Text

Rev 0 to ASME Code Evaluation of Braidwood Unit 2 Nozzle F to Include Effects of Proposed Grindouts
	ML20141D987
Person / Time
Site:	Braidwood
Issue date:	02/28/1986
From:	Brandlund B, Marisa Herrera, Ranganath S; GENERAL ELECTRIC CO.
To:	;
Shared Package
ML20141D981	List: ML20141D976; ML20141D987;
References
	MDE-41-0386, MDE-41-386, NUDOCS 8604080348
	Download: ML20141D987 (91)
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J GENERAL $ ELECTRIC MDE#41-0386 3 Rev.0 DRF A00-02669

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ASME CODE EVALUATION OF THE BRAIDWOOD UNIT 2 N0ZZLE F TO INCLUDE EFFECTS OF PROPOSED GRIND 0UTS C

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February 28, 1986 Q

Performed by: /

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M.,0. Herrera, Senior Engineer Structural Analysis Servicer l

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l B. J. Branlund, Engineer Structural Analysis Services l

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Approved by: M n

l S. Ranganath," Manager Structural Analysis Services p

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MDE#41-0386

~' Rev.0 GENER AL h ELECTRIC The document listed below reconciles the original ASME Code Stress Report (Thermal / Mechanical Anal.ysis of the inlet Nozzle Report #5 for Westinghouse Nuclear Energy Systees Rev.1 by Babcock and Wilcox, March 2 1983), to include the effects of the planned grindout in the Braidwood Unit 2 Nozzle F. The listed document considers only the changes related to the proposed repair. All other results are covered by the original certified report.

s The document listed below along with the original certified report J comprise the stress analysis report for the inlet nozzle. I certify that to the best of my knowledge and belief, the Stress Analysis described in the listed decurent is correct and complete and in compliance with the requirements of Paragraph NA-3350 of the ASME Boiler and Pressure Vessel Code (1971 Edition including addenda up to Summer 1973),Section III, Nuclear Power Plant Components.

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LISTED DOCUMENT Type of Title Document Revision Document Number Number Stress Report ASME Code Evaluation MDE 41-0386 0 of the Braidwood Unit 2 Nozzle F to include

-J Effects of Proposed Grindouts Certified by Q ) % c_ \ _

P.E. Number: tw m m i:e l Registered Professional Engineer State: Cnh n:m Date: M4/PA, AQi5?!k'..

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TABLE OF CONTENTS

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1. INTRODUCTION 1

2. ASME CODE REOUIREMENTS 2 O ,

3. ANALYSIS 4 3.1 Finite Element Model 4 3.2 Pressure Case 6 3.3 A>.ial Load Case 6 3.4 Merent Lead Cese 17 (3 3.5 Lineartzation of Stresses 17 3.6 Local Prinary Stress 19 3.7 Primary F1 tis Secondary Stress 20 3.6 Fatigue Lvaluation 20

4. RESULTS 22 0

5. RFFEEENCES 23 APPENLIX 1 - PROCSAP STRDIS Al-1 APPEND 1X 2 - UNIT LOAD CASE RESULTS AND CALCULATIONS A2-1 APP END :' 2 - CALCULATIONS FOR 3/4" GRINDOUT A 3- 1 APPENDIX 4 - CALCULATIONS FOR 1" GRINDOUT A4-1 APPENDIX 5 - CALCULATIONS FOR 1/2" GRIND 0CT A5-1 O

ATPENDIN 6 - TEERMAL RACHETING A6-1 APPENDIN ~ - AREA 0F REINFORCEMENT A7-1

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, MDE#41-0386 Rw.0 GENERAL $ ELECTRIC D 1. INTRODUCTION This report presents the evaluation and results of the Braidwood Unit 2 Reactor Inlet Nozzle F analysis to include the effects of proposed grindeuts. An indication was found in veld WR-19 located at 45' from nozzle top dead center. A prior American Society of Mechanical Engineers (ASME) Code evaluation var performed for the nozzle (Reference 1). The original analysis showed compliance with all ASME Code O requirements. However, the proposed grindeuts vill cause a localized concentration of stress requiring a re-evaluation and reconciliation of the original report to include the grindout effects.

T) The depth of the detected indication has been reported at approximately 3/4 of an inch. However, due to uncertainty in detection accuracy, the analysis considered grindout depths of 1/2, 3/4 and I". A three to one tapering of the grindeut was used for the finite element D modeling.

Results of the analysis show that all ASME Code requirements are maintained even with the grindouts. Therefore, the inlet nozzle is

") acceptable with a grindout of up to 1" in depth and a three to one tapering.

The conclusions in the original report (Reference 1) are still C valid since the grindout vill have a localized effect only.

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MDE#41-0386 R:v.0 GENERAL h ELECTRIC s 2. ASME CODE REQUIREMENTS Nuclear power plant pressure vessel components are designed to satisfy the ISME Code Section III requirements. The key requirements to O be satisfied are (i) primary stress limits to prevent rupture, and (ii) fatigue usage limits to prevent fatigue crack initiation. For a nozzle, the primary stress limits are P <S and P +P < 1.5 S ,where P is b

the primary membrane stress, P is the primary local membrane stress and O P is the primary bending stress.

b S,is the ASME Code design stress intensity for the low alloy steel material. The proposed grindouts vill be at the nozzle to vessel junction. Therefore, the membrane stress due to pressure can be classified as a local primary stress (Section NB-3200, paragraph NB-3217 ASME Code, Reference 2). In addition, the 3

bending stress due to pressure, axial loading and moment loading are classified as a secondary bending stress per the same Section in the Code. The requirements for the section of interest are therefore.

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1) Local primary stress (Pt ) <1.5 S,

2) Local primary stress (P ) +

0 secondary stress (Q) <3 5 (Not required for faulted conditions)

Further checks are required if requirement 2 is violated. Thesc

? additional checks are:

3) P + Q -(Thermal Bending) <3 S, O 4) Assure that thermal racheting does not occur.

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MDE#41-0386 (3~

R:v.0 GENERAL h ELECTRIC ,

J The second requirement in the ASME Code is the limit on fatigue usage. This requirement assures that fatigue induced crack initiation J' does dot occur.

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In addition, it must be verified that removal of the material does not cause area of reinforcement requirements to be violated.

C) The analysis given in this report re-evaluates all of the above requirements at the grindout location.

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MDEf41-0386 R v.0 GENERAL $ ELECTRIC

3. ANALYSIS

.- A finite element model was developed and the actual applied' loads and

) pressures were used to determine the stress at the ligament of interest.

The original stress report (Reference 1) was conservative since Bijlaard type analysis and shell modeling techniques were used. The thermal analyses were not redone. Instead, the thermal stress results in Reference I were used and magnified by a conservative factor.

3.1 Finite Element Model

The finite element model was developed using the ANSYS finite element program (Reference 3). Reference 4 was used to obtain the necessary geometric dimensions. The finite element model is shown in Figure 1. The model is axisymmetric using isoparametric quadrilateral elements (STIF42) of the ANSYS library. The location of the proposed grindout is shown in Figure 1. The radius of the vessel portion of the model is 1.5 times the radius of the actual vessel. This provides an effective stress equal to the average of the hoop and axial stress in the cylindrical vessel. Since the proposed grindouts are at 45* from the top-dead-center of the nozzle, 1.5 times the radius of the vessel is an appropriate value. It should be noted that the cladding on the inside portion of the vessel was not included in the model.

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The grindout configuration was incorporated in the model by modifying the region in the vicinity of the nozzle to vessel weld.

Since the model is axisymmetric, the grindout is conservatively codeled as a fully circumferential grindout. This is conservative since the grindout will only locally affect the stresses, and the surrounding material will provide reinforcement to the grindout area.

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MDE#41-0386 R;v.0 GENERAL $ ELECTRIC Three grindout depths were considered; 1 inch, 3/4 inch and 1/2 inch. A three to one taper was used for each cace. Figures__ 2 through 4

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show the model in the vicinity of the grindout.

The vessel vall farthest from the nozzle was fixed in the circumferential direction to simulate symmetry. The same edge was allowed to expand radially.

To evaluate all of the requirements, three unit cases were performed for each grindout depth. These were,

1) Internal pressure (1000 psi)

2) Axial load on pipe edge (2447 kips)

3) Moment loading on pipe edge (91580 in-kips)

Each of these cases are described in the following sections.

3.2 Pressure Case An internal pressure of 1000 psi was applied to all internal surfaces. An axial load of PR/(2t) was applied at the pipe end to simulate a closed system. Figure 5 shows the applied loading. Figures 6 through 11 show the results for the unit pressure case. Plots are given for SX (stress parallel to surface) and SZ (hoop stress) for the three grindout depts. The effect of the grindout can be seen in these figures.

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3.3 Axial Load Case To simulate an axial load, a pressure load was applied at the pipe end. The applied pressure was -10000 psi which is equivalent to 2447.38

_i_ in-kips. Figure 5 shows the applied loading.

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3.4 Moment Load Case

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To determine the stress due to an applied soment at th pipe end.

O the non-axisymmetric loading capability of AFSYS (ST1F25) was used.

This ANSYS option allows non-axisymmetric loading on an axisymmetric model and gives the maximum stress results as output. The unit moment was 91580 in-kips. Figure 5 shows the applied loading.

U The results of the three unit cases can be scaled to determine the actual stress for the particular loadings.

O" 3.5 Linearization of Stresses To assure that rupture does not occur, the ASME Code has requirements on primary stress and secordary stress. In accordance with O.

Section NB-3200 of the ASME Code, to check against these requirements the stress at the ligament of interest must be separated into a membrane (constant) stress, and a bending stress. This procedure is illustrated in Figure 12.

