*10**N'bI...11;"1".*00000m-IZa::'0000"'000U)4000JDOO*20001000'iO.00210100'0 ***'"CGAP=3.0000INCHESJ4**,**0)I,.I*,*'1O*).**,*trtIJ4**,.,1rfP*RINLBS.PRRRMETRICFORElRST}PIPEWHIPRESRAINTS.(Applicablebnlytosteam*saturatedwae+orsteam-watbr*1.26)I..v,-.------..,...------.,..--------;------,10000c:1000coetoHGOIlOOIDOO".tOO211tOl FORPIPEWHIP(Applicableonlytoorsteam-watir*1.26)=0.0650lNCHESJ.***,t.O*P)(A***,.'1ctINLBS.J**""lcfJ*""'1 SEABROOKUPDATEDFSARAPPENDIX3FVERIFICATIONOFCOMPUTERPROGRAMSUSEDFORSTRUCTURALANALYSISANDDESIGNTheinformationcontainedinthisappendixwasnotrevised,buthasbeenextractedfromtheoriginalFSARandisprovidedforhistoricalinformation.

SB1&2FSARAPPENDIX3FVERIFICATIONOFCOMPUTERPROGRAMSUSEDFORSTRUCTURALANALYSISANDDESIGNAmendment54February1985ComputerprogramsusedforstructuralanalysisanddesignhavebeenverifiedaccordingtothecriteriadescribedintheUSNRCStandardReviewPlan3.8.1,SectionII-4(e).(a)Thefollowingcomputerprogramsarerecognizedinthepublicdomain,andhavehadsufficienthistorytojustifytheirapplicabilityandvaliditywithoutfurtherdemonstration:HardwareSourceSTARDYNECDCCDC(l)MARC-CDCCDCCDC(l)STRU-PAl<CDCCDC(l)SystemProfessionalCDCCDC(l)ANSYSCDCCDC(l)STRUDLUCCELPSDI(2)UEMENUUCCELUCCEL(3)(1)CDC-(2)PSDI-(3)UCCEL-ControlDataCorporationP.O.Box0,HQWOSHMinneapolis,Minnesota55440ProgramsforStructuralDesign,Inc.14StoryStreetCambridge,Massachusetts02138UCCELCorporationP.O.Box84028Dallas,Texas75284(b)Thefollowingcomputerprogramshavebeenverifiedbysolvingtestproblemswithasimilarandindependently-writtenandrecognizedprograminthepublicdomain:SAG058(ResponseSpectra)3F-l SB1&2FSARAmendment54February1985Asummaryofcomparisonresultsisshown1nTable3F-l.AX2(AxisymmetricShellProgram)AverificationmanualcomparingAX2withresultsobtainedfromeitherANSYSorBOSOR4(LockheadMissileandSpaceCompany-PaloAlto,CA)canbeobtainedfromPittsburgh-DesMoinesCorporation,3400GrandAvenue,NevilleIsland,Pittsburgh,PA15225(c)Thefollowingcomputerprogramshavebeenverifiedbycomparisonwithanalyticalresultspublishedintechnicalliterature:SAG001SAGO10(WILSON1)(WILSON2,DYN)SummariesofcomparisonresultsareshowninTables3F-2and3F-3,respectively.(d)Thefollowingcomputerprogramshavebeenverifiedbycomparisonwithhandcalculationsfortestproblemswhicharerepresentativeofthetypeusedinactualanalyses:AsummaryofcomparisonresultsisshowninTables3F-4through3F-8.SAG008SAGOI7SAG024SAG025PM-9IO*PM-906(TAPAS)(FOUREXP)(MMIC)(SECTION)(LESCAL)(STRAP)I54(e)Thefollowingcomputerprogramsareverifiedbyinspectionofthegraphicaloutputdata.SAG054(ResponseEnvelope)AtypicalverificationexampleispresentedinTable3F-9.*DocumentationofSTRAPisavailableintheFinalSafetyAnalysiskeportfortheCarolinaPowerandLightCo.,Brunswick1&2,USNRCDocketNos.50-324and50-325.3F-2 SB1&2FSARTABLE3F-lSAG058(RESPONSESPECTRA)SAG058(1)isverifiedagainstSTARDYNE,sub-routineDYNRE5.TheinputT/Hisof22secondduration,withatimeintervalof0.01secondsandamaximumaccelerationofI.Dg.SpectralAcceleration(g)Frequency0.5%Damping2%Damping(Hz)SAG058DYNRE5SAG058DYNRE50.330.910.980.790.831.002.682.672.032.032.008.238.234.334.323.036.046.024.314.324.005.205.184.404.375.005.255.213.953.946.257.517.424.474.387.145.335.253.943.908.334.874.803.689.097.096.934.964.8110.005.004.973.373.3520.002.612.601.771.7733.331.221.221.131.14(1)SAG058isanin-housecomputerprogramrunontheControlDataCorporationCYBER-175andisusedasatoSTARDYNEprogram.

