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XA030061 0
SYNTHESIS OF ANALYTICAL ANDEXPERIMENTAL DATA CAPACITY
EVALUATION
Chi-Wen LinConsultant, Martinez, California, USA
WORKSHOP ON"SEISMIC DESIGN ASSESSMENT BY EXPERIMENTAL METHODS"9
NUCLEAR POWER INSTITUTE OF CHINA (NPIC)CHENGDU, CHINA, 10-14 SEPTEMBER 2001
-53 5
NATIONAL WORKSHOP"SEISMIC DESIGN ASSESSMENT BY EXPERIMENTAL METHODS`
NPIC-CHENGDU, CHINA
SEPTEMBE 10-14, 2001
NO. 9: SYNTHESIS OF ANALYTICAL AND EXPERIMENTAL DATA,CAPACITY EVALUATION
BY:CHI-WEN LIN, Ph.D.
CONSULTANTMARTINEZ, CALIFORNIA, USA
INTRODUCTION
THIS PART OF THE PRESENTATION DEALS WITH THE SYNTHESIS OFANALYTICAL AND EXPERIMENTAL DATA AND CAPACITY EVALUATION.
FIRST, A TYPICAL TEST FLOW DIAGRAM WILL BE DISCUSSED TO IDENTIFYKEY ASPECTS OF THE TEST PROGRAM WHERE ANALYSIS IS TO BEPERFORMED. NEXT, ACTUAL COMPONENT TEST AND ANALYSIS PROGRAMSWILL BE PRESENTED TO ILLUSTRATE SOME IMPORTANT PARAMETERS TO BECONSIDERED IN THE MODELLING PROCESS. THEN, TWO COMBINED TEST ANDANALYSIS PROJECTS WILL BE REVIEWED TO DEMONSTRATE THE POTENTIALUSE OF SUBSTRUCTURING IN THE MODEL TESTING TO REDUCE THE SIZE OFTHE MODEL TO BE TESTED. THIS WILL BE FOLLOWED BY AN INELASTICRESPONSE SPECTRAL REACTOR COOLANT LOOP ANALYSIS, WHICH WAS USEDTO STUDY A HIGH LEVEL SEISMIC TEST CONDUCTED FOR A PWR REACTORCOOLANT SYSTEM. THE POTENTIAL USE OF AN IMPROVED IMPACTCALCULATION METHOD WILL BE DISCUSSED AFTER THAT. AS A CLOSURE TOTHE TEST AND ANALYSIS SYNTHESIS PROCESS, A REACTOR INTERNALQUALIFICATION PROCESS WILL BE DISCUSSED.
FINALLY, CAPACITY EVALUATION WILL BE DISCUSSED, FOLLOWING THEREQUIREMENTS OF ASME SECTION III CODE FOR CLASS 1 PRESSUREVESSEL, CLASS 1 PIPING WHICH INCLUDES THE REACTOR COOLANT LOOPPIPING, AND THE REACTOR INTERNALS.
THE FOLLOWING LISTS THE SUBSECTIONS INCLUDED IN THIS PART OFPRESENTATION WHICH COVERS THE ABOVE MENTIONED SUBJECTS:
SECTION 9/1. TYPICAL COMPONENT TEST AND ANALYSIS RESULTSSECTION 9/2. COMBINED TEST AND ANALYSIS PROCESSSECTION 9/3. A SIMPLIFIED INELASTIC RESPONSE SPECTRAL
ANALYSIS OF REACTOR COOLANT LOOPSECTION 9/4. AN IMPROVED IMPACT ANALYSIS METHODOLOGYSECTION 9/5. REACTOR COOLANT SYSTEM AND CORE INTERNAL
QUALIFICATION PROCESS
SECTION 9/6. ASME SECTION III CODE, DESIGN BY ANALYSIS OFCLASS 1 PRESSURE VESSEL
1 2
SECTION 9/7. ASME SECTION III CODE, DESIGN BY ANALYSIS OFCLASS 1 PIPING
SECTION 9/8. ASME SECTION III CODE, DESIGN BY ANALYSIS OFREACTOR CORE INTERNALS
SIMILAR TO SECTION NO. 8, THE PERTINENT REFERENCES USED IN THEPRESENTATION ARE IDENTIFIED AT THE BOTTOM OF THE PAGE, AND THEREWILL BE NO SEPARATE REFERENCE SECTION PROVIDED.
