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| number = ML16147A185 | | number = ML16147A185 | ||
| issue date = 04/29/2016 | | issue date = 04/29/2016 | ||
| title = | | title = 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 ... | ||
| author name = | | author name = | ||
| author affiliation = NextEra Energy Seabrook, LLC | | author affiliation = NextEra Energy Seabrook, LLC | ||
| Line 15: | Line 15: | ||
| page count = 37 | | page count = 37 | ||
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{{#Wiki_filter:SEABROOK UPDATED FSAR APPENDIX 3D PROCEDURE FOR CALCULATING ELASTO-PLASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY ENERGY BALANCE METHOD The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information. | |||
SB 1&2 FSAR Amendment 56 November lQHS A simplified mathematical model ason the next page can be used for elascic-plastic design of pipe restraints. | |||
An energy balance approach has been used to formulate the calculations for determining the plastic deformation in the restraints. | |||
In applying the plastic deformation design for restraints, the regulatory guides require that either one of the following upper bound design limits for metallic ductile materials be met..(3)50%of the minimum ultimate uniform strain (the strain at the maximum stress of an engineering stress-strain curve based on actual material tests for the restraint),'or (b)50%0: the percent elongation as specified in an applicable ASHE.ASTH, etc.Code, specification, or standard when demonstrated to be less than 50%of the minimum ultimate uniform strain based on representative test results.3D-l S1&2 FSAR Simolified approach for elasto-?lastic i\mendnlent 5G November 19R5 If the restraint is to go into the plastic region, then the restraint deflection, d cax* consist of an ela3tic and a portion as sho.wn belov.(Figure 1.0)Restraint DeflectionFigure 1.0-Idealized Restrain: | |||
where, de Restraint elastic deflection at yield stress d max Maximum allowable restraint deflection Rp Maximum restraint resistance Rp=ked e k e Restraint elastic structural stiffness If'F'denotes the applied forcing Function (i.e.*aload in case of a pipe break)and'h'denotes the gap the piping and the restraint, an energy balance relation for this case gives)(see 2.0).-Rp (d cax-de)2 3D-2 SB 1&2 FSAR Amendment 56 November 1985 Ca)Before Impact h(b)After Impact Figure 2.0 Energy balance Analvsis Hodel Rearranging, (Ro-F)2 TIlerefore, d max=1 2 2Fh.;.Rpd e 2 (Rp-F)(1)The above formulation can be further sinlplif:ed in 2Fh is much larg-:r th2n Therefore, assuming.Rpd e<<2Fh Equation (1)gives, dmax:(Rp-F)(2)After determining Cmax.either by equation (1)or equation (2)above (as applicable), the resulting strain in the member should be calculated 3nd should be checked against the criteria give in page 1. | |||
For uniaxial members, the strain e is taken to be equal to L yhere L is the original length of the restraint member.3D-3 SB 1&2 FSAR Pages 4 and 5 Deleted in Amendment 56 Amendment 56 November 1985 SEABROOK UPDATED FSAR APPENDIX 3E PROCEDURE FOR CALCULATING ELASTO-PLASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY EQUIVALENT STATIC ANALYSIS METHOD The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information. | |||
SB 1&.2 FSAR APPENDIX 3E PROCEDURE FOR CALCULATING ELASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY EQUIVALENT STATIC ANALYSIS METHOD PREPARED BY: REVIDVED BY::1/.1.11}1 F.JAN MECHANICAL | |||
.'lliALYSIS11/29/77 R.F.PERRY.{l. | |||
A..'IALYS IS GROCP In order to evaluate the response of an elastically designed pipe whip to a pipe break load by using the equivalent static analysis approach, the load factor associated with the applicable forcing function'and the clearance (gap)becween the pipe and the restraint has to be A simplified mathematical model as shown the oext page,' be used to the dynamic load factor.Since the pipe size effects are already being.reflected in the magnitude of the pipe break load, the pipe size alone is not considered again as a model parameter. | |||
The load factor (DL'F)*thus determined is used to calculate the restraint: | |||
load (R)as follows: R*a X DLF.-where:{1.26 for steam-saturated water ct.: 2.0 for subcooled non-flashingu.s.NRC Standard Review Plan, 3.6.2 (III)(2)(c)(42]P*Operating PressureA*Pipe Break Area A series of curves for determining the restraint loads for steam-saturated water or steam-water mixturesare given in Pages3-14. A S1J1PLE MODEL FOR LOAD FACTOR By substituting (3)into (2), we have F(h+d)=1/2{...L\d 2 dstJ F d eS k F(h+d)1/2 kd!From (1).k&..!....d st (1)(2)(3)Fh F.\d--.----L.//#1//F/l/CD..CD Or, (d2 dstJ-2(...!-\-2(-!:""\c 0\d st') DLF d*-z: d st Where, F*Applied Load(Pipe Rupture Load)d st c Restraint deflection for statically applied Fd*Maximum restraint deflectionh-Gap sizek*Restraint stiffness DLF C Dynamic load factor )*I*,*'1 C*,***,., i,.I*,"1 rf 2.J*,*.,*t 1 0'P-A INLBS.=O.f2 00 INCHES FOR ELRSTIl PIPE WHIP RES(Applicable nly to wa er or r mixtures, 2 1.26))**.7.tleT FOR ElRSTI PIPE RES RRINTS.(Applicable I nly to steam1saturated Ya er or steam-wat r 1.26)GRP=0.25 00 INCHES J'.,*,.'1 rf*,""'1 rJ IN LBS.**"'1 cJP*A J*,*,.'1 ct 2** | |||
4I*,*'1 0'.: 'c'."*'1 O*IN LBS.GRP=0.50 00 INCHES J***,..0 4P*R FOR ELASTl'PIPE WHIP(Applicable nly to.steamr!saturated wa er or steam-wat r | |||
*1.26).)*I*"'1I.10= GRP=0.75 00 lNCHES FOR ELASTI PIPE WHIP RES RAINTS.(Applicable nly to steam*saturated.wa er or steam-wat r mixtures ,a*1.26)J 4 I*,,'1 0'2.J*"*,.'1 rt IN LBS.J***.,.'1 O*P*R | |||
CURVES FOR PI?E WHIP RES RRtNTS.(Applicable 6nly to stearn'saturated water , or steam-W8lrr*1.26)-7-*,*"', rj IN LBS.=1.00 00 INCHES)***,." 0'P*R:*I*,*'1 cr CU FOR PIPE(Applicable to steam+saturated wa er or steam-wat' r mixtures, l-1.26)4*,.,.'1 rJ IN LBS.=1.25 00 INCHES IC CU.YES FOR1PIWHIP RESI NTS.I to steac saturated water or steam-wa ler mixtures,*1.26)GRP=1.50 00 INCHES J 4 J,*"'1 O*P*)*I*1,'ilt IN LBS.J***, 1'1 O*)4,., tl lC , I , 4 , 4,*t o',*&4 7.'I 0 5 IN lBS.GRP=1.7500 INCHES ,*I*, 8'1 O*P*A PARAMETRIC CU VES FOR ELASTI PIPE WHIP RES RRINTS.(Applicable nly to steam wa er or steam-wat r mixtures,Q1.26), 4,*,*t 0'1 0'I., 0It#I"')N"0 en CD ,...CD lI)*trl N'b (1)cD ,...CD V)f'I")*U UP'S/IN.100000 enQ),...10000 (,,()V).000* f'I')2000 N b 5 8l e 8 1 O*IN LBS.GRP=2.00 00 INCHES ,I e 7 ,*J 0'P*A PRRRHETR1C CU V£S FOR ELRSTI PIPE RES(Applicable only to steam saturated wa er or steam-wa er | |||
=1.26)J*I*,.e 0'I.-1", N po.0 en CD t-ao V)*C'I")N b (7)CD r-CD\f)I{..,'N I{I'S/IN.100000 N (J)(D-J z"b enr-CD V)fI")N b m CD f"-lOC CD&I).0.." 10 , 0'GAP=2.50 00 INCHES CU YES FOR ELASTI PIPE WHIP RES RAINTS.(Applicable nly to steam saturated waler or steam-wat r e 1.26)J 4**,**I J,*, i*O*S 4 i 87*I 0 6 IP*A IN LBS.I*10**N'b I...11;"1".*00000m-I Z a:: '0000"'000 U)4000 JDOO*2000 1000'iO.00 210 100'0 ***'" C GAP=3.00 00 INCHES J 4**,**0)I ,.I*,*'1 O*).**,*t rt I J 4**,., 1 rfP*R IN LBS.PRRRMETRIC FOR ElRST}PIPE WHIP RES RAINTS.(Applicable bnly to steam*saturated wa e+or steam-watbr | |||
*1.26)I..v,-.------..,...------.,..--------;------, 10000 c: 1000 coeto HGO IlOO IDOO".tOO 211 tOl FOR PIPE WHIP(Applicable only to or steam-watir | |||
*1.26)=0.06 50 lNCHES J.***, t.O*P)(A***,.'1 ct IN LBS.J**""lcf J*""'1 SEABROOK UPDATED FSAR APPENDIX 3F VERIFICATION OF COMPUTER PROGRAMS USED FOR STRUCTURAL ANALYSIS AND DESIGN The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information. | |||
SB 1&2 FSAR APPENDIX 3F VERIFICATION OF COMPUTER PROGRAMS USED FOR STRUCTURAL ANALYSIS AND DESIGN Amendment 54 February 1985 Computer programs used for structural analysis and design have been verified according to the criteria described in the US NRC Standard Review Plan 3.8.1, Section II-4(e).(a)The following computer programs are recognized in the public domain, and have had sufficient history to justify their applicability and validity without further demonstration: | |||
Hardware Source STARDYNE CDC CDC(l)MARC-CDC CDC CDC(l)STRU-PAl<CDC CDC(l)System Professional CDC CDC(l)ANSYS CDC CDC(l)STRUDL UCCEL PSDI(2)UEMENU UCCEL UCCEL(3)(1)CDC-(2)PSDI-(3)UCCEL-Control Data Corporation P.O.Box 0, HQWOSH Minneapolis, Minnesota 55440 Programs for Structural Design, Inc.14 Story Street Cambridge, Massachusetts 02138 UCCEL Corporation P.O.Box 84028 Dallas, Texas 75284 (b)The following computer programs have been verified by solving test problems with a similar and independently-written and recognized program in the public domain: SAG058 (Response Spectra)3F-l SB 1&2 FSAR Amendment 54 February 1985 A summary of comparison results is shown 1n Table 3F-l.AX2 (Axisymmetric Shell Program)A verification manual comparing AX2 with results obtained from either ANSYS or BOSOR4 (Lockhead Missile and Space Company-Palo Alto, CA)can be obtained from Pittsburgh | |||
-Des Moines Corporation, 3400 Grand Avenue, Neville Island, Pittsburgh, PA 15225 (c)The following computer programs have been verified by comparison with analytical results published in technical literature: | |||
