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{{#Wiki_filter:SEABROOKUPDATEDFSARAPPENDIX3DPROCEDUREFORCALCULATINGELASTO-PLASTICALLYDESIGNEDPIPEWHIPRESTRAINTLOADSBYENERGYBALANCEMETHODTheinformationcontainedinthisappendixwasnotrevised,buthasbeenextractedfromtheoriginalFSARandisprovidedforhistoricalinformation.
{{#Wiki_filter:SEABROOKUPDATEDFSARAPPENDIX3DPROCEDURE FORCALCULATING ELASTO-PLASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYENERGYBALANCEMETHODTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.
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&2FSARAmendment 56NovemberlQHSAsimplified mathematical modelasonthenextpagecanbeusedforelascic-plastic designofpiperestraints.
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&#xa3;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.
Anenergybalanceapproachhasbeenusedtoformulate thecalculations fordetermining theplasticdeformation intherestraints.
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.
Inapplyingtheplasticdeformation designforrestraints, theregulatory guidesrequirethateitheroneofthefollowing upperbounddesignlimitsformetallicductilematerials bemet..(3)50%oftheminimumultimateuniformstrain(thestrainatthemaximumstressofanengineering stress-strain curvebasedonactualmaterialtestsfortherestraint),
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.
'or(b)50%0:the percentelongation asspecified inanapplicable ASHE.ASTH,etc.Code,specification, orstandardwhendemonstrated tobelessthan50%oftheminimumultimateuniformstrainbasedonrepresentative testresults.3D-l S1&2FSARSimolified approachfor elasto-?lastic i\mendnlent 5GNovember19R5Iftherestraint is togointotheplasticregion,thenthe restraint deflection, dcax*consistofanela3tic anda portionassho.wnbelov.(Figure1.0)Restraint DeflectionFigure1.0-Idealized Restrain:
SB1&2FSARTABLE3F-3SAG010(WILSON2,DYN)TheoriginalversionofSAGOla,"DynamicStressAnalysisofAxisymmetricStructuresUnderArbitraryLoading,"writtenbyGhoshandWilsonwasrevisedbyUE&CinSeptember,1975.TheprogramisdistributedinthepublicdomainbytheEarthquakeEngineeringResearchCenter,UniversityofCalifornia,Berkeley,California.Theprogramhasbeenverifiedagainstaseriesofproblemswhoseresultsarepublishedintechnicalliterature.DocumentationofthisverificationiscontainedinthereportEERC69-10whichcanbeobtainedfromtheEarthquakeEngineeringResearchCenter.SAGOlaisrunontheHoneywell66/60System.
where,deRestraint elasticdeflection atyieldstressdmaxMaximumallowable restraint deflection RpMaximumrestraint resistance Rp=kedekeRestraint elasticstructural stiffness If'F'denotestheappliedforcingFunction(i.e.*aloadincaseofapipebreak)and'h'denotesthegap thepipingandtherestraint, anenergybalancerelationforthiscasegives)(see 2.0).-Rp(dcax-de)23D-2 SB1&2FSARAmendment 56November1985Ca)BeforeImpacth(b)AfterImpactFigure2.0EnergybalanceAnalvsisHodelRearranging, (Ro-F)2TIlerefore, dmax=122Fh.;.Rpde2(Rp-F)(1)Theaboveformulation canbefurthersinlplif:ed in2Fhismuchlarg-:rth2nTherefore, assuming.
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
Rpde<<2FhEquation(1)gives,dmax:(Rp-F)(2)Afterdetermining Cmax.eitherbyequation(1)orequation(2)above(asapplicable),
theresulting straininthemembershouldbecalculated 3ndshouldbecheckedagainstthecriteriagiveinpage1.
Foruniaxialmembers,thestraineistakentobeequaltoLyhereListheoriginallengthoftherestraint member.3D-3 SB1&2FSARPages4and5DeletedinAmendment 56Amendment 56November1985 SEABROOKUPDATEDFSARAPPENDIX3EPROCEDURE FORCALCULATING ELASTO-PLASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYEQUIVALENT STATICANALYSISMETHODTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.
SB1&.2FSARAPPENDIX3EPROCEDURE FORCALCULATING ELASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYEQUIVALENT STATICANALYSISMETHODPREPAREDBY:REVIDVEDBY::1/.1.11}1F.JANMECHANICAL
.'lliALYSIS11/29/77R.F.PERRY.{l.
A..'IALYS ISGROCP Inordertoevaluatetheresponseofanelastically designedpipewhip toapipebreakloadbyusingtheequivalent staticanalysisapproach, the loadfactorassociated withtheapplicable forcingfunction'and theclearance (gap)becweenthepipeandtherestraint hastobe Asimplified mathematical modelasshowntheoextpage,'beusedto thedynamicloadfactor.Sincethepipesizeeffectsarealreadybeing.reflected inthemagnitude ofthepipebreakload,thepipesizealoneisnotconsidered againasamodelparameter.
The loadfactor(DL'F)*thusdetermined isusedtocalculate therestraint:
load(R)asfollows:R*a XDLF.-where:{1.26forsteam-saturated waterct.:2.0forsubcooled non-flashingu.s.NRCStandardReviewPlan,3.6.2(III)(2)(c)(42]P*Operating PressureA*PipeBreakAreaAseriesof curvesfordetermining therestraint loadsforsteam-saturated waterorsteam-water mixturesaregiveninPages3-14. AS1J1PLEMODELFOR LOADFACTORBysubstituting (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)dstcRestraint deflection forstatically appliedFd*Maximumrestraint deflectionh-Gapsizek*Restraint stiffness DLFCDynamicloadfactor )*I*,*'1C*,***,.,i,.I*,"1rf2.J*,*.,*t10'P-AINLBS.=O.f200INCHES FORELRSTIlPIPEWHIPRES (Applicable nlyto waeror rmixtures, 21.26))**.7.tleT  FORElRSTIPIPE RESRRINTS.(Applicable Inlytosteam1saturated Yaerorsteam-wat r
1.26)GRP=0.2500INCHESJ'.,*,.'1rf*,""'1rJINLBS.**"'1cJP*AJ*,*,.'1ct  2**
4I*,*'10'.:'c'."*'1O*INLBS.GRP=0.5000INCHESJ***,..04P*R FORELASTl'PIPEWHIP (Applicable nlyto.steamr!saturated waerorsteam-wat r
*1.26).)*I*"'1I.10=  GRP=0.7500lNCHES FORELASTIPIPEWHIPRESRAINTS.(Applicable nlytosteam*saturated.wa erorsteam-wat rmixtures,a*1.26)J4I*,,'10'2.J*"*,.'1rtINLBS.J***.,.'1O*P*R  
 