AGAIN, ALTHOUGH NO SPECIFIC MENTION WILL BE MADE WITH RESPECT TOTHE IAEA SAFETY GUIDES, THE PRINCIPLES DISCUSSED, THE METHODSREVIEWED, AND THE REGULATORY REQUIREMENTS CITED ARE CONSISTENTWITH THE REQUIREMENTS OF IAEA SAFETY GUIDES.
SECTION 9/1. TYPICAL COMPONENT TEST AND ANALYSIS RESULTS
FIGS. 9/1 THROUGH 9/5 PRESENT A COMPARISON OF THE TEST ANDANALYSIS MODAL DATA OF AN UPPER HEAD INJECTION VALVE. THECONNECTING BOLTS OF THE VALVE WAS IDENTIFIED AS A SOURCE OFANALYTICAL ERROR WHICH REQUIRED CORRECTION. THE ANALYSIS ALSOIDENTIFIED THAT THE TEST SUPPORT OF THE VALVE, ALTHOUGH APPEAREDTO BE RIGID, WAS ACTUALLY WEAK IN TORSIONAL RESISTANCE. THIS LEDTO A MODIFICATION OF THE TEST SUPPORT ARRANGEMENTS.
FIGS. 9/6 THROUGH 9/9 SHOW THE RESULTS OF A STUDY PERFORMED FORVERTICAL TANKS. THESE RESULTS INDICATE THAT THE FUNDAMENTFREQUENCIES OF THE SKIRT SUPPORTED TANKS ARE BELOW 25 Hz.HOWEVER, THE SECOND MODE FREQUENCIES ARE GENERALLY HIGHER THAN 33Hz. THEREFORE, WHEN CONDUCTING A MODEL TESTING, THE FUNDAMENTALNATURAL FREQUENCIES ARE KEY. HOWEVER, IN ORDER TO CAPTURE THERIGID BODY MODE, THE SECOND MODE MAY STILL NEED TO BE ASSESSED.
FIGS. 9/10, 9/11, AND 9/12 SHOW NATURAL FREQUENCY PLOTS OFTYPICAL TANKS, VALVES, PUMPS, AND A TYPICAL PUMP MODEL. THEYINDICATE THAT, EXCEPT FOR VERY LARGE VALVES AND PUMPS, THENATURAL FREQUENCIES OF THESE EQUIPMENT ARE GENERALLY QUITE HIGH.
M ~~~~~~~9/1
LATERAL SUPPORT TEST FIXTURE
SUPPORTS S~ '~~-WOODEN BLOCKS
Diagram of Upper Head InjectionValve as Mounted on Test Fixture
ANALYSIS TEST 9/2
ROTATORY SPRING
Comparison of Analytical Mode Shape With Test ModeShape for the 9.55 Hz Natural Frequency of UI Valve
ANALYSIS TEST
9/3
ROTATORY SPRING
Comparison of Analytical Mode Shape Widi1 Test ModeShape for the 56 Hz Natural Frequency of UHI Valve
9/4
NATURAL FREQUENCY = 8.5 Hz
00
Mode Shape Corresponding to First Natural Frequencyof UI Valve in Flow Direction (From Tests)
5 - 7
9/5
NATURAL FREQUENCY =21.5 Hz
Mode Shape Corresponding to Second Natural Frequencyof UHI1 Valve in Flow Direction (From Tests)
9/6
p 6p~~/ / p
I I~~~~~0
H
Motion Due to Translational Inertia Effect
Lin, Chi-Wen, "A Simplified Approach to Compute Natural Frequenciesof Vertical Tanks and Heat Exchanges with Skirt Supports", ASCEConference Proceedings, 1974.