SAG001 SAGO10 (WILSON 1)(WILSON 2, DYN)Summaries of comparison results are shown in Tables 3F-2 and 3F-3, respectively.(d)The following computer programs have been verified by comparison with hand calculations for test problems which are representative of the type used in actual analyses: A summary of comparison results is shown in Tables 3F-4 through 3F-8.SAG008 SAGOI7 SAG024 SAG025 PM-9IO*PM-906 (TAPAS)(FOUREXP)(MMIC)(SECTION)(LESCAL)(STRAP)I 54 (e)The following computer programs are verified by inspection of the graphical output data.SAG054 (Response Envelope)A typical verification example is presented in Table 3F-9.*Documentation of STRAP is available in the Final Safety Analysis keport for the Carolina Power and Light Co., Brunswick 1&2, US NRC Docket Nos.50-324 and 50-325.3F-2 SB 1&2 FSAR TABLE 3F-l SAG058 (RESPONSE SPECTRA)SAG058 (1)is verified against STARDYNE, sub-routine DYNRE5.The input T/H is of 22 second duration, with a time interval of 0.01 seconds and a maximum acceleration of I.Dg.Spectral Acceleration (g)Frequency 0.5%Damping 2%Damping (Hz)SAG058 DYNRE5 SAG058 DYNRE5 0.33 0.91 0.98 0.79 0.83 1.00 2.68 2.67 2.03 2.03 2.00 8.23 8.23 4.33 4.32 3.03 6.04 6.02 4.31 4.32 4.00 5.20 5.18 4.40 4.37 5.00 5.25 5.21 3.95 3.94 6.25 7.51 7.42 4.47 4.38 7.14 5.33 5.25 3.94 3.90 8.33 4.87 4.80 3.68 9.09 7.09 6.93 4.96 4.81 10.00 5.00 4.973.373.35 20.00 2.61 2.60 1.77 1.77 33.33 1.22 1.22 1.13 1.14 (1)SAG058 is an in-house computer program run on the Control Data Corporation CYBER-175 and is used as a toSTARDYNE program. | |||
SB 1&2 FSAR TABLE 3F-2 SAG001 (WILSON 1)The following is a comparison of the results from SAGOOI with results obtained from published technical literature. | |||
SAGOOI runs on the Honeywell 66/60 system with the GeOS operating system.Samnle Problem No.1 Analysis of a thick-walled cylinder subjected to an internal pressure.Reference-Gallagher, R.H., Finite Element Analysis, Figure 11.5)pg.317, Prentice-Hall, Inc., 1975.Comparison of the theoretical solution with the WILSON 1 solution is shown on Figure 3F-l for the radial stress and the hoop stress.Sample Problem No.2 Analysis of a cylindrical shell, fixed at both ends and subjected to an internal pressure.Reference-Timoshenko, S., Woinowsky-Krieger, S., Theory of Plates and Shells, Second Edition, pg.475, McGraw-Hill, 1959.Comparison of the theore*tical solution with the WILSON 1 solution is shown on Figures 3F-2 andfor the radial shear and meridional moment, respectively. | |||
SB 1&2 FSAR TABLE 3F-3 SAG010 (WILSON 2, DYN)The original version of SAGOla,"Dynamic Stress Analysis of Axisymmetric Structures Under Arbitrary Loading," written by Ghosh and Wilson was revised by UE&C in September, 1975.The program is distributed in the public domain by the Earthquake Engineering Research Center, University of California, Berkeley, California. | |||
The program has been verified against a series of problems whose results are published in technical literature. | |||
Documentation of this verification is contained in the report EERC 69-10 which can be obtained from the Earthquake Engineering Research Center.SAGOla is run on the Honeywell 66/60 System. | |||
SB 1&2 FSAR TABLE 3F-4 SAGOOa (TAPAS)The following is a comparison of the results from SAG008, which computes the temperature distribution through plane and axisymmetric solids, with hand calculations. | |||
The sample results are for the temperature distribution through the thickness of a hemispherical concrete dome which is 42 inches thick and subject to 1200F inside and (-)lOOF outside.Element No.724 848 972 1096 1220 1344 SAGOoa(l)(OF)110.38 88.89 65.33 42.12 19.26 (-)1.04 Hand Calculation (OF@Mid Pt.of Elem.)110.7143 89.048 65.833 42.619 19.405 (-)0.7143 SAGOOB runs on the Honeywell 66/60 system | |||
==References:== | |||
(1)Wilson, E.L., Nickell, R.E.,"Application of the Finite Element," Journal of Nuclear Engineering and Design, 4, 1966. | |||
SB 1&2 FSAR TABLE 3F-5 SAGO!7 (FOUREXP)Amendment 56 November 1985 The following is a verification of SAGOl7 with hand calculations for arbitrary loading distribution which is an even function and can be expanded using a cosine Fourier Series.The periodic*function is,£(6)=-ne<01 La Q<8S.1TJ Comparison of Fourier Coefficients: | |||
o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'17 18 19 20 SAG017(1)1.5699-1.2739-0.0019-0.1421-0.0019.-0.0516-0.0020-0.0266-0.0021-0.0164-000022-0.0112-0.0023-0.0082-0.0025-0.0063-0.0028-0.0051-0.0031-0.0042-0.0036 Hand Calculations(2) 1.5708-1.2732 o-0.1415 o-0.0509 o-0.0260 o-0.0157 o-0.0105 o-0.0075 o-0.0057 o-0.0044 o-0.0035 o I 5{, SAGOI7 runs on the Honeywell 66/60 syst.em. | |||
==References:== | |||
(1)The Fourier coefficients are computed for a digitized function by a recursive technique described in Mathematical Methods for Digital Computers, by Rolsten and Wilfs John Wiley and Sons, New York, 1960, Chapter 24.The solution technique is from subroutine FORII in the.IBM Scientific Subroutine package.The program is run on the Honeywell 66/60 system.(2)Wylie, C.R;, Advanced Engineering Mathematics, 4th Ed., McGraw-Hill, 1975. | |||
SB 1&2 FSAR TABLE 3F-6 SAG024 (MMIC)The following is a comparison of the results of hand calculations with SAG024 for the weight of a typcial lumped mass point in la dynamic model of a shear building.Parameter SAG024 (1)XcM (X-Coordinate of the Center of Mass)0-ft.26.19 Y CM (Y-Coordinate of the Center of Mass)-ft.0.08 W T (Total Weight of Mass Point)-Kips 1444 IMX (Rotary Weight Moment of Inertia about X-Axis)K-ft 2 162,323 IMY (Rotary Weight Moment of Inertia about Y-Axis)K-ft 2 379,552 IMZ (Rotary Weight Moment of Inertia about Z-Axis)K-ft 2 470,152 Hand Calculation 26.19 0.08 1444 162,320 379,550 470,150 SAG024 runs on the Honeywell 66/60 system. | |||
==Reference:== | |||
(1)Bear, F.P.and Johnston, R.E., Jr., Vector Mechanics'for Engineers: | |||
Static and:DYnamics, McGraw-Hill t 1962, pps.343-347. | |||
SB 1&2 FSAR TABLE 3F-7 SAG025 (SECTION)The follo\Jing is a comparison of the results of hand calculations with SAG025 for a system of resisting structural elements between floors in a typcial shear building.SAG025 Hand Calculations XeR (X-Coordinate of Center of Rigidity)-ft.26.3 26.257 Y CR (Y-Coordinate of Center of Rigidity)-ft.0.0 0.0 Atr (Area)-ft 466.0 466.0 SFX (Shear Shape Factor about X-Axis).456 0.456 SFY (Shear Shape Factor about Y-Axis).555 0.555 I XX (Moment of Inertia about X-Axis)-ft.11,100 11,079 I yy (Moment of Inertia about Y-Axis)-ft.44,000 43,957 J (Torsional Constant)-ft.117,000 117,470 SAG025 runs on the Honeywell 66/60 system. | |||
SB 1&2 FSAR TABLE 3F-8 (Sheet 1 of 2)PM-910 (LESCAL)Amendment 56 November 1985 The following is a comparison of the results from the LESCAL computer program with hand calculations. | |||
LESCAL calculates the stresses and strains in rebars and/or concrete in accordance with the criteria set forth in Subarticle3511.1 of ASME Section III, Division II.The section is concrete reinforced with horizontal, vertical and/or diagonal rebars, subjected to axial force and moment on a vertical and horizontal face and in-plane shear.When inplane shear forces are" included, a solution is obtained by solving Duchon's equations(l). | |||
5&.Hand Load Condition Parameter LESCAL (Ksi)Calculations I 5fD.D+Fa+E s f m outside 29.39 29.46 Applied@e.g-of fh outside 23.08 23.05 I Concrete Section fseis.(3)52.26 52.35 5G,.fsets.(4)0.21 0.21 f m inside 26.67 26.75 f h inside 23.82 23.77 D+1.25Pa+l.25Eo f m outside-2.22-2.99 Applied@C.9-of f n outside-0.41-0.16 Concrete Section fseis.(3)9.70 SG 9.47 fseis*.(4)-12.34-12.63 f m inside 38.37 39.34 fh inside 1.98 2.12 D+P a+E s f m outside 37.70 37.70 Applied@e.g.f h outside 25.08 25.07 of Rebar fseis.(3)57.41 57.41 fseis.(4)5.37*5.37 f m inside 12.74 12.73 fh inside 19.01 19.01 SB 1&2 FSAR TABLE 3F-8 (Sheetof 2)Amendment S6 November 1985 Load Condition D+l.25Pa+l.25Eo Applie,d@c.g.of Rebar Parameter f m outside f h outside fseis.(3)fseis.(4)f m inside fh inside Hand LESCAL (Ksi)Calculations-2.01-1.77 7.33 7.82 16.07 16.08-10.76-10.02 40.94 40.64 9.54 10.06 LESCAL runs on the Honeywell 66/60 system.Notes (3)and (4)indicate directions of seismic rebars. | |||
==References:== | |||
(1)Duchon, N.B.,"Analysis of Reinforced Concrete Membrane Subject to Tension and Shear," ACI Journal, September 1972, pp.578-583. | |||
SB 1&2 FSAR TABLE 3F-9 SAG054 (RESPONSE ENVELOPE)SAG054 is a post-processing program for STARDYNE yhich is used in seismic analysis The program spreads the peaks of the amplified response spectra created by SAG058 (See Table 3F-l)by a predetermined amount and tabulates the ordinates and abscissas of the resulting curve.Verification of this program is accomplished by visual inspection of the graphical output to insure that the raw data has, in fact, been enveloped. | |||
SAG054 runs on the CDC CYBER-175 svstem. | |||
I<t SYM.I r----I (0)FINITE ELEMENT | |||
(-.2607)-.{R-STRESS)x 10 psi (+0.9218)(+0.7915)(+0.5997)o SAG 001-EXACT SOLUTION RADIUS-4(T-STR ESS)X lOps i 1.8 1.6 1.4 1.2 1.0 b 0.8 V1 V1 w 0.6 a=::.-V1--I<<0.4a=:: 0 0.2 z 0 0.5-0.2-0.4-0.6-0.8-1.0 (b)CALCULATED STRESSES ANALYSIS OF THICK-WALLED CYLINDER UNDER INTERNAL PRESSURE | |||
==REFERENCE:== | |||
GALLAGHER, R.H., FINITE ELEMENT ANALYSIS, PRENTICE-HALL/INC. | |||
1975.FIGURE 11.5, PG.317 PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SAG001 SAMPLE PROBLEM NO.1 SEABROOK STATION-UNITS 1&2 FINAL SAFETY ANALYSIS REPORT I FIGURE 3F-1 w O o liN....J'-><LL_N o M o co o f"'-..d 0Z UJ I 0 V")0-.0 0<!)d<t: t-V")I I 0 0 Ll)0....JIN"-><d 0 0 0 0 0 0 0.5 0 0 0 0 0 0 0 0'" 0 0 0 0 0 0..0 0-.0 N N-.0 0++I I 7'"+I co 0........(!sd) | |||
Z PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SAG001 SAMPLE PROBLEM NO.2 SEABROOK STATION-UNITS 1&2 RADIAL SHEAR FINAL SAFETY ANALYSIS REPORT I FIGURE.3F-2 CD oo ro o C\J 0 0 0 z w a Q..lJ.J-.JIC\J\0 x"-LL x 0 J: CJ)...--lJ.J::r: to-CI)0 w wCJ)0 a:: w<t0 z z U 1J...W J: (5 0<D CJ)0 0 0 0:E (!)(!)<t<t to-CJ)CJ)0<:>L{)0 0000 a00 8 0g2 a 00000o 00000o 00000 lO C\J V<.0 CD 0 (\JIII IT" V I (U!/#U!)lN3WOW PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SEABROOK STATION-UNITS1&2 FINAL SAFETY ANALYSIS REPORT SAG001 SAMPLE PROBLEM NO.2 MERIDIONAL MOMENT I FIGURE 3.F-3 SEABROOK UPDATED FSAR APPENDIX 3D PROCEDURE FOR CALCULATING ELASTO-PLASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY ENERGY BALANCE METHOD The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information. | |||