CURVESFOR PI?EWHIPRESRRtNTS.(Applicable 6nlytostearn'saturated water,orsteam-W8lrr
*1.26)-7-*,*"',rjINLBS.=1.0000INCHES)***,."0'P*R:*I*,*'1cr  CUFOR PIPE (Applicabletosteam+saturated waerorsteam-wat' rmixtures, l-1.26)4*,.,.'1rJINLBS.=1.2500INCHES  ICCU.YESFOR1PIWHIPRESINTS.I tosteacsaturated waterorsteam-walermixtures,
*1.26)GRP=1.5000INCHESJ4 J,*"'1O*P*)*I*1,'iltINLBS.J***,1'1O*)4,.,tllC  ,I,4,4,*to',*&47.'I05INlBS.GRP=1.7500INCHES,*I*,8'1O*P*APARAMETRIC CUVESFORELASTIPIPEWHIPRESRRINTS.(Applicable nlytosteam waerorsteam-wat rmixtures,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*APRRRHETR1C CUV&#xa3;SFORELRSTIPIPERES (Applicable onlytosteamsaturated waerorsteam-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=2.5000INCHES CUYESFORELASTIPIPEWHIPRESRAINTS.(Applicable nlytosteamsaturated walerorsteam-wat r
e1.26)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.PRRRMETRIC FORElRST}PIPEWHIPRESRAINTS.(Applicable bnlytosteam*saturated wae+orsteam-watbr
*1.26)I..v,-.------..,...------.,..--------;------,10000c:1000coetoHGOIlOOIDOO".tOO211tOl  FOR PIPEWHIP (Applicable onlyto orsteam-watir
*1.26)=0.0650lNCHESJ.***,t.O*P)(A***,.'1ctINLBS.J**""lcfJ*""'1 SEABROOKUPDATEDFSARAPPENDIX3FVERIFICATION OFCOMPUTERPROGRAMSUSEDFORSTRUCTURAL ANALYSISANDDESIGNTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.
SB1&2FSARAPPENDIX3FVERIFICATION OFCOMPUTERPROGRAMSUSEDFORSTRUCTURAL ANALYSISANDDESIGNAmendment 54February1985Computerprogramsusedforstructural analysisanddesignhavebeenverifiedaccording tothecriteriadescribed intheUSNRCStandardReviewPlan3.8.1,SectionII-4(e).(a)Thefollowing computerprogramsarerecognized inthepublicdomain,andhavehadsufficient historytojustifytheirapplicability andvaliditywithoutfurtherdemonstration:
HardwareSourceSTARDYNECDCCDC(l)MARC-CDCCDCCDC(l)STRU-PAl<
CDCCDC(l)SystemProfessional CDCCDC(l)ANSYSCDCCDC(l)STRUDLUCCELPSDI(2)UEMENUUCCELUCCEL(3)(1)CDC-(2)PSDI-(3)UCCEL-ControlDataCorporation P.O.Box0,HQWOSHMinneapolis, Minnesota 55440ProgramsforStructural Design,Inc.14StoryStreetCambridge, Massachusetts 02138UCCELCorporation P.O.Box84028Dallas,Texas75284(b)Thefollowing computerprogramshavebeenverifiedbysolvingtestproblemswithasimilarandindependently-written andrecognized programinthepublicdomain:SAG058(Response Spectra)3F-l SB1&2FSARAmendment 54February1985Asummaryofcomparison resultsisshown1nTable3F-l.AX2(Axisymmetric ShellProgram)Averification manualcomparing AX2withresultsobtainedfromeitherANSYSorBOSOR4(Lockhead MissileandSpaceCompany-PaloAlto,CA)canbeobtainedfromPittsburgh
-DesMoinesCorporation, 3400GrandAvenue,NevilleIsland,Pittsburgh, PA15225(c)Thefollowing computerprogramshavebeenverifiedbycomparison withanalytical resultspublished intechnical literature:
SAG001SAGO10(WILSON1)(WILSON2,DYN)Summaries ofcomparison resultsareshowninTables3F-2and3F-3,respectively.
(d)Thefollowing computerprogramshavebeenverifiedbycomparison withhandcalculations fortestproblemswhicharerepresentative ofthetypeusedinactualanalyses:
Asummaryofcomparison resultsisshowninTables3F-4through3F-8.SAG008SAGOI7SAG024SAG025PM-9IO*PM-906(TAPAS)(FOUREXP)(MMIC)(SECTION)(LESCAL)(STRAP)I54(e)Thefollowing computerprogramsareverifiedbyinspection ofthegraphical outputdata.SAG054(Response Envelope)
Atypicalverification exampleispresented inTable3F-9.*Documentation ofSTRAPisavailable intheFinalSafetyAnalysiskeportfortheCarolinaPowerandLightCo.,Brunswick 1&2,USNRCDocketNos.50-324and50-325.3F-2 SB1&2FSARTABLE3F-lSAG058(RESPONSE SPECTRA)SAG058(1)isverifiedagainstSTARDYNE, sub-routine DYNRE5.TheinputT/Hisof22secondduration, withatimeintervalof0.01secondsandamaximumacceleration ofI.Dg.SpectralAcceleration (g)Frequency 0.5%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-housecomputerprogramrunontheControlDataCorporation CYBER-175 andisusedasa toSTARDYNEprogram.
SB1&2FSARTABLE3F-2SAG001(WILSON1)Thefollowing isacomparison oftheresultsfromSAGOOIwithresultsobtainedfrompublished technical literature.
SAGOOIrunsontheHoneywell 66/60systemwiththeGeOSoperating system.SamnleProblemNo.1Analysisofathick-walled cylindersubjected toaninternalpressure.
Reference
-Gallagher, R.H.,FiniteElementAnalysis, Figure11.5)pg.317,Prentice-Hall, Inc.,1975.Comparison ofthetheoretical solutionwiththeWILSON1solutionisshownonFigure3F-lfortheradialstressandthehoopstress.SampleProblemNo.2Analysisofacylindrical shell,fixedatbothendsandsubjected toaninternalpressure.
Reference
-Timoshenko, S.,Woinowsky-Krieger,S.,TheoryofPlatesandShells,SecondEdition,pg.475,McGraw-Hill, 1959.Comparison ofthetheore*tical solutionwiththeWILSON1solutionisshownonFigures3F-2andfortheradialshearandmeridional moment,respectively.
SB1&2FSARTABLE3F-3SAG010(WILSON2,DYN)TheoriginalversionofSAGOla,"DynamicStressAnalysisofAxisymmetric Structures UnderArbitrary Loading,"
writtenbyGhoshandWilsonwasrevisedbyUE&CinSeptember, 1975.Theprogramisdistributed inthepublicdomainbytheEarthquake Engineering ResearchCenter,University ofCalifornia,
: Berkeley, California.
Theprogramhasbeenverifiedagainstaseriesofproblemswhoseresultsarepublished intechnical literature.
Documentation ofthisverification iscontained inthereportEERC69-10whichcanbeobtainedfromtheEarthquake Engineering ResearchCenter.SAGOlaisrunontheHoneywell 66/60System.
SB1&2FSARTABLE3F-4SAGOOa(TAPAS)Thefollowing isacomparison oftheresultsfromSAG008,whichcomputesthetemperature distribution throughplaneandaxisymmetric solids,withhandcalculations.
Thesampleresultsareforthetemperature distribution throughthethickness ofahemispherical concretedomewhichis42inchesthickandsubjectto1200Finsideand(-)lOOFoutside.ElementNo.724848972109612201344SAGOoa(l)
(OF)110.3888.8965.3342.1219.26(-)1.04HandCalculation (OF@MidPt.ofElem.)110.714389.04865.83342.61919.405(-)0.7143 SAGOOBrunsontheHoneywell 66/60system


==References:==
==References:==
(1)Wilson,E.L.,Nickell,R.E.,"ApplicationoftheFiniteElement,"JournalofNuclearEngineeringandDesign,4,1966.
 
SB1&2FSARTABLE3F-5SAGO!7(FOUREXP)Amendment56November1985ThefollowingisaverificationofSAGOl7withhandcalculationsforarbitraryloadingdistributionwhichisanevenfunctionandcanbeexpandedusingacosineFourierSeries.Theperiodic*functionis,&#xa3;(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.
(1)Wilson,E.L.,Nickell,R.E.,"Application oftheFiniteElement,"
JournalofNuclearEngineering andDesign,4,1966.
SB1&2FSARTABLE3F-5SAGO!7(FOUREXP)
Amendment 56November1985Thefollowing isaverification ofSAGOl7withhandcalculations forarbitrary loadingdistribution whichisanevenfunctionandcanbeexpandedusingacosineFourierSeries.Theperiodic*function is,&#xa3;(6)=-ne<01LaQ<8S.1TJComparison ofFourierCoefficients:
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{,SAGOI7runsontheHoneywell 66/60syst.em.


==References:==
==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.
(1)TheFouriercoefficients arecomputedforadigitized functionbyarecursive technique described inMathematical MethodsforDigitalComputers, byRolstenandWilfsJohnWileyandSons,NewYork,1960,Chapter24.Thesolutiontechnique isfromsubroutine FORIIinthe.IBMScientific Subroutine package.TheprogramisrunontheHoneywell 66/60system.(2)Wylie,C.R;,AdvancedEngineering Mathematics, 4thEd.,McGraw-Hill, 1975.
SB1&2FSARTABLE3F-6SAG024(MMIC)Thefollowing isacomparison oftheresultsofhandcalculations withSAG024fortheweightofatypciallumpedmasspointinladynamicmodelofashearbuilding.
Parameter SAG024(1)XcM(X-Coordinate oftheCenterofMass)0-ft.26.19YCM(Y-Coordinate oftheCenterofMass)-ft.0.08WT(TotalWeightofMassPoint)-Kips1444IMX(RotaryWeightMomentofInertiaaboutX-Axis)K-ft2162,323IMY(RotaryWeightMomentofInertiaaboutY-Axis)K-ft2379,552IMZ(RotaryWeightMomentofInertiaaboutZ-Axis)K-ft2470,152HandCalculation 26.190.081444162,320379,550470,150SAG024runsontheHoneywell 66/60system.


==Reference:==
==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.
(1)Bear,F.P.andJohnston, R.E.,Jr.,VectorMechanics
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.
'forEngineers:
Staticand:DYnamics, McGraw-Hill t1962,pps.343-347.
SB1&2FSARTABLE3F-7SAG025(SECTION)
Thefollo\Jing isacomparison oftheresultsofhandcalculations withSAG025forasystemofresisting structural elementsbetweenfloorsinatypcialshearbuilding.
SAG025HandCalculations XeR(X-Coordinate ofCenterofRigidity)
-ft.26.326.257YCR(Y-Coordinate ofCenterofRigidity)
-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(Torsional Constant)
-ft.117,000117,470SAG025runsontheHoneywell 66/60system.
SB1&2FSARTABLE3F-8(Sheet1of2)PM-910(LESCAL)Amendment 56November1985Thefollowing isacomparison oftheresultsfromtheLESCALcomputerprogramwithhandcalculations.
LESCALcalculates thestressesandstrainsinrebarsand/orconcreteinaccordance withthecriteriasetforthinSubarticle3511.1ofASMESectionIII,DivisionII.Thesectionisconcretereinforced withhorizontal, verticaland/ordiagonalrebars,subjected toaxialforceandmomentonaverticalandhorizontal faceandin-planeshear.Wheninplaneshearforcesare"included, asolutionisobtainedbysolvingDuchon'sequations(l).
5&.HandLoadCondition Parameter LESCAL(Ksi)Calculations I5fD.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.25Eo fmoutside-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)Amendment S6November1985LoadCondition D+l.25Pa+l.25Eo Applie,d@c.g.ofRebarParameter fmoutsidefhoutsidefseis.(3)fseis.(4)fminsidefhinsideHandLESCAL(Ksi)Calculations-2.01-1.777.337.8216.0716.08-10.76-10.0240.9440.649.5410.06LESCALrunsontheHoneywell 66/60system.Notes(3)and(4)indicatedirections ofseismicrebars.