9/7
M
Motin De toRotry nerta Efec
9/8
50
a (D 3t h 3W )112* MULTI-DEGREE-OF-FREEDOM
40 -COMPUTER AIDED, EXACT, SOLUTIONo SOLUTION USING PRESENT METHOD
30-
20 -T
0 I
0.0 0.01 0.02 0.03 0.04 0.05a
Comparison of the First Mode Natural Frequency
9/9
120a =(D
3t/C3W) 112
* MULTI - DEGREE-OF-FREEDOM100 COMPUTER AIDED, EXACT, SOLUTION
o SOLUTION USING PRESENT METHOD
80-
360
0~
40
20t
0.0 0.01 0.02 0.03 0.04 0.05a
Comparison of the Second Mode Natural Frequency
9/10
cs
1 30 I[
~~~ ~SA
120-
110 *I 1cl100 RH Typical
SAccH Tanks
90 0ABA
80
70C)( 0 Computed
60~~~~~ 60~ ~ ~~
.0/
CV 0~50
40 / 'AFitted
30 - 1
20//
10 o
0 1 2 3 4 5 6
MODE NUMBERS
FrequeŽncy )iqtrib1ut ion.of the [ll•
9/11
- 2~~~~ 14 3 S~~ 1~t ) 1 2
12(
1 10:*, 4 100
9 0 3'i-
80 ~~~~~~~~~~~~~~8 Typical
12 Valves
U 2~~~~~~~~~)16 0
6 0~ ~ ~~~
5 0 /--Computed0/
40 6/
301-Fitted
201
10
o 2 3 4 5 6 7
MODE NUMBER
FreqencyDistributionof ie \:.Ilves
9/12
IR
300 C
2 801si
260 )C
2 40
220 0.
I S~~~~~~~~~~~~s
-'180
160 ~ ~ ~ ~~~oCS Typical
140 - / ~~~~~~~~~~~~~~~~s-'j.1
120~~~~~~~~~~ Computed
100 -
o ~ ~ ---~-~*-L- Fitted
80-
60
.0 1 2 3 4 5 6 7 8
MODE NUMBERS
Frequicc 1)1st ribut ion1
9/12. 1
TABLE 3 STRESSES OF THE CHARGING AND SAFETY INJECTION P4PS (900 HP)
FREQUENC IES(CPS)
38.136
51.613
72.947
84.221
85.161
JOINT STRESS LOCATION______ (PSI)
4 2220 End Motor Shaft5 595 Center Motor Shaft
6 1119 Center Motor Shaft
7 2163 End Motor Shaft
8 439 End Motor Closing
14 2048 End L.S. Shaft
29 482 Speed Increaser Base
34 1560 Pump Shaft at Bearing
35 527 Center Pump Shaft
36 521 Center Pump Shaft
37 1564 Pump Shaft at Bearing
5 6 7 13 14 1516 174 - 0* 8
3 2! f 81 31 32 3334 35 36 37 38 39
y 10 /127 /71/7 429 30
X ~~~~~~~~48 44 41
z
CHARGING AND SAFETY INJECTION PUMP (900 HP)
1 3
SECTION 9/2. COMBINED TEST AND ANALYSIS PROCESS
FIG. 9/13 SHOWS THE MODEL OF A SET OF PIPING SYSTEMS SUPPORTED BYA STEEL FRAMED STRUCTURE. THE STEEL STRUCTURE WAS DESIGNED TOSIMULATE THE NATURAL FREQUENCIES AND VIBRATION MODESHAPES TYPICALOF THE AUXILIARY BUILDING. THE PIPING WAS ARRANGED WITH TYPICALBENDS AND ELBOWS SIMILAR TO A REAL SYSTEM, WITH COMMONLY USEDSUPPORTS (e.g., SUBBERS, LIMIT STOPS, ROD HANGERS). CONCRETEBLOCKS WERE ADDED TO INCREASE THE WEIGHT OF THE STRUCTURE.BOTTOM PART OF FIG. 9/13 SHOWS THE PIPING MODEL AND DIMENSION.
FIG. 9/13.1 PRESENTS THE 2% DAMPING RESPONSE SPECTRA PLOTS FROMTESTS. TWO PEAKS CAN BE OBSERVED FROM THE PLOTS, REPRESENTINGTHE TWO FUNDAMENTAL MODES OF THE TWO INTER-CONNECTED STRUCTURES.
FIG. 9/13.2 ARE THE PIPING ACCELERATIONS AND SUPPORT LOADSCALCULATED AND TESTED. BOTH ENVELOP RESPONSE SPECTRUM APPROACHAND MULTIPLE SUPPORT RESPONSE SPECTRA METHOD WERE USED. IT ISOBVIOUS THAT THE ANALYTICAL CALCULATIONS ARE MUCH MORECONSERVATIVE THAN TEST RESULTS. THIS COMPARISON IS ONE OF THEBASES USED TO JUSTIFY THE ACCEPTANCE OF THE MULTIPLE SUPPORTRESPONSE SPECTRA TECHNIQUE.
FIG. 9/14 SHOWS ANOTHER COMBINED ANALYSIS AND TESTS. IN THISFIGURE, THE EXTRACTED MODAL INFORMATION FOR ONE CONTROL BOARD WASUSED TO CONSTRUCT A CONNECTED FIVE-BOARD ACTUAL LAYOUT, SINCE TEBOARDS HAVE SIMILAR DESIGN AND CHARACTERISTICS.