SB 1&2 FSAR Amendment 56 November lQHS A simplified mathematical model ason the next page can be used for elascic-plastic design of pipe restraints. | |||
An energy balance approach has been used to formulate the calculations for determining the plastic deformation in the restraints. | |||
In applying the plastic deformation design for restraints, the regulatory guides require that either one of the following upper bound design limits for metallic ductile materials be met..(3)50%of the minimum ultimate uniform strain (the strain at the maximum stress of an engineering stress-strain curve based on actual material tests for the restraint),'or (b)50%0: the percent elongation as specified in an applicable ASHE.ASTH, etc.Code, specification, or standard when demonstrated to be less than 50%of the minimum ultimate uniform strain based on representative test results.3D-l S1&2 FSAR Simolified approach for elasto-?lastic i\mendnlent 5G November 19R5 If the restraint is to go into the plastic region, then the restraint deflection, d cax* consist of an ela3tic and a portion as sho.wn belov.(Figure 1.0)Restraint DeflectionFigure 1.0-Idealized Restrain: | |||
where, de Restraint elastic deflection at yield stress d max Maximum allowable restraint deflection Rp Maximum restraint resistance Rp=ked e k e Restraint elastic structural stiffness If'F'denotes the applied forcing Function (i.e.*aload in case of a pipe break)and'h'denotes the gap the piping and the restraint, an energy balance relation for this case gives)(see 2.0).-Rp (d cax-de)2 3D-2 SB 1&2 FSAR Amendment 56 November 1985 Ca)Before Impact h(b)After Impact Figure 2.0 Energy balance Analvsis Hodel Rearranging, (Ro-F)2 TIlerefore, d max=1 2 2Fh.;.Rpd e 2 (Rp-F)(1)The above formulation can be further sinlplif:ed in 2Fh is much larg-:r th2n Therefore, assuming.Rpd e<<2Fh Equation (1)gives, dmax:(Rp-F)(2)After determining Cmax.either by equation (1)or equation (2)above (as applicable), the resulting strain in the member should be calculated 3nd should be checked against the criteria give in page 1. | |||
For uniaxial members, the strain e is taken to be equal to L yhere L is the original length of the restraint member.3D-3 SB 1&2 FSAR Pages 4 and 5 Deleted in Amendment 56 Amendment 56 November 1985 SEABROOK UPDATED FSAR APPENDIX 3E PROCEDURE FOR CALCULATING ELASTO-PLASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY EQUIVALENT STATIC ANALYSIS METHOD The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information. | |||
SB 1&.2 FSAR APPENDIX 3E PROCEDURE FOR CALCULATING ELASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY EQUIVALENT STATIC ANALYSIS METHOD PREPARED BY: REVIDVED BY::1/.1.11}1 F.JAN MECHANICAL | |||
.'lliALYSIS11/29/77 R.F.PERRY.{l. | |||
A..'IALYS IS GROCP In order to evaluate the response of an elastically designed pipe whip to a pipe break load by using the equivalent static analysis approach, the load factor associated with the applicable forcing function'and the clearance (gap)becween the pipe and the restraint has to be A simplified mathematical model as shown the oext page,' be used to the dynamic load factor.Since the pipe size effects are already being.reflected in the magnitude of the pipe break load, the pipe size alone is not considered again as a model parameter. | |||
The load factor (DL'F)*thus determined is used to calculate the restraint: | |||
load (R)as follows: R*a X DLF.-where:{1.26 for steam-saturated water ct.: 2.0 for subcooled non-flashingu.s.NRC Standard Review Plan, 3.6.2 (III)(2)(c)(42]P*Operating PressureA*Pipe Break Area A series of curves for determining the restraint loads for steam-saturated water or steam-water mixturesare given in Pages3-14. A S1J1PLE MODEL FOR LOAD FACTOR By substituting (3)into (2), we have F(h+d)=1/2{...L\d 2 dstJ F d eS k F(h+d)1/2 kd!From (1).k&..!....d st (1)(2)(3)Fh F.\d--.----L.//#1//F/l/CD..CD Or, (d2 dstJ-2(...!-\-2(-!:""\c 0\d st') DLF d*-z: d st Where, F*Applied Load(Pipe Rupture Load)d st c Restraint deflection for statically applied Fd*Maximum restraint deflectionh-Gap sizek*Restraint stiffness DLF C Dynamic load factor )*I*,*'1 C*,***,., i,.I*,"1 rf 2.J*,*.,*t 1 0'P-A INLBS.=O.f2 00 INCHES FOR ELRSTIl PIPE WHIP RES(Applicable nly to wa er or r mixtures, 2 1.26))**.7.tleT FOR ElRSTI PIPE RES RRINTS.(Applicable I nly to steam1saturated Ya er or steam-wat r 1.26)GRP=0.25 00 INCHES J'.,*,.'1 rf*,""'1 rJ IN LBS.**"'1 cJP*A J*,*,.'1 ct 2** | |||
4I*,*'1 0'.: 'c'."*'1 O*IN LBS.GRP=0.50 00 INCHES J***,..0 4P*R FOR ELASTl'PIPE WHIP(Applicable nly to.steamr!saturated wa er or steam-wat r | |||
*1.26).)*I*"'1I.10= GRP=0.75 00 lNCHES FOR ELASTI PIPE WHIP RES RAINTS.(Applicable nly to steam*saturated.wa er or steam-wat r mixtures ,a*1.26)J 4 I*,,'1 0'2.J*"*,.'1 rt IN LBS.J***.,.'1 O*P*R | |||
CURVES FOR PI?E WHIP RES RRtNTS.(Applicable 6nly to stearn'saturated water , or steam-W8lrr*1.26)-7-*,*"', rj IN LBS.=1.00 00 INCHES)***,." 0'P*R:*I*,*'1 cr CU FOR PIPE(Applicable to steam+saturated wa er or steam-wat' r mixtures, l-1.26)4*,.,.'1 rJ IN LBS.=1.25 00 INCHES IC CU.YES FOR1PIWHIP RESI NTS.I to steac saturated water or steam-wa ler mixtures,*1.26)GRP=1.50 00 INCHES J 4 J,*"'1 O*P*)*I*1,'ilt IN LBS.J***, 1'1 O*)4,., tl lC , I , 4 , 4,*t o',*&4 7.'I 0 5 IN lBS.GRP=1.7500 INCHES ,*I*, 8'1 O*P*A PARAMETRIC CU VES FOR ELASTI PIPE WHIP RES RRINTS.(Applicable nly to steam wa er or steam-wat r mixtures,Q1.26), 4,*,*t 0'1 0'I., 0It#I"')N"0 en CD ,...CD lI)*trl N'b (1)cD ,...CD V)f'I")*U UP'S/IN.100000 enQ),...10000 (,,()V).000* f'I')2000 N b 5 8l e 8 1 O*IN LBS.GRP=2.00 00 INCHES ,I e 7 ,*J 0'P*A PRRRHETR1C CU V£S FOR ELRSTI PIPE RES(Applicable only to steam saturated wa er or steam-wa er | |||
=1.26)J*I*,.e 0'I.-1", N po.0 en CD t-ao V)*C'I")N b (7)CD r-CD\f)I{..,'N I{I'S/IN.100000 N (J)(D-J z"b enr-CD V)fI")N b m CD f"-lOC CD&I).0.." 10 , 0'GAP=2.50 00 INCHES CU YES FOR ELASTI PIPE WHIP RES RAINTS.(Applicable nly to steam saturated waler or steam-wat r e 1.26)J 4**,**I J,*, i*O*S 4 i 87*I 0 6 IP*A IN LBS.I*10**N'b I...11;"1".*00000m-I Z a:: '0000"'000 U)4000 JDOO*2000 1000'iO.00 210 100'0 ***'" C GAP=3.00 00 INCHES J 4**,**0)I ,.I*,*'1 O*).**,*t rt I J 4**,., 1 rfP*R IN LBS.PRRRMETRIC FOR ElRST}PIPE WHIP RES RAINTS.(Applicable bnly to steam*saturated wa e+or steam-watbr | |||
*1.26)I..v,-.------..,...------.,..--------;------, 10000 c: 1000 coeto HGO IlOO IDOO".tOO 211 tOl FOR PIPE WHIP(Applicable only to or steam-watir | |||
*1.26)=0.06 50 lNCHES J.***, t.O*P)(A***,.'1 ct IN LBS.J**""lcf J*""'1 SEABROOK UPDATED FSAR APPENDIX 3F VERIFICATION OF COMPUTER PROGRAMS USED FOR STRUCTURAL ANALYSIS AND DESIGN The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information. | |||
SB 1&2 FSAR APPENDIX 3F VERIFICATION OF COMPUTER PROGRAMS USED FOR STRUCTURAL ANALYSIS AND DESIGN Amendment 54 February 1985 Computer programs used for structural analysis and design have been verified according to the criteria described in the US NRC Standard Review Plan 3.8.1, Section II-4(e).(a)The following computer programs are recognized in the public domain, and have had sufficient history to justify their applicability and validity without further demonstration: | |||
Hardware Source STARDYNE CDC CDC(l)MARC-CDC CDC CDC(l)STRU-PAl<CDC CDC(l)System Professional CDC CDC(l)ANSYS CDC CDC(l)STRUDL UCCEL PSDI(2)UEMENU UCCEL UCCEL(3)(1)CDC-(2)PSDI-(3)UCCEL-Control Data Corporation P.O.Box 0, HQWOSH Minneapolis, Minnesota 55440 Programs for Structural Design, Inc.14 Story Street Cambridge, Massachusetts 02138 UCCEL Corporation P.O.Box 84028 Dallas, Texas 75284 (b)The following computer programs have been verified by solving test problems with a similar and independently-written and recognized program in the public domain: SAG058 (Response Spectra)3F-l SB 1&2 FSAR Amendment 54 February 1985 A summary of comparison results is shown 1n Table 3F-l.AX2 (Axisymmetric Shell Program)A verification manual comparing AX2 with results obtained from either ANSYS or BOSOR4 (Lockhead Missile and Space Company-Palo Alto, CA)can be obtained from Pittsburgh | |||
-Des Moines Corporation, 3400 Grand Avenue, Neville Island, Pittsburgh, PA 15225 (c)The following computer programs have been verified by comparison with analytical results published in technical literature: | |||
SAG001 SAGO10 (WILSON 1)(WILSON 2, DYN)Summaries of comparison results are shown in Tables 3F-2 and 3F-3, respectively.(d)The following computer programs have been verified by comparison with hand calculations for test problems which are representative of the type used in actual analyses: A summary of comparison results is shown in Tables 3F-4 through 3F-8.SAG008 SAGOI7 SAG024 SAG025 PM-9IO*PM-906 (TAPAS)(FOUREXP)(MMIC)(SECTION)(LESCAL)(STRAP)I 54 (e)The following computer programs are verified by inspection of the graphical output data.SAG054 (Response Envelope)A typical verification example is presented in Table 3F-9.*Documentation of STRAP is available in the Final Safety Analysis keport for the Carolina Power and Light Co., Brunswick 1&2, US NRC Docket Nos.50-324 and 50-325.3F-2 SB 1&2 FSAR TABLE 3F-l SAG058 (RESPONSE SPECTRA)SAG058 (1)is verified against STARDYNE, sub-routine DYNRE5.The input T/H is of 22 second duration, with a time interval of 0.01 seconds and a maximum acceleration of I.Dg.Spectral Acceleration (g)Frequency 0.5%Damping 2%Damping (Hz)SAG058 DYNRE5 SAG058 DYNRE5 0.33 0.91 0.98 0.79 0.83 1.00 2.68 2.67 2.03 2.03 2.00 8.23 8.23 4.33 4.32 3.03 6.04 6.02 4.31 4.32 4.00 5.20 5.18 4.40 4.37 5.00 5.25 5.21 3.95 3.94 6.25 7.51 7.42 4.47 4.38 7.14 5.33 5.25 3.94 3.90 8.33 4.87 4.80 3.68 9.09 7.09 6.93 4.96 4.81 10.00 5.00 4.973.373.35 20.00 2.61 2.60 1.77 1.77 33.33 1.22 1.22 1.13 1.14 (1)SAG058 is an in-house computer program run on the Control Data Corporation CYBER-175 and is used as a toSTARDYNE program. | |||