==References:==
==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.
(1)Duchon,N.B.,"Analysis ofReinforced ConcreteMembraneSubjecttoTensionandShear,"ACIJournal,September 1972,pp.578-583.
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
SB1&2FSARTABLE3F-9SAG054(RESPONSE ENVELOPE)
SAG054isapost-processing programforSTARDYNEyhichisusedinseismicanalysisTheprogramspreadsthepeaksoftheamplified responsespectracreatedbySAG058(SeeTable3F-l)byapredetermined amountandtabulates theordinates andabscissas oftheresulting curve.Verification ofthisprogramisaccomplished byvisualinspection ofthegraphical outputtoinsurethattherawdatahas,infact,beenenveloped.
SAG054runsontheCDCCYBER-175 svstem.
I<tSYM.Ir----I(0)FINITEELEMENT
(-.2607)-.{R-STRESS)x 10psi(+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)CALCULATED STRESSESANALYSISOFTHICK-WALLED CYLINDERUNDERINTERNALPRESSURE


==REFERENCE:==
==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.
GALLAGHER, R.H.,FINITEELEMENTANALYSIS, PRENTICE-HALL/INC.
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&#xa3;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.
1975.FIGURE11.5,PG.317PUBLICSERVICECOMPANYOFNEWHAMPSHIRE SAG001SAMPLEPROBLEMNO.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)
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.
ZPUBLICSERVICECOMPANYOFNEWHAMPSHIRE SAG001SAMPLEPROBLEMNO.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!)lN3WOW PUBLICSERVICECOMPANYOFNEWHAMPSHIRE SEABROOKSTATION-UNITS1&2FINALSAFETYANALYSISREPORTSAG001SAMPLEPROBLEMNO.2MERIDIONAL MOMENTIFIGURE3.F-3 SEABROOKUPDATEDFSARAPPENDIX3DPROCEDURE FORCALCULATING ELASTO-PLASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYENERGYBALANCEMETHODTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.
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&2FSARAmendment 56NovemberlQHSAsimplified mathematical modelasonthenextpagecanbeusedforelascic-plastic designofpiperestraints.
SB1&2FSARTABLE3F-3SAG010(WILSON2,DYN)TheoriginalversionofSAGOla,"DynamicStressAnalysisofAxisymmetricStructuresUnderArbitraryLoading,"writtenbyGhoshandWilsonwasrevisedbyUE&CinSeptember,1975.TheprogramisdistributedinthepublicdomainbytheEarthquakeEngineeringResearchCenter,UniversityofCalifornia,Berkeley,California.Theprogramhasbeenverifiedagainstaseriesofproblemswhoseresultsarepublishedintechnicalliterature.DocumentationofthisverificationiscontainedinthereportEERC69-10whichcanbeobtainedfromtheEarthquakeEngineeringResearchCenter.SAGOlaisrunontheHoneywell66/60System.
Anenergybalanceapproachhasbeenusedtoformulate thecalculations fordetermining theplasticdeformation intherestraints.
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
Inapplyingtheplasticdeformation designforrestraints, theregulatory guidesrequirethateitheroneofthefollowing upperbounddesignlimitsformetallicductilematerials bemet..(3)50%oftheminimumultimateuniformstrain(thestrainatthemaximumstressofanengineering stress-strain curvebasedonactualmaterialtestsfortherestraint),
'or(b)50%0:the percentelongation asspecified inanapplicable ASHE.ASTH,etc.Code,specification, orstandardwhendemonstrated tobelessthan50%oftheminimumultimateuniformstrainbasedonrepresentative testresults.3D-l S1&2FSARSimolified approachfor elasto-?lastic i\mendnlent 5GNovember19R5Iftherestraint is togointotheplasticregion,thenthe restraint deflection, dcax*consistofanela3tic anda portionassho.wnbelov.(Figure1.0)Restraint DeflectionFigure1.0-Idealized Restrain:
where,deRestraint elasticdeflection atyieldstressdmaxMaximumallowable restraint deflection RpMaximumrestraint resistance Rp=kedekeRestraint elasticstructural stiffness If'F'denotestheappliedforcingFunction(i.e.*aloadincaseofapipebreak)and'h'denotesthegap thepipingandtherestraint, anenergybalancerelationforthiscasegives)(see 2.0).-Rp(dcax-de)23D-2 SB1&2FSARAmendment 56November1985Ca)BeforeImpacth(b)AfterImpactFigure2.0EnergybalanceAnalvsisHodelRearranging, (Ro-F)2TIlerefore, dmax=122Fh.;.Rpde2(Rp-F)(1)Theaboveformulation canbefurthersinlplif:ed in2Fhismuchlarg-:rth2nTherefore, assuming.
Rpde<<2FhEquation(1)gives,dmax:(Rp-F)(2)Afterdetermining Cmax.eitherbyequation(1)orequation(2)above(asapplicable),
theresulting straininthemembershouldbecalculated 3ndshouldbecheckedagainstthecriteriagiveinpage1.
Foruniaxialmembers,thestraineistakentobeequaltoLyhereListheoriginallengthoftherestraint member.3D-3 SB1&2FSARPages4and5DeletedinAmendment 56Amendment 56November1985 SEABROOKUPDATEDFSARAPPENDIX3EPROCEDURE FORCALCULATING ELASTO-PLASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYEQUIVALENT STATICANALYSISMETHODTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.
SB1&.2FSARAPPENDIX3EPROCEDURE FORCALCULATING ELASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYEQUIVALENT STATICANALYSISMETHODPREPAREDBY:REVIDVEDBY::1/.1.11}1F.JANMECHANICAL
.'lliALYSIS11/29/77R.F.PERRY.{l.
A..'IALYS ISGROCP Inordertoevaluatetheresponseofanelastically designedpipewhip toapipebreakloadbyusingtheequivalent staticanalysisapproach, the loadfactorassociated withtheapplicable forcingfunction'and theclearance (gap)becweenthepipeandtherestraint hastobe Asimplified mathematical modelasshowntheoextpage,'beusedto thedynamicloadfactor.Sincethepipesizeeffectsarealreadybeing.reflected inthemagnitude ofthepipebreakload,thepipesizealoneisnotconsidered againasamodelparameter.
The loadfactor(DL'F)*thusdetermined isusedtocalculate therestraint:
load(R)asfollows:R*a XDLF.-where:{1.26forsteam-saturated waterct.:2.0forsubcooled non-flashingu.s.NRCStandardReviewPlan,3.6.2(III)(2)(c)(42]P*Operating PressureA*PipeBreakAreaAseriesof curvesfordetermining therestraint loadsforsteam-saturated waterorsteam-water mixturesaregiveninPages3-14. AS1J1PLEMODELFOR LOADFACTORBysubstituting (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)dstcRestraint deflection forstatically appliedFd*Maximumrestraint deflectionh-Gapsizek*Restraint stiffness DLFCDynamicloadfactor )*I*,*'1C*,***,.,i,.I*,"1rf2.J*,*.,*t10'P-AINLBS.=O.f200INCHES FORELRSTIlPIPEWHIPRES (Applicable nlyto waeror rmixtures, 21.26))**.7.tleT  FORElRSTIPIPE RESRRINTS.(Applicable Inlytosteam1saturated Yaerorsteam-wat r
1.26)GRP=0.2500INCHESJ'.,*,.'1rf*,""'1rJINLBS.**"'1cJP*AJ*,*,.'1ct  2**
4I*,*'10'.:'c'."*'1O*INLBS.GRP=0.5000INCHESJ***,..04P*R FORELASTl'PIPEWHIP (Applicable nlyto.steamr!saturated waerorsteam-wat r
*1.26).)*I*"'1I.10=  GRP=0.7500lNCHES FORELASTIPIPEWHIPRESRAINTS.(Applicable nlytosteam*saturated.wa erorsteam-wat rmixtures,a*1.26)J4I*,,'10'2.J*"*,.'1rtINLBS.J***.,.'1O*P*R  
 