SB1&2FSARTABLE3F-2SAG001(WILSON1)ThefollowingisacomparisonoftheresultsfromSAGOOIwithresultsobtainedfrompublishedtechnicalliterature.SAGOOIrunsontheHoneywell66/60systemwiththeGeOSoperatingsystem.SamnleProblemNo.1Analysisofathick-walledcylindersubjectedtoaninternalpressure.Reference-Gallagher,R.H.,FiniteElementAnalysis,Figure11.5)pg.317,Prentice-Hall,Inc.,1975.ComparisonofthetheoreticalsolutionwiththeWILSON1solutionisshownonFigure3F-lfortheradialstressandthehoopstress.SampleProblemNo.2Analysisofacylindricalshell,fixedatbothendsandsubjectedtoaninternalpressure.Reference-Timoshenko,S.,Woinowsky-Krieger,S.,TheoryofPlatesandShells,SecondEdition,pg.475,McGraw-Hill,1959.Comparisonofthetheore*ticalsolutionwiththeWILSON1solutionisshownonFigures3F-2andfortheradialshearandmeridionalmoment,respectively.

SB1&2FSARTABLE3F-3SAG010(WILSON2,DYN)TheoriginalversionofSAGOla,"DynamicStressAnalysisofAxisymmetricStructuresUnderArbitraryLoading,"writtenbyGhoshandWilsonwasrevisedbyUE&CinSeptember,1975.TheprogramisdistributedinthepublicdomainbytheEarthquakeEngineeringResearchCenter,UniversityofCalifornia,Berkeley,California.Theprogramhasbeenverifiedagainstaseriesofproblemswhoseresultsarepublishedintechnicalliterature.DocumentationofthisverificationiscontainedinthereportEERC69-10whichcanbeobtainedfromtheEarthquakeEngineeringResearchCenter.SAGOlaisrunontheHoneywell66/60System.

SB1&2FSARTABLE3F-4SAGOOa(TAPAS)ThefollowingisacomparisonoftheresultsfromSAG008,whichcomputesthetemperaturedistributionthroughplaneandaxisymmetricsolids,withhandcalculations.Thesampleresultsareforthetemperaturedistributionthroughthethicknessofahemisphericalconcretedomewhichis42inchesthickandsubjectto1200Finsideand(-)lOOFoutside.ElementNo.724848972109612201344SAGOoa(l)(OF)110.3888.8965.3342.1219.26(-)1.04HandCalculation(OF@MidPt.ofElem.)110.714389.04865.83342.61919.405(-)0.7143SAGOOBrunsontheHoneywell66/60system

References:

(1)Wilson,E.L.,Nickell,R.E.,"ApplicationoftheFiniteElement,"JournalofNuclearEngineeringandDesign,4,1966.

SB1&2FSARTABLE3F-5SAGO!7(FOUREXP)Amendment56November1985ThefollowingisaverificationofSAGOl7withhandcalculationsforarbitraryloadingdistributionwhichisanevenfunctionandcanbeexpandedusingacosineFourierSeries.Theperiodic*functionis,£(6)=-ne<01LaQ<8S.1TJComparisonofFourierCoefficients:o12345678910111213141516'17181920SAG017(1)1.5699-1.2739-0.0019-0.1421-0.0019.-0.0516-0.0020-0.0266-0.0021-0.0164-000022-0.0112-0.0023-0.0082-0.0025-0.0063-0.0028-0.0051-0.0031-0.0042-0.0036HandCalculations(2)1.5708-1.2732o-0.1415o-0.0509o-0.0260o-0.0157o-0.0105o-0.0075o-0.0057o-0.0044o-0.0035oI5{,SAGOI7runsontheHoneywell66/60syst.em.

References:

(1)TheFouriercoefficientsarecomputedforadigitizedfunctionbyarecursivetechniquedescribedinMathematicalMethodsforDigitalComputers,byRolstenandWilfsJohnWileyandSons,NewYork,1960,Chapter24.ThesolutiontechniqueisfromsubroutineFORIIinthe.IBMScientificSubroutinepackage.TheprogramisrunontheHoneywell66/60system.(2)Wylie,C.R;,AdvancedEngineeringMathematics,4thEd.,McGraw-Hill,1975.

SB1&2FSARTABLE3F-6SAG024(MMIC)ThefollowingisacomparisonoftheresultsofhandcalculationswithSAG024fortheweightofatypciallumpedmasspointinladynamicmodelofashearbuilding.ParameterSAG024(1)XcM(X-CoordinateoftheCenterofMass)0-ft.26.19YCM(Y-CoordinateoftheCenterofMass)-ft.0.08WT(TotalWeightofMassPoint)-Kips1444IMX(RotaryWeightMomentofInertiaaboutX-Axis)K-ft2162,323IMY(RotaryWeightMomentofInertiaaboutY-Axis)K-ft2379,552IMZ(RotaryWeightMomentofInertiaaboutZ-Axis)K-ft2470,152HandCalculation26.190.081444162,320379,550470,150SAG024runsontheHoneywell66/60system.

Reference:

(1)Bear,F.P.andJohnston,R.E.,Jr.,VectorMechanics'forEngineers:Staticand:DYnamics,McGraw-Hillt1962,pps.343-347.