SB 1&2 FSAR TABLE 3F-2 SAG001 (WILSON 1)The following is a comparison of the results from SAGOOI with results obtained from published technical literature. | |||
SAGOOI runs on the Honeywell 66/60 system with the GeOS operating system.Samnle Problem No.1 Analysis of a thick-walled cylinder subjected to an internal pressure.Reference-Gallagher, R.H., Finite Element Analysis, Figure 11.5)pg.317, Prentice-Hall, Inc., 1975.Comparison of the theoretical solution with the WILSON 1 solution is shown on Figure 3F-l for the radial stress and the hoop stress.Sample Problem No.2 Analysis of a cylindrical shell, fixed at both ends and subjected to an internal pressure.Reference-Timoshenko, S., Woinowsky-Krieger, S., Theory of Plates and Shells, Second Edition, pg.475, McGraw-Hill, 1959.Comparison of the theore*tical solution with the WILSON 1 solution is shown on Figures 3F-2 andfor the radial shear and meridional moment, respectively. | |||
SB 1&2 FSAR TABLE 3F-3 SAG010 (WILSON 2, DYN)The original version of SAGOla,"Dynamic Stress Analysis of Axisymmetric Structures Under Arbitrary Loading," written by Ghosh and Wilson was revised by UE&C in September, 1975.The program is distributed in the public domain by the Earthquake Engineering Research Center, University of California, Berkeley, California. | |||
The program has been verified against a series of problems whose results are published in technical literature. | |||
Documentation of this verification is contained in the report EERC 69-10 which can be obtained from the Earthquake Engineering Research Center.SAGOla is run on the Honeywell 66/60 System. | |||
SB 1&2 FSAR TABLE 3F-4 SAGOOa (TAPAS)The following is a comparison of the results from SAG008, which computes the temperature distribution through plane and axisymmetric solids, with hand calculations. | |||
The sample results are for the temperature distribution through the thickness of a hemispherical concrete dome which is 42 inches thick and subject to 1200F inside and (-)lOOF outside.Element No.724 848 972 1096 1220 1344 SAGOoa(l)(OF)110.38 88.89 65.33 42.12 19.26 (-)1.04 Hand Calculation (OF@Mid Pt.of Elem.)110.7143 89.048 65.833 42.619 19.405 (-)0.7143 SAGOOB runs on the Honeywell 66/60 system | |||
==References:== | |||
(1)Wilson, E.L., Nickell, R.E.,"Application of the Finite Element," Journal of Nuclear Engineering and Design, 4, 1966. | |||
SB 1&2 FSAR TABLE 3F-5 SAGO!7 (FOUREXP)Amendment 56 November 1985 The following is a verification of SAGOl7 with hand calculations for arbitrary loading distribution which is an even function and can be expanded using a cosine Fourier Series.The periodic*function is,£(6)=-ne<01 La Q<8S.1TJ Comparison of Fourier Coefficients: | |||
o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'17 18 19 20 SAG017(1)1.5699-1.2739-0.0019-0.1421-0.0019.-0.0516-0.0020-0.0266-0.0021-0.0164-000022-0.0112-0.0023-0.0082-0.0025-0.0063-0.0028-0.0051-0.0031-0.0042-0.0036 Hand Calculations(2) 1.5708-1.2732 o-0.1415 o-0.0509 o-0.0260 o-0.0157 o-0.0105 o-0.0075 o-0.0057 o-0.0044 o-0.0035 o I 5{, SAGOI7 runs on the Honeywell 66/60 syst.em. | |||
==References:== | |||
(1)The Fourier coefficients are computed for a digitized function by a recursive technique described in Mathematical Methods for Digital Computers, by Rolsten and Wilfs John Wiley and Sons, New York, 1960, Chapter 24.The solution technique is from subroutine FORII in the.IBM Scientific Subroutine package.The program is run on the Honeywell 66/60 system.(2)Wylie, C.R;, Advanced Engineering Mathematics, 4th Ed., McGraw-Hill, 1975. | |||
SB 1&2 FSAR TABLE 3F-6 SAG024 (MMIC)The following is a comparison of the results of hand calculations with SAG024 for the weight of a typcial lumped mass point in la dynamic model of a shear building.Parameter SAG024 (1)XcM (X-Coordinate of the Center of Mass)0-ft.26.19 Y CM (Y-Coordinate of the Center of Mass)-ft.0.08 W T (Total Weight of Mass Point)-Kips 1444 IMX (Rotary Weight Moment of Inertia about X-Axis)K-ft 2 162,323 IMY (Rotary Weight Moment of Inertia about Y-Axis)K-ft 2 379,552 IMZ (Rotary Weight Moment of Inertia about Z-Axis)K-ft 2 470,152 Hand Calculation 26.19 0.08 1444 162,320 379,550 470,150 SAG024 runs on the Honeywell 66/60 system. | |||
==Reference:== | |||
(1)Bear, F.P.and Johnston, R.E., Jr., Vector Mechanics'for Engineers: | |||
Static and:DYnamics, McGraw-Hill t 1962, pps.343-347. | |||
SB 1&2 FSAR TABLE 3F-7 SAG025 (SECTION)The follo\Jing is a comparison of the results of hand calculations with SAG025 for a system of resisting structural elements between floors in a typcial shear building.SAG025 Hand Calculations XeR (X-Coordinate of Center of Rigidity)-ft.26.3 26.257 Y CR (Y-Coordinate of Center of Rigidity)-ft.0.0 0.0 Atr (Area)-ft 466.0 466.0 SFX (Shear Shape Factor about X-Axis).456 0.456 SFY (Shear Shape Factor about Y-Axis).555 0.555 I XX (Moment of Inertia about X-Axis)-ft.11,100 11,079 I yy (Moment of Inertia about Y-Axis)-ft.44,000 43,957 J (Torsional Constant)-ft.117,000 117,470 SAG025 runs on the Honeywell 66/60 system. | |||
SB 1&2 FSAR TABLE 3F-8 (Sheet 1 of 2)PM-910 (LESCAL)Amendment 56 November 1985 The following is a comparison of the results from the LESCAL computer program with hand calculations. | |||
LESCAL calculates the stresses and strains in rebars and/or concrete in accordance with the criteria set forth in Subarticle3511.1 of ASME Section III, Division II.The section is concrete reinforced with horizontal, vertical and/or diagonal rebars, subjected to axial force and moment on a vertical and horizontal face and in-plane shear.When inplane shear forces are" included, a solution is obtained by solving Duchon's equations(l). | |||
5&.Hand Load Condition Parameter LESCAL (Ksi)Calculations I 5fD.D+Fa+E s f m outside 29.39 29.46 Applied@e.g-of fh outside 23.08 23.05 I Concrete Section fseis.(3)52.26 52.35 5G,.fsets.(4)0.21 0.21 f m inside 26.67 26.75 f h inside 23.82 23.77 D+1.25Pa+l.25Eo f m outside-2.22-2.99 Applied@C.9-of f n outside-0.41-0.16 Concrete Section fseis.(3)9.70 SG 9.47 fseis*.(4)-12.34-12.63 f m inside 38.37 39.34 fh inside 1.98 2.12 D+P a+E s f m outside 37.70 37.70 Applied@e.g.f h outside 25.08 25.07 of Rebar fseis.(3)57.41 57.41 fseis.(4)5.37*5.37 f m inside 12.74 12.73 fh inside 19.01 19.01 SB 1&2 FSAR TABLE 3F-8 (Sheetof 2)Amendment S6 November 1985 Load Condition D+l.25Pa+l.25Eo Applie,d@c.g.of Rebar Parameter f m outside f h outside fseis.(3)fseis.(4)f m inside fh inside Hand LESCAL (Ksi)Calculations-2.01-1.77 7.33 7.82 16.07 16.08-10.76-10.02 40.94 40.64 9.54 10.06 LESCAL runs on the Honeywell 66/60 system.Notes (3)and (4)indicate directions of seismic rebars. | |||
==References:== | |||
(1)Duchon, N.B.,"Analysis of Reinforced Concrete Membrane Subject to Tension and Shear," ACI Journal, September 1972, pp.578-583. | |||
SB 1&2 FSAR TABLE 3F-9 SAG054 (RESPONSE ENVELOPE)SAG054 is a post-processing program for STARDYNE yhich is used in seismic analysis The program spreads the peaks of the amplified response spectra created by SAG058 (See Table 3F-l)by a predetermined amount and tabulates the ordinates and abscissas of the resulting curve.Verification of this program is accomplished by visual inspection of the graphical output to insure that the raw data has, in fact, been enveloped. | |||
SAG054 runs on the CDC CYBER-175 svstem. | |||
I<t SYM.I r----I (0)FINITE ELEMENT | |||
(-.2607)-.{R-STRESS)x 10 psi (+0.9218)(+0.7915)(+0.5997)o SAG 001-EXACT SOLUTION RADIUS-4(T-STR ESS)X lOps i 1.8 1.6 1.4 1.2 1.0 b 0.8 V1 V1 w 0.6 a=::.-V1--I<<0.4a=:: 0 0.2 z 0 0.5-0.2-0.4-0.6-0.8-1.0 (b)CALCULATED STRESSES ANALYSIS OF THICK-WALLED CYLINDER UNDER INTERNAL PRESSURE | |||
==REFERENCE:== | |||
GALLAGHER, R.H., FINITE ELEMENT ANALYSIS, PRENTICE-HALL/INC. | |||
1975.FIGURE 11.5, PG.317 PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SAG001 SAMPLE PROBLEM NO.1 SEABROOK STATION-UNITS 1&2 FINAL SAFETY ANALYSIS REPORT I FIGURE 3F-1 w O o liN....J'-><LL_N o M o co o f"'-..d 0Z UJ I 0 V")0-.0 0<!)d<t: t-V")I I 0 0 Ll)0....JIN"-><d 0 0 0 0 0 0 0.5 0 0 0 0 0 0 0 0'" 0 0 0 0 0 0..0 0-.0 N N-.0 0++I I 7'"+I co 0........(!sd) | |||
Z PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SAG001 SAMPLE PROBLEM NO.2 SEABROOK STATION-UNITS 1&2 RADIAL SHEAR FINAL SAFETY ANALYSIS REPORT I FIGURE.3F-2 CD oo ro o C\J 0 0 0 z w a Q..lJ.J-.JIC\J\0 x"-LL x 0 J: CJ)...--lJ.J::r: to-CI)0 w wCJ)0 a:: w<t0 z z U 1J...W J: (5 0<D CJ)0 0 0 0:E (!)(!)<t<t to-CJ)CJ)0<:>L{)0 0000 a00 8 0g2 a 00000o 00000o 00000 lO C\J V<.0 CD 0 (\JIII IT" V I (U!/#U!)lN3WOW PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SEABROOK STATION-UNITS1&2 FINAL SAFETY ANALYSIS REPORT SAG001 SAMPLE PROBLEM NO.2 MERIDIONAL MOMENT I FIGURE 3.F-3}} | |||
Latest revision as of 00:21, 3 April 2019
Text
SEABROOK UPDATED FSAR APPENDIX 3D PROCEDURE FOR CALCULATING ELASTO-PLASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY ENERGY BALANCE METHOD The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information.