FIG. 9/15 SHOWS THE MODEL OF THE SINGLE BOARD AND NATURALFREQUENCIES FOR THREE FUNDAMENTAL MODES.
FIG. 9/15.1 COMPARES THE RESPONSE ACCELERATIONS OBTAINED FROM THESINGLE BOARD AND COUPLED FIVE-BOARD. FIG. 9/15.2 SHOWS THE FIRSTTHREE MODESHPAES OF THE COUPLED BOARD. IT IS INTERESTING TO NOTETHAT BOARD TWISTING BECOMES A SIGNIFICANT MOTION.
THE DATA OBTAINED FROM THE FIVE-BOARD ANALYSIS PROVIDED IMPORTANTINFORMATION TO ALLOW THE EXTRACTION OF THE TEST DATA FROM ONLYONE BOARD TO A FIVE-BOARD COUPLED DESIGN.
THE FUNDAMENTAL NATURAL FREQUENCIES LISTED ON FIG. 9/16 FOR MAJORCOMPONENTS OF THE REACTOR SYSTEM INDICATE THAT THE SG FORDIFFERENT LOOPS ARE SIMILARLY SUPPORTED. THE SAME IS ALSO TRUEFOR THE REACTOR COOLANT PUMP. ALSO, THE MAJOR COMPONENTS ARE THECONTROLLING FACTORS TO THE VIBRATION RESPONSE OF THE REACTORSYSTEM. INTER-CONNECTING PIPING DOES NOT PROVIDE SIGNIFICANTSUPPORT NOR INFLUENCE THE MAJOR COMPONENT MOTION. THEREFORE, ITIS JUDGED THAT WHEN CONDUCTING A TEST PROGRAM. A SUBSTRUCTURINGTECHNIQUE COULD BE EMPLOYED TO ALLOW TESTS TO BE CONDUCTED FOREACH OF THE MAJOR COMPONENTS SEPARATELY. THE RESULTS COULD THENBE RE-ASSEMBLED TO REPRESENT THE ENTIRE SYSTEM, AS HAS BEEN DONEFOR THE COUPLED CONTROL BOARD DISCUSSED EARLIER.
Y
WE A 1
z9/13
64~~~~~~~~~~~~~6
36
46
F ~~~~~ 7724- 4--- 2-A- 4o
Elevation Showing Frames Side by Side on Table
I
0 PIPE FLAN~~~~~FLOR
FLOOR~~~~~~~~~~~~~~FO
4 TOOCY
Second Pipe/Support System (Rod Hangers & Snubbers)
I �7.J. .1-. &
.1.91LI
'I..
S..
� .�.
S.. .� 3*
8. 5
'I..
I -. I
I� .8.9 8.6
** .*.. �** **
�
3.
I I9-fl - I.
" �
I *..
2W.6 S.,
aV.. �,n a. S. S
ft.i44a.�
a. a. S
3.* -. LU
a . . .-. N-- . . S . - --..
� *bC*
95 5.9 *C.* *t.* fl*. S.�aA, a-I.
2% Damping Response Spectra Reported from Test -
El Centro 750 Span Braced Frame
9/13 .2
COMPARISON OF AVERAGES FOR THREE INPUTS
ENV MS (SRSS) MS (ABS) TEST
Support Loads 0.51 0.37 0.69 0.25(k ips)
Piping Accelerations 5.02 2.50 4.25 1.96
COMPARISON OF AVERAGES FOR 12 INPUTS
ENV MS (SRSS) TEST
Support Loads 0.52 0.41 0.29(k ips)
Piping Accelerations 4.94 2.90 2.34
(g)
TABLE 3
* 0. 610' -- - 639' COMPUTED DYNAMIC CHARACTERISTICS FORTHE ONE MASS POINT MODEL
_ -. J Mode Natural Frequency Mode Shape Modal Effective Mass
3RD MODE SHAPE _____ ~~~~ ~ ~~~~~~~~~~~~~~ ~~(Hz) Translational Rotational (0) With Me Without
1 lsI moDE SHAPE Radian Degree
1 14.01 Side to Side .0091 .52 2953.44 11.91
2ND MODE SHAPE ~ ~ ~~~2 26.47 Front to Back 0 0 6.24 6.24
3 41.95 Side to Side -.0122 *699 30834.3 .971
3 ~~~~~~~~~~~~~~~~~~~~TABLE 4
NATURAL FREQUENCIES OF THE CONTROL BOARD
2 ~~~~~~~~~~~~~~~~~~~~~WITH ALL FIVE SECTIONS CONNECTED
~~~~~r)7 ~~~~~~~~~~~~~MODE FREQUENCY
1 14.3
2 17.71
5 ~~~~~~~~~~~~3 23.38
4 28.64
5 29.05
Y ~~~~~~~~~~~~~~~~~6 31.89
7 33.51
Figure 4. Coupled Model for the Control BoardWith Five Sections Connected.