Per Section NB-3200 of Reference 2. the menbrane (constant) stress due to pressure, moment, and external load are classified as local membrane (PL ). The bending components are classified as secondary O bending (Qb )*

To perform the linearization of the stress distributions, a computer code was used. The code is given in Appendix 1. The stress u~ values through the ligament thickness at the location of the grindout were input into the program. The output consists of membrane stress, bending stress and peak stress at the inside and outside surfaces.

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ACTUAL PEAK STRESS STRESS O

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-e EQUIVALENT g SECTION _ MEM3FBE g THICl2;ESS STRESS V -

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, FIGURE 12 LIliEARIZATION OF STRESS THROUCH A SECTION THICKNESS

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MDE#41-0385 R;v.0 GENER AL $ ELECTRIC Although the ligament located at the deepest part of the grindout will obviously give the highest stress concentration for fatigue, it is not obvious that the P and P +Q values vill also be maximut there.

J Therefore, for the P and P +Q checks, all of the ligaments which are t

located at the grindout were examiaed. However, the results tabuinted present only the results for the ligament at the deepest grindout location. The results for all of the ligaments are given in Reference 5.

Appendix 2 gives the through wall stress distribution and linearized stress results at the liga =ent of interest for the three grindout depth cases.

3.6 Local Primary Stress To determine the local primary stress at the ligaments of interest, the information in Appendix 2 is scaled to the appropriate values and combined. As stated earlier, the limit on P is 1.5 S ,. P is composed of the ecebrane stress due to pressure, applied axial load and applied moment. The cases investigated by the original report are shown in Table 1.

TABLE 1 CASES USED IN P CHECK Case 3+X q

3-X 15+X 15-X 16+X

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MDE#41-0386 g Rsv.0 GENERAL $ ELECTRIC O

3.7 Primary Plus Secondary Stress (P+Q)

.- The original analysis (Reference 1) showed that P+Q eiceeded 3 S, O ,

without the grindout effects. It is expected that this condition will also occur considering the grindout effects. Therefore, the requirement on P+Q -(thermal bending) was evaluated directly. It should be noted that P+Q <3 S ,is not a limiting condition as long as a simplified O elastic-plastic evaluation is performed consistent with Paragraph NB-3228.3 of Reference 2.

3.8 Fatigue Evaluation O

In the original report (Reference 1), the outside surface of the vessel located at the grindout location was determined to be the most severe with respect to fatigue. Therefore, only the outside surface of O the ligament located at the maximum grindout depth will be evaluated for fatigue initiation. The peak stress values were obtained from the base cases and magnified by the appropriate factors.

O The selection of the stress state combinations for fatigue evaluation was performed in Reference 1. These same combinations were used for the fatigue evaluation considering the grindout.

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MDEf41-0386 ['

IO Rev.0 i

j I GENERAL $ ELECTRIC

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! The detailed calculations for the 3/4", 1" and 1/2" grindouts are given in Appendices 3, 4 and 5. respectively. -

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lO Appendix 6 gives the detailed calculation for racheting.

i Appendix 7 gives the detailed calculation for required area of

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reinforcement.

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MDE#41-0386 R:v.0 GENERAL $ ELECTRIC 4.0 Results

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- The results of the analysis are summarized in Table 4. .

TABLE 4.1 ANALYSIS RESULTS (ksi)

P +Q- FATIGUE GRINDOUT CASE P ALLOWABLE THERMAL BENDING ALLOWABLE USAGE 1/2" 30.24 1.55 ,=40.1 59.48 35 ,=80.1 . 531 <1 Faulted 60.55 1.055,=84 a '

3/4" 31.62 40.1 63.3 3S,=80.1 .586<1 Faulted $2.71 84 -

1" 30.5 40.1 64.6 3S,=80.1 .614<1 Faulted 54.39 84 -

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The requirement to prevent racheting was satisfied, and the requirement on area of reinforcement was satisfied.

Results of the analysis indicate that all the ASME Code requirements are satisfied for the three grindout configurations.

Therefore, the inlet nozzle is acceptable with the planned grindout repairs.

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MDE#41-0386 R;v.0 GENERAL $ ELECTRIC a

REFERENCES

1. " Thermal / Mechanical Analysis of the Inlet Nozzle Report #5" for

,- Westinghouse Nuclear Energy Systems Rev.1. Performed ~by The Babcock and Wilcox Company, March 1983.

2. ASME Boiler and Pressure Vessel Code,Section III, 1971 Edition with Summer 1973 Addenda.

3. ANSYS Engineering Analysis System Version 4.1. Swanson Analysis

]) Systems, Inc., Houston, PA, 1983.

4. B&W Drawing #185 338-0 Inlet Nozzle Details and Assembly.

5. Design Record File #A00-02669. General Electric Company.

6. "Pipt and Support Loading on Primary Nozzles", Report No. 4 for

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Westinghouse Nuclear Energy Systems, Rev.1. Performed by The Babcock and Wilcox Company, March 1983.

7. " Addendum to B&W Co. Contract #640-0016-51/52, Reactor Vessel Stress Report for Braidwood Unit No. 2 (Excessive Feedwater Flow

" Transient Evaluation)", Westinghouse Nuclear Energy Systems, December 1983.

8. Reactor Vessel Stress Report for Braidwood Unit 2 Report No.1, Revision 1, Pages B-76 through B-104 Inclusive, dated 3/83.

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f MDEf41-0386 3 Rev.0 GENERAL $ ELECTRIC O

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O APPENDIX 1 LISTING OF PROGRAM STRDIS O

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MDE#41-0386 R;v.0 GENERAL $ ELECTRIC LIST /hlH/STRDIS 10 REAL NENSTRehEMEEND.NEWSTE,NUAVG5. NUDIE.he-A;e.MO ENT 20 REAL H,hAAr2 30 DInENSION NELN(25 8.C06 Ex t 27) .5TF5(27) .IIE Av0(2' * .5T AVG t 2').TSTE(27) .

403 NEWSTR(27),NUAVG5(27),NUDI5 : 27) .n0.- AF.5 2 s .n0mErs' .27 4.h00Nn 9? ; >

50 LIPENSION H(27), harm 2(27' 60 CALL ATTACht01.'F588?6/ntr/DAIA13*.I.C.15'. >

70 CALL ATTACH (02. 'FE554 0 /rLH '0U11i' 2.C .15Ti . >

80 DO 300 L=1,979 90 N5TR5=0 100 READ (01,500)NEL 110 500 F0hnAT(v) 120 IFtNEL.LE.0)GOTO 301 130 LOCATE =NEtt2 140 READt02,50.siNorESI 150 IF(N0tE51.EG.0 EDTO 11 160 00T0 12 170 11 00N11NUE 150 READ (01 500)(COFDr(I'..i=1.LO(Alt.

190C 200 12 CONTINUE 210 N5TPs= LOCATE 220 FE AbiOI .500 )(EThi.( . > .):1.wiik r i 230 TOTSTF=0.

240 10TDIE=0.

250 DC 100 A=1.(N.,TFS-1+

260 S T A'16 ' h / = ( S T hi '. r. ) + b : R s ( t 4 ] > . . .

270 DISAVG(F )= 4 0FDXe rA1 > -C0%s e r i 280 TETRth)= ETAVG:r)*Di!ader 290 T015TR = TOTS TF +15TR(t. .

300 TOTDI5=T. TD15+Di>A'JC (r -

310 100 CONTINUE 320 hE hSTF = TOT Ll L/ T01 D15 330 T0in09:0.

1 340 DD 101 I=1,r45tLE 350 101 NEWSTR(1)=57R5(1 -nin51R 360 IiG 102 I=1,(NSTks-1>

370 H t I ) =rJEUS TR e l + 1 )-NEud !k( I )

390 NUD15(It= CORiur!+;)-Curuffi Al-2

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- 390 MDMARM(I)=(CORDX(I )-COEM (1) ) M C04 t(I +11-CORL * (! > > /2.

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400 MARM2(I)=c0RDx(I)-c0RDx(1)+(2./3. ) (c0F Dr(141)-c0F nx(I))

410 MOMENT ( I ) = NEWS T R ( I ) *NUDI S ( I )

M ON AR M ( I ) + 0. 58 N'JD I S ( I )

H ( I )

M art'2 ( I )

420 TOTMOM= TOTMON+ MOMENT (I) 430 102 CONTINUE 440 SEEND=(6*TOTMOM)/(TOTDIS TOTDIS) 450 SFEND1= ABS (SEFND)

O 460 SPEND 2=SFEND14(-1.)

470 SPEND =AFS(EFEND) 4E0 IF (NEMSTR.GE.O.0)GOTO 13 490 MEMBEND=MEMSTR-SPEN 1' 500 GOTO 14 510 13 MEM3ENL=MEMSTR+SF5ND U, 520 14 IF(STR5(11.LT.S!kS!NSTRS) tC TO 400 530 PEAASl=STRH 1)-NFMS W-SPE @2 540 PEAAS2=STRE:NST P!. )-tiLn.r i k- S tut ?

550 GO TO 401 560 400 FEALSl=5TRS(1)-MEMSTR-SEEND2 570 F E ANS2=STF S ( N S TR S )-MENS T R- 51FND :

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580 401 CONTINUE 570 WRITE (02 503) 600 WRlrEt02 504) 610 503 FORMAT (' *)

620 504 FORMAT ('IN-UT SThESiES AkE:')

630 WRI TE( 02,202) s S1 FS. I r . : =1,NSTP D

,C 640 WRITE (02 50$?