SB 1&2 FSAR Amendment 56 November lQHS A simplified mathematical model ason the next page can be used for elascic-plastic design of pipe restraints.
An energy balance approach has been used to formulate the calculations for determining the plastic deformation in the restraints.
In applying the plastic deformation design for restraints, the regulatory guides require that either one of the following upper bound design limits for metallic ductile materials be met..(3)50%of the minimum ultimate uniform strain (the strain at the maximum stress of an engineering stress-strain curve based on actual material tests for the restraint),'or (b)50%0: the percent elongation as specified in an applicable ASHE.ASTH, etc.Code, specification, or standard when demonstrated to be less than 50%of the minimum ultimate uniform strain based on representative test results.3D-l S1&2 FSAR Simolified approach for elasto-?lastic i\mendnlent 5G November 19R5 If the restraint is to go into the plastic region, then the restraint deflection, d cax* consist of an ela3tic and a portion as sho.wn belov.(Figure 1.0)Restraint DeflectionFigure 1.0-Idealized Restrain:
where, de Restraint elastic deflection at yield stress d max Maximum allowable restraint deflection Rp Maximum restraint resistance Rp=ked e k e Restraint elastic structural stiffness If'F'denotes the applied forcing Function (i.e.*aload in case of a pipe break)and'h'denotes the gap the piping and the restraint, an energy balance relation for this case gives)(see 2.0).-Rp (d cax-de)2 3D-2 SB 1&2 FSAR Amendment 56 November 1985 Ca)Before Impact h(b)After Impact Figure 2.0 Energy balance Analvsis Hodel Rearranging, (Ro-F)2 TIlerefore, d max=1 2 2Fh.;.Rpd e 2 (Rp-F)(1)The above formulation can be further sinlplif:ed in 2Fh is much larg-:r th2n Therefore, assuming.Rpd e<<2Fh Equation (1)gives, dmax:(Rp-F)(2)After determining Cmax.either by equation (1)or equation (2)above (as applicable), the resulting strain in the member should be calculated 3nd should be checked against the criteria give in page 1.
For uniaxial members, the strain e is taken to be equal to L yhere L is the original length of the restraint member.3D-3 SB 1&2 FSAR Pages 4 and 5 Deleted in Amendment 56 Amendment 56 November 1985 SEABROOK UPDATED FSAR APPENDIX 3E PROCEDURE FOR CALCULATING ELASTO-PLASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY EQUIVALENT STATIC ANALYSIS METHOD The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information.
SB 1&.2 FSAR APPENDIX 3E PROCEDURE FOR CALCULATING ELASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY EQUIVALENT STATIC ANALYSIS METHOD PREPARED BY: REVIDVED BY::1/.1.11}1 F.JAN MECHANICAL
.'lliALYSIS11/29/77 R.F.PERRY.{l.
A..'IALYS IS GROCP In order to evaluate the response of an elastically designed pipe whip to a pipe break load by using the equivalent static analysis approach, the load factor associated with the applicable forcing function'and the clearance (gap)becween the pipe and the restraint has to be A simplified mathematical model as shown the oext page,' be used to the dynamic load factor.Since the pipe size effects are already being.reflected in the magnitude of the pipe break load, the pipe size alone is not considered again as a model parameter.
The load factor (DL'F)*thus determined is used to calculate the restraint:
load (R)as follows: R*a X DLF.-where:{1.26 for steam-saturated water ct.: 2.0 for subcooled non-flashingu.s.NRC Standard Review Plan, 3.6.2 (III)(2)(c)(42]P*Operating PressureA*Pipe Break Area A series of curves for determining the restraint loads for steam-saturated water or steam-water mixturesare given in Pages3-14. A S1J1PLE MODEL FOR LOAD FACTOR By substituting (3)into (2), we have F(h+d)=1/2{...L\d 2 dstJ F d eS k F(h+d)1/2 kd!From (1).k&..!....d st (1)(2)(3)Fh F.\d--.----L.//#1//F/l/CD..CD Or, (d2 dstJ-2(...!-\-2(-!:""\c 0\d st') DLF d*-z: d st Where, F*Applied Load(Pipe Rupture Load)d st c Restraint deflection for statically applied Fd*Maximum restraint deflectionh-Gap sizek*Restraint stiffness DLF C Dynamic load factor )*I*,*'1 C*,***,., i,.I*,"1 rf 2.J*,*.,*t 1 0'P-A INLBS.=O.f2 00 INCHES FOR ELRSTIl PIPE WHIP RES(Applicable nly to wa er or r mixtures, 2 1.26))**.7.tleT FOR ElRSTI PIPE RES RRINTS.(Applicable I nly to steam1saturated Ya er or steam-wat r 1.26)GRP=0.25 00 INCHES J'.,*,.'1 rf*,""'1 rJ IN LBS.**"'1 cJP*A J*,*,.'1 ct 2**
4I*,*'1 0'.: 'c'."*'1 O*IN LBS.GRP=0.50 00 INCHES J***,..0 4P*R FOR ELASTl'PIPE WHIP(Applicable nly to.steamr!saturated wa er or steam-wat r
- 1.26).)*I*"'1I.10= GRP=0.75 00 lNCHES FOR ELASTI PIPE WHIP RES RAINTS.(Applicable nly to steam*saturated.wa er or steam-wat r mixtures ,a*1.26)J 4 I*,,'1 0'2.J*"*,.'1 rt IN LBS.J***.,.'1 O*P*R
CURVES FOR PI?E WHIP RES RRtNTS.(Applicable 6nly to stearn'saturated water , or steam-W8lrr*1.26)-7-*,*"', rj IN LBS.=1.00 00 INCHES)***,." 0'P*R:*I*,*'1 cr CU FOR PIPE(Applicable to steam+saturated wa er or steam-wat' r mixtures, l-1.26)4*,.,.'1 rJ IN LBS.=1.25 00 INCHES IC CU.YES FOR1PIWHIP RESI NTS.I to steac saturated water or steam-wa ler mixtures,*1.26)GRP=1.50 00 INCHES J 4 J,*"'1 O*P*)*I*1,'ilt IN LBS.J***, 1'1 O*)4,., tl lC , I , 4 , 4,*t o',*&4 7.'I 0 5 IN lBS.GRP=1.7500 INCHES ,*I*, 8'1 O*P*A PARAMETRIC CU VES FOR ELASTI PIPE WHIP RES RRINTS.(Applicable nly to steam wa er or steam-wat r mixtures,Q1.26), 4,*,*t 0'1 0'I., 0It#I"')N"0 en CD ,...CD lI)*trl N'b (1)cD ,...CD V)f'I")*U UP'S/IN.100000 enQ),...10000 (,,()V).000* f'I')2000 N b 5 8l e 8 1 O*IN LBS.GRP=2.00 00 INCHES ,I e 7 ,*J 0'P*A PRRRHETR1C CU V£S FOR ELRSTI PIPE RES(Applicable only to steam saturated wa er or steam-wa er
=1.26)J*I*,.e 0'I.-1", N po.0 en CD t-ao V)*C'I")N b (7)CD r-CD\f)I{..,'N I{I'S/IN.100000 N (J)(D-J z"b enr-CD V)fI")N b m CD f"-lOC CD&I).0.." 10 , 0'GAP=2.50 00 INCHES CU YES FOR ELASTI PIPE WHIP RES RAINTS.(Applicable nly to steam saturated waler or steam-wat r e 1.26)J 4**,**I J,*, i*O*S 4 i 87*I 0 6 IP*A IN LBS.I*10**N'b I...11;"1".*00000m-I Z a:: '0000"'000 U)4000 JDOO*2000 1000'iO.00 210 100'0 ***'" C GAP=3.00 00 INCHES J 4**,**0)I ,.I*,*'1 O*).**,*t rt I J 4**,., 1 rfP*R IN LBS.PRRRMETRIC FOR ElRST}PIPE WHIP RES RAINTS.(Applicable bnly to steam*saturated wa e+or steam-watbr
- 1.26)I..v,-.------..,...------.,..--------;------, 10000 c: 1000 coeto HGO IlOO IDOO".tOO 211 tOl FOR PIPE WHIP(Applicable only to or steam-watir
- 1.26)=0.06 50 lNCHES J.***, t.O*P)(A***,.'1 ct IN LBS.J**""lcf J*""'1 SEABROOK UPDATED FSAR APPENDIX 3F VERIFICATION OF COMPUTER PROGRAMS USED FOR STRUCTURAL ANALYSIS AND DESIGN The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information.
SB 1&2 FSAR APPENDIX 3F VERIFICATION OF COMPUTER PROGRAMS USED FOR STRUCTURAL ANALYSIS AND DESIGN Amendment 54 February 1985 Computer programs used for structural analysis and design have been verified according to the criteria described in the US NRC Standard Review Plan 3.8.1, Section II-4(e).(a)The following computer programs are recognized in the public domain, and have had sufficient history to justify their applicability and validity without further demonstration:
Hardware Source STARDYNE CDC CDC(l)MARC-CDC CDC CDC(l)STRU-PAl<CDC CDC(l)System Professional CDC CDC(l)ANSYS CDC CDC(l)STRUDL UCCEL PSDI(2)UEMENU UCCEL UCCEL(3)(1)CDC-(2)PSDI-(3)UCCEL-Control Data Corporation P.O.Box 0, HQWOSH Minneapolis, Minnesota 55440 Programs for Structural Design, Inc.14 Story Street Cambridge, Massachusetts 02138 UCCEL Corporation P.O.Box 84028 Dallas, Texas 75284 (b)The following computer programs have been verified by solving test problems with a similar and independently-written and recognized program in the public domain: SAG058 (Response Spectra)3F-l SB 1&2 FSAR Amendment 54 February 1985 A summary of comparison results is shown 1n Table 3F-l.AX2 (Axisymmetric Shell Program)A verification manual comparing AX2 with results obtained from either ANSYS or BOSOR4 (Lockhead Missile and Space Company-Palo Alto, CA)can be obtained from Pittsburgh
-Des Moines Corporation, 3400 Grand Avenue, Neville Island, Pittsburgh, PA 15225 (c)The following computer programs have been verified by comparison with analytical results published in technical literature:
SAG001 SAGO10 (WILSON 1)(WILSON 2, DYN)Summaries of comparison results are shown in Tables 3F-2 and 3F-3, respectively.(d)The following computer programs have been verified by comparison with hand calculations for test problems which are representative of the type used in actual analyses: A summary of comparison results is shown in Tables 3F-4 through 3F-8.SAG008 SAGOI7 SAG024 SAG025 PM-9IO*PM-906 (TAPAS)(FOUREXP)(MMIC)(SECTION)(LESCAL)(STRAP)I 54 (e)The following computer programs are verified by inspection of the graphical output data.SAG054 (Response Envelope)A typical verification example is presented in Table 3F-9.*Documentation of STRAP is available in the Final Safety Analysis keport for the Carolina Power and Light Co., Brunswick 1&2, US NRC Docket Nos.50-324 and 50-325.3F-2 SB 1&2 FSAR TABLE 3F-l SAG058 (RESPONSE SPECTRA)SAG058 (1)is verified against STARDYNE, sub-routine DYNRE5.The input T/H is of 22 second duration, with a time interval of 0.01 seconds and a maximum acceleration of I.Dg.Spectral Acceleration (g)Frequency 0.5%Damping 2%Damping (Hz)SAG058 DYNRE5 SAG058 DYNRE5 0.33 0.91 0.98 0.79 0.83 1.00 2.68 2.67 2.03 2.03 2.00 8.23 8.23 4.33 4.32 3.03 6.04 6.02 4.31 4.32 4.00 5.20 5.18 4.40 4.37 5.00 5.25 5.21 3.95 3.94 6.25 7.51 7.42 4.47 4.38 7.14 5.33 5.25 3.94 3.90 8.33 4.87 4.80 3.68 9.09 7.09 6.93 4.96 4.81 10.00 5.00 4.973.373.35 20.00 2.61 2.60 1.77 1.77 33.33 1.22 1.22 1.13 1.14 (1)SAG058 is an in-house computer program run on the Control Data Corporation CYBER-175 and is used as a toSTARDYNE program.