9/15
Mmy, H
2
K K 0
Figure 1. Top View of the Full Size ControlBoard With Five Sections.K
X
Y
C. g.
TOP VEW
SIDE V I EW Figure '3 Single Mass Point M el With
F gure 2. Schernac View of a Singic Section.
TABLE 1 TABLE 2
DYNAMIC CHARACTERISTICS OF THE IM4 SECTION COMPUTED PARAMETERS FOR THECALCULATED FROM THE FINITE ELEMENT MODEL ONE MASS POINT MODEL
Mode Natural Frequency Mode Shape Modal Effective Mans (in) 67.3189(Hz) (lb -Sec
2lin)nlTranslational Rotational W0) Ke ( 1.4571 x 109
Radian Degree (rad.
14.01 Side to Side .0091 .52 9.688 K% (lin) 1.6123 x 105
2 26.45 Front to Back 0 0 6.24 KV(lin) 1.729 x 05
3 41.62 Side to Side -0.0122 -0.699 3.209 in-ib_________________ __________________ ~~~~~~~~~~M -71 33720.
sec2
Lin, . w., 1"Seismic Qualification of the Full size Main controlBoards - sequoyah and Watts Bar Nuclear Power Plants", WCAP-8540,1975.
9/15. 1COMPARISON OF UNCOUPLED AND COUPLED
MODEL MAXIMUM ACCELERATIONS
Maximum Acceleration (gs) Maximum Acceleration (g's)Node Uncoupled Model Coupled Model
ss FB3 ss FB
1 1.19 1.08 1.12 1.07
3 1.19 1.08 1.12 1.08
5 1.19 1.08 1.12 1.07
MODE I~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~MD I f :14.3 l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 3z3N
/ /~~~~~~~~~~~~M D
UNDERFORMED OSiIioII
Figure f. Mode Shapes of the Five Coupled Sections (Continued).
Figure 6. Mode Shapes of the Five Coupled Sections.
9/16-COMPARISO.PH 0F NATAL FLEQ'JUIVES (z).
CCAMO>ENT __ DRCT 0) TDI;MY~! YCc.
. .94 7.90 'Steam Generator X 7.11' 7.O0S
(First Horizontal) 7.19 7.067.20 7.90
Y 8.52 7.85 -
(Second Horizontal) 8.52 7.858.69 8.72
8.70 8.19
Reactor Coolant X 6.74~ 5.55Pump (First Horizontal 6. G6 6.4
6.91 ~~~5.53
(Second Horizontal) 7.34 6.817.50 6.67
7.65 6.27
Reactor ressure X 1 11.67 8.07Vessel (First Horizontal)
Y I 11.80 7.14(Second orizontal)!
interior Concrcte X 1.980Structure (First Horizontal)
v 138913.65(Second [Horfzontal)
Shear Wave 3600 ft/sec 9000 ft/scc
*Based on ve~rage values.
14
SECTION 9/3. A SIMPLIFIED INELASTIC RESPONSE SPECTRAL ANALYSISOF REACTOR COOLANT LOOP
FIG. 9/17 PRESENTS THE REDUCED TEST MODEL OF A TYPICAL REACTORCOOLANT LOOP, THE ANALYSIS MODEL USED TO SIMULATE THE HIGH LEVELINELASTIC PIPING RESPONSE MOTION. BOTH TIME HISTORY SOLUTION ANDA SIMPLIFIED INELASTIC RESPONSE SPECTRA TECHNIQUE WERE EMPLOYED.FIG. 9/18 SHOWS THE PROCESS USED FOR THE DEVELOPMENT OF THEINELASTIC RESPONSE SPECTRUM.