CURVESFOR PI?EWHIPRESRRtNTS.(Applicable 6nlytostearn'saturated water,orsteam-W8lrr
*1.26)-7-*,*"',rjINLBS.=1.0000INCHES)***,."0'P*R:*I*,*'1cr  CUFOR PIPE (Applicabletosteam+saturated waerorsteam-wat' rmixtures, l-1.26)4*,.,.'1rJINLBS.=1.2500INCHES  ICCU.YESFOR1PIWHIPRESINTS.I tosteacsaturated waterorsteam-walermixtures,
*1.26)GRP=1.5000INCHESJ4 J,*"'1O*P*)*I*1,'iltINLBS.J***,1'1O*)4,.,tllC  ,I,4,4,*to',*&47.'I05INlBS.GRP=1.7500INCHES,*I*,8'1O*P*APARAMETRIC CUVESFORELASTIPIPEWHIPRESRRINTS.(Applicable nlytosteam waerorsteam-wat rmixtures,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*APRRRHETR1C CUV&#xa3;SFORELRSTIPIPERES (Applicable onlytosteamsaturated waerorsteam-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=2.5000INCHES CUYESFORELASTIPIPEWHIPRESRAINTS.(Applicable nlytosteamsaturated walerorsteam-wat r
e1.26)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.PRRRMETRIC FORElRST}PIPEWHIPRESRAINTS.(Applicable bnlytosteam*saturated wae+orsteam-watbr
*1.26)I..v,-.------..,...------.,..--------;------,10000c:1000coetoHGOIlOOIDOO".tOO211tOl  FOR PIPEWHIP (Applicable onlyto orsteam-watir
*1.26)=0.0650lNCHESJ.***,t.O*P)(A***,.'1ctINLBS.J**""lcfJ*""'1 SEABROOKUPDATEDFSARAPPENDIX3FVERIFICATION OFCOMPUTERPROGRAMSUSEDFORSTRUCTURAL ANALYSISANDDESIGNTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.
SB1&2FSARAPPENDIX3FVERIFICATION OFCOMPUTERPROGRAMSUSEDFORSTRUCTURAL ANALYSISANDDESIGNAmendment 54February1985Computerprogramsusedforstructural analysisanddesignhavebeenverifiedaccording tothecriteriadescribed intheUSNRCStandardReviewPlan3.8.1,SectionII-4(e).(a)Thefollowing computerprogramsarerecognized inthepublicdomain,andhavehadsufficient historytojustifytheirapplicability andvaliditywithoutfurtherdemonstration:
HardwareSourceSTARDYNECDCCDC(l)MARC-CDCCDCCDC(l)STRU-PAl<
CDCCDC(l)SystemProfessional CDCCDC(l)ANSYSCDCCDC(l)STRUDLUCCELPSDI(2)UEMENUUCCELUCCEL(3)(1)CDC-(2)PSDI-(3)UCCEL-ControlDataCorporation P.O.Box0,HQWOSHMinneapolis, Minnesota 55440ProgramsforStructural Design,Inc.14StoryStreetCambridge, Massachusetts 02138UCCELCorporation P.O.Box84028Dallas,Texas75284(b)Thefollowing computerprogramshavebeenverifiedbysolvingtestproblemswithasimilarandindependently-written andrecognized programinthepublicdomain:SAG058(Response Spectra)3F-l SB1&2FSARAmendment 54February1985Asummaryofcomparison resultsisshown1nTable3F-l.AX2(Axisymmetric ShellProgram)Averification manualcomparing AX2withresultsobtainedfromeitherANSYSorBOSOR4(Lockhead MissileandSpaceCompany-PaloAlto,CA)canbeobtainedfromPittsburgh
-DesMoinesCorporation, 3400GrandAvenue,NevilleIsland,Pittsburgh, PA15225(c)Thefollowing computerprogramshavebeenverifiedbycomparison withanalytical resultspublished intechnical literature:
SAG001SAGO10(WILSON1)(WILSON2,DYN)Summaries ofcomparison resultsareshowninTables3F-2and3F-3,respectively.
(d)Thefollowing computerprogramshavebeenverifiedbycomparison withhandcalculations fortestproblemswhicharerepresentative ofthetypeusedinactualanalyses:
Asummaryofcomparison resultsisshowninTables3F-4through3F-8.SAG008SAGOI7SAG024SAG025PM-9IO*PM-906(TAPAS)(FOUREXP)(MMIC)(SECTION)(LESCAL)(STRAP)I54(e)Thefollowing computerprogramsareverifiedbyinspection ofthegraphical outputdata.SAG054(Response Envelope)
Atypicalverification exampleispresented inTable3F-9.*Documentation ofSTRAPisavailable intheFinalSafetyAnalysiskeportfortheCarolinaPowerandLightCo.,Brunswick 1&2,USNRCDocketNos.50-324and50-325.3F-2 SB1&2FSARTABLE3F-lSAG058(RESPONSE SPECTRA)SAG058(1)isverifiedagainstSTARDYNE, sub-routine DYNRE5.TheinputT/Hisof22secondduration, withatimeintervalof0.01secondsandamaximumacceleration ofI.Dg.SpectralAcceleration (g)Frequency 0.5%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-housecomputerprogramrunontheControlDataCorporation CYBER-175 andisusedasa toSTARDYNEprogram.
SB1&2FSARTABLE3F-2SAG001(WILSON1)Thefollowing isacomparison oftheresultsfromSAGOOIwithresultsobtainedfrompublished technical literature.
SAGOOIrunsontheHoneywell 66/60systemwiththeGeOSoperating system.SamnleProblemNo.1Analysisofathick-walled cylindersubjected toaninternalpressure.
Reference
-Gallagher, R.H.,FiniteElementAnalysis, Figure11.5)pg.317,Prentice-Hall, Inc.,1975.Comparison ofthetheoretical solutionwiththeWILSON1solutionisshownonFigure3F-lfortheradialstressandthehoopstress.SampleProblemNo.2Analysisofacylindrical shell,fixedatbothendsandsubjected toaninternalpressure.
Reference
-Timoshenko, S.,Woinowsky-Krieger,S.,TheoryofPlatesandShells,SecondEdition,pg.475,McGraw-Hill, 1959.Comparison ofthetheore*tical solutionwiththeWILSON1solutionisshownonFigures3F-2andfortheradialshearandmeridional moment,respectively.
SB1&2FSARTABLE3F-3SAG010(WILSON2,DYN)TheoriginalversionofSAGOla,"DynamicStressAnalysisofAxisymmetric Structures UnderArbitrary Loading,"
writtenbyGhoshandWilsonwasrevisedbyUE&CinSeptember, 1975.Theprogramisdistributed inthepublicdomainbytheEarthquake Engineering ResearchCenter,University ofCalifornia,
: Berkeley, California.
Theprogramhasbeenverifiedagainstaseriesofproblemswhoseresultsarepublished intechnical literature.
Documentation ofthisverification iscontained inthereportEERC69-10whichcanbeobtainedfromtheEarthquake Engineering ResearchCenter.SAGOlaisrunontheHoneywell 66/60System.
SB1&2FSARTABLE3F-4SAGOOa(TAPAS)Thefollowing isacomparison oftheresultsfromSAG008,whichcomputesthetemperature distribution throughplaneandaxisymmetric solids,withhandcalculations.
Thesampleresultsareforthetemperature distribution throughthethickness ofahemispherical concretedomewhichis42inchesthickandsubjectto1200Finsideand(-)lOOFoutside.ElementNo.724848972109612201344SAGOoa(l)
(OF)110.3888.8965.3342.1219.26(-)1.04HandCalculation (OF@MidPt.ofElem.)110.714389.04865.83342.61919.405(-)0.7143 SAGOOBrunsontheHoneywell 66/60system


==References:==
==References:==
(1)Wilson,E.L.,Nickell,R.E.,"ApplicationoftheFiniteElement,"JournalofNuclearEngineeringandDesign,4,1966.
 
SB1&2FSARTABLE3F-5SAGO!7(FOUREXP)Amendment56November1985ThefollowingisaverificationofSAGOl7withhandcalculationsforarbitraryloadingdistributionwhichisanevenfunctionandcanbeexpandedusingacosineFourierSeries.Theperiodic*functionis,&#xa3;(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.
(1)Wilson,E.L.,Nickell,R.E.,"Application oftheFiniteElement,"
JournalofNuclearEngineering andDesign,4,1966.
SB1&2FSARTABLE3F-5SAGO!7(FOUREXP)
Amendment 56November1985Thefollowing isaverification ofSAGOl7withhandcalculations forarbitrary loadingdistribution whichisanevenfunctionandcanbeexpandedusingacosineFourierSeries.Theperiodic*function is,&#xa3;(6)=-ne<01LaQ<8S.1TJComparison ofFourierCoefficients:
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{,SAGOI7runsontheHoneywell 66/60syst.em.


==References:==
==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.
(1)TheFouriercoefficients arecomputedforadigitized functionbyarecursive technique described inMathematical MethodsforDigitalComputers, byRolstenandWilfsJohnWileyandSons,NewYork,1960,Chapter24.Thesolutiontechnique isfromsubroutine FORIIinthe.IBMScientific Subroutine package.TheprogramisrunontheHoneywell 66/60system.(2)Wylie,C.R;,AdvancedEngineering Mathematics, 4thEd.,McGraw-Hill, 1975.
SB1&2FSARTABLE3F-6SAG024(MMIC)Thefollowing isacomparison oftheresultsofhandcalculations withSAG024fortheweightofatypciallumpedmasspointinladynamicmodelofashearbuilding.
Parameter SAG024(1)XcM(X-Coordinate oftheCenterofMass)0-ft.26.19YCM(Y-Coordinate oftheCenterofMass)-ft.0.08WT(TotalWeightofMassPoint)-Kips1444IMX(RotaryWeightMomentofInertiaaboutX-Axis)K-ft2162,323IMY(RotaryWeightMomentofInertiaaboutY-Axis)K-ft2379,552IMZ(RotaryWeightMomentofInertiaaboutZ-Axis)K-ft2470,152HandCalculation 26.190.081444162,320379,550470,150SAG024runsontheHoneywell 66/60system.


==Reference:==
==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.
(1)Bear,F.P.andJohnston, R.E.,Jr.,VectorMechanics
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.
'forEngineers:
Staticand:DYnamics, McGraw-Hill t1962,pps.343-347.
SB1&2FSARTABLE3F-7SAG025(SECTION)
Thefollo\Jing isacomparison oftheresultsofhandcalculations withSAG025forasystemofresisting structural elementsbetweenfloorsinatypcialshearbuilding.
SAG025HandCalculations XeR(X-Coordinate ofCenterofRigidity)
-ft.26.326.257YCR(Y-Coordinate ofCenterofRigidity)
-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(Torsional Constant)
-ft.117,000117,470SAG025runsontheHoneywell 66/60system.
SB1&2FSARTABLE3F-8(Sheet1of2)PM-910(LESCAL)Amendment 56November1985Thefollowing isacomparison oftheresultsfromtheLESCALcomputerprogramwithhandcalculations.
LESCALcalculates thestressesandstrainsinrebarsand/orconcreteinaccordance withthecriteriasetforthinSubarticle3511.1ofASMESectionIII,DivisionII.Thesectionisconcretereinforced withhorizontal, verticaland/ordiagonalrebars,subjected toaxialforceandmomentonaverticalandhorizontal faceandin-planeshear.Wheninplaneshearforcesare"included, asolutionisobtainedbysolvingDuchon'sequations(l).
5&.HandLoadCondition Parameter LESCAL(Ksi)Calculations I5fD.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.25Eo fmoutside-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)Amendment S6November1985LoadCondition D+l.25Pa+l.25Eo Applie,d@c.g.ofRebarParameter fmoutsidefhoutsidefseis.(3)fseis.(4)fminsidefhinsideHandLESCAL(Ksi)Calculations-2.01-1.777.337.8216.0716.08-10.76-10.0240.9440.649.5410.06LESCALrunsontheHoneywell 66/60system.Notes(3)and(4)indicatedirections ofseismicrebars.