650 505 FORMA 1( *IN'OT L:0URtc ARE :')

l 660 WRITE (02 203)(C0tts.<}..I=1.LttAi()

j 670 20 WRITE (02,200. MEnSTR.5tOD.CE Ard-) .cEA> S2.rt. 5END

! 680 300 CONTINt'E l 690 301 WRITE (02 204)

O 700 200 FORMAT (/.4x,'MEMFRANE tTFt!5 = '.1:0.c.4,.

7101 ' BENDING STRESSES =(+ 06-) ',Fjo..'.e.4 .

7201 'F E AK51 =' . F10. 2,4's ,

0t ANS2 = ' . 819. 2. u .

7301 4X,'MEMPRANE Pt.US FEN!@3 STRE% =' .f le. ";. . ' i 740 202 FORFAT(4x,6F10.1) 750 203 FORnAT(4X.6F12.3s 1

0 760 204 FORMAT (//)

770 STOP 780 END C

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t MDEf41-0386 O Rev.0 GENER AL h ELECTRIC O

APPENDIX 2 WIT L E CASE RESMS O ,

AND CALCULATIONS O

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UNIT LOAD CASE RESULTS - 1/2" CRINDOUT

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The stress distribution at the section with the deepest grindout depth is given in the following tables.

1/2" CRINDOUT STRESS DISTRIBUTION (ksi) DOE TO INTERNAL PRESSURE LOADING (1000 psi)

STRESS ID ELEMENT ** OD COMPONENT SURFACE 1 2 3 4 5 6 7 8 9 10 11 SURFACE r/ 55 .9 1.5 2.1 2. 0- 3.1 3.6 4.1 4 51 6.19 1.17 12. 2 L 17.25 m o

ay" - 1. o .% .75 .6 .38 .i2 .I9 . C, l.o 1.47 i.S4 1. l

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o-;~ 3.s, 9.s 3 9 .34 9.is ,a s a s.ss s.s4 2.ss 9.x, n.sr iO.3 i o ., s 2 e Stress parallel to surface O

gj7. CRINDOUT Radial Stress E STRESS DISTRIBUTION (ksi) DUE TO **" E

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"88

"8 AXIAL FORCE LOADING (2447 kips) :sp O

STRESS ID ELEMENT ** OD 2 3 4 5 6 7 8 9 10 11 SURFACE COMPONENT SURFACE 1 2.4 z -l.y .33 .bl 1.56 7.60 3 3L 5.37 7.9 3o.73 15.1 i t. 6 7 c, ~3.o 03 .' Is i77 1.5 19 2 .31 2.75 2. D 2 5T o.o 79 o.o . 2. 1 11 0.0 .01 .I ,18 . 3'I .49 ,bl .71 74 99 ' S9

O.0 ,5 by o.o e>

.1,3 ,05 .'5 7 1. t i 1.74 2.36 3.05 3 79 9. 5'l 6.71 7.33 7 41 ." C G ,9 l C e '

t w

U U U U U U C O O O O 1/2" GRINDOUT '

STRESS DISTRIBUTION (ksi) DUE TO MOMENT LOADING

91580 in-ktps)

STRESS ID FLEMENT** OD COMPONENT SURFACE i 2 3 4 5 6 7 8 9 10 11 SURFACE

@ -10.6 - 4.1 - 6.16 - 1. --l. 91 .32 2,(, g,3 3 64 13Rf

. 2o.32 3l,65' 39.vt

.03 .29 .32 f.52 2.'A 3.15 4.25 5 n (..L5 (o.o? 4.14 o 0y o

.,42 .9 f.49 2 lE 3.M 3.? 6 4.2l o

'Ly 0 .L .34 .z5 .c4 9,36 i4,7z is 7 7.o Ia - 5,4 - 4.4<1 -2.N -l.it ,4 i s 3.si r.it 11. 5 8' m

m 2

m

n F-

Conservatively unes 3/4" grindnut results

- Stresses at eiement centroid m

FT9 F=

FTt O

-4

D 5 M' s

.* !2 C

a s

a

O u O 0 0 0 0 0 J U e UNIT LOAD CASE RESULTS - 3/4" CRINDOUT The stress distribution at the section with the deepest grindout is given in the following tables.

3/4" CRINDOUT STRESS DISTRIBUTION (ksi) DUE TO INTERNAL PRESSIIRE LOADING (1000 psi) FOR 3/4" GRINDOUT ID ELEMENT ** OD STRESS SURFACE 2 3 4 5 6 7 8 9 10 11 SURFACE COMPONENT 1

. 55' 9 1.61 2.Z'l Z ?f 2 3 5r 4.19 4.rt 5.81 7.w 4.4 13.6 L 16 A9 Cii

.S G .4 mI . 2. .6 f.I f.6 1.9 lT o.O (Ty - l. o -l.o l' '

l4 O*

'L, 0.0 .; . 2.L . M. --A s .A1 .A9 -A) .sl .I3 a

9. A9 9 51 10 8*6 l ' A "

O~y 9.t, n.g 9. y. 9.is 9.t G 't . c't 't.01 9.ct 'I. G z m

M r-D 3/4" CRINDOUT O

m STRESS DISTRIBUTION (ksi) DUE TO ,

m AXIA1. FORCE LOADING (2447 kips) c7

-4 ID ELEMENT ** OD :x STRESS COMPONENT SURFACE 1 2 3 4 5 6 7 8 9 10 11 SURFACE g

- 2.<i r -2.4s -l.4 4 6 .i1 .96 I.Y 2.7 5.'/ 5 T.92 7.r7 12 Y 7 15.?3 0<

o,s . to 5 %s .G7 .U I. 2 I.6 139 2^ 2. !L I 7i O.o cy, , ci;

. ] l' 'l- ' '4I' I*L I O'O

~

o1 .I - . 0 S' .05 .l1 .'E .55 Lay C.O 4N

, q t, I.49 2.01 2.61 LD 4 '3 4.76 6.IT

,T z ,ct o .L4 _ .. , 43 yg

?Q a

u a

O .

..O O .

. . . .O, O O O O O O O 3/4" GRINDOUT ,

.,. STRESS DISTRIBUTION (kal) DUE TO MOMENT LOADING 91580 in-kips)

s .,,

STRESS ID ELEMENT ** OD COMPONENT SURFACE 1 2 3 4 5 6 7 8 9 10 11 SURFACE c- -to. 6 <1. i 4.% <1. -- l. M , 2i2. 2.6 53 f. 64 83.9 / 20,sz 31.68 39, ur

.1'1 ,74 I.52 2 F# 3.25 ') 23 5~ 27 6.23 6.u? 4.44 o,o Jy O.O .o3

,M ,42 .90 1.45' 2.sF g.o? 3.% 4.2/ O0 0.0 ,2. ,M 723

't< 7 14 , 7 2. / 5,7 o 1,'? 5 3.Sl F, /6 7.o 7,36 /t. 59 (5 - 5..q - 4,49 -2,78 -l.i6 ,4 e

m 2

m

- Stressen at Element Centroid no r-9 @

FT1 W

FTg C"3

==4 llU

.0 C

e 4

e

O O u O O O G J G (

UNIT LOAD CASE RESITLTS - 1" CRINDOUT

't The stress distribution at the section with the deepest grindout depth is given in the following table. ,

STRESS DISTRIBUTION (ksi) DUE TO INTERNAL PRESSIIRE LOADING (1000 psi) FOR 1" CRINDOUT STRESS ID ELEMENT ** OD COMPONENT SURFACE 1 2 3 4 5 6 7 8 9 10 11 StfRFACE Gs 55 .G5 l.SA 2.tS 2.Y L1 A.DL A. 71 S.b 2.12. Q.Il 83 9 lb.5

.76 .W m 2t . 6' .44 .il I.44 i.51 1.e4 o.o ,

0y -I.o --l .05 .9 3-m t f o .03 . 2.1 .33 .41 - 47 .Ti -SL .47 .r7 ,o 3 53 o .0 z m

t 9 T#l 1/lb 9 . 51 9 .11 9. i 1.05 S.19 9.0 9.01 9. %' 7.E to.7 ll.l8 p

" m

& 1" CRINDOUT r m

STRESS DISTRIBUTION (ksi) DUE TO AXIAL FORCE LOADING (2447 kips) a W

~~

STRESS ID ELEMENT ** OD n COMPONENT SURFACE 1 2 3 4 5 6 7 8 9 10 11 SifRFACE E -2.9S -2..S -l Al '.5s .21 1.o5 f.qs 2.17 4.3 6.4 9.0 P. 7 16 .73 3y -l o o c, .1 . 11 .Ss .I l . 2 s' l.64 2. c6 2 44 2.4 i l.7F o.O

.h .W 1. 2. o.*

ty o. o .i3 .li .I 01 . 8 5' .Si l.ot i. LS

,91 .65 .45 .19 1.59 2.1 2 . 71 2, A 4.3 5.t 6.4T 6.04 O, .;

h E' @

?!

C a

se

n ,,

p .

,s -

C v J v ,v. . (v b.., (v., v v

v UNIT LOAD CASE RESUI.TS - 1" CRINDOUT STRESS DISTRIBUTION (ksi) DUE TO MOMENT I.0ADING (91580 in-kips) 'e ID ELEMENT ** OD STRESS SURFACE 2 3 4 5 6 7 8 9 10 11 SURFACE COMPONENT 1 L 2.6 c.1 ct.o 14.7 28.6 33 3 ef t.o G- -II. t cl. (, -(,J7 -4.3 -2.0 2.5 3.4 4.T f.5 6.4 6.o 4.1 o.0 0y o. o.o o.3 c.9 l. 6

.3 -.z .l . b- I.o IS 2.I 2. b' 3.I 2.2 o.O T,y O. .t 7.1 12.l I S'. 2 16 1 o.1 2.o 3. [, .r. 5 et . ~ 7 (r. --5. 0 -4. '7 -2.9 -l.L ci m

2 m

23 3>

r=

c m r"

m

("3

-4 33 Eh

<c a

u a

MDE#41-0386

') Rev.0 GENER AL $ ELECTRIC IJ These stress distributions were input into the timeshare program STRDIS (See Appendix 1) to determine the membrane, bending and peak

, components. The results of the linearization are given below. Note that

) the values for bending are for the outer surface since the outside surface was determined to be limiting.