FIRST, THE RESPONSE SPECTRUM WAS REDUCED TO ALLOW ONLY THEPLASTIC HINGE FORMATION AT THE MOST HIGHLY STRESS NODE. THEN AMOMENT HINGE WAS INTRODUCED IN THE ANALYSIS AT THE MOST HIGHLYSTRESSED LOCATION. THE RESPONSE SPECTRUM ACCELERATIONS WEREINCREASED AND APPLIED TO THE NEW 1-HINGE MODEL UNTIL A SECONDMOMENT HINGE IS FORMED. THE PROCESS REPEATS ITSELF.
THEN, A REDUCED INELASTIC RESPONSE SPECTRUM IS CONSTRUCTED USINGTHE PLASTIC FREQUENCY REDUCTION FACTOR FROM THE LITERATURE. THEDUCTILITY FACTOR WAS BASED ON THE DISPLACEMENT DUCTILITY, WHICHIS APPROXIMATED BY DIVIDING THE SYSTEM'S MAXIMUM DISPLACEMENT BYTHE DISPLACEMENT AT THAT LOCATION WHEN THE FIRST HINGE FORMED.THE REDUCED INELASTIC RESPONSE SPECTRUM CAN THEN BE CONSTRUCTEDUSING THE RIDDEL-NEWMARK PROCEDURE.
THE CURVE CONSTRUCTED USING THE LOAD LEVELS CORRESPONDING TO THEFIRST HINGE FORMATION AND SECOND HINGE FORMATION, AND SO ON, CANTHEN BE PLOTTED AGAINST THE REDUCED INELASTIC RESPONSE SPECTRUM.THE INTERSECTION POINT OF THE TWO CURVES WOULD THEN INDICATE THEAPPROPRIATE LOAD LEVEL OF THE SYSTEM. THE SYSTEM CAN THEN BESTUDIED WITH THE APPROPRIATE NUMBER OF PLASTIC HINGES AT THE LOADLEVEL DETERMINED.
FIG. 9/19 PRESENTS A COMPARISON OF THE INCREMENTAL HINGEPREDICTION AND THE TEST MEASUREMENT. A COMPARISON WAS ALSO MADEFOR THE NONLINEAR TIME HISTORY ANALYSIS PREDICTION TO THE TESTMEASUREMENTS. THE INCREMENTAL HINGE METHOD APPEARS TO BECOMPARABLE TO THE NONLINEAR TIME HISTORY ANALYSIS. BOTH METHODS,HOWEVER, UNDER-ESTIMATED THE RESPONSE AT THE TOP OF THE SG ALONGY DIRECTION.
TRUNCATED TOP STEAM GENERATOR
REA~~~~tOR ~~~~~ 9/17
___ - ~~~~~~~~~~~~~~~~REACTOR COOLANT pUMp
I) ~ ~ ~ ~ ~ -R S BERE
RCP~~~~(C
REVISED SUPPOFg.R0TSP8 HLT Mde
~SNAXE S~ABTEBLE
S IC S~BE
Fig. 1 HLVT Test Setup SA86 LW ode1k~~~~~~~~~~I
SOVERTE 1211
INFORCU~~~~~~ENRC
Fig. 1 HLW Testig 11ABQU HLSeecod od
REMOOEE T'
REMOVEDRMOE ~l - .-
PINNIED-N---' - ~LOWER
SUPPORT Ia I
Fig. 2 HLVT Steam Generator Modifications Fig. 12 SAP86 HLVT Hot Leg Model
Jaquay, K., et al, Nonlinear Dynamic Analysis of Seismic Tests ofa Modified Scale Model PWR Primary Coolant Loop, P-Vol.220,1991.
(pp -q)r91
where,
q =3.00B1 0 .3 0 g(*
r 0 .48B5O.08
These were developed for ground motions havingEa broad frequency content versus the narrowband frequency content found in building- C1T
filtered loadings. The refined I adjusts EFE'IV
for the effect of frequency tuning/detuning by DCLA EE
using at-frequency response accelerations and go cf) M. VALnUE AT TED
the Lazzeri (1987) ductility-based frequencyEDC-reduction factor, , plotted in Fig. 7 imOENYv DUCTILITY
6.0 * *~~~~~~~~~~~~~~~~~~~~~~~.