==References:==
==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.
(1)Duchon,N.B.,"Analysis ofReinforced ConcreteMembraneSubjecttoTensionandShear,"ACIJournal,September 1972,pp.578-583.
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
SB1&2FSARTABLE3F-9SAG054(RESPONSE ENVELOPE)
SAG054isapost-processing programforSTARDYNEyhichisusedinseismicanalysisTheprogramspreadsthepeaksoftheamplified responsespectracreatedbySAG058(SeeTable3F-l)byapredetermined amountandtabulates theordinates andabscissas oftheresulting curve.Verification ofthisprogramisaccomplished byvisualinspection ofthegraphical outputtoinsurethattherawdatahas,infact,beenenveloped.
SAG054runsontheCDCCYBER-175 svstem.
I<tSYM.Ir----I(0)FINITEELEMENT
(-.2607)-.{R-STRESS)x 10psi(+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)CALCULATED STRESSESANALYSISOFTHICK-WALLED CYLINDERUNDERINTERNALPRESSURE


==REFERENCE:==
==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}}
 
GALLAGHER, R.H.,FINITEELEMENTANALYSIS, PRENTICE-HALL/INC.
1975.FIGURE11.5,PG.317PUBLICSERVICECOMPANYOFNEWHAMPSHIRE SAG001SAMPLEPROBLEMNO.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)
ZPUBLICSERVICECOMPANYOFNEWHAMPSHIRE SAG001SAMPLEPROBLEMNO.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!)lN3WOW PUBLICSERVICECOMPANYOFNEWHAMPSHIRE SEABROOKSTATION-UNITS1&2FINALSAFETYANALYSISREPORTSAG001SAMPLEPROBLEMNO.2MERIDIONAL MOMENTIFIGURE3.F-3}}

Revision as of 07:11, 30 June 2018

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
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SEABROOKUPDATEDFSARAPPENDIX3DPROCEDURE FORCALCULATING ELASTO-PLASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYENERGYBALANCEMETHODTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.

SB1&2FSARAmendment 56NovemberlQHSAsimplified mathematical modelasonthenextpagecanbeusedforelascic-plastic designofpiperestraints.

Anenergybalanceapproachhasbeenusedtoformulate thecalculations fordetermining theplasticdeformation intherestraints.

Inapplyingtheplasticdeformation designforrestraints, theregulatory guidesrequirethateitheroneofthefollowing upperbounddesignlimitsformetallicductilematerials bemet..(3)50%oftheminimumultimateuniformstrain(thestrainatthemaximumstressofanengineering stress-strain curvebasedonactualmaterialtestsfortherestraint),

'or(b)50%0:the percentelongation asspecified inanapplicable ASHE.ASTH,etc.Code,specification, orstandardwhendemonstrated tobelessthan50%oftheminimumultimateuniformstrainbasedonrepresentative testresults.3D-l S1&2FSARSimolified approachfor elasto-?lastic i\mendnlent 5GNovember19R5Iftherestraint is togointotheplasticregion,thenthe restraint deflection, dcax*consistofanela3tic anda portionassho.wnbelov.(Figure1.0)Restraint DeflectionFigure1.0-Idealized Restrain:

where,deRestraint elasticdeflection atyieldstressdmaxMaximumallowable restraint deflection RpMaximumrestraint resistance Rp=kedekeRestraint elasticstructural stiffness If'F'denotestheappliedforcingFunction(i.e.*aloadincaseofapipebreak)and'h'denotesthegap thepipingandtherestraint, anenergybalancerelationforthiscasegives)(see 2.0).-Rp(dcax-de)23D-2 SB1&2FSARAmendment 56November1985Ca)BeforeImpacth(b)AfterImpactFigure2.0EnergybalanceAnalvsisHodelRearranging, (Ro-F)2TIlerefore, dmax=122Fh.;.Rpde2(Rp-F)(1)Theaboveformulation canbefurthersinlplif:ed in2Fhismuchlarg-:rth2nTherefore, assuming.

Rpde<<2FhEquation(1)gives,dmax:(Rp-F)(2)Afterdetermining Cmax.eitherbyequation(1)orequation(2)above(asapplicable),

theresulting straininthemembershouldbecalculated 3ndshouldbecheckedagainstthecriteriagiveinpage1.

Foruniaxialmembers,thestraineistakentobeequaltoLyhereListheoriginallengthoftherestraint member.3D-3 SB1&2FSARPages4and5DeletedinAmendment 56Amendment 56November1985 SEABROOKUPDATEDFSARAPPENDIX3EPROCEDURE FORCALCULATING ELASTO-PLASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYEQUIVALENT STATICANALYSISMETHODTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.

SB1&.2FSARAPPENDIX3EPROCEDURE FORCALCULATING ELASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYEQUIVALENT STATICANALYSISMETHODPREPAREDBY:REVIDVEDBY::1/.1.11}1F.JANMECHANICAL

.'lliALYSIS11/29/77R.F.PERRY.{l.

A..'IALYS ISGROCP Inordertoevaluatetheresponseofanelastically designedpipewhip toapipebreakloadbyusingtheequivalent staticanalysisapproach, the loadfactorassociated withtheapplicable forcingfunction'and theclearance (gap)becweenthepipeandtherestraint hastobe Asimplified mathematical modelasshowntheoextpage,'beusedto thedynamicloadfactor.Sincethepipesizeeffectsarealreadybeing.reflected inthemagnitude ofthepipebreakload,thepipesizealoneisnotconsidered againasamodelparameter.

The loadfactor(DL'F)*thusdetermined isusedtocalculate therestraint:

load(R)asfollows:R*a XDLF.-where:{1.26forsteam-saturated waterct.:2.0forsubcooled non-flashingu.s.NRCStandardReviewPlan,3.6.2(III)(2)(c)(42]P*Operating PressureA*PipeBreakAreaAseriesof curvesfordetermining therestraint loadsforsteam-saturated waterorsteam-water mixturesaregiveninPages3-14. AS1J1PLEMODELFOR LOADFACTORBysubstituting (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)dstcRestraint deflection forstatically appliedFd*Maximumrestraint deflectionh-Gapsizek*Restraint stiffness DLFCDynamicloadfactor )*I*,*'1C*,***,.,i,.I*,"1rf2.J*,*.,*t10'P-AINLBS.=O.f200INCHES FORELRSTIlPIPEWHIPRES (Applicable nlyto waeror rmixtures, 21.26))**.7.tleT FORElRSTIPIPE RESRRINTS.(Applicable Inlytosteam1saturated Yaerorsteam-wat r

1.26)GRP=0.2500INCHESJ'.,*,.'1rf*,""'1rJINLBS.**"'1cJP*AJ*,*,.'1ct 2**

4I*,*'10'.:'c'."*'1O*INLBS.GRP=0.5000INCHESJ***,..04P*R FORELASTl'PIPEWHIP (Applicable nlyto.steamr!saturated waerorsteam-wat r

  • 1.26).)*I*"'1I.10= GRP=0.7500lNCHES FORELASTIPIPEWHIPRESRAINTS.(Applicable nlytosteam*saturated.wa erorsteam-wat rmixtures,a*1.26)J4I*,,'10'2.J*"*,.'1rtINLBS.J***.,.'1O*P*R

CURVESFOR PI?EWHIPRESRRtNTS.(Applicable 6nlytostearn'saturated water,orsteam-W8lrr

  • 1.26)-7-*,*"',rjINLBS.=1.0000INCHES)***,."0'P*R:*I*,*'1cr CUFOR PIPE (Applicabletosteam+saturated waerorsteam-wat' rmixtures, l-1.26)4*,.,.'1rJINLBS.=1.2500INCHES ICCU.YESFOR1PIWHIPRESINTS.I tosteacsaturated waterorsteam-walermixtures,
  • 1.26)GRP=1.5000INCHESJ4 J,*"'1O*P*)*I*1,'iltINLBS.J***,1'1O*)4,.,tllC ,I,4,4,*to',*&47.'I05INlBS.GRP=1.7500INCHES,*I*,8'1O*P*APARAMETRIC CUVESFORELASTIPIPEWHIPRESRRINTS.(Applicable nlytosteam waerorsteam-wat rmixtures,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*APRRRHETR1C CUV£SFORELRSTIPIPERES (Applicable onlytosteamsaturated waerorsteam-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=2.5000INCHES CUYESFORELASTIPIPEWHIPRESRAINTS.(Applicable nlytosteamsaturated walerorsteam-wat r

e1.26)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.PRRRMETRIC FORElRST}PIPEWHIPRESRAINTS.(Applicable bnlytosteam*saturated wae+orsteam-watbr

  • 1.26)I..v,-.------..,...------.,..--------;------,10000c:1000coetoHGOIlOOIDOO".tOO211tOl FOR PIPEWHIP (Applicable onlyto orsteam-watir
  • 1.26)=0.0650lNCHESJ.***,t.O*P)(A***,.'1ctINLBS.J**""lcfJ*""'1 SEABROOKUPDATEDFSARAPPENDIX3FVERIFICATION OFCOMPUTERPROGRAMSUSEDFORSTRUCTURAL ANALYSISANDDESIGNTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.