TABLE A2-1 LINEARIZATION RESULTS FOR 3/4" CRINDOUT g

PRESSURE RESULTS (ksi)

MEMBRANE MEMBRANE + BENDING

3 c 5.4 12.2 o .5 0 y

T .2 .2 Ky c, 9.5 10.1 O

AXIAL LOAD REST *LTS (ksi)

MEMBRANE MEMEPJLNE + BEhTING

[? e 3.2 11.5 c 1.1 2.2 y

T .5 1.3 xy a 2.3 6.1 z

O MOMENT LOAD RESULTS (ksi)

MEMBRANE MEMBRANE + BESTING 1) c 3.67 20.6 c 2.86 6.27 y

T 1.1 3.33 xy 3.22 12.38 z

9-O A2-8

MDE#41-0386 GENERAL h ELECTRIC u

TABLE A2-2 LINEARIZATION RESULTS FOR 1" GRIND 0UT PRESSURE RESULTS (ksi)

O ,

MEMBRANE MEMBRANE + BEhTING c 5.3 12 x

O o .1 1.5 y

T .2 0 c, 9.4 9.9 O

AXIAL LOAD RESULTS (ksi)

MEMBRANE MEM3RANE + BENDING O

e 3.51 12.24 x

e 1.12 2.3 y

T 4 1.13 lC c, 2.45 6.46 i

i l

l l

!O MOMENT LOAD RESULTS (ksi)

MEMBRANE MEMBRA' + BENDINC

'O c 3.8 21.65 X

o 2.96 6.38 7

T 1.08 3.09 x

3.31 12.82 1 a o

'd A2-9

MDE#47-0386 v

R:v.0 GENERAL h ELECTRIC v

TABLE A2-3 LINEARIZATION 1(ES"LTS FOR 1/2" GRIND 0UT

~~

.- PRESSURE RESULTS (kst)

n v

MEMBRANE MEMBkANE + BENDING c 4.76 10.68 X

c .22 1.54 Y

T .67 -1.06 xy c, 9.3 9.56 AXIAL LOAD RESULTS (ksi)

MEMBRANE MEMBRANE + BENDING c 4.35 14.24 m x

'-' c 1.36 2.76 y

T .28 41 xy c 2.76 7.18 z

,O MOMENT LOAD RESULTS* (ksi)

MEMBRANE MEMBRANE + BEh' JING q

'~'

c 3.67 20.6 x

c 2.86 6.27 y

1.1 3.33 xy c 3.22 12.38 z

<)

s.

Conservatively use 3/4" Grindout Results q The results given in Table A2-1 through Table A2-3 can be magnified i

by the appropriate halues depending upon the specific case loading.

" A2-10

MDEll41-0386 O Rev.0 GENERAL $ ELECTRIC

O

!O O

APPENDIX 3 CALCUI.ATIONS FOR lO 3/4" GRIND 0UT l

'O i

lO O

O 9.

l l

t

^3-1 O

n MDE#41-0386

'J Rev.0 GENERAL $ ELECTRIC 0

P CALCULATIONS, 3/4" GRINDOUT

~~

O ,

The cases examined in Reference 1 are:

3+X 3-X O 15+x 15-X 16+X 16-X O

Case 3+X From Reference 1, the applied loads are:

O FX = 517.7 kips FZ = 1911 kips MY = - 63275.81 in-kips O FY = - 318 kips MZ = -31069.38 in-kips MX - -58470 in-kips O

o

_o A3-2 g

MDE#41-0386 O Rev.0 GENERAL h ELECTRIC O

The loads are applied consistent with Figure A3-1.

's O

ALL L ADS ARE ORIENTED AS - ' VESSEL CENTERLINE O GIVEN BEL 0k':

7 d

F y

O Z

F, 3

SUPPORT N0ZZLE j O CENTERLINE F

\ vz NOTE: MOMENTS FOLLOW X RIGHT liAND RULE E

O y 0

FIGURE A3-1 SCHEMATIC OF LOADING ORIENTATION O

O 33_3

MDE#41-0386 R:v.0 GENERAL $ ELECTRIC Taking the square root of the sum of the squares (SRSS) of the moments gives M=/M 8+M x y 23 z2 = / (58470)8+(63275.81) +(31069.38)2'

_ M= 91585.34 in-kips M may be combined with FX to produce an equivalent FX. FX produces the same maximum axial stress at the pipe end as if M and FX vere applied separately and then the stresses combined. This combination is shown g

below.

Stress due to M O

f 8

Z= (16.55 - 14 ) = 1737 in 16.55

'- o = 91585.34 in-kips 1737 in 8 a = 52.72 ksi This stress can be produced by an axial force of the magnitude F ,

F = r(16.55 2_ 34 )2 52.72 = 12902.58 kips The equivalent axial load is F=F +F = 518 kips + 12902 kips g

= 13420 kips Since the unit axial load case used 2447 kips, the appropriate scaling factor is q

R = 13420 = 5.484 2447 The internal pressure for 3+X is 2.485 ksi. Therefore the scaling factor for pressure is R = 2.485 = 2.485 p

1.0 A3-4

MDEf41-0386 Rev.0 GENER AL $ ELECTRIC J

Ra and Rp can be used to scale the stress linearization results given in Appendix 2. Note that the applied moment was conservatively

.' combined with the axial load. However, the axisi loading U ,

is more severe than an equivalent moment.

Pressure Stress (ksi) (R = 2.485)

# T x y z xy 13.42 -1.24 23.61 .497 Axial Load Stress (ksi) (R, = 5.484)

C C C T J x y 2 xy 17.55 6.03 12.61 2.742 Combining Pressure and Axial Load gives

] Pressure + Axial Load. (ksi)

# # I y z xy

_ x_

30.97 4.79 36.22 2.245

The principal stresses are o,c' = 36.22, 31.16, 4.6 ksi g 2 3 The stress intensity is the maximum absolute value of

~# -# -# # -#

12 1 2' 23 " #2 3 31 " #3 1 Therefore, the stress intensity is S = 36.22 - 4.6 = 31.62 ksi l; The allowable value on P is 1.5 S,. From Reference 1, 1.5 S is 40.1 ksi. Therefore P <1.5 S .

m, 3 A3-5

g _ __

MDE#41-0386 Rev.O i

GENERAL $ ELECTRIC

.O Case 3-X From Reference 1, Section B-9 the applied loads are: i

[ FX = -482.3 kips

~

.O FZ = 1911 kips i ,' MY = -63275.81 in-kips FY = -318 kips MZ = -31069 in-kips MX = -58470 in-kips

.O M =/M 2+M x y 23 z2 =

/(63275.81)2+(31069)2+(58470)2 j

= 91585.34 in-kips F = -482.3 kips lO The stress due to M is equivalent to the 3+X case o = 52.72 ksi

The equivalen'. axial load is

,0 F= Fx + F,= -482.3 + 12902.58 kips ;

= 12420.28 kips ,

Since F is less than F for case 3+X, and the pressure is the same,

.O F <1.5 S . '

L m i i

l l

l I I

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(

I O

O A3-6 t

- - - , ~ . . . - , . . - - - - . - . , , - , - - - - - , , _ . . -

~.

MDE#41-0386 U Rev.0 GENERAL $ ELECTRIC J

Case 15+X From Reference 1 Section B-9 the applied loads are: ,-

C) FX = 2168.82 kips FZ = 6110.3 kips MY = -179227.3 in-kips FY = 5519.02 kips MZ = 103495.78 in-kips MX = -146117.2 in-kips O

M=/M 2.g 2.g 2 ,

/ (146117.2)2+(179227.3)2+(103495.78)2 x y z M= 253345.7 in-kips Stress due to M, J

o= M Z

o = 253345.7 = 145.84 ksi 1737

)

F = w(16.55 2_g4 2)(145.84) = 35692.6 kips F= F +F = 2168.82 + 35692.6 x C

= 37861.4 kips

[)

The axial lead scaling factor is, R

a

= 37861.4 = 15.5 2447 C') The internal pressure for 15+X (using faulted condition pressure) is 3.097 ksi. The pressure scaling factor is.