DUCTILITY
Fig. IHM Determination lastic ResponseAcceleration
6.0
-j A1 3, o MS
0. . . . 5 0F070. . . M 54M 2INLSI UQECILSTCFEUNY
Fi.7PatcFeunyRdcinFcooj54 f
A~ ~~ M~F I Cf Il~~~~~Er ~ h~ 5 l;.i ',C. HtL
2.0 ACEEAIOIsF LSI R 111E oINPUT9SI-EC;RA t~UP12
QUENCY Hot L.9II
1.0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. b
IWELSTI FROUECY(LASTICFREOUENCY.m DUTLT / . .
Fig. 7 plastic Frequenig. 4 y TeductionionFactorpin
DUCTILITY~~~~~~~-0. L4
Fig. 8 JHM Ini,'.it Wad curve Developmento)..Sfl ~5g. on.c .
Table 2 Comparison of IH11 HLVT Predictions to Table 3 Comparison of ABAQUS HT PredictionsTest Measurements to Test Measurements 91
Comparison Note Comparison NoteLocation Response (1) .OMPR 0.4MPR 0.1MPR Location Response (1) 1.OMPR 0.4NPR 0.1MPR
…- - - - - - - - - - - - - - - -All First A 3.72 3.72 3.72 All First A 3.37 3.37 3.26
Modal T 3.15 3.15 3.15 Modal T 3.15 3.15 3.15Frequeny R 1.18 1.18 1.18 Frequeny R 1.07 1.07 1.03
Second A 6.64 6.64 6.80 Second A 6.55 6.55 6.54Modal T 6.64 6.64 6.38 Modal T 6.64 6.64 6.38Frequency R 1.00 1.00 1.06 Frequency R 0.99 0.99 1.02
…~~~~~~~~~~~~~~~~~- - - - - - - - -Top of DX (cm) A 6.38 3.89 0.89 Top of DX (cm) A 6.78 3.63 0.94SG T 7.64 3.8B 0.95 SG T 7.64 3.88 0.95
R 0.84 1.00 0.94 R 0.89 0.94 0.99
DY (cm) A 0.40 0.27 0.05 DY (cm) A 0.64 0.32 0.04T 3.04 0.92 0.14 T 3.04 0.92 0.14R 0.13 0.29 0.36 R 0.21 0.35 0.30
AX (gal) A 8130 6380 1630 AX (gal) A 6460 4890 1670T 7280 5470 1630 T 7280 5470 1630R 1.11 1.17 1.00 R 0.89 0.89 1.02
AY (gal) A 5000 3030 760 AY (gal) A 750 350 65T 600 510 210 T 600 510 210R 8.33 5.94 3.57 R 1.25 0.70 0.31
…~~~-- - - - - - - - - - - - - - - - - -Top of DX (cm) A 0.14 0.09 0.02 Top of DX (cm) A n.o. 0.10 0.02RCP T 0.10 0.08 0.02 RCP T 0.10 0.08 0.02
R 1.35 1.13 0.95 R 1.30 1.00
DY (cm) A 0.08 0.04 0.01 DY (cm) A 0.07 0.04 0.01T 0.05 0.04 0.01 T 0.05 0.04 0.01R 1.58 1.03 0.73 R 1.47 0.97 0.53
AX (gal) A 2790 1350 220 AX (gal) A 4670 1710 n.o.T 3800 1610 400 T 3800 1610 400R 0.73 0.84 0.54 R 1.23 1.06
AY (gal) A 3380 1540 260 AY (gal) A 1790 680 n.o.T 1230 830 180 T 1230 830 180R 2.75 1.87 1.47 R 1.46 0.83
…~~~~~~~~~~~~~~~~- - - - - - - - - - - -
Note ():A = 111 predictionT = Test measurement (Park et al. 1991)R = AT (A and T values without roundoff)
15
SECTION 9/4. AN IMPROVED IMPACT ANALYSIS METHODOLOGY
PRESENTED IN THIS SECTION IS AN IMPROVED IMPACT FORCE CALCULATIONMETHOD. THE KEY PART OF THIS METHOD, FIGS. 9/20 AND 9/21 HAVEBEEN PUBLISHED IN THE LITERATURE. THE METHOD TRIES TO MINIMIZETHE SQUARED VALUE OF THE DIFFERENCE OF THE RESTORING FORCE DUE TOIMPACT AND THE FORCE OBTAINED FROM AN EQUIVALENT LINEAR SPRING,REPRESENTING THE GAPED SUPPORT.
THE PROCESS REQUIRES A TRY-AND-ERROR CONVERGENCE CALCULATION.HOWEVER, SINCE THE METHOD USES ONLY A RESPONSE SPECTRUM AS INPUT,THE PROCESS IS SIMPLE TO EXECUTE.