SB1&2FSARTABLE3F-7SAG025(SECTION)Thefollo\JingisacomparisonoftheresultsofhandcalculationswithSAG025forasystemofresistingstructuralelementsbetweenfloorsinatypcialshearbuilding.SAG025HandCalculationsXeR(X-CoordinateofCenterofRigidity)-ft.26.326.257YCR(Y-CoordinateofCenterofRigidity)-ft.0.00.0Atr(Area)-ft466.0466.0SFX(ShearShapeFactoraboutX-Axis).4560.456SFY(ShearShapeFactoraboutY-Axis).5550.555IXX(MomentofInertiaaboutX-Axis)-ft.11,10011,079Iyy(MomentofInertiaaboutY-Axis)-ft.44,00043,957J(TorsionalConstant)-ft.117,000117,470SAG025runsontheHoneywell66/60system.

SB1&2FSARTABLE3F-8(Sheet1of2)PM-910(LESCAL)Amendment56November1985ThefollowingisacomparisonoftheresultsfromtheLESCALcomputerprogramwithhandcalculations.LESCALcalculatesthestressesandstrainsinrebarsand/orconcreteinaccordancewiththecriteriasetforthinSubarticle3511.1ofASMESectionIII,DivisionII.Thesectionisconcretereinforcedwithhorizontal,verticaland/ordiagonalrebars,subjectedtoaxialforceandmomentonaverticalandhorizontalfaceandin-planeshear.Wheninplaneshearforcesare"included,asolutionisobtainedbysolvingDuchon'sequations(l).5&.HandLoadConditionParameterLESCAL(Ksi)CalculationsI5fD.D+Fa+Esfmoutside29.3929.46Applied@e.g-offhoutside23.0823.05IConcreteSectionfseis.(3)52.2652.355G,.fsets.(4)0.210.21fminside26.6726.75fhinside23.8223.77D+1.25Pa+l.25Eofmoutside-2.22-2.99Applied@C.9-offnoutside-0.41-0.16ConcreteSectionfseis.(3)9.70SG9.47fseis*.(4)-12.34-12.63fminside38.3739.34fhinside1.982.12D+Pa+Esfmoutside37.7037.70Applied@e.g.fhoutside25.0825.07ofRebarfseis.(3)57.4157.41fseis.(4)5.37*5.37fminside12.7412.73fhinside19.0119.01 SB1&2FSARTABLE3F-8(Sheetof2)AmendmentS6November1985LoadConditionD+l.25Pa+l.25EoApplie,d@c.g.ofRebarParameterfmoutsidefhoutsidefseis.(3)fseis.(4)fminsidefhinsideHandLESCAL(Ksi)Calculations-2.01-1.777.337.8216.0716.08-10.76-10.0240.9440.649.5410.06LESCALrunsontheHoneywell66/60system.Notes(3)and(4)indicatedirectionsofseismicrebars.

References:

(1)Duchon,N.B.,"AnalysisofReinforcedConcreteMembraneSubjecttoTensionandShear,"ACIJournal,September1972,pp.578-583.

SB1&2FSARTABLE3F-9SAG054(RESPONSEENVELOPE)SAG054isapost-processingprogramforSTARDYNEyhichisusedinseismicanalysisTheprogramspreadsthepeaksoftheamplifiedresponsespectracreatedbySAG058(SeeTable3F-l)byapredeterminedamountandtabulatestheordinatesandabscissasoftheresultingcurve.Verificationofthisprogramisaccomplishedbyvisualinspectionofthegraphicaloutputtoinsurethattherawdatahas,infact,beenenveloped.SAG054runsontheCDCCYBER-175svstem.

I<tSYM.Ir----I(0)FINITEELEMENT(-.2607)-.{R-STRESS)x10psi(+0.9218)(+0.7915)(+0.5997)oSAG001-EXACTSOLUTIONRADIUS-4(T-STRESS)XlOpsi1.81.61.41.21.0b0.8V1V1w0.6a=::.-V1--I<<0.4a=::00.2z00.5-0.2-0.4-0.6-0.8-1.0(b)CALCULATEDSTRESSESANALYSISOFTHICK-WALLEDCYLINDERUNDERINTERNALPRESSURE

REFERENCE:

GALLAGHER,R.H.,FINITEELEMENTANALYSIS,PRENTICE-HALL/INC.1975.FIGURE11.5,PG.317PUBLICSERVICECOMPANYOFNEWHAMPSHIRESAG001SAMPLEPROBLEMNO.1SEABROOKSTATION-UNITS1&2FINALSAFETYANALYSISREPORTIFIGURE3F-1 wOoliN....J'-><LL_NoMocoof"'-..d0ZUJI0V")0-.00<!)d<t:t-V")II00Ll)0....JIN"-><d0000000.500000000'"000000..00-.0NN-.00++II7'"+Ico0........(!sd)ZPUBLICSERVICECOMPANYOFNEWHAMPSHIRESAG001SAMPLEPROBLEMNO.2SEABROOKSTATION-UNITS1&2RADIALSHEARFINALSAFETYANALYSISREPORTIFIGURE.3F-2 CDoorooC\J000zwaQ..lJ.J-.JIC\J\0x"-LLx0J:CJ)...--lJ.J::r:to-CI)0wwCJ)0a::w<t0zzU1J...WJ:(50<DCJ)0000:E(!)(!)<t<tto-CJ)CJ)0<:>L{)00000a0080g2a00000o00000o00000lOC\JV<.0CD0(\JIIIIT"VI(U!/#U!)lN3WOWPUBLICSERVICECOMPANYOFNEWHAMPSHIRESEABROOKSTATION-UNITS1&2FINALSAFETYANALYSISREPORTSAG001SAMPLEPROBLEMNO.2MERIDIONALMOMENTIFIGURE3.F-3 SEABROOKUPDATEDFSARAPPENDIX3DPROCEDUREFORCALCULATINGELASTO-PLASTICALLYDESIGNEDPIPEWHIPRESTRAINTLOADSBYENERGYBALANCEMETHODTheinformationcontainedinthisappendixwasnotrevised,buthasbeenextractedfromtheoriginalFSARandisprovidedforhistoricalinformation.

SB1&2FSARAmendment56NovemberlQHSAsimplifiedmathematicalmodelasonthenextpagecanbeusedforelascic-plasticdesignofpiperestraints.Anenergybalanceapproachhasbeenusedtoformulatethecalculationsfordeterminingtheplasticdeformationintherestraints.Inapplyingtheplasticdeformationdesignforrestraints,theregulatoryguidesrequirethateitheroneofthefollowingupperbounddesignlimitsformetallicductilematerialsbemet..(3)50%oftheminimumultimateuniformstrain(thestrainatthemaximumstressofanengineeringstress-straincurvebasedonactualmaterialtestsfortherestraint),'or(b)50%0:thepercentelongationasspecifiedinanapplicableASHE.ASTH,etc.Code,specification,orstandardwhendemonstratedtobelessthan50%oftheminimumultimateuniformstrainbasedonrepresentativetestresults.3D-l S1&2FSARSimolifiedapproachforelasto-?lastici\mendnlent5GNovember19R5Iftherestraintistogointotheplasticregion,thentherestraintdeflection,dcax*consistofanela3ticandaportionassho.wnbelov.(Figure1.0)RestraintDeflectionFigure1.0-IdealizedRestrain:where,deRestraintelasticdeflectionatyieldstressdmaxMaximumallowablerestraintdeflectionRpMaximumrestraintresistanceRp=kedekeRestraintelasticstructuralstiffnessIf'F'denotestheappliedforcingFunction(i.e.*aloadincaseofapipebreak)and'h'denotesthegapthepipingandtherestraint,anenergybalancerelationforthiscasegives)(see2.0).-Rp(dcax-de)23D-2 SB1&2FSARAmendment56November1985Ca)BeforeImpacth(b)AfterImpactFigure2.0EnergybalanceAnalvsisHodelRearranging,(Ro-F)2TIlerefore,dmax=122Fh.;.Rpde2(Rp-F)(1)Theaboveformulationcanbefurthersinlplif:edin2Fhismuchlarg-:rth2nTherefore,assuming.Rpde<<2FhEquation(1)gives,dmax:(Rp-F)(2)AfterdeterminingCmax.eitherbyequation(1)orequation(2)above(asapplicable),theresultingstraininthemembershouldbecalculated3ndshouldbecheckedagainstthecriteriagiveinpage1.Foruniaxialmembers,thestraineistakentobeequaltoLyhereListheoriginallengthoftherestraintmember.3D-3 SB1&2FSARPages4and5DeletedinAmendment56Amendment56November1985 SEABROOKUPDATEDFSARAPPENDIX3EPROCEDUREFORCALCULATINGELASTO-PLASTICALLYDESIGNEDPIPEWHIPRESTRAINTLOADSBYEQUIVALENTSTATICANALYSISMETHODTheinformationcontainedinthisappendixwasnotrevised,buthasbeenextractedfromtheoriginalFSARandisprovidedforhistoricalinformation.