SB1&2FSARAPPENDIX3FVERIFICATION OFCOMPUTERPROGRAMSUSEDFORSTRUCTURAL ANALYSISANDDESIGNAmendment 54February1985Computerprogramsusedforstructural analysisanddesignhavebeenverifiedaccording tothecriteriadescribed intheUSNRCStandardReviewPlan3.8.1,SectionII-4(e).(a)Thefollowing computerprogramsarerecognized inthepublicdomain,andhavehadsufficient historytojustifytheirapplicability andvaliditywithoutfurtherdemonstration:

HardwareSourceSTARDYNECDCCDC(l)MARC-CDCCDCCDC(l)STRU-PAl<

CDCCDC(l)SystemProfessional CDCCDC(l)ANSYSCDCCDC(l)STRUDLUCCELPSDI(2)UEMENUUCCELUCCEL(3)(1)CDC-(2)PSDI-(3)UCCEL-ControlDataCorporation P.O.Box0,HQWOSHMinneapolis, Minnesota 55440ProgramsforStructural Design,Inc.14StoryStreetCambridge, Massachusetts 02138UCCELCorporation P.O.Box84028Dallas,Texas75284(b)Thefollowing computerprogramshavebeenverifiedbysolvingtestproblemswithasimilarandindependently-written andrecognized programinthepublicdomain:SAG058(Response Spectra)3F-l SB1&2FSARAmendment 54February1985Asummaryofcomparison resultsisshown1nTable3F-l.AX2(Axisymmetric ShellProgram)Averification manualcomparing AX2withresultsobtainedfromeitherANSYSorBOSOR4(Lockhead MissileandSpaceCompany-PaloAlto,CA)canbeobtainedfromPittsburgh

-DesMoinesCorporation, 3400GrandAvenue,NevilleIsland,Pittsburgh, PA15225(c)Thefollowing computerprogramshavebeenverifiedbycomparison withanalytical resultspublished intechnical literature:

SAG001SAGO10(WILSON1)(WILSON2,DYN)Summaries ofcomparison resultsareshowninTables3F-2and3F-3,respectively.

(d)Thefollowing computerprogramshavebeenverifiedbycomparison withhandcalculations fortestproblemswhicharerepresentative ofthetypeusedinactualanalyses:

Asummaryofcomparison resultsisshowninTables3F-4through3F-8.SAG008SAGOI7SAG024SAG025PM-9IO*PM-906(TAPAS)(FOUREXP)(MMIC)(SECTION)(LESCAL)(STRAP)I54(e)Thefollowing computerprogramsareverifiedbyinspection ofthegraphical outputdata.SAG054(Response Envelope)

Atypicalverification exampleispresented inTable3F-9.*Documentation ofSTRAPisavailable intheFinalSafetyAnalysiskeportfortheCarolinaPowerandLightCo.,Brunswick 1&2,USNRCDocketNos.50-324and50-325.3F-2 SB1&2FSARTABLE3F-lSAG058(RESPONSE SPECTRA)SAG058(1)isverifiedagainstSTARDYNE, sub-routine DYNRE5.TheinputT/Hisof22secondduration, withatimeintervalof0.01secondsandamaximumacceleration ofI.Dg.SpectralAcceleration (g)Frequency 0.5%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-housecomputerprogramrunontheControlDataCorporation CYBER-175 andisusedasa toSTARDYNEprogram.

SB1&2FSARTABLE3F-2SAG001(WILSON1)Thefollowing isacomparison oftheresultsfromSAGOOIwithresultsobtainedfrompublished technical literature.

SAGOOIrunsontheHoneywell 66/60systemwiththeGeOSoperating system.SamnleProblemNo.1Analysisofathick-walled cylindersubjected toaninternalpressure.

Reference

-Gallagher, R.H.,FiniteElementAnalysis, Figure11.5)pg.317,Prentice-Hall, Inc.,1975.Comparison ofthetheoretical solutionwiththeWILSON1solutionisshownonFigure3F-lfortheradialstressandthehoopstress.SampleProblemNo.2Analysisofacylindrical shell,fixedatbothendsandsubjected toaninternalpressure.

Reference

-Timoshenko, S.,Woinowsky-Krieger,S.,TheoryofPlatesandShells,SecondEdition,pg.475,McGraw-Hill, 1959.Comparison ofthetheore*tical solutionwiththeWILSON1solutionisshownonFigures3F-2andfortheradialshearandmeridional moment,respectively.

SB1&2FSARTABLE3F-3SAG010(WILSON2,DYN)TheoriginalversionofSAGOla,"DynamicStressAnalysisofAxisymmetric Structures UnderArbitrary Loading,"

writtenbyGhoshandWilsonwasrevisedbyUE&CinSeptember, 1975.Theprogramisdistributed inthepublicdomainbytheEarthquake Engineering ResearchCenter,University ofCalifornia,

Berkeley, California.

Theprogramhasbeenverifiedagainstaseriesofproblemswhoseresultsarepublished intechnical literature.

Documentation ofthisverification iscontained inthereportEERC69-10whichcanbeobtainedfromtheEarthquake Engineering ResearchCenter.SAGOlaisrunontheHoneywell 66/60System.

SB1&2FSARTABLE3F-4SAGOOa(TAPAS)Thefollowing isacomparison oftheresultsfromSAG008,whichcomputesthetemperature distribution throughplaneandaxisymmetric solids,withhandcalculations.

Thesampleresultsareforthetemperature distribution throughthethickness ofahemispherical concretedomewhichis42inchesthickandsubjectto1200Finsideand(-)lOOFoutside.ElementNo.724848972109612201344SAGOoa(l)

(OF)110.3888.8965.3342.1219.26(-)1.04HandCalculation (OF@MidPt.ofElem.)110.714389.04865.83342.61919.405(-)0.7143 SAGOOBrunsontheHoneywell 66/60system

References:

(1)Wilson,E.L.,Nickell,R.E.,"Application oftheFiniteElement,"

JournalofNuclearEngineering andDesign,4,1966.

SB1&2FSARTABLE3F-5SAGO!7(FOUREXP)

Amendment 56November1985Thefollowing isaverification ofSAGOl7withhandcalculations forarbitrary loadingdistribution whichisanevenfunctionandcanbeexpandedusingacosineFourierSeries.Theperiodic*function is,£(6)=-ne<01LaQ<8S.1TJComparison ofFourierCoefficients:

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{,SAGOI7runsontheHoneywell 66/60syst.em.

References:

(1)TheFouriercoefficients arecomputedforadigitized functionbyarecursive technique described inMathematical MethodsforDigitalComputers, byRolstenandWilfsJohnWileyandSons,NewYork,1960,Chapter24.Thesolutiontechnique isfromsubroutine FORIIinthe.IBMScientific Subroutine package.TheprogramisrunontheHoneywell 66/60system.(2)Wylie,C.R;,AdvancedEngineering Mathematics, 4thEd.,McGraw-Hill, 1975.

SB1&2FSARTABLE3F-6SAG024(MMIC)Thefollowing isacomparison oftheresultsofhandcalculations withSAG024fortheweightofatypciallumpedmasspointinladynamicmodelofashearbuilding.

Parameter SAG024(1)XcM(X-Coordinate oftheCenterofMass)0-ft.26.19YCM(Y-Coordinate oftheCenterofMass)-ft.0.08WT(TotalWeightofMassPoint)-Kips1444IMX(RotaryWeightMomentofInertiaaboutX-Axis)K-ft2162,323IMY(RotaryWeightMomentofInertiaaboutY-Axis)K-ft2379,552IMZ(RotaryWeightMomentofInertiaaboutZ-Axis)K-ft2470,152HandCalculation 26.190.081444162,320379,550470,150SAG024runsontheHoneywell 66/60system.

Reference:

(1)Bear,F.P.andJohnston, R.E.,Jr.,VectorMechanics

'forEngineers:

Staticand:DYnamics, McGraw-Hill t1962,pps.343-347.

SB1&2FSARTABLE3F-7SAG025(SECTION)

Thefollo\Jing isacomparison oftheresultsofhandcalculations withSAG025forasystemofresisting structural elementsbetweenfloorsinatypcialshearbuilding.

SAG025HandCalculations XeR(X-Coordinate ofCenterofRigidity)

-ft.26.326.257YCR(Y-Coordinate ofCenterofRigidity)

-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(Torsional Constant)

-ft.117,000117,470SAG025runsontheHoneywell 66/60system.

SB1&2FSARTABLE3F-8(Sheet1of2)PM-910(LESCAL)Amendment 56November1985Thefollowing isacomparison oftheresultsfromtheLESCALcomputerprogramwithhandcalculations.

LESCALcalculates thestressesandstrainsinrebarsand/orconcreteinaccordance withthecriteriasetforthinSubarticle3511.1ofASMESectionIII,DivisionII.Thesectionisconcretereinforced withhorizontal, verticaland/ordiagonalrebars,subjected toaxialforceandmomentonaverticalandhorizontal faceandin-planeshear.Wheninplaneshearforcesare"included, asolutionisobtainedbysolvingDuchon'sequations(l).

5&.HandLoadCondition Parameter LESCAL(Ksi)Calculations I5fD.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.25Eo fmoutside-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)Amendment S6November1985LoadCondition D+l.25Pa+l.25Eo Applie,d@c.g.ofRebarParameter fmoutsidefhoutsidefseis.(3)fseis.(4)fminsidefhinsideHandLESCAL(Ksi)Calculations-2.01-1.777.337.8216.0716.08-10.76-10.0240.9440.649.5410.06LESCALrunsontheHoneywell 66/60system.Notes(3)and(4)indicatedirections ofseismicrebars.

References:

(1)Duchon,N.B.,"Analysis ofReinforced ConcreteMembraneSubjecttoTensionandShear,"ACIJournal,September 1972,pp.578-583.

SB1&2FSARTABLE3F-9SAG054(RESPONSE ENVELOPE)

SAG054isapost-processing programforSTARDYNEyhichisusedinseismicanalysisTheprogramspreadsthepeaksoftheamplified responsespectracreatedbySAG058(SeeTable3F-l)byapredetermined amountandtabulates theordinates andabscissas oftheresulting curve.Verification ofthisprogramisaccomplished byvisualinspection ofthegraphical outputtoinsurethattherawdatahas,infact,beenenveloped.

SAG054runsontheCDCCYBER-175 svstem.

I<tSYM.Ir----I(0)FINITEELEMENT

(-.2607)-.{R-STRESS)x 10psi(+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)CALCULATED STRESSESANALYSISOFTHICK-WALLED CYLINDERUNDERINTERNALPRESSURE

REFERENCE:

GALLAGHER, R.H.,FINITEELEMENTANALYSIS, PRENTICE-HALL/INC.