R = 3.097 - 3.097 P g,o

() Stress (ksi)

I x y z xy Pressure 16.72 -1.55 29.42 .619 Axial Load 49.5 17.02 35.58 7.784 Total 66.22 15.47 65.0 7.12 A3-7

MDE#41-0386 g Rev.0 GENERAL $ ELECTRIC O

The principal stresses are .

c' = 67.2, 65.0, 14.49 ksi

, 1 2' 3 O The stress intensity is ,

S= 67.2 - 14.49 = 52.71 ksi 52.71 ksi <1.05 S,= 84 ksi O

O O

!O I

i

!O

^3-8 O

MDE#41-0386 J R:v.0 GENERAL $ ELECTRIC J

Case 15-X From Reference 1. Section B-9 the applied loads are: ,

c3 FX e -3501.33 kips FZ = 6110.3 kips KY = -179227.27 in-kips FY = 5519.02 kips M2 = 103495.78 in-kips MX = -146117.2 in-kips M = /M 2.g 2 g 2 x y z

= /(146117.2)2+(179227.3)2+(103495.78)2 M = 253345.7 in-kips The stress due to M is equivalent to the 15+X case n

a= 145.04 ksi The equivalent axial load is 35692.6 (from 15+X)

F=F +F = 35692.6 - 3501 x 2

= 32191.6 kips Since F is less than F for Case 15+X and the internal pressure is the same, P <1.05 S .

t I

O

~.J

_)

v' l

A A3-9 g

l

" "l- 386 O Rev.0 GENERAL $ ELECTRIC O'

Case 16+X From Reference 1. Section B-9 the applied loads are:

~~

.- FX = 2168.82 kips O FZ = 6110.3 kips

,- MY = -179227.27 in-kips FY = -669.82 kips MZ = -56143.95 in-kips MX = -146117.2 in-kips

') M= /M 2+M 2+M,2 . / (179227.27)2+(56143.95)8+(146117.2)

M= 237959,65 in-kips The stress due to M is g a=M = 237959.65 = 136.98 ksi 2 1737 The equivalent axial load is F = w(16.55 8-14 2)(136.98) = 33524.2 kips O The equivalent axial load is F = 7 +F,= 33524.2 + 2168.82

= 35693 kips O Since F is less than F for 15+X and the internal pressure is the same, P (1.05 S,.

t O

O

.O_

O A3_lo

MDEf41-0386 O Rev.0 GENERAL $ ELECTRIC O

Case 16-X From Reference 1 Section B-9the applied loads are:

.~ FX = -3501.33 kips O FZ = 6110.3 kips MY = -179227.27 in-kips FY = -669.82 kips MZ = -56143.95 in-kips MX = -146117.2 in-kips O M = / M x* +M * +Mz '

y

- / (179227.27)2+(56143.95)'+(146117.2)2 M = 237959.65 in-kips From Case 16+X O F,- 33524.2 kips The equivalent load is F = 33524.2 - 3501.33 O = 30022.87 kips Since F is less than F for 15+X and the internal pressure is the same, P <1.05 S

t u O

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O i-i

^3-11

!O i

1

MDEf41-0386 R:v.0 GENERAL $ ELECTRIC P + Q CALCULATIONS In Reference 1, it was found that the value of P + Q exceeded 3 S .

m

~

The maximum range occurs between iteration 10-2 with external load set J 7+X, and iteration 10-4 with external load set 11R-X. Therefore, the value of P + Q will not be recalculated. Instead, the value of P + Q

-(thermal bending) will be determined and compared to 3 S .

) The loads for 7+X and 11R-X vere obtained from Reference 6.

7+X 11R-X FX = L'".7 kips FX = -430 kips FY -298 kips FY = 136 kips FZ = 510 kips FZ = -430 kips MX = -18830 in-kips MX = 10300 in-kips MY = -24720 in-kips MY = 13000 in-kips MZ = -18510 in-kips MZ = 10300 in-kips FZ = 1400 kips FZ = -1400 kips FY = 981 kips These loads can be applied at the pipe end to give the equivalent loads at the stress plane of interest. The translation results are, 7+X 11R-X i) FX = 518.7 kips FX FY

=

-430 kips 1117 kips FY = -298 kips FZ = 1910 kips FZ = -1830 kips MX = -58030 in-kips MX = 49500 in-kips MY = -63124.1 in-kips MY = 48531 in-hips MZ = -29211.18 in-kips M2 = 15183.8 in-kips

.)

Using these effective loads, the stress at the grindout can be determined. Since the grindout is located at 45' from top dead center, it is conservative to apply the moment which results from the SRSS calculation as was done in the P check. Therefore, the orientation of the grindout with respect to the in-plane moments was considered.

T A3-12

)

MDE#41-0386 R:v.0 l

GENERAL h ELECTRIC

)

Case 7+X The in-plane moment loads are _,

_) M = -6312.1 in-kips y

M = -29211.18 in-kips The stress due to the unit loading (91580 in-kips) is then used to determine the stress at the grindout. The stress due to either M or M*

7 j is:

a= .707 (My or M2 )(cP) 91580 where .707 = reduction in moment due to grindeut being at 45' J, angle from top dead center.

91580 = unit moment (in-kips) o = peak (eembrane + bending) due to either Mx or Mz p

j Scaling the unit moment stresses gives the folleving results Axial stress due to M = 19.05 ksi Y

Axial stress due to Mz = 8.814 ksi

? Total stress due to M +M Z = 27.86 ksi Y

The equivalent moment which produce 27.86 ksi is, M = 27.86 (91580) = 65254 in-kips 39.1 J

where 39.1 = peak stress from unit coment case.

M can then be combined with *M to give the total moment at the grindout.

M = / (65254)2+(58030)2 = 87324 in-kips T

() A3-13

s MDE#41-0386 3 Rev.0 GENERAL $ ELECTRIC b Case 11R-X The in-plane moment loads are

.- M = 48531 in-kips 3 . M = 15183.8 in-kips

- z Scaling the unit moment stresses gives the following results:

Axial stress due to M = 14.64 ksi y

3 Axial stress due to M = 4.582 ksi Total stress due to M +M = 19.22 ksi y z The equivalent coment which produces 19.22 ksi is.

O M= 19.22 (91580) = 45020 in-kips 39.1 M can then be combined with M to give the total moment at the grindeut 3 M = / (45.02)2 + (49.5)2 = 66910 in-kips T

D O

O l

l' A3-14 3

s -

j MDEf41-0386 R:v.0 GENERAL $ ELECTRIC

.)

For case 7+X we have the following ratios to be applied to the unit Cases.

Pressure, R = 2485 = 2.485 .

,- P 1000 g

v Axial load, R = 518 .21 2447 Moment, R = 87.32 = .951 91.85 w)

The table below shows the results of the scaling, 7+X Stress (ksi) o o o T em X y Z Xy V

Pressure 30.3 4.448 25.099 1.24 Axial Load 2.415 46 1.28 .27 Moment 19.58 5.96 11.77 3.166 q

s Total 52.295 10.868 38.149 4.676 For case 11R-X the ratios are,

[) Pressure = 0 Axial Load = -430 = .176 2447 Moment = -66.91 = .728

[] 91.58 The table below shows the results of the scaling, I 11R-X Stress (ksi)

'^) o o o T X y 2 Xy Pressure 0 0 0 0 Axial Load -2.02 .387 -1.07 .228 Moment -14.97 -4.564 -9.013 -2.425

,C)_

Total -16.99 -4.951 -10.083 -2.653 C) A3-15 l

MDE#41-0386

- R:v.0 GENERAL $ ELECTRIC Taking the difference between each stress component of 7+X and 11R-X gives ac = 69.285 ksi x

. oc = 15.819 ksi y

l) ac 2

= 48.23 ksi at xy

= 7.329 ksi The principal stress using these differences in stress values gives 3 e,c' 2 3

= 0.27, 48.23, 14.83 ksi The range is therefore, 70.27 - 14.83 = 55.44 ksi E) However, the above calculation does not include the thermal stress contribution. Since the thermal analyses were not redone for this analysis, the values from Reference I were used. From Section B-8 of Reference 1, the thermal membrane stress intensity is 2.31 ksi and -2.93 J ksi for iteration 10-2 and 10-4 respectively. These stress intensity values must be magnified to compensate for the grindout location. A factor of 1.5 was applied to the thermal membrane component. This is conservative since it was found that the membrane stress intensity due to 3 pressure was magnified by approximately 10% due to the grindout. The magnification of thermal stress is also expected to be less than the magnification due to pressure. Therefore, the factor of 1.5 is considered conservative.

%)

Adding the thermal membrane stress intensity range to the previously calculated range gives P+Q -(Thermal bending) = 55.44 + (2.93+2.31)1.5 m- = 63.3 ksi Since P+Q - (Thermal bending) is less than 3 S , (80.1 ksi), this ASME requirement is satisfied.

O-In addition, since P+Q exceeded 3 S,, and P+Q -(Thermal bending) <3 S,,

an additional check to assure against racheting must be performed. This calculation is given in Appendix 6.

3 A3-16

c3 MDE#41-0386 R v.0 GENERAL h ELECTRIC

~,

FATIGUE USAGE CALCULATION - 3/4" GRINDOUT

,- In Reference 1. the load and transient combinations for T the fatigue

'J usage evaluation was performed. These same stress combinations will be used in this analysis to determine the effect of the grindout on fatigue usage. The combinations are shown in Table A3-1.

C)

TABLE A-31 STRESS STATE COMBINATIONS FOR FATIGUE EVALUATION

2) Combination Stress State 1 Stress State 2 1 7+X and Iter

10-2 11R-X and Iter 10-4

) 2 7+X and Iter 10-2 11R-X and Iter 10-2 3 11R-X and Iter 10-4 7+X and Iter 10-4 i

I) 4 Iter 10-2 Iter 10-4 5 Iter 1-1B Iter 1-3B C) 6 Iter 10-1 Iter 9-2C 7 Iter 6-2 Iter 9-2C I) 8 Iter 6-2 Iter 5-1 9 Iter 6-2 Iter 9-1C c,

_2. 10 Iter 8-3 Iter 8-2

Iter - Iteration A3-17

m MDE#41-0386 R:v.0 GENERAL $ ELECTRIC Combination 1

, K, Factor Calculation q_

Since for combination 1, P+Q exceeded 3 5 , a K factor must be applied to the stress range. In Paragraph NB-3228.3 of the ASME Code (Reference 2), the K, factor is defined as, q

K =1+ (1-n) S )

n(m-1)[2 -1 l i 3S, /

where n = .2 3 m=2 S = Range of P+Q O S can be found by adding themal bending to P+Q -(thermal bending) results previously obtained. P+Q -(Thermal bending) was 63.3 ksi. The thermal bending stress intensities were determined in Section B-8 Reference 1. For Iter 10-2 thermal bending stress intensity was -16.73

') ksi and for Itcr 10-4 the themal bending stress intensity was 19.25 ksi.