SB1&.2FSARAPPENDIX3EPROCEDUREFORCALCULATINGELASTICALLYDESIGNEDPIPEWHIPRESTRAINTLOADSBYEQUIVALENTSTATICANALYSISMETHODPREPAREDBY:REVIDVEDBY::1/.1.11}1F.JANMECHANICAL.'lliALYSIS11/29/77R.F.PERRY.{l.A..'IALYSISGROCP Inordertoevaluatetheresponseofanelasticallydesignedpipewhiptoapipebreakloadbyusingtheequivalentstaticanalysisapproach,theloadfactorassociatedwiththeapplicableforcingfunction'andtheclearance(gap)becweenthepipeandtherestrainthastobeAsimplifiedmathematicalmodelasshowntheoextpage,'beusedtothedynamicloadfactor.Sincethepipesizeeffectsarealreadybeing.reflectedinthemagnitudeofthepipebreakload,thepipesizealoneisnotconsideredagainasamodelparameter.Theloadfactor(DL'F)*thusdeterminedisusedtocalculatetherestraint:load(R)asfollows:R*aXDLF.-where:{1.26forsteam-saturatedwaterct.:2.0forsubcoolednon-flashingu.s.NRCStandardReviewPlan,3.6.2(III)(2)(c)(42]P*OperatingPressureA*PipeBreakAreaAseriesofcurvesfordeterminingtherestraintloadsforsteam-saturatedwaterorsteam-watermixturesaregiveninPages3-14. AS1J1PLEMODELFORLOADFACTORBysubstituting(3)into(2),wehaveF(h+d)=1/2{...L\d2dstJFdeSkF(h+d)1/2kd!From(1).k&..!....dst(1)(2)(3)FhF.\d--.----L.//#1//F/l/CD..CDOr,(d2dstJ-2(...!-\-2(-!:""\c0\dst')DLFd*-z:dstWhere,F*AppliedLoad(PipeRuptureLoad)dstcRestraintdeflectionforstaticallyappliedFd*Maximumrestraintdeflectionh-Gapsizek*RestraintstiffnessDLFCDynamicloadfactor )*I*,*'1C*,***,.,i,.I*,"1rf2.J*,*.,*t10'P-AINLBS.=O.f200INCHESFORELRSTIlPIPEWHIPRES(Applicablenlytowaerorrmixtures,21.26))**.7.tleT FORElRSTIPIPERESRRINTS.(ApplicableInlytosteam1saturatedYaerorsteam-watr1.26)GRP=0.2500INCHESJ'.,*,.'1rf*,""'1rJINLBS.**"'1cJP*AJ*,*,.'1ct 2**4I*,*'10'.:'c'."*'1O*INLBS.GRP=0.5000INCHESJ***,..04P*RFORELASTl'PIPEWHIP(Applicablenlyto.steamr!saturatedwaerorsteam-watr*1.26).)*I*"'1I.10= GRP=0.7500lNCHESFORELASTIPIPEWHIPRESRAINTS.(Applicablenlytosteam*saturated.waerorsteam-watrmixtures,a*1.26)J4I*,,'10'2.J*"*,.'1rtINLBS.J***.,.'1O*P*R CURVESFORPI?EWHIPRESRRtNTS.(Applicable6nlytostearn'saturatedwater,orsteam-W8lrr*1.26)-7-*,*"',rjINLBS.=1.0000INCHES)***,."0'P*R:*I*,*'1cr CUFORPIPE(Applicabletosteam+saturatedwaerorsteam-wat'rmixtures,l-1.26)4*,.,.'1rJINLBS.=1.2500INCHES ICCU.YESFOR1PIWHIPRESINTS.Itosteacsaturatedwaterorsteam-walermixtures,*1.26)GRP=1.5000INCHESJ4J,*"'1O*P*)*I*1,'iltINLBS.J***,1'1O*)4,.,tllC ,I,4,4,*to',*&47.'I05INlBS.GRP=1.7500INCHES,*I*,8'1O*P*APARAMETRICCUVESFORELASTIPIPEWHIPRESRRINTS.(Applicablenlytosteamwaerorsteam-watrmixtures,Q1.26),4,*,*t0'10'I.,0It#I"')N"0enCD,...CDlI)*trlN'b(1)cD,...CDV)f'I")*UUP'S/IN.100000enQ),...10000(,,()V).000*f'I')2000Nb 58le81O*INLBS.GRP=2.0000INCHES,Ie7,*J0'P*APRRRHETR1CCUV£SFORELRSTIPIPERES(Applicableonlytosteamsaturatedwaerorsteam-waer=1.26)J*I*,.e0'I.-1",Npo.0enCDt-aoV)*C'I")Nb(7)CDr-CD\f)I{..,'NI{I'S/IN.100000N(J)(D-Jz"benr-CDV)fI")NbmCDf"-lOCCD&I).0.."10, 0'GAP=2.5000INCHESCUYESFORELASTIPIPEWHIPRESRAINTS.(Applicablenlytosteamsaturatedwalerorsteam-watre1.26)J4**,**IJ,*,i*O*S4i87*I06IP*AINLBS.I*10**N'bI...11;"1".*00000m-IZa::'0000"'000U)4000JDOO*20001000'iO.00210100'0 ***'"CGAP=3.0000INCHESJ4**,**0)I,.I*,*'1O*).**,*trtIJ4**,.,1rfP*RINLBS.PRRRMETRICFORElRST}PIPEWHIPRESRAINTS.(Applicablebnlytosteam*saturatedwae+orsteam-watbr*1.26)I..v,-.------..,...------.,..--------;------,10000c:1000coetoHGOIlOOIDOO".tOO211tOl FORPIPEWHIP(Applicableonlytoorsteam-watir*1.26)=0.0650lNCHESJ.***,t.O*P)(A***,.'1ctINLBS.J**""lcfJ*""'1 SEABROOKUPDATEDFSARAPPENDIX3FVERIFICATIONOFCOMPUTERPROGRAMSUSEDFORSTRUCTURALANALYSISANDDESIGNTheinformationcontainedinthisappendixwasnotrevised,buthasbeenextractedfromtheoriginalFSARandisprovidedforhistoricalinformation.