SB 1&2 FSAR TABLE 3F-2 SAG001 (WILSON 1)The following is a comparison of the results from SAGOOI with results obtained from published technical literature.
SAGOOI runs on the Honeywell 66/60 system with the GeOS operating system.Samnle Problem No.1 Analysis of a thick-walled cylinder subjected to an internal pressure.Reference-Gallagher, R.H., Finite Element Analysis, Figure 11.5)pg.317, Prentice-Hall, Inc., 1975.Comparison of the theoretical solution with the WILSON 1 solution is shown on Figure 3F-l for the radial stress and the hoop stress.Sample Problem No.2 Analysis of a cylindrical shell, fixed at both ends and subjected to an internal pressure.Reference-Timoshenko, S., Woinowsky-Krieger, S., Theory of Plates and Shells, Second Edition, pg.475, McGraw-Hill, 1959.Comparison of the theore*tical solution with the WILSON 1 solution is shown on Figures 3F-2 andfor the radial shear and meridional moment, respectively.
SB 1&2 FSAR TABLE 3F-3 SAG010 (WILSON 2, DYN)The original version of SAGOla,"Dynamic Stress Analysis of Axisymmetric Structures Under Arbitrary Loading," written by Ghosh and Wilson was revised by UE&C in September, 1975.The program is distributed in the public domain by the Earthquake Engineering Research Center, University of California, Berkeley, California.
The program has been verified against a series of problems whose results are published in technical literature.
Documentation of this verification is contained in the report EERC 69-10 which can be obtained from the Earthquake Engineering Research Center.SAGOla is run on the Honeywell 66/60 System.
SB 1&2 FSAR TABLE 3F-4 SAGOOa (TAPAS)The following is a comparison of the results from SAG008, which computes the temperature distribution through plane and axisymmetric solids, with hand calculations.
The sample results are for the temperature distribution through the thickness of a hemispherical concrete dome which is 42 inches thick and subject to 1200F inside and (-)lOOF outside.Element No.724 848 972 1096 1220 1344 SAGOoa(l)(OF)110.38 88.89 65.33 42.12 19.26 (-)1.04 Hand Calculation (OF@Mid Pt.of Elem.)110.7143 89.048 65.833 42.619 19.405 (-)0.7143 SAGOOB runs on the Honeywell 66/60 system
References:
(1)Wilson, E.L., Nickell, R.E.,"Application of the Finite Element," Journal of Nuclear Engineering and Design, 4, 1966.
SB 1&2 FSAR TABLE 3F-5 SAGO!7 (FOUREXP)Amendment 56 November 1985 The following is a verification of SAGOl7 with hand calculations for arbitrary loading distribution which is an even function and can be expanded using a cosine Fourier Series.The periodic*function is,£(6)=-ne<01 La Q<8S.1TJ Comparison of Fourier Coefficients:
o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'17 18 19 20 SAG017(1)1.5699-1.2739-0.0019-0.1421-0.0019.-0.0516-0.0020-0.0266-0.0021-0.0164-000022-0.0112-0.0023-0.0082-0.0025-0.0063-0.0028-0.0051-0.0031-0.0042-0.0036 Hand Calculations(2) 1.5708-1.2732 o-0.1415 o-0.0509 o-0.0260 o-0.0157 o-0.0105 o-0.0075 o-0.0057 o-0.0044 o-0.0035 o I 5{, SAGOI7 runs on the Honeywell 66/60 syst.em.
References:
(1)The Fourier coefficients are computed for a digitized function by a recursive technique described in Mathematical Methods for Digital Computers, by Rolsten and Wilfs John Wiley and Sons, New York, 1960, Chapter 24.The solution technique is from subroutine FORII in the.IBM Scientific Subroutine package.The program is run on the Honeywell 66/60 system.(2)Wylie, C.R;, Advanced Engineering Mathematics, 4th Ed., McGraw-Hill, 1975.
SB 1&2 FSAR TABLE 3F-6 SAG024 (MMIC)The following is a comparison of the results of hand calculations with SAG024 for the weight of a typcial lumped mass point in la dynamic model of a shear building.Parameter SAG024 (1)XcM (X-Coordinate of the Center of Mass)0-ft.26.19 Y CM (Y-Coordinate of the Center of Mass)-ft.0.08 W T (Total Weight of Mass Point)-Kips 1444 IMX (Rotary Weight Moment of Inertia about X-Axis)K-ft 2 162,323 IMY (Rotary Weight Moment of Inertia about Y-Axis)K-ft 2 379,552 IMZ (Rotary Weight Moment of Inertia about Z-Axis)K-ft 2 470,152 Hand Calculation 26.19 0.08 1444 162,320 379,550 470,150 SAG024 runs on the Honeywell 66/60 system.
Reference:
(1)Bear, F.P.and Johnston, R.E., Jr., Vector Mechanics'for Engineers:
Static and:DYnamics, McGraw-Hill t 1962, pps.343-347.
SB 1&2 FSAR TABLE 3F-7 SAG025 (SECTION)The follo\Jing is a comparison of the results of hand calculations with SAG025 for a system of resisting structural elements between floors in a typcial shear building.SAG025 Hand Calculations XeR (X-Coordinate of Center of Rigidity)-ft.26.3 26.257 Y CR (Y-Coordinate of Center of Rigidity)-ft.0.0 0.0 Atr (Area)-ft 466.0 466.0 SFX (Shear Shape Factor about X-Axis).456 0.456 SFY (Shear Shape Factor about Y-Axis).555 0.555 I XX (Moment of Inertia about X-Axis)-ft.11,100 11,079 I yy (Moment of Inertia about Y-Axis)-ft.44,000 43,957 J (Torsional Constant)-ft.117,000 117,470 SAG025 runs on the Honeywell 66/60 system.
SB 1&2 FSAR TABLE 3F-8 (Sheet 1 of 2)PM-910 (LESCAL)Amendment 56 November 1985 The following is a comparison of the results from the LESCAL computer program with hand calculations.
LESCAL calculates the stresses and strains in rebars and/or concrete in accordance with the criteria set forth in Subarticle3511.1 of ASME Section III, Division II.The section is concrete reinforced with horizontal, vertical and/or diagonal rebars, subjected to axial force and moment on a vertical and horizontal face and in-plane shear.When inplane shear forces are" included, a solution is obtained by solving Duchon's equations(l).
5&.Hand Load Condition Parameter LESCAL (Ksi)Calculations I 5fD.D+Fa+E s f m outside 29.39 29.46 Applied@e.g-of fh outside 23.08 23.05 I Concrete Section fseis.(3)52.26 52.35 5G,.fsets.(4)0.21 0.21 f m inside 26.67 26.75 f h inside 23.82 23.77 D+1.25Pa+l.25Eo f m outside-2.22-2.99 Applied@C.9-of f n outside-0.41-0.16 Concrete Section fseis.(3)9.70 SG 9.47 fseis*.(4)-12.34-12.63 f m inside 38.37 39.34 fh inside 1.98 2.12 D+P a+E s f m outside 37.70 37.70 Applied@e.g.f h outside 25.08 25.07 of Rebar fseis.(3)57.41 57.41 fseis.(4)5.37*5.37 f m inside 12.74 12.73 fh inside 19.01 19.01 SB 1&2 FSAR TABLE 3F-8 (Sheetof 2)Amendment S6 November 1985 Load Condition D+l.25Pa+l.25Eo Applie,d@c.g.of Rebar Parameter f m outside f h outside fseis.(3)fseis.(4)f m inside fh inside Hand LESCAL (Ksi)Calculations-2.01-1.77 7.33 7.82 16.07 16.08-10.76-10.02 40.94 40.64 9.54 10.06 LESCAL runs on the Honeywell 66/60 system.Notes (3)and (4)indicate directions of seismic rebars.
References:
(1)Duchon, N.B.,"Analysis of Reinforced Concrete Membrane Subject to Tension and Shear," ACI Journal, September 1972, pp.578-583.
SB 1&2 FSAR TABLE 3F-9 SAG054 (RESPONSE ENVELOPE)SAG054 is a post-processing program for STARDYNE yhich is used in seismic analysis The program spreads the peaks of the amplified response spectra created by SAG058 (See Table 3F-l)by a predetermined amount and tabulates the ordinates and abscissas of the resulting curve.Verification of this program is accomplished by visual inspection of the graphical output to insure that the raw data has, in fact, been enveloped.
SAG054 runs on the CDC CYBER-175 svstem.
I<t SYM.I r----I (0)FINITE ELEMENT
(-.2607)-.{R-STRESS)x 10 psi (+0.9218)(+0.7915)(+0.5997)o SAG 001-EXACT SOLUTION RADIUS-4(T-STR ESS)X lOps i 1.8 1.6 1.4 1.2 1.0 b 0.8 V1 V1 w 0.6 a=::.-V1--I<<0.4a=:: 0 0.2 z 0 0.5-0.2-0.4-0.6-0.8-1.0 (b)CALCULATED STRESSES ANALYSIS OF THICK-WALLED CYLINDER UNDER INTERNAL PRESSURE
REFERENCE:
GALLAGHER, R.H., FINITE ELEMENT ANALYSIS, PRENTICE-HALL/INC.
1975.FIGURE 11.5, PG.317 PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SAG001 SAMPLE PROBLEM NO.1 SEABROOK STATION-UNITS 1&2 FINAL SAFETY ANALYSIS REPORT I FIGURE 3F-1 w O o liN....J'-><LL_N o M o co o f"'-..d 0Z UJ I 0 V")0-.0 0<!)d<t: t-V")I I 0 0 Ll)0....JIN"-><d 0 0 0 0 0 0 0.5 0 0 0 0 0 0 0 0'" 0 0 0 0 0 0..0 0-.0 N N-.0 0++I I 7'"+I co 0........(!sd)
Z PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SAG001 SAMPLE PROBLEM NO.2 SEABROOK STATION-UNITS 1&2 RADIAL SHEAR FINAL SAFETY ANALYSIS REPORT I FIGURE.3F-2 CD oo ro o C\J 0 0 0 z w a Q..lJ.J-.JIC\J\0 x"-LL x 0 J: CJ)...--lJ.J::r: to-CI)0 w wCJ)0 a:: w<t0 z z U 1J...W J: (5 0<D CJ)0 0 0 0:E (!)(!)<t<t to-CJ)CJ)0<:>L{)0 0000 a00 8 0g2 a 00000o 00000o 00000 lO C\J V<.0 CD 0 (\JIII IT" V I (U!/#U!)lN3WOW PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SEABROOK STATION-UNITS1&2 FINAL SAFETY ANALYSIS REPORT SAG001 SAMPLE PROBLEM NO.2 MERIDIONAL MOMENT I FIGURE 3.F-3 SEABROOK UPDATED FSAR APPENDIX 3D PROCEDURE FOR CALCULATING ELASTO-PLASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY ENERGY BALANCE METHOD The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information.