The range in thermal bending is 19.25 + 16.73 - 35.98 ksi. As was done with the themal membrane stress intensity, a magnification of 1.5 will be applied to the thermal bending stress. In Reference 5 a factor of 1.4 U was found for internal pressure loading for the 3/4" grindout.

Therefore, a factor of 1.5 is considered conservative since magnification due to pressure is expected to be higher than for themal loading.

O S can be calculated as, Sn = 63.3 + 35.98(1.5) = 117.27 Substituting into K gives, 2 K 1+1 .2 117.27 - 1

.2(2-1) 80.1

= 2.856 I-) A3-18

~

r 1 MDE#41-0386

~# Rev.0 1

GENERAL $ ELECTRIC Next the stress at the outer surface must be determined. The

$) outside surface stress at the deepest grindout location is given below.

Case 7+X T s o C 0

- x y z xy ;

S) Pressure 40.98 0 27.7 0 Axial 3.32 0 1.38 0 Moment 37.25 0 14.96 0 C) Total 81.55 0 44.04 0 Case 11R-X

# # T x y _

z xy

7) Pressure 0 0 0 0 Axial -2.76 0 -1.15 0 Moment -28.4 C[ -11.44 C[

I) Total -31.16 0 -12.59 0 The difference in the stress components is, oc x

= 112.71 ksi g

v Ac = 0 V.

Ac = 56.63 ksi z

LT = 0 xy C) The maximum differenca is 112.71 ksi. The thermal stress values must also be added to the 112.71 ksi. As was done previously a factor of 1.5 is applied to the thermal values. The total stress range is, S

R" * *(* * * * *

') = 174.39 ksi It should be noted that the thermal membrane and thermal bending components are opposite in sign. Therefore it is conservative to add them as done above.

"GL The alternating stress can then be calculated l Sa = 2.856 (174.39) = 249 ksi 2

I

',, A3-19 o

l MDEf41-0386 II Rev.0 GENERAL $ ELECTRIC j However, to use the ASME Code f atigue curve, the value of S musta be 6

modified by E*/E, where E* = 30X10 psi is the basis for the ASME curve and E is Youngs Modulus used in the analysis (E*/E = 1.085) __ l 1

1 db Therefore ;

S, = 1.085 (249.03) = 270.2 ksi 9

From Figure I-9-1, Reference 2, the number of allowable cycles is

45. Therefore the fatigue usage due to this combination is 1

10 = .222 (D 45 Combination 2 and 3 .

l For combinat.on 2 and 3, a conservative factor of 1.87 was applied II to S from Reference 1. This is conservative since 1.87 is the magnification of the outside surface pressure stress due to the grindout.

The stress in combinations 2 and 3 from Reference 1 are 18.5 ksi and l 18.2 ksi respectively.

+1 l l

Therefore S (Combination 2) = 18.5(1.87) = 34.6 ksi l

S* (Combination 3) = 18.2(1.87) = 34.03 ksi 9

The allowable number of cycles is (Reference 2) 1 1

N (Combination 2) = 12000 3

N (Combination 3) = 12000 ,

1 l

The usage due to combination 2 and 3 is l E- U (Case 2) = 190/12000 = .016 l

U (Case 3) = 190/12000 = .016 A3-20 J

.______J

~_

MDE#41-0386 O Rev.0 GENERAL $ ELECTRIC o

Combination 4

[ The two stress states for combination 4 are iter 10-2 and iter 10-4 O Combination 10-2 and 10-4 are comprised entirely of internal pressure and thermal loading. Since the thermal analyses were not performed in this analysis, the thermal stress can be determined from the stress values given in the original report. The thermal stress can be det,rmined e by O subtracting out the pressure stress as predicted by the original report (Reference 1). The pressure stress can be determined by using an internal pressure only transient, iter 10-1. A pressure of 3107 psi was used for iter 10-1.

O The thermal stress is 27.53 ksi The stress due to pressure from the unit pressure case is 40.98 ksi.

The stress on the outside surface for iter 10-2 is c = 40.98 (1.085) + 27.53(1.5) 0= 87 ksi

'O' 29.12 where, 30 = E* from Reference 1 Section B-6 29.12 E O

Iter 10-4 is comprised entirely of thermal stress since internal pressure is O psi. The stress given for 10-4 in Reference 1 is 31.6 ksi. Therefore, the stress range is SR = 87 + 31.6(1.5)(30/29.51) = 135.2 ksi l

l

! The alternating stress is lO S, = 135.2 = 67.6 ksi l 2 O A3-21

MDE#41-0386

{) R:v.0 GENERAL $ ELECTRIC From Figure I-9-1 of Reference 2, the number of allowable cycles is 1700. The contribution to fatigue usage for this combination is U = 270 = .16

) .' 1700 Combination 5 The two stress states for combination 5 are iter 1-1B and 1-3B. The same procedure shown in combination 4 to determine the thermal stress will be carried out for Case 5.

i The stress for iter 1-1B and iter 1-3B from Reference 1 is 80.5 ksi and -21.6 ksi respectively.

The thermal stress for each stress state is, iter 1-1B 29.34 ksi D

iter 1-3B -31.91 ksi For iter 1-1B, the stress on the outside surface using the unit pressure case is 38.21 ksi. The stress on the outside surface for iter 1-1B is a = 38.21 (1.085) + 29.34(1.5) }J!

26.14

= 88.34 ksi For iter 1-3B, the stress on the outside surface using the unit

[)

pressure case is 31.91 ksi. The stress on the outside surface fer iter i

1-3B is e = -31.91 }jl (1.5) + 7.72 (1,085) = -40.3 ksi 29.51 lO V

A3-22 7)

\

MDE041-0386 3 R:v.0 GENERAL $ ELECTRIC

] The stress range is S = 88.34 + 40.3 = 128.64 ksi R

The alternating stress is 128.64/2 = 64.32 kai .

~)

From Figure I-9-1 of Reference 2, the number of allowable cycles is 2100. The contribution to fa:igue usage for this combination is U= 200 = .095 2100 3

Combination 6 The two stress states for Combination 6 are iter 10-1 and 9-2C. The thermal stress for iter 10-1 is O since 10-1 is a pressure only case.

l} The stress for iter 9-2C from Reference 1 is -14 ksi.

The thermat stress for 9-2C is -25.13 ksi The stress on the outside surface using the unit pressure case is 8.31 ksi and 51.23 ksi for iter 9-2C and 10-1 respectively.

.3 The total range is 51.23 (1.085) + [(25.13 30 (1.5) - 8.31 (1.085] = 87.2 ksi 27.85

D The alternating stress is S = 87.2 = 43.6 ksi 2

From Figure I-9-1 of Reference 2 the number of allovable cycles is

D 6000. The contribution to fatigue usage due to this combination is U = 10/6000 = .0017 1

+

?)

A3-23

[)

~,

MDEf41-0386

2) R:v.0 GENER AL $ ELECTRIC D

Combination 7 The two stress states for combination 7 are iter 6-2 and 9-2C.

. Values for 9-2C can be obtained from combination 6.

The stress for iter 6-2 from Reference 1 is 64.2 ksi.

~

The thermal stress for iter 6-2 is 4.4 ksi The stress on the outside surface from the unit pressure case is 44.69 ksi and 8.31 ksi for iter 6-2 and 9-2C respectively.

D The total range is SR = 44.69 (1.085) + 4.4 30 (1.5) + [(25.13 30 (1.5)-8.31(1.085)]

27.7 27.85

= 87.23 ksi The alternating stress range is S = 87.23 = 43.6 ksi

~') 2 From Figure I-9-1 of Reference 2, the number of allowable cycles is 6400. The contribution to fatigue usage from this combination is U =

10/6000 = .0017

,.r-

~J l

l l

w)

7) A3-24

u q MDE#41-0386 II R:v.0 GENERAL h ELECTRIC lD Combination 8 The two stress states for combination 8 are iter 6-2 and iter 5-1.

_, Values for iter 6-2 can be obtained from combination 7. -

O The stress for iter 5-1 from Reference 1 is -13.9 ksi.

The thermal stress for iter 5-1 ic 14.24 ksi.

O The stress on the outside surface from the unit pressure case is 44.69 ksi and .251 ksi for iter 6-2 and 5-1, respectively.

The total range is S =

.69 (1.085) + 4.4 30 (1.5) .251 (1.085)+14.24 30 (1.5)

R 27.7 29.74 O

= 76.91 ksi The alternating stress is S, = 76.91 = 38.5 ksi 2

From Figure I-9-1 of Reference 2, the number of allowable cycles is

) 9000. The contribution to fatigue usage from this combination is U = 80/9000 = .009 m

a A3-25

]

o MDE#41-0386

'# R:v 0 GENERAL $ ELECTRIC O

Combination 9

.~

n" The two stress states for combination 9 are iter 6-2 and iter 9-1C.

Values for iter 6-2 can be obtained from combination 7.

The stress for iter 9-1C from Reference 1 is -36.56 kai.

O The thermal stress is -50.1 ksi The stress on the outside surface from the unit pressure case is O' 44.69 and 27.21 respectively.

The total ranFe is a

S R

= .69 (1.089 + /. 4 30 0.9 -27.210.08H + 50.1 30 U.M 27.7 27.94

= 106.81 ksi O

The alternating stress is 1

S = 106.81 = 53.4 ksi

, a 2

From Figure I-9-1 of Ref 2, the number of allowable cycles is 3000.