SB1&2FSARAPPENDIX3FVERIFICATIONOFCOMPUTERPROGRAMSUSEDFORSTRUCTURALANALYSISANDDESIGNAmendment54February1985ComputerprogramsusedforstructuralanalysisanddesignhavebeenverifiedaccordingtothecriteriadescribedintheUSNRCStandardReviewPlan3.8.1,SectionII-4(e).(a)Thefollowingcomputerprogramsarerecognizedinthepublicdomain,andhavehadsufficienthistorytojustifytheirapplicabilityandvaliditywithoutfurtherdemonstration:HardwareSourceSTARDYNECDCCDC(l)MARC-CDCCDCCDC(l)STRU-PAl<CDCCDC(l)SystemProfessionalCDCCDC(l)ANSYSCDCCDC(l)STRUDLUCCELPSDI(2)UEMENUUCCELUCCEL(3)(1)CDC-(2)PSDI-(3)UCCEL-ControlDataCorporationP.O.Box0,HQWOSHMinneapolis,Minnesota55440ProgramsforStructuralDesign,Inc.14StoryStreetCambridge,Massachusetts02138UCCELCorporationP.O.Box84028Dallas,Texas75284(b)Thefollowingcomputerprogramshavebeenverifiedbysolvingtestproblemswithasimilarandindependently-writtenandrecognizedprograminthepublicdomain:SAG058(ResponseSpectra)3F-l SB1&2FSARAmendment54February1985Asummaryofcomparisonresultsisshown1nTable3F-l.AX2(AxisymmetricShellProgram)AverificationmanualcomparingAX2withresultsobtainedfromeitherANSYSorBOSOR4(LockheadMissileandSpaceCompany-PaloAlto,CA)canbeobtainedfromPittsburgh-DesMoinesCorporation,3400GrandAvenue,NevilleIsland,Pittsburgh,PA15225(c)Thefollowingcomputerprogramshavebeenverifiedbycomparisonwithanalyticalresultspublishedintechnicalliterature:SAG001SAGO10(WILSON1)(WILSON2,DYN)SummariesofcomparisonresultsareshowninTables3F-2and3F-3,respectively.(d)Thefollowingcomputerprogramshavebeenverifiedbycomparisonwithhandcalculationsfortestproblemswhicharerepresentativeofthetypeusedinactualanalyses:AsummaryofcomparisonresultsisshowninTables3F-4through3F-8.SAG008SAGOI7SAG024SAG025PM-9IO*PM-906(TAPAS)(FOUREXP)(MMIC)(SECTION)(LESCAL)(STRAP)I54(e)Thefollowingcomputerprogramsareverifiedbyinspectionofthegraphicaloutputdata.SAG054(ResponseEnvelope)AtypicalverificationexampleispresentedinTable3F-9.*DocumentationofSTRAPisavailableintheFinalSafetyAnalysiskeportfortheCarolinaPowerandLightCo.,Brunswick1&2,USNRCDocketNos.50-324and50-325.3F-2 SB1&2FSARTABLE3F-lSAG058(RESPONSESPECTRA)SAG058(1)isverifiedagainstSTARDYNE,sub-routineDYNRE5.TheinputT/Hisof22secondduration,withatimeintervalof0.01secondsandamaximumaccelerationofI.Dg.SpectralAcceleration(g)Frequency0.5%Damping2%Damping(Hz)SAG058DYNRE5SAG058DYNRE50.330.910.980.790.831.002.682.672.032.032.008.238.234.334.323.036.046.024.314.324.005.205.184.404.375.005.255.213.953.946.257.517.424.474.387.145.335.253.943.908.334.874.803.689.097.096.934.964.8110.005.004.973.373.3520.002.612.601.771.7733.331.221.221.131.14(1)SAG058isanin-housecomputerprogramrunontheControlDataCorporationCYBER-175andisusedasatoSTARDYNEprogram.

SB1&2FSARTABLE3F-2SAG001(WILSON1)ThefollowingisacomparisonoftheresultsfromSAGOOIwithresultsobtainedfrompublishedtechnicalliterature.SAGOOIrunsontheHoneywell66/60systemwiththeGeOSoperatingsystem.SamnleProblemNo.1Analysisofathick-walledcylindersubjectedtoaninternalpressure.Reference-Gallagher,R.H.,FiniteElementAnalysis,Figure11.5)pg.317,Prentice-Hall,Inc.,1975.ComparisonofthetheoreticalsolutionwiththeWILSON1solutionisshownonFigure3F-lfortheradialstressandthehoopstress.SampleProblemNo.2Analysisofacylindricalshell,fixedatbothendsandsubjectedtoaninternalpressure.Reference-Timoshenko,S.,Woinowsky-Krieger,S.,TheoryofPlatesandShells,SecondEdition,pg.475,McGraw-Hill,1959.Comparisonofthetheore*ticalsolutionwiththeWILSON1solutionisshownonFigures3F-2andfortheradialshearandmeridionalmoment,respectively.