SHOWN IN FIGS. 9/22 THROUGH 9/25 IS A METHOD DEVELOPED TO PROVIDEFURTHER IMPROVEMENT TO THE FORCE CALCULATION METHOD REPORTED INFIGS. 9/20 AND 9/21 DISCUSSED ABOVE. THE METHOD IS DEVELOPED BYTHIS PRESENTER, NEVER PUBLISHED AND IS ONLY IN EXISTENCE IN ITSHAND WRITTEN FORM.
FIG. 9/22 SHOWS A SCHEMATIC DIAGRAM OF AN VIBRATING OBJECTIMPACTING BOTH LEFT AND RIGHT TARGETS. THE METHOD CONSIDERS THETRAVELLING OTION OF THE OBJECT AND ATTEMPTS TO EQUATE THEIMPULSE GENERATED DURING IMPACT WITH THE CHANGE IN MOMENTUM OFTHE TARGET DURING IMPACT. A CLOSED FORM SOLUTION IS OBTAINED FORTHE IMPACT FORCE. THE COMPARISON WITH ACTUAL PIPING TESTS APPEARTO BE MUCH MORE REASONABLE THAN THE METHOD REPORTED EARLIER. THEANALYSIS RESULTS ARE ALSO MORE REALISTIC THAN A FINITE ELEMENTCOMPUTER SOLUTION BASED SOLELY ON THE USE OF RESTITUTIONCOEFFICIENT. FURTHER, IT COMPARES VERY WELL WITH TEST RESULTS,WHICH CAN BE WITNESSED FROM FIG. 9/25.1.
x(t) = A(t) cos 9(t)) Figure 3 shows the typical force-displacement relationship of a symmetricSeismic Stop. The support stiffness qa
where ~~(t) = wt-0(t). to zero until the gap is closed, afto --at,the stiffness is K Let 6 denote the
The variable A(t) and (t) are assumed dimension of the gap. Then, the supportto be random. restoring force ay e written as
Let D(x(t)) be the difference between r o when xl 6the restoring force, F(x), for the gapped F(x) (6)support and that for the equivalent linear Kg(Ix(t)l-6)support. Then, when 1l > 6
D~x~t))= F~x~t) - klxt) (2) where denotes the absolute value.
Substituting from Eqns.(1) and (6) into
where k,1 s the equivalent linear support Eqn.(5) and integrating yieldstiffness for quasi-harmonic response n aparticular mode. klA , for ASS(7
kic is determined by requiring that the- (2Kgft)[cos1 (6A)mean squared value of be a minimum for each -.(&/A)(1-.($/A)2)1, for A>6
individual support over any one cycle ofoscillation of x(t). Since A(t) and (t) are OZ
assumed to be slowly varying, they willremain nearly constant over any one cycle.
JKgHence, the mean squared value of D(x)
will be:
DISPIC~~i
T
Din5 =f (D(x(t)))2 dt (3)
0
where T=2r/w is the period of the modal
response. ~~~~~~~ ~~Fig. 3 Force-Displacement of Symmetric
A necessary and sufficient condition for Gapped SupportDs to be a minimum with respect to Ic is
d~~~~~as ~~~~~Due to its irregular appearance and
=0 (4) broad frequency band, earthquake excitationdk 1 ~~~~~~~~~~~i often modeled as a random process. For adki ~~~~~~~~~random excitation process, the response will
also be random. For the assumed case of
where cl's denote the differentials. narrow-banded response within mode-likecomponents, the amplitude of quasi-harmonic
Performing the differentiation indicated response, A, must therefore be a randomyields an algebraic equation for k, which may variable.be written as a function of "A"l in the formFoasnged reo-feom SDF
system, a direct linearization analysis may2W ~~~be performed considering A to be slowly
1 fvarying random variable. In this case, thekl(A) = F(x)cosede (5) minimization criterion used is the
A J minimization of the expected value of D (seeo Eqn. (3) ) Lb)1. This leads to the following
where e isdefined i Eqn.(1).expression for the effective linear supportwhere 8 is defined in Eqn.(l).stiffness,
E[A 2 k(A)]
KLin - 2~ (6)E[A I
Yang, M. S., et al, Analysis of Piping Systems with GappedSupports Using the Response Spectrum Method, PVP-Vol.155, 1989.
LINEARIZED STIFFNESS FOR ASYMMETRIC GAPPED The