1975.FIGURE11.5,PG.317PUBLICSERVICECOMPANYOFNEWHAMPSHIRE SAG001SAMPLEPROBLEMNO.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)

ZPUBLICSERVICECOMPANYOFNEWHAMPSHIRE SAG001SAMPLEPROBLEMNO.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!)lN3WOW PUBLICSERVICECOMPANYOFNEWHAMPSHIRE SEABROOKSTATION-UNITS1&2FINALSAFETYANALYSISREPORTSAG001SAMPLEPROBLEMNO.2MERIDIONAL MOMENTIFIGURE3.F-3 SEABROOKUPDATEDFSARAPPENDIX3DPROCEDURE FORCALCULATING ELASTO-PLASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYENERGYBALANCEMETHODTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.

SB1&2FSARAmendment 56NovemberlQHSAsimplified mathematical modelasonthenextpagecanbeusedforelascic-plastic designofpiperestraints.

Anenergybalanceapproachhasbeenusedtoformulate thecalculations fordetermining theplasticdeformation intherestraints.

Inapplyingtheplasticdeformation designforrestraints, theregulatory guidesrequirethateitheroneofthefollowing upperbounddesignlimitsformetallicductilematerials bemet..(3)50%oftheminimumultimateuniformstrain(thestrainatthemaximumstressofanengineering stress-strain curvebasedonactualmaterialtestsfortherestraint),

'or(b)50%0:the percentelongation asspecified inanapplicable ASHE.ASTH,etc.Code,specification, orstandardwhendemonstrated tobelessthan50%oftheminimumultimateuniformstrainbasedonrepresentative testresults.3D-l S1&2FSARSimolified approachfor elasto-?lastic i\mendnlent 5GNovember19R5Iftherestraint is togointotheplasticregion,thenthe restraint deflection, dcax*consistofanela3tic anda portionassho.wnbelov.(Figure1.0)Restraint DeflectionFigure1.0-Idealized Restrain:

where,deRestraint elasticdeflection atyieldstressdmaxMaximumallowable restraint deflection RpMaximumrestraint resistance Rp=kedekeRestraint elasticstructural stiffness If'F'denotestheappliedforcingFunction(i.e.*aloadincaseofapipebreak)and'h'denotesthegap thepipingandtherestraint, anenergybalancerelationforthiscasegives)(see 2.0).-Rp(dcax-de)23D-2 SB1&2FSARAmendment 56November1985Ca)BeforeImpacth(b)AfterImpactFigure2.0EnergybalanceAnalvsisHodelRearranging, (Ro-F)2TIlerefore, dmax=122Fh.;.Rpde2(Rp-F)(1)Theaboveformulation canbefurthersinlplif:ed in2Fhismuchlarg-:rth2nTherefore, assuming.

Rpde<<2FhEquation(1)gives,dmax:(Rp-F)(2)Afterdetermining Cmax.eitherbyequation(1)orequation(2)above(asapplicable),

theresulting straininthemembershouldbecalculated 3ndshouldbecheckedagainstthecriteriagiveinpage1.

Foruniaxialmembers,thestraineistakentobeequaltoLyhereListheoriginallengthoftherestraint member.3D-3 SB1&2FSARPages4and5DeletedinAmendment 56Amendment 56November1985 SEABROOKUPDATEDFSARAPPENDIX3EPROCEDURE FORCALCULATING ELASTO-PLASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYEQUIVALENT STATICANALYSISMETHODTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.

SB1&.2FSARAPPENDIX3EPROCEDURE FORCALCULATING ELASTICALLY DESIGNEDPIPEWHIPRESTRAINT LOADSBYEQUIVALENT STATICANALYSISMETHODPREPAREDBY:REVIDVEDBY::1/.1.11}1F.JANMECHANICAL

.'lliALYSIS11/29/77R.F.PERRY.{l.

A..'IALYS ISGROCP Inordertoevaluatetheresponseofanelastically designedpipewhip toapipebreakloadbyusingtheequivalent staticanalysisapproach, the loadfactorassociated withtheapplicable forcingfunction'and theclearance (gap)becweenthepipeandtherestraint hastobe Asimplified mathematical modelasshowntheoextpage,'beusedto thedynamicloadfactor.Sincethepipesizeeffectsarealreadybeing.reflected inthemagnitude ofthepipebreakload,thepipesizealoneisnotconsidered againasamodelparameter.

The loadfactor(DL'F)*thusdetermined isusedtocalculate therestraint:

load(R)asfollows:R*a XDLF.-where:{1.26forsteam-saturated waterct.:2.0forsubcooled non-flashingu.s.NRCStandardReviewPlan,3.6.2(III)(2)(c)(42]P*Operating PressureA*PipeBreakAreaAseriesof curvesfordetermining therestraint loadsforsteam-saturated waterorsteam-water mixturesaregiveninPages3-14. AS1J1PLEMODELFOR LOADFACTORBysubstituting (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)dstcRestraint deflection forstatically appliedFd*Maximumrestraint deflectionh-Gapsizek*Restraint stiffness DLFCDynamicloadfactor )*I*,*'1C*,***,.,i,.I*,"1rf2.J*,*.,*t10'P-AINLBS.=O.f200INCHES FORELRSTIlPIPEWHIPRES (Applicable nlyto waeror rmixtures, 21.26))**.7.tleT FORElRSTIPIPE RESRRINTS.(Applicable Inlytosteam1saturated Yaerorsteam-wat r

1.26)GRP=0.2500INCHESJ'.,*,.'1rf*,""'1rJINLBS.**"'1cJP*AJ*,*,.'1ct 2**

4I*,*'10'.:'c'."*'1O*INLBS.GRP=0.5000INCHESJ***,..04P*R FORELASTl'PIPEWHIP (Applicable nlyto.steamr!saturated waerorsteam-wat r

  • 1.26).)*I*"'1I.10= GRP=0.7500lNCHES FORELASTIPIPEWHIPRESRAINTS.(Applicable nlytosteam*saturated.wa erorsteam-wat rmixtures,a*1.26)J4I*,,'10'2.J*"*,.'1rtINLBS.J***.,.'1O*P*R

CURVESFOR PI?EWHIPRESRRtNTS.(Applicable 6nlytostearn'saturated water,orsteam-W8lrr

  • 1.26)-7-*,*"',rjINLBS.=1.0000INCHES)***,."0'P*R:*I*,*'1cr CUFOR PIPE (Applicabletosteam+saturated waerorsteam-wat' rmixtures, l-1.26)4*,.,.'1rJINLBS.=1.2500INCHES ICCU.YESFOR1PIWHIPRESINTS.I tosteacsaturated waterorsteam-walermixtures,
  • 1.26)GRP=1.5000INCHESJ4 J,*"'1O*P*)*I*1,'iltINLBS.J***,1'1O*)4,.,tllC ,I,4,4,*to',*&47.'I05INlBS.GRP=1.7500INCHES,*I*,8'1O*P*APARAMETRIC CUVESFORELASTIPIPEWHIPRESRRINTS.(Applicable nlytosteam waerorsteam-wat rmixtures,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*APRRRHETR1C CUV£SFORELRSTIPIPERES (Applicable onlytosteamsaturated waerorsteam-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=2.5000INCHES CUYESFORELASTIPIPEWHIPRESRAINTS.(Applicable nlytosteamsaturated walerorsteam-wat r

e1.26)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.PRRRMETRIC FORElRST}PIPEWHIPRESRAINTS.(Applicable bnlytosteam*saturated wae+orsteam-watbr

  • 1.26)I..v,-.------..,...------.,..--------;------,10000c:1000coetoHGOIlOOIDOO".tOO211tOl FOR PIPEWHIP (Applicable onlyto orsteam-watir
  • 1.26)=0.0650lNCHESJ.***,t.O*P)(A***,.'1ctINLBS.J**""lcfJ*""'1 SEABROOKUPDATEDFSARAPPENDIX3FVERIFICATION OFCOMPUTERPROGRAMSUSEDFORSTRUCTURAL ANALYSISANDDESIGNTheinformation contained inthisappendixwasnotrevised,buthasbeenextracted fromtheoriginalFSARandisprovidedforhistorical information.

SB1&2FSARAPPENDIX3FVERIFICATION OFCOMPUTERPROGRAMSUSEDFORSTRUCTURAL ANALYSISANDDESIGNAmendment 54February1985Computerprogramsusedforstructural analysisanddesignhavebeenverifiedaccording tothecriteriadescribed intheUSNRCStandardReviewPlan3.8.1,SectionII-4(e).(a)Thefollowing computerprogramsarerecognized inthepublicdomain,andhavehadsufficient historytojustifytheirapplicability andvaliditywithoutfurtherdemonstration:

HardwareSourceSTARDYNECDCCDC(l)MARC-CDCCDCCDC(l)STRU-PAl<

CDCCDC(l)SystemProfessional CDCCDC(l)ANSYSCDCCDC(l)STRUDLUCCELPSDI(2)UEMENUUCCELUCCEL(3)(1)CDC-(2)PSDI-(3)UCCEL-ControlDataCorporation P.O.Box0,HQWOSHMinneapolis, Minnesota 55440ProgramsforStructural Design,Inc.14StoryStreetCambridge, Massachusetts 02138UCCELCorporation P.O.Box84028Dallas,Texas75284(b)Thefollowing computerprogramshavebeenverifiedbysolvingtestproblemswithasimilarandindependently-written andrecognized programinthepublicdomain:SAG058(Response Spectra)3F-l SB1&2FSARAmendment 54February1985Asummaryofcomparison resultsisshown1nTable3F-l.AX2(Axisymmetric ShellProgram)Averification manualcomparing AX2withresultsobtainedfromeitherANSYSorBOSOR4(Lockhead MissileandSpaceCompany-PaloAlto,CA)canbeobtainedfromPittsburgh

-DesMoinesCorporation, 3400GrandAvenue,NevilleIsland,Pittsburgh, PA15225(c)Thefollowing computerprogramshavebeenverifiedbycomparison withanalytical resultspublished intechnical literature:

SAG001SAGO10(WILSON1)(WILSON2,DYN)Summaries ofcomparison resultsareshowninTables3F-2and3F-3,respectively.