The contribut #on to fatigue usage from this combination is O

u - 30 .01 3000 0

O A3-26

m s

e. EDEf41-0386 V R::v.0 GENERAL $ ELECTRIC C

Combination 10

.' For combination 10, a factor of 1.87 was applied to the stress range n'

. in Reference 1. This results in an alternating stress of 10.8 (1.87) = 20.2 ksi From Figure 1-9-1 of Reference 2, the number of allowable cycles is 90000. The contribution to fatigue usage due to this combination is O

U = 390 = .0043 90000 Excessive Feedwater Flow Transient (EFT) Addendum O

in Reference 7 an addendue to Reference 1 was made to evaluate the effect of the Excessive Feedwater Flow Transient (EFT). The report concluded that the effect of this transient on the inlet nozzle fatigue

"**8' "** "i"i"*l* T i"'1"d* 'hi" ""*8' 1" *hi" *"*1 Y 'i 'h*

O alternating stress determined for EFT in Reference 7 will be conservatively multiplied by 1.87 (magnification factor on outside diameter pressure induced peak stress)

O S,= 55.59 (1.87) = 104 ksi The number of allowable cycles fron Reference 2 is 600. The c neribution to the usage factor is (30 cycles of EFT from Reference 7)

O U = 30 = .05 600 The overall usage factor is the sum of the usage factor from each O combination evaluated.

10 U =

7U +U EFT i=1 O U = . 222 + .016 + .016 + .16 + .095 + .0017 + .0017 + .009 +

.01 + .0043 + .05 2

U = .586 *1 O A3-27 1

MDE#41-0386 O Rev.0 GENERAL & ELECTRIC

'O

~

O '

APPENDIX 4 CALCUI.ATIONS FOR 1" CRINDOUT C

O

.O

-O O

O O

.O A4-1

__ _ _ _ _ _ . - - _-. m _ ._._ ._

MDEf41-0386

() Rev.0 GENERAL $ ELECTRIC o

P CALCULATIONS, 1" GRIND 0UT t

Case 3+X [

() ,

From Appendix 3 for Case 3+X. the axial load scaling factor is R, = 5.484 The internal pressure scaling factor is

(

C) R = 2.485 P

}

The resulta after scaling are given below x y z xy

() Pressure 13.17 .25 23.36 .5 Axial Load 19.25 6.14 13.43 2.19 Total 32.42 6.39 36.79 1.69 O

The principal stress values are

= 36.79, 32.53, 6.28 l' #2' #3 Therefore, the stress intensity is S = 36.79 - 6.28 = 30.5 kai The allowable value on P is 1.5 S,. From Reference 2. 1.5 S, is 40.1 ksi. Therefore, P' (1.5 S".

O O

O A4-2 C)

_ MDE#41-0386 R:v.0 GENERAL $ ELECTRis

-s J

Case 3-X As shown in Appendix 3 for the 3/4" grindeut, Case 3+X. bounds Case

-m a

3-X. Therefore P L <1.5 Sm.

Case 15+X From Appendix 3, the scaling ratios are, 7)

R = 15.5 a

, R = 3.097 s p The results of the stress scaling are

-) Stress o a e, t ,

Pressure 16.414 .31 29.112 .619 Axial Load 54.52 17.39 37.90 6.19 7)

Total 70.93 17.7 67.01 5.57 The principal stresses are 7)

= 71.51, 67.01, 17.12 ksi c '

l '2' C3 PL = 71.51 - 17.12 = 54.39 kai <1.05 S u Case 15-X, 16+X and 16-X As shown in Appendix 3 for the 3/4" grindeut, case 15+X bounds cases g

15-X, 16+X and 16-X. Therefore, P <l.5 S,.

A4-3 m

~)

.. _ _ _ _ . _ __ _ -. . - _ _ . _. _ _ _ _ _ _ . . . . _ = - . . - - . . ~ - - - . . - .

t ._m. -

MDEf41-0386 g --

Rev.0 i GENERAL $ ELECTRIC P l

P + Q CALCULATIONS - ,,

~

I As stated in Appendix 3 the value of P+Q -(thermal bending) will be f determined and compared to 3 S,.

From Appendix 3 the equivalent loads and ratios are,

.O <

7+X 11R-X l

FX = 518.7 kips FX = -430 kips FY = -298 kips FY = 1117 kips FZ = 1910 kips FZ = -1830 kips MX = -58030 in-kips MX = 49500 in-kips MY = -63124.1 in-kips FY = 48531 in-kips ,

O MZ = -29211.18 in-kips MZ = 15183.8 in-kips e

M = 87.32 in-kips M = 66.91 in-kips T T O R = 2.485 R = 0 l p P R = .21 R = .176 ;

a a ,

O R = .951 R = .728 m m l

The table below shows the results of the scaling, LO l

f 1

l A4-4

MDEf41-0386

() Rav.0 GENERAL $ ELECTRIC O

7+X Stress (ksi) s

() ,

x y "r xy Pressure 29.82 3.728 24.6 0 Axial Load 2.57 .483 1.357 .24 Moment 20.59 6.07 12.19 2.94

()

Total 52.98 10.28 38.15 3.18 11R-X Stress (ksi)

O

# # I x y z xy Pressure 0 0 0 0 Axial Load -2.151 .404 -1.14 .2

()

Moment -15.77 -4.64 -9.33 -2.25 Total -17.92 -5.04 -10.47 2.45

'O Taking the difference between the different stress components of 7+X and 11R-X gives 40,= 70.9 ksi Ac = 15.32 kai

()

60 z

= 48.62 kai at = 5.63 kai xy 0

O

() A4-5

4

""E#4'- 386

'O i

Rav.0 GENERAL $ ELECTRIC

~O F

The principal stress using these differences in stress values gives.

- 71.46, 48.62, 14.75

. l' 2' 3 ,

O The range is therefore,

! 71.46 - 14.75 = 56.71 ksi l Adding the thermal membrane contribution (see Appendix 3) gives the i

O total range of P+Q -(Thermal Bending),

P+Q-(thermal bending) = 56.71 + (2.93+2.31)(1.5) = 64.6 kai

The value of P+Q -(thermal bending) is less than 3 S, (80.1 kai),

4

O therefore this ASME requirement is satisfied.

Since P+Q exceeded 3 S ,, and P+Q -(thermal bending)<3 S,, an 3 additional check to assure against racheting must be performed. This IO calculation is performed in Appendix 6.

.O

.O i

l

O i

l l-

O F

A4-6 lO

r MDE#41-0386 R;v.0 GENER AL $ ELECTRIC FATIGUE EVALUATION - 1" CRINDOUT The stress on the outside surface due to pressure is essentially the same for the 3/4" and 1" grindout cases. Also, the thermal stress

~

contributions for the 3/4" and 1" cases is determined by multiplying the thermal stress values in Reference 1 by 1.5. The only major dif ference between the 1" and 3/4" grindout case is in the calculation of the K, factor. Therefore, only the K, factor will be recalculated and the fatigue usage for combination 1 re-evaluated. The fatigue usage for the other combination vill be taken as equivalent to those for the 3/4" grindout case.

K, Calculation The value of S can be determined by adding thermal bending to P+Q

-(thermal bending) calculated earlier. The value of P+Q -(therr.al bending) = 64.6 ksi. Adding the thereal tending to this value gives S .

Sn - 64.6 + (19.25 + 16.73) 1.5

- 118.57 ksi Substituting into K gives s

K = 1 + l .2

[118.57-1)/

.2(2-1) \ 80.1

- 2.921

/)

A4-7

MDEf41-0386 g Rsv.0 GENERAL $ ELECTRIC o The stress values at the outside surface are tabulated below.

Case 7+X

~

'x 'y 'z t,y

< Pressure 41.0 0 27.78 0 Axial 3.52 0 1.44 0 Moment 39.0 O_ 15.6 0 O Total 83.52 0 44.82 0 Case 11R-X O 8 x

U y 'r T xy Pressure 0 0 0 0 Axial -2.949 0 -1.968 0 O -11.94 Moment -29.85 0 0 Total -32.8 0 -13.91 0 The difference in the stress components is, O

Ac, = 116.32 ksi Ac, = 58.73 ksi The total range is O SR = 116.32 + (2.31 + 2.93 + 16.73 + 19.25) 1.5 = 178.2 kai The alternating stress is S* = 178.2 (1.085) (2.92) = 282.3 O 2 From Figure 1-9-1 of Reference 2, the number of allowable cycles in

40. The contribution to fatigue usage is 10/40 = .25.

O O A4-8

~,

MDE#41-0386 O Rev.0 GENERAL $ ELECTRIC O

The overall usage factor is the sum of the usage factor for each combination evaluated.

10 ,-

q U =

[

i=1 U, + U EFT U = .25 + .016 + .016 + .16 + .095

+ .0017 + .0017 + .009 + .01 + .0043 + .05 O U - .614 <1 O

O O

O i

'],

A 1

A4-9

.O 2

MDE#41-0386 O Rev.0 GENERAL h ELECTRIC o

APPENDIX 5

~O CALCULATIONS FOR 1/2" GRINDOUT O

^O

'O

'O LO I

i O

l 4

AS-1 l - - -

m MDEf41-0386 U Rsv.0 GENERAL $ ELECTRIC 0- P calculations, 1/2" Crindout Case 3+X .

O From Appendix 3 for case 3+X, the axial load scaling factor is R, = 5.484 The internal pressure scaling factor is .

O- R = 2.485 p

The results after scaling are given below.

x y "r xy g

Pressure 11.83 .55 23.11 -1.66 Axial Load 23.85 7.46 15.13 1.54 O Total 35.68 8.0 38.24 .12 The principal stress values are o, 3,

= 38.24, 35.68, 8.0 g 2' Therefore, the stress intensity is Q

S = 38.24 - 8 = 30.24 kai The allowable value on tP is 1.5 5,. From Reference 1, 1.5 S, is 40.1 ksi. Therefore, P '1.5 S, O

O

,0 O A5-2

MDEf41-0386 O Rsv.0 GENERAL $ ELECTRIC o

Case 3-X As shown in Appendix 3 for the 3/4" grindout, case 3+X bounds case

.- 3-X . Therefore PL <1.5 S,.