SB1&2FSARTABLE3F-3SAG010(WILSON2,DYN)TheoriginalversionofSAGOla,"DynamicStressAnalysisofAxisymmetricStructuresUnderArbitraryLoading,"writtenbyGhoshandWilsonwasrevisedbyUE&CinSeptember,1975.TheprogramisdistributedinthepublicdomainbytheEarthquakeEngineeringResearchCenter,UniversityofCalifornia,Berkeley,California.Theprogramhasbeenverifiedagainstaseriesofproblemswhoseresultsarepublishedintechnicalliterature.DocumentationofthisverificationiscontainedinthereportEERC69-10whichcanbeobtainedfromtheEarthquakeEngineeringResearchCenter.SAGOlaisrunontheHoneywell66/60System.

SB1&2FSARTABLE3F-4SAGOOa(TAPAS)ThefollowingisacomparisonoftheresultsfromSAG008,whichcomputesthetemperaturedistributionthroughplaneandaxisymmetricsolids,withhandcalculations.Thesampleresultsareforthetemperaturedistributionthroughthethicknessofahemisphericalconcretedomewhichis42inchesthickandsubjectto1200Finsideand(-)lOOFoutside.ElementNo.724848972109612201344SAGOoa(l)(OF)110.3888.8965.3342.1219.26(-)1.04HandCalculation(OF@MidPt.ofElem.)110.714389.04865.83342.61919.405(-)0.7143SAGOOBrunsontheHoneywell66/60system

References:

(1)Wilson,E.L.,Nickell,R.E.,"ApplicationoftheFiniteElement,"JournalofNuclearEngineeringandDesign,4,1966.

SB1&2FSARTABLE3F-5SAGO!7(FOUREXP)Amendment56November1985ThefollowingisaverificationofSAGOl7withhandcalculationsforarbitraryloadingdistributionwhichisanevenfunctionandcanbeexpandedusingacosineFourierSeries.Theperiodic*functionis,£(6)=-ne<01LaQ<8S.1TJComparisonofFourierCoefficients:o12345678910111213141516'17181920SAG017(1)1.5699-1.2739-0.0019-0.1421-0.0019.-0.0516-0.0020-0.0266-0.0021-0.0164-000022-0.0112-0.0023-0.0082-0.0025-0.0063-0.0028-0.0051-0.0031-0.0042-0.0036HandCalculations(2)1.5708-1.2732o-0.1415o-0.0509o-0.0260o-0.0157o-0.0105o-0.0075o-0.0057o-0.0044o-0.0035oI5{,SAGOI7runsontheHoneywell66/60syst.em.

References:

(1)TheFouriercoefficientsarecomputedforadigitizedfunctionbyarecursivetechniquedescribedinMathematicalMethodsforDigitalComputers,byRolstenandWilfsJohnWileyandSons,NewYork,1960,Chapter24.ThesolutiontechniqueisfromsubroutineFORIIinthe.IBMScientificSubroutinepackage.TheprogramisrunontheHoneywell66/60system.(2)Wylie,C.R;,AdvancedEngineeringMathematics,4thEd.,McGraw-Hill,1975.

SB1&2FSARTABLE3F-6SAG024(MMIC)ThefollowingisacomparisonoftheresultsofhandcalculationswithSAG024fortheweightofatypciallumpedmasspointinladynamicmodelofashearbuilding.ParameterSAG024(1)XcM(X-CoordinateoftheCenterofMass)0-ft.26.19YCM(Y-CoordinateoftheCenterofMass)-ft.0.08WT(TotalWeightofMassPoint)-Kips1444IMX(RotaryWeightMomentofInertiaaboutX-Axis)K-ft2162,323IMY(RotaryWeightMomentofInertiaaboutY-Axis)K-ft2379,552IMZ(RotaryWeightMomentofInertiaaboutZ-Axis)K-ft2470,152HandCalculation26.190.081444162,320379,550470,150SAG024runsontheHoneywell66/60system.

Reference:

(1)Bear,F.P.andJohnston,R.E.,Jr.,VectorMechanics'forEngineers:Staticand:DYnamics,McGraw-Hillt1962,pps.343-347.

SB1&2FSARTABLE3F-7SAG025(SECTION)Thefollo\JingisacomparisonoftheresultsofhandcalculationswithSAG025forasystemofresistingstructuralelementsbetweenfloorsinatypcialshearbuilding.SAG025HandCalculationsXeR(X-CoordinateofCenterofRigidity)-ft.26.326.257YCR(Y-CoordinateofCenterofRigidity)-ft.0.00.0Atr(Area)-ft466.0466.0SFX(ShearShapeFactoraboutX-Axis).4560.456SFY(ShearShapeFactoraboutY-Axis).5550.555IXX(MomentofInertiaaboutX-Axis)-ft.11,10011,079Iyy(MomentofInertiaaboutY-Axis)-ft.44,00043,957J(TorsionalConstant)-ft.117,000117,470SAG025runsontheHoneywell66/60system.