SB 1&2 FSAR Amendment 56 November lQHS A simplified mathematical model ason the next page can be used for elascic-plastic design of pipe restraints.
An energy balance approach has been used to formulate the calculations for determining the plastic deformation in the restraints.
In applying the plastic deformation design for restraints, the regulatory guides require that either one of the following upper bound design limits for metallic ductile materials be met..(3)50%of the minimum ultimate uniform strain (the strain at the maximum stress of an engineering stress-strain curve based on actual material tests for the restraint),'or (b)50%0: the percent elongation as specified in an applicable ASHE.ASTH, etc.Code, specification, or standard when demonstrated to be less than 50%of the minimum ultimate uniform strain based on representative test results.3D-l S1&2 FSAR Simolified approach for elasto-?lastic i\mendnlent 5G November 19R5 If the restraint is to go into the plastic region, then the restraint deflection, d cax* consist of an ela3tic and a portion as sho.wn belov.(Figure 1.0)Restraint DeflectionFigure 1.0-Idealized Restrain:
where, de Restraint elastic deflection at yield stress d max Maximum allowable restraint deflection Rp Maximum restraint resistance Rp=ked e k e Restraint elastic structural stiffness If'F'denotes the applied forcing Function (i.e.*aload in case of a pipe break)and'h'denotes the gap the piping and the restraint, an energy balance relation for this case gives)(see 2.0).-Rp (d cax-de)2 3D-2 SB 1&2 FSAR Amendment 56 November 1985 Ca)Before Impact h(b)After Impact Figure 2.0 Energy balance Analvsis Hodel Rearranging, (Ro-F)2 TIlerefore, d max=1 2 2Fh.;.Rpd e 2 (Rp-F)(1)The above formulation can be further sinlplif:ed in 2Fh is much larg-:r th2n Therefore, assuming.Rpd e<<2Fh Equation (1)gives, dmax:(Rp-F)(2)After determining Cmax.either by equation (1)or equation (2)above (as applicable), the resulting strain in the member should be calculated 3nd should be checked against the criteria give in page 1.
For uniaxial members, the strain e is taken to be equal to L yhere L is the original length of the restraint member.3D-3 SB 1&2 FSAR Pages 4 and 5 Deleted in Amendment 56 Amendment 56 November 1985 SEABROOK UPDATED FSAR APPENDIX 3E PROCEDURE FOR CALCULATING ELASTO-PLASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY EQUIVALENT STATIC ANALYSIS METHOD The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information.
SB 1&.2 FSAR APPENDIX 3E PROCEDURE FOR CALCULATING ELASTICALLY DESIGNED PIPE WHIP RESTRAINT LOADS BY EQUIVALENT STATIC ANALYSIS METHOD PREPARED BY: REVIDVED BY::1/.1.11}1 F.JAN MECHANICAL
.'lliALYSIS11/29/77 R.F.PERRY.{l.
A..'IALYS IS GROCP In order to evaluate the response of an elastically designed pipe whip to a pipe break load by using the equivalent static analysis approach, the load factor associated with the applicable forcing function'and the clearance (gap)becween the pipe and the restraint has to be A simplified mathematical model as shown the oext page,' be used to the dynamic load factor.Since the pipe size effects are already being.reflected in the magnitude of the pipe break load, the pipe size alone is not considered again as a model parameter.
The load factor (DL'F)*thus determined is used to calculate the restraint:
load (R)as follows: R*a X DLF.-where:{1.26 for steam-saturated water ct.: 2.0 for subcooled non-flashingu.s.NRC Standard Review Plan, 3.6.2 (III)(2)(c)(42]P*Operating PressureA*Pipe Break Area A series of curves for determining the restraint loads for steam-saturated water or steam-water mixturesare given in Pages3-14. A S1J1PLE MODEL FOR LOAD FACTOR By substituting (3)into (2), we have F(h+d)=1/2{...L\d 2 dstJ F d eS k F(h+d)1/2 kd!From (1).k&..!....d st (1)(2)(3)Fh F.\d--.----L.//#1//F/l/CD..CD Or, (d2 dstJ-2(...!-\-2(-!:""\c 0\d st') DLF d*-z: d st Where, F*Applied Load(Pipe Rupture Load)d st c Restraint deflection for statically applied Fd*Maximum restraint deflectionh-Gap sizek*Restraint stiffness DLF C Dynamic load factor )*I*,*'1 C*,***,., i,.I*,"1 rf 2.J*,*.,*t 1 0'P-A INLBS.=O.f2 00 INCHES FOR ELRSTIl PIPE WHIP RES(Applicable nly to wa er or r mixtures, 2 1.26))**.7.tleT FOR ElRSTI PIPE RES RRINTS.(Applicable I nly to steam1saturated Ya er or steam-wat r 1.26)GRP=0.25 00 INCHES J'.,*,.'1 rf*,""'1 rJ IN LBS.**"'1 cJP*A J*,*,.'1 ct 2**
4I*,*'1 0'.: 'c'."*'1 O*IN LBS.GRP=0.50 00 INCHES J***,..0 4P*R FOR ELASTl'PIPE WHIP(Applicable nly to.steamr!saturated wa er or steam-wat r
- 1.26).)*I*"'1I.10= GRP=0.75 00 lNCHES FOR ELASTI PIPE WHIP RES RAINTS.(Applicable nly to steam*saturated.wa er or steam-wat r mixtures ,a*1.26)J 4 I*,,'1 0'2.J*"*,.'1 rt IN LBS.J***.,.'1 O*P*R
CURVES FOR PI?E WHIP RES RRtNTS.(Applicable 6nly to stearn'saturated water , or steam-W8lrr*1.26)-7-*,*"', rj IN LBS.=1.00 00 INCHES)***,." 0'P*R:*I*,*'1 cr CU FOR PIPE(Applicable to steam+saturated wa er or steam-wat' r mixtures, l-1.26)4*,.,.'1 rJ IN LBS.=1.25 00 INCHES IC CU.YES FOR1PIWHIP RESI NTS.I to steac saturated water or steam-wa ler mixtures,*1.26)GRP=1.50 00 INCHES J 4 J,*"'1 O*P*)*I*1,'ilt IN LBS.J***, 1'1 O*)4,., tl lC , I , 4 , 4,*t o',*&4 7.'I 0 5 IN lBS.GRP=1.7500 INCHES ,*I*, 8'1 O*P*A PARAMETRIC CU VES FOR ELASTI PIPE WHIP RES RRINTS.(Applicable nly to steam wa er or steam-wat r mixtures,Q1.26), 4,*,*t 0'1 0'I., 0It#I"')N"0 en CD ,...CD lI)*trl N'b (1)cD ,...CD V)f'I")*U UP'S/IN.100000 enQ),...10000 (,,()V).000* f'I')2000 N b 5 8l e 8 1 O*IN LBS.GRP=2.00 00 INCHES ,I e 7 ,*J 0'P*A PRRRHETR1C CU V£S FOR ELRSTI PIPE RES(Applicable only to steam saturated wa er or steam-wa er
=1.26)J*I*,.e 0'I.-1", N po.0 en CD t-ao V)*C'I")N b (7)CD r-CD\f)I{..,'N I{I'S/IN.100000 N (J)(D-J z"b enr-CD V)fI")N b m CD f"-lOC CD&I).0.." 10 , 0'GAP=2.50 00 INCHES CU YES FOR ELASTI PIPE WHIP RES RAINTS.(Applicable nly to steam saturated waler or steam-wat r e 1.26)J 4**,**I J,*, i*O*S 4 i 87*I 0 6 IP*A IN LBS.I*10**N'b I...11;"1".*00000m-I Z a:: '0000"'000 U)4000 JDOO*2000 1000'iO.00 210 100'0 ***'" C GAP=3.00 00 INCHES J 4**,**0)I ,.I*,*'1 O*).**,*t rt I J 4**,., 1 rfP*R IN LBS.PRRRMETRIC FOR ElRST}PIPE WHIP RES RAINTS.(Applicable bnly to steam*saturated wa e+or steam-watbr
- 1.26)I..v,-.------..,...------.,..--------;------, 10000 c: 1000 coeto HGO IlOO IDOO".tOO 211 tOl FOR PIPE WHIP(Applicable only to or steam-watir
- 1.26)=0.06 50 lNCHES J.***, t.O*P)(A***,.'1 ct IN LBS.J**""lcf J*""'1 SEABROOK UPDATED FSAR APPENDIX 3F VERIFICATION OF COMPUTER PROGRAMS USED FOR STRUCTURAL ANALYSIS AND DESIGN The information contained in this appendix was not revised, but has been extracted from the original FSAR and is provided for historical information.
SB 1&2 FSAR APPENDIX 3F VERIFICATION OF COMPUTER PROGRAMS USED FOR STRUCTURAL ANALYSIS AND DESIGN Amendment 54 February 1985 Computer programs used for structural analysis and design have been verified according to the criteria described in the US NRC Standard Review Plan 3.8.1, Section II-4(e).(a)The following computer programs are recognized in the public domain, and have had sufficient history to justify their applicability and validity without further demonstration:
Hardware Source STARDYNE CDC CDC(l)MARC-CDC CDC CDC(l)STRU-PAl<CDC CDC(l)System Professional CDC CDC(l)ANSYS CDC CDC(l)STRUDL UCCEL PSDI(2)UEMENU UCCEL UCCEL(3)(1)CDC-(2)PSDI-(3)UCCEL-Control Data Corporation P.O.Box 0, HQWOSH Minneapolis, Minnesota 55440 Programs for Structural Design, Inc.14 Story Street Cambridge, Massachusetts 02138 UCCEL Corporation P.O.Box 84028 Dallas, Texas 75284 (b)The following computer programs have been verified by solving test problems with a similar and independently-written and recognized program in the public domain: SAG058 (Response Spectra)3F-l SB 1&2 FSAR Amendment 54 February 1985 A summary of comparison results is shown 1n Table 3F-l.AX2 (Axisymmetric Shell Program)A verification manual comparing AX2 with results obtained from either ANSYS or BOSOR4 (Lockhead Missile and Space Company-Palo Alto, CA)can be obtained from Pittsburgh
-Des Moines Corporation, 3400 Grand Avenue, Neville Island, Pittsburgh, PA 15225 (c)The following computer programs have been verified by comparison with analytical results published in technical literature:
SAG001 SAGO10 (WILSON 1)(WILSON 2, DYN)Summaries of comparison results are shown in Tables 3F-2 and 3F-3, respectively.(d)The following computer programs have been verified by comparison with hand calculations for test problems which are representative of the type used in actual analyses: A summary of comparison results is shown in Tables 3F-4 through 3F-8.SAG008 SAGOI7 SAG024 SAG025 PM-9IO*PM-906 (TAPAS)(FOUREXP)(MMIC)(SECTION)(LESCAL)(STRAP)I 54 (e)The following computer programs are verified by inspection of the graphical output data.SAG054 (Response Envelope)A typical verification example is presented in Table 3F-9.*Documentation of STRAP is available in the Final Safety Analysis keport for the Carolina Power and Light Co., Brunswick 1&2, US NRC Docket Nos.50-324 and 50-325.3F-2 SB 1&2 FSAR TABLE 3F-l SAG058 (RESPONSE SPECTRA)SAG058 (1)is verified against STARDYNE, sub-routine DYNRE5.The input T/H is of 22 second duration, with a time interval of 0.01 seconds and a maximum acceleration of I.Dg.Spectral Acceleration (g)Frequency 0.5%Damping 2%Damping (Hz)SAG058 DYNRE5 SAG058 DYNRE5 0.33 0.91 0.98 0.79 0.83 1.00 2.68 2.67 2.03 2.03 2.00 8.23 8.23 4.33 4.32 3.03 6.04 6.02 4.31 4.32 4.00 5.20 5.18 4.40 4.37 5.00 5.25 5.21 3.95 3.94 6.25 7.51 7.42 4.47 4.38 7.14 5.33 5.25 3.94 3.90 8.33 4.87 4.80 3.68 9.09 7.09 6.93 4.96 4.81 10.00 5.00 4.973.373.35 20.00 2.61 2.60 1.77 1.77 33.33 1.22 1.22 1.13 1.14 (1)SAG058 is an in-house computer program run on the Control Data Corporation CYBER-175 and is used as a toSTARDYNE program.