Case 15+X From Appendix 3 the scaling ratios are.

R

= 15.5 Q R = 3.097 P

The results of the stress scaling is Stress o o o, t O 14.74 .681 28.80 -2.075 Pressure Axial Load 67.4 21.08 42.78 4.34 Total 82.14 21.76 71.58 2.265 O

The principal stresses are, o,c' g

= 82.22, 71.75, 21.67 2 3 P = 82.22 - 21.67 = 60.55 kai <1.05 S, Case 15-X, 16+X and 16-X As shown in Appendix 3 for the 3/4" grindout, case 15+X bounds cases 15-X, 16+X and 16-X. Therefore P <1.05 5,

.O O

l A5-3 L

O

~,

MDE#41-0386 g Rev.0 GENERAL $ ELECTRIC P+Q Calculations As stated in Appendix 3, the value of P+Q -(thermal bending) will be determined and compared to 3 S,.

From Appendix 3 the equivalent loads and ratios are, ,-

O ,

7+X 11R-X FX = $18.7 kips FX = -430 kips FY = -298 kips FY = 1117 kips FZ = 1910 kips FZ = -1830 kips MX = -58030 in-kips MX = 49500 in-kips O MY = -63124.1 in-kips MY = 48531 in-kips MZ = -29211.18 in-kips MZ = 15183.E in-kips MT = 87324 in-kips g= 66910.8 in-kips R = 2.485 R = 0 P P 0

R = .21 R = .176 a a R = .951 R = .728 The following table shows the results of the scaling, O

O lO l

)

l

]

O i

[O

'O A5-4 j

2

MDEf41-0386 O dsv.0 GENERAL $ ELECTRIC Q

7+X Stress (ksi)

'x 'y 'z t,y ,.

O Pressure 26.54 3.827 23.757 -2.634 Axial Load 2.99 .58 1.51 .086 Moment 19.59 5.96 11.77 3.167 O Total 49 12 10.37 37.04 .619 IIR-X Stress (ksi)

7 * *7 O 0 Pressure 0 0 0 Axial Load -2.51 .486 -1.262 .072 Moment -15.0 -4.564 -9.01 -2.425 O

Total -17.51 -5.05 -10.273 -2.497 Taking the difference between the different stress components of 7+X and 11R-X gives O Ac - 66.63 kai x

Le y

= 15.42 kai Ae,

= 47.31 kai O at xy - 3.116 ksi O

O O A5-5

I MDE#41-0386 (g R2v.0 l

1 GENERAL $ ELECTRIC

,0 The principal stress using these differences in stress values gives, l

0 = 66.82, 47.3, 15.2 kai 3, 02' 3

.O *

. The range is therefore, l

66.82 - 15.2 = 51.62 kai O

Adding the thertal membrane contribution (see Appendix 3) gives the total range of P+Q -(thermal bending),

P+Q =(thermal bending) = $1.62 + (2.31 + 2.93)(1.5)

.O

= 59.48 kai

'O Since P+Q -(therual bending) is less than 3 S, (80.1 ksi), this ASME requirement is satisfied.

Since P+Q exceeded 3 S u

, and P+Q -(thermal bending) <3 S,, an additional check e assure against racheting must de performed. This

!O calculation is given in Appendix 6.

.O l

O o

O A5-6

MDE#41-0386 g Rav.0 GENERAL $ ELECTRIC O ,

FATIGUE CAI.CULATION - 1/2" CRINDOUT

~

- The value of S can be determined by adding thermal bending to P+Q O -(thermal bending) calculated earlier. The value of P+Q -(thermal bending) = 59.48 ksi. Add!.bg the thermal bending to this value gives S .

S n

= . + . + 6.73) 1.5 O = 113.45 ksi Substituting into K, gives K = 1 + l .2

/113.45-1

.2(2-1) \ 80.1 O

= 2.66 The stress values at the outside surface are tabulated below.

Case 7+X O

'x 'y C T

xy Pressure 37.85 0 26.71 0 Axial 3.92 0 1.6 0 0 14.93 Moment 37.17 O_ , O_

Total 78.94 0 43,24 0

~

0 ;

Case 11R-X x y z xy Pressure 0 0 0 0 0 J Axial -3.29 0 -1.3 0 I Moment -28.45 O_ -11.43 O_

Total -31.74 0 -12.73 0 0

e O 45 7

E EN 1-0386 O Rev.0 GENERAL $ ELECTRIC O

The difference in the stress components is, Ae x

= 110.68 kai .-

O .

Ac z

= 55.97 ksi The total range is SR = 110.68 + (2.31 + 2.93 e 16.73 + 19.25) 1.5 O = 172.51 ksi The alternating stress is s,= 172.51 (1.085) (2.66) 2 0

= 248.94 kai From Reference 1, the number of allowable cycles is 57. The contribution to fatigue usage is 10/57 = .175.

O The overall usage factor is the sume of the usage factor for each combination evaluated 10 U =[Ug+UEFT O i-1 U = .167 + .016 + .016 + .16 + .095

+ .0017 + .0017 + .009 + .01 + .0043 + .05 O U = .531 l

f 40 .

u I

!O l

F

.O AS-8 i

l MDE#41-0386

.O Rev.0 l GENERAL $ ELECTRIC

'O I .-

APPENDIX 6 O -

i THERMA 1. RACHETING l

O O

.O O

'O O

O O A6-1

MDE#41-0386

() --

Rev.0 GENERAL $ ELECTRIC o

Thermal Racheting As noted in Section 3 P+Q exceeded 3 S,. As a consequence, the possibility of thermal racheting must be evaluated. Paragraph 3222.5 of

()

.' Reference 2 gives guidelines for the thermal rachetirg calculation and limits. The calculation will be performed for the 1" grindout case only.

The 3/4" grindeut and 1/2" grindout cases will be bounded by the 1" grindout.

)

Let Y = Maximum allowable range of thermal stress computed on an elastic basis divided by the yield strength, S O

X = Maximum general membrane stress due to pressure divided by the yield strength. S y

From the pressure unit case results, the general membrane stress is

()

2317 ksi. Therefore, the genersi membrane stress is (2.317)(9.4) =

21.78 ksi.

X = 21.78 = .512 X >.5 C) 42.5 For X >.5, Y = 4(1-X)

Y = 4(1 .512) = 1.952 O

Th Y = 1.952 = S all S

y

!O Solving for Th

{ all i

lC) Th

___ S,11

= 1.952 (S ) = 82.96 ksi

' In Section B-8 of Reference 1, the maximum range occurs between iter 10-2 and 10-4. It was also found in Seetion B-8 of Reference 1.

j

A6-2 b 4

MDE#41-0386 d,,

Rev.0 GENERAL $ ELECTRIC O

that for iter 10-2 Th

., c, = 2.31 .

O Th Th Th a m

+ c b

= -14.42 ksi

= -16.73 b

and for iter 10-4 O Th o, = -2.93 Th Th Th a + c = 16.32

D

= 19.25 b

O The total range is 16.32 -(14.42) = 30.7 ksi Multiplying by 1.5 to consider the grindout effect, S = 30.7(1.5) = 46.1 ksi O Th S = 46.1 ksi < 82.96 ksi nO l

l

'O

!O 4-A6-3 lO

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l n MDEll41-0386 l

" Rev.0 1 GENERAL $ ELECTRIC o

Case 2 Parabolic Variation of Temperature For X = .512 .-

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Y a 2.5 !

Th S,g = 2.5 (42.5) = 106.25 To consider the grindout effect use 30.7 ksi as given in Case 1.

O S = 46.1 ksi < 106.25 ksi, in both cases, per Section 8 Reference 3 the range due to the thermal expansion pipe loads will be insignificant at the steady state transient condition.

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APPENDIX 7 O

AREA 0F REINFORCEMENT CALCULATICN O

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~O In this section the area of reinforcement is calculated and checked

, against the required value. In Reference 8, an area of reinforcement

.~ calculation was performed for the design condition. The cal'tulation in

0

. , Reference 8 was performed for the worst condition. In reality, the location of the grindout is at 45* from top dead center, and the vessel wall is cuived at this location. Therefore, by using the value given in Reference 8, a conservative liciiting condition is considered.

'O in addition it should be noted that the 1983 Edition of the ASME i Code does not require area of reinforcement calculations if all stress requirements are met. However, since the inlet nozzle was designed per

.O the 1971 ASME Code, the calculation will be performed.

From Reference 8. the required area of reinforcement is 145.42 in , z 4

The actual area of reinforcement is 149.172 2in . This results in an

O extra 3.752 in2 of reinforcement. Therefore, if the groundout area for the 1" depth case is less than 3.752 in 2 this requirement is satisfied.

Due to the complex geometry, the area of reinforcement is checked by i

(O two methods. The first is by assuming a simplified geometry as shown in Figure A-8-1.

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f 3,,

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Area of cutout =arca of pie + area of triangles D

Area of cutout = 2(1/2((3.0))

+ w (1) 2(18.43)+ 45 360 A7-2 3.714 in' O =

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This value is less than the 3.752 in' maximum cutout allowed.

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The second method to calculate the area of the cutout is to integrate the area from a scale drawing of the nozzle / vessel including the grindout. Reference 5 contains this drawing and calculation. The 2

total area is approximately 3.5 in .

O Therefore, the required area of reinforcement is satisfied.

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