SB1&2FSARTABLE3F-8(Sheet1of2)PM-910(LESCAL)Amendment56November1985ThefollowingisacomparisonoftheresultsfromtheLESCALcomputerprogramwithhandcalculations.LESCALcalculatesthestressesandstrainsinrebarsand/orconcreteinaccordancewiththecriteriasetforthinSubarticle3511.1ofASMESectionIII,DivisionII.Thesectionisconcretereinforcedwithhorizontal,verticaland/ordiagonalrebars,subjectedtoaxialforceandmomentonaverticalandhorizontalfaceandin-planeshear.Wheninplaneshearforcesare"included,asolutionisobtainedbysolvingDuchon'sequations(l).5&.HandLoadConditionParameterLESCAL(Ksi)CalculationsI5fD.D+Fa+Esfmoutside29.3929.46Applied@e.g-offhoutside23.0823.05IConcreteSectionfseis.(3)52.2652.355G,.fsets.(4)0.210.21fminside26.6726.75fhinside23.8223.77D+1.25Pa+l.25Eofmoutside-2.22-2.99Applied@C.9-offnoutside-0.41-0.16ConcreteSectionfseis.(3)9.70SG9.47fseis*.(4)-12.34-12.63fminside38.3739.34fhinside1.982.12D+Pa+Esfmoutside37.7037.70Applied@e.g.fhoutside25.0825.07ofRebarfseis.(3)57.4157.41fseis.(4)5.37*5.37fminside12.7412.73fhinside19.0119.01 SB1&2FSARTABLE3F-8(Sheetof2)AmendmentS6November1985LoadConditionD+l.25Pa+l.25EoApplie,d@c.g.ofRebarParameterfmoutsidefhoutsidefseis.(3)fseis.(4)fminsidefhinsideHandLESCAL(Ksi)Calculations-2.01-1.777.337.8216.0716.08-10.76-10.0240.9440.649.5410.06LESCALrunsontheHoneywell66/60system.Notes(3)and(4)indicatedirectionsofseismicrebars.

References:

(1)Duchon,N.B.,"AnalysisofReinforcedConcreteMembraneSubjecttoTensionandShear,"ACIJournal,September1972,pp.578-583.

SB1&2FSARTABLE3F-9SAG054(RESPONSEENVELOPE)SAG054isapost-processingprogramforSTARDYNEyhichisusedinseismicanalysisTheprogramspreadsthepeaksoftheamplifiedresponsespectracreatedbySAG058(SeeTable3F-l)byapredeterminedamountandtabulatestheordinatesandabscissasoftheresultingcurve.Verificationofthisprogramisaccomplishedbyvisualinspectionofthegraphicaloutputtoinsurethattherawdatahas,infact,beenenveloped.SAG054runsontheCDCCYBER-175svstem.

I<tSYM.Ir----I(0)FINITEELEMENT(-.2607)-.{R-STRESS)x10psi(+0.9218)(+0.7915)(+0.5997)oSAG001-EXACTSOLUTIONRADIUS-4(T-STRESS)XlOpsi1.81.61.41.21.0b0.8V1V1w0.6a=::.-V1--I<<0.4a=::00.2z00.5-0.2-0.4-0.6-0.8-1.0(b)CALCULATEDSTRESSESANALYSISOFTHICK-WALLEDCYLINDERUNDERINTERNALPRESSURE

REFERENCE:

GALLAGHER,R.H.,FINITEELEMENTANALYSIS,PRENTICE-HALL/INC.1975.FIGURE11.5,PG.317PUBLICSERVICECOMPANYOFNEWHAMPSHIRESAG001SAMPLEPROBLEMNO.1SEABROOKSTATION-UNITS1&2FINALSAFETYANALYSISREPORTIFIGURE3F-1 wOoliN....J'-><LL_NoMocoof"'-..d0ZUJI0V")0-.00<!)d<t:t-V")II00Ll)0....JIN"-><d0000000.500000000'"000000..00-.0NN-.00++II7'"+Ico0........(!sd)ZPUBLICSERVICECOMPANYOFNEWHAMPSHIRESAG001SAMPLEPROBLEMNO.2SEABROOKSTATION-UNITS1&2RADIALSHEARFINALSAFETYANALYSISREPORTIFIGURE.3F-2 CDoorooC\J000zwaQ..lJ.J-.JIC\J\0x"-LLx0J:CJ)...--lJ.J::r:to-CI)0wwCJ)0a::w<t0zzU1J...WJ:(50<DCJ)0000:E(!)(!)<t<tto-CJ)CJ)0<:>L{)00000a0080g2a00000o00000o00000lOC\JV<.0CD0(\JIIIIT"VI(U!/#U!)lN3WOWPUBLICSERVICECOMPANYOFNEWHAMPSHIRESEABROOKSTATION-UNITS1&2FINALSAFETYANALYSISREPORTSAG001SAMPLEPROBLEMNO.2MERIDIONALMOMENTIFIGURE3.F-3