SB 1&2 FSAR TABLE 3F-2 SAG001 (WILSON 1)The following is a comparison of the results from SAGOOI with results obtained from published technical literature.
SAGOOI runs on the Honeywell 66/60 system with the GeOS operating system.Samnle Problem No.1 Analysis of a thick-walled cylinder subjected to an internal pressure.Reference-Gallagher, R.H., Finite Element Analysis, Figure 11.5)pg.317, Prentice-Hall, Inc., 1975.Comparison of the theoretical solution with the WILSON 1 solution is shown on Figure 3F-l for the radial stress and the hoop stress.Sample Problem No.2 Analysis of a cylindrical shell, fixed at both ends and subjected to an internal pressure.Reference-Timoshenko, S., Woinowsky-Krieger, S., Theory of Plates and Shells, Second Edition, pg.475, McGraw-Hill, 1959.Comparison of the theore*tical solution with the WILSON 1 solution is shown on Figures 3F-2 andfor the radial shear and meridional moment, respectively.
SB 1&2 FSAR TABLE 3F-3 SAG010 (WILSON 2, DYN)The original version of SAGOla,"Dynamic Stress Analysis of Axisymmetric Structures Under Arbitrary Loading," written by Ghosh and Wilson was revised by UE&C in September, 1975.The program is distributed in the public domain by the Earthquake Engineering Research Center, University of California, Berkeley, California.
The program has been verified against a series of problems whose results are published in technical literature.
Documentation of this verification is contained in the report EERC 69-10 which can be obtained from the Earthquake Engineering Research Center.SAGOla is run on the Honeywell 66/60 System.
SB 1&2 FSAR TABLE 3F-4 SAGOOa (TAPAS)The following is a comparison of the results from SAG008, which computes the temperature distribution through plane and axisymmetric solids, with hand calculations.
The sample results are for the temperature distribution through the thickness of a hemispherical concrete dome which is 42 inches thick and subject to 1200F inside and (-)lOOF outside.Element No.724 848 972 1096 1220 1344 SAGOoa(l)(OF)110.38 88.89 65.33 42.12 19.26 (-)1.04 Hand Calculation (OF@Mid Pt.of Elem.)110.7143 89.048 65.833 42.619 19.405 (-)0.7143 SAGOOB runs on the Honeywell 66/60 system
References:
(1)Wilson, E.L., Nickell, R.E.,"Application of the Finite Element," Journal of Nuclear Engineering and Design, 4, 1966.
SB 1&2 FSAR TABLE 3F-5 SAGO!7 (FOUREXP)Amendment 56 November 1985 The following is a verification of SAGOl7 with hand calculations for arbitrary loading distribution which is an even function and can be expanded using a cosine Fourier Series.The periodic*function is,£(6)=-ne<01 La Q<8S.1TJ Comparison of Fourier Coefficients:
o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16'17 18 19 20 SAG017(1)1.5699-1.2739-0.0019-0.1421-0.0019.-0.0516-0.0020-0.0266-0.0021-0.0164-000022-0.0112-0.0023-0.0082-0.0025-0.0063-0.0028-0.0051-0.0031-0.0042-0.0036 Hand Calculations(2) 1.5708-1.2732 o-0.1415 o-0.0509 o-0.0260 o-0.0157 o-0.0105 o-0.0075 o-0.0057 o-0.0044 o-0.0035 o I 5{, SAGOI7 runs on the Honeywell 66/60 syst.em.
References:
(1)The Fourier coefficients are computed for a digitized function by a recursive technique described in Mathematical Methods for Digital Computers, by Rolsten and Wilfs John Wiley and Sons, New York, 1960, Chapter 24.The solution technique is from subroutine FORII in the.IBM Scientific Subroutine package.The program is run on the Honeywell 66/60 system.(2)Wylie, C.R;, Advanced Engineering Mathematics, 4th Ed., McGraw-Hill, 1975.
SB 1&2 FSAR TABLE 3F-6 SAG024 (MMIC)The following is a comparison of the results of hand calculations with SAG024 for the weight of a typcial lumped mass point in la dynamic model of a shear building.Parameter SAG024 (1)XcM (X-Coordinate of the Center of Mass)0-ft.26.19 Y CM (Y-Coordinate of the Center of Mass)-ft.0.08 W T (Total Weight of Mass Point)-Kips 1444 IMX (Rotary Weight Moment of Inertia about X-Axis)K-ft 2 162,323 IMY (Rotary Weight Moment of Inertia about Y-Axis)K-ft 2 379,552 IMZ (Rotary Weight Moment of Inertia about Z-Axis)K-ft 2 470,152 Hand Calculation 26.19 0.08 1444 162,320 379,550 470,150 SAG024 runs on the Honeywell 66/60 system.
Reference:
(1)Bear, F.P.and Johnston, R.E., Jr., Vector Mechanics'for Engineers:
Static and:DYnamics, McGraw-Hill t 1962, pps.343-347.
SB 1&2 FSAR TABLE 3F-7 SAG025 (SECTION)The follo\Jing is a comparison of the results of hand calculations with SAG025 for a system of resisting structural elements between floors in a typcial shear building.SAG025 Hand Calculations XeR (X-Coordinate of Center of Rigidity)-ft.26.3 26.257 Y CR (Y-Coordinate of Center of Rigidity)-ft.0.0 0.0 Atr (Area)-ft 466.0 466.0 SFX (Shear Shape Factor about X-Axis).456 0.456 SFY (Shear Shape Factor about Y-Axis).555 0.555 I XX (Moment of Inertia about X-Axis)-ft.11,100 11,079 I yy (Moment of Inertia about Y-Axis)-ft.44,000 43,957 J (Torsional Constant)-ft.117,000 117,470 SAG025 runs on the Honeywell 66/60 system.
SB 1&2 FSAR TABLE 3F-8 (Sheet 1 of 2)PM-910 (LESCAL)Amendment 56 November 1985 The following is a comparison of the results from the LESCAL computer program with hand calculations.
LESCAL calculates the stresses and strains in rebars and/or concrete in accordance with the criteria set forth in Subarticle3511.1 of ASME Section III, Division II.The section is concrete reinforced with horizontal, vertical and/or diagonal rebars, subjected to axial force and moment on a vertical and horizontal face and in-plane shear.When inplane shear forces are" included, a solution is obtained by solving Duchon's equations(l).
5&.Hand Load Condition Parameter LESCAL (Ksi)Calculations I 5fD.D+Fa+E s f m outside 29.39 29.46 Applied@e.g-of fh outside 23.08 23.05 I Concrete Section fseis.(3)52.26 52.35 5G,.fsets.(4)0.21 0.21 f m inside 26.67 26.75 f h inside 23.82 23.77 D+1.25Pa+l.25Eo f m outside-2.22-2.99 Applied@C.9-of f n outside-0.41-0.16 Concrete Section fseis.(3)9.70 SG 9.47 fseis*.(4)-12.34-12.63 f m inside 38.37 39.34 fh inside 1.98 2.12 D+P a+E s f m outside 37.70 37.70 Applied@e.g.f h outside 25.08 25.07 of Rebar fseis.(3)57.41 57.41 fseis.(4)5.37*5.37 f m inside 12.74 12.73 fh inside 19.01 19.01 SB 1&2 FSAR TABLE 3F-8 (Sheetof 2)Amendment S6 November 1985 Load Condition D+l.25Pa+l.25Eo Applie,d@c.g.of Rebar Parameter f m outside f h outside fseis.(3)fseis.(4)f m inside fh inside Hand LESCAL (Ksi)Calculations-2.01-1.77 7.33 7.82 16.07 16.08-10.76-10.02 40.94 40.64 9.54 10.06 LESCAL runs on the Honeywell 66/60 system.Notes (3)and (4)indicate directions of seismic rebars.
References:
(1)Duchon, N.B.,"Analysis of Reinforced Concrete Membrane Subject to Tension and Shear," ACI Journal, September 1972, pp.578-583.
SB 1&2 FSAR TABLE 3F-9 SAG054 (RESPONSE ENVELOPE)SAG054 is a post-processing program for STARDYNE yhich is used in seismic analysis The program spreads the peaks of the amplified response spectra created by SAG058 (See Table 3F-l)by a predetermined amount and tabulates the ordinates and abscissas of the resulting curve.Verification of this program is accomplished by visual inspection of the graphical output to insure that the raw data has, in fact, been enveloped.
SAG054 runs on the CDC CYBER-175 svstem.
I<t SYM.I r----I (0)FINITE ELEMENT
(-.2607)-.{R-STRESS)x 10 psi (+0.9218)(+0.7915)(+0.5997)o SAG 001-EXACT SOLUTION RADIUS-4(T-STR ESS)X lOps i 1.8 1.6 1.4 1.2 1.0 b 0.8 V1 V1 w 0.6 a=::.-V1--I<<0.4a=:: 0 0.2 z 0 0.5-0.2-0.4-0.6-0.8-1.0 (b)CALCULATED STRESSES ANALYSIS OF THICK-WALLED CYLINDER UNDER INTERNAL PRESSURE
REFERENCE:
GALLAGHER, R.H., FINITE ELEMENT ANALYSIS, PRENTICE-HALL/INC.
1975.FIGURE 11.5, PG.317 PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SAG001 SAMPLE PROBLEM NO.1 SEABROOK STATION-UNITS 1&2 FINAL SAFETY ANALYSIS REPORT I FIGURE 3F-1 w O o liN....J'-><LL_N o M o co o f"'-..d 0Z UJ I 0 V")0-.0 0<!)d<t: t-V")I I 0 0 Ll)0....JIN"-><d 0 0 0 0 0 0 0.5 0 0 0 0 0 0 0 0'" 0 0 0 0 0 0..0 0-.0 N N-.0 0++I I 7'"+I co 0........(!sd)
Z PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SAG001 SAMPLE PROBLEM NO.2 SEABROOK STATION-UNITS 1&2 RADIAL SHEAR FINAL SAFETY ANALYSIS REPORT I FIGURE.3F-2 CD oo ro o C\J 0 0 0 z w a Q..lJ.J-.JIC\J\0 x"-LL x 0 J: CJ)...--lJ.J::r: to-CI)0 w wCJ)0 a:: w<t0 z z U 1J...W J: (5 0<D CJ)0 0 0 0:E (!)(!)<t<t to-CJ)CJ)0<:>L{)0 0000 a00 8 0g2 a 00000o 00000o 00000 lO C\J V<.0 CD 0 (\JIII IT" V I (U!/#U!)lN3WOW PUBLIC SERVICE COMPANY OF NEW HAMPSHIRE SEABROOK STATION-UNITS1&2 FINAL SAFETY ANALYSIS REPORT SAG001 SAMPLE PROBLEM NO.2 MERIDIONAL MOMENT I FIGURE 3.F-3