(d)Thefollowing computerprogramshavebeenverifiedbycomparison withhandcalculations fortestproblemswhicharerepresentative ofthetypeusedinactualanalyses:

Asummaryofcomparison resultsisshowninTables3F-4through3F-8.SAG008SAGOI7SAG024SAG025PM-9IO*PM-906(TAPAS)(FOUREXP)(MMIC)(SECTION)(LESCAL)(STRAP)I54(e)Thefollowing computerprogramsareverifiedbyinspection ofthegraphical outputdata.SAG054(Response Envelope)

Atypicalverification exampleispresented inTable3F-9.*Documentation ofSTRAPisavailable intheFinalSafetyAnalysiskeportfortheCarolinaPowerandLightCo.,Brunswick 1&2,USNRCDocketNos.50-324and50-325.3F-2 SB1&2FSARTABLE3F-lSAG058(RESPONSE SPECTRA)SAG058(1)isverifiedagainstSTARDYNE, sub-routine DYNRE5.TheinputT/Hisof22secondduration, withatimeintervalof0.01secondsandamaximumacceleration ofI.Dg.SpectralAcceleration (g)Frequency 0.5%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-housecomputerprogramrunontheControlDataCorporation CYBER-175 andisusedasa toSTARDYNEprogram.

SB1&2FSARTABLE3F-2SAG001(WILSON1)Thefollowing isacomparison oftheresultsfromSAGOOIwithresultsobtainedfrompublished technical literature.

SAGOOIrunsontheHoneywell 66/60systemwiththeGeOSoperating system.SamnleProblemNo.1Analysisofathick-walled cylindersubjected toaninternalpressure.

Reference

-Gallagher, R.H.,FiniteElementAnalysis, Figure11.5)pg.317,Prentice-Hall, Inc.,1975.Comparison ofthetheoretical solutionwiththeWILSON1solutionisshownonFigure3F-lfortheradialstressandthehoopstress.SampleProblemNo.2Analysisofacylindrical shell,fixedatbothendsandsubjected toaninternalpressure.

Reference

-Timoshenko, S.,Woinowsky-Krieger,S.,TheoryofPlatesandShells,SecondEdition,pg.475,McGraw-Hill, 1959.Comparison ofthetheore*tical solutionwiththeWILSON1solutionisshownonFigures3F-2andfortheradialshearandmeridional moment,respectively.

SB1&2FSARTABLE3F-3SAG010(WILSON2,DYN)TheoriginalversionofSAGOla,"DynamicStressAnalysisofAxisymmetric Structures UnderArbitrary Loading,"

writtenbyGhoshandWilsonwasrevisedbyUE&CinSeptember, 1975.Theprogramisdistributed inthepublicdomainbytheEarthquake Engineering ResearchCenter,University ofCalifornia,

Berkeley, California.

Theprogramhasbeenverifiedagainstaseriesofproblemswhoseresultsarepublished intechnical literature.

Documentation ofthisverification iscontained inthereportEERC69-10whichcanbeobtainedfromtheEarthquake Engineering ResearchCenter.SAGOlaisrunontheHoneywell 66/60System.

SB1&2FSARTABLE3F-4SAGOOa(TAPAS)Thefollowing isacomparison oftheresultsfromSAG008,whichcomputesthetemperature distribution throughplaneandaxisymmetric solids,withhandcalculations.

Thesampleresultsareforthetemperature distribution throughthethickness ofahemispherical concretedomewhichis42inchesthickandsubjectto1200Finsideand(-)lOOFoutside.ElementNo.724848972109612201344SAGOoa(l)

(OF)110.3888.8965.3342.1219.26(-)1.04HandCalculation (OF@MidPt.ofElem.)110.714389.04865.83342.61919.405(-)0.7143 SAGOOBrunsontheHoneywell 66/60system

References:

(1)Wilson,E.L.,Nickell,R.E.,"Application oftheFiniteElement,"

JournalofNuclearEngineering andDesign,4,1966.

SB1&2FSARTABLE3F-5SAGO!7(FOUREXP)

Amendment 56November1985Thefollowing isaverification ofSAGOl7withhandcalculations forarbitrary loadingdistribution whichisanevenfunctionandcanbeexpandedusingacosineFourierSeries.Theperiodic*function is,£(6)=-ne<01LaQ<8S.1TJComparison ofFourierCoefficients:

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{,SAGOI7runsontheHoneywell 66/60syst.em.

References:

(1)TheFouriercoefficients arecomputedforadigitized functionbyarecursive technique described inMathematical MethodsforDigitalComputers, byRolstenandWilfsJohnWileyandSons,NewYork,1960,Chapter24.Thesolutiontechnique isfromsubroutine FORIIinthe.IBMScientific Subroutine package.TheprogramisrunontheHoneywell 66/60system.(2)Wylie,C.R;,AdvancedEngineering Mathematics, 4thEd.,McGraw-Hill, 1975.

SB1&2FSARTABLE3F-6SAG024(MMIC)Thefollowing isacomparison oftheresultsofhandcalculations withSAG024fortheweightofatypciallumpedmasspointinladynamicmodelofashearbuilding.

Parameter SAG024(1)XcM(X-Coordinate oftheCenterofMass)0-ft.26.19YCM(Y-Coordinate oftheCenterofMass)-ft.0.08WT(TotalWeightofMassPoint)-Kips1444IMX(RotaryWeightMomentofInertiaaboutX-Axis)K-ft2162,323IMY(RotaryWeightMomentofInertiaaboutY-Axis)K-ft2379,552IMZ(RotaryWeightMomentofInertiaaboutZ-Axis)K-ft2470,152HandCalculation 26.190.081444162,320379,550470,150SAG024runsontheHoneywell 66/60system.

Reference:

(1)Bear,F.P.andJohnston, R.E.,Jr.,VectorMechanics

'forEngineers:

Staticand:DYnamics, McGraw-Hill t1962,pps.343-347.

SB1&2FSARTABLE3F-7SAG025(SECTION)

Thefollo\Jing isacomparison oftheresultsofhandcalculations withSAG025forasystemofresisting structural elementsbetweenfloorsinatypcialshearbuilding.

SAG025HandCalculations XeR(X-Coordinate ofCenterofRigidity)

-ft.26.326.257YCR(Y-Coordinate ofCenterofRigidity)

-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(Torsional Constant)

-ft.117,000117,470SAG025runsontheHoneywell 66/60system.

SB1&2FSARTABLE3F-8(Sheet1of2)PM-910(LESCAL)Amendment 56November1985Thefollowing isacomparison oftheresultsfromtheLESCALcomputerprogramwithhandcalculations.

LESCALcalculates thestressesandstrainsinrebarsand/orconcreteinaccordance withthecriteriasetforthinSubarticle3511.1ofASMESectionIII,DivisionII.Thesectionisconcretereinforced withhorizontal, verticaland/ordiagonalrebars,subjected toaxialforceandmomentonaverticalandhorizontal faceandin-planeshear.Wheninplaneshearforcesare"included, asolutionisobtainedbysolvingDuchon'sequations(l).

5&.HandLoadCondition Parameter LESCAL(Ksi)Calculations I5fD.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.25Eo fmoutside-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)Amendment S6November1985LoadCondition D+l.25Pa+l.25Eo Applie,d@c.g.ofRebarParameter fmoutsidefhoutsidefseis.(3)fseis.(4)fminsidefhinsideHandLESCAL(Ksi)Calculations-2.01-1.777.337.8216.0716.08-10.76-10.0240.9440.649.5410.06LESCALrunsontheHoneywell 66/60system.Notes(3)and(4)indicatedirections ofseismicrebars.

References:

(1)Duchon,N.B.,"Analysis ofReinforced ConcreteMembraneSubjecttoTensionandShear,"ACIJournal,September 1972,pp.578-583.

SB1&2FSARTABLE3F-9SAG054(RESPONSE ENVELOPE)

SAG054isapost-processing programforSTARDYNEyhichisusedinseismicanalysisTheprogramspreadsthepeaksoftheamplified responsespectracreatedbySAG058(SeeTable3F-l)byapredetermined amountandtabulates theordinates andabscissas oftheresulting curve.Verification ofthisprogramisaccomplished byvisualinspection ofthegraphical outputtoinsurethattherawdatahas,infact,beenenveloped.

SAG054runsontheCDCCYBER-175 svstem.

I<tSYM.Ir----I(0)FINITEELEMENT

(-.2607)-.{R-STRESS)x 10psi(+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)CALCULATED STRESSESANALYSISOFTHICK-WALLED CYLINDERUNDERINTERNALPRESSURE

REFERENCE:

GALLAGHER, R.H.,FINITEELEMENTANALYSIS, PRENTICE-HALL/INC.

1975.FIGURE11.5,PG.317PUBLICSERVICECOMPANYOFNEWHAMPSHIRE SAG001SAMPLEPROBLEMNO.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)

ZPUBLICSERVICECOMPANYOFNEWHAMPSHIRE SAG001SAMPLEPROBLEMNO.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!)lN3WOW PUBLICSERVICECOMPANYOFNEWHAMPSHIRE SEABROOKSTATION-UNITS1&2FINALSAFETYANALYSISREPORTSAG001SAMPLEPROBLEMNO.2MERIDIONAL MOMENTIFIGURE3.F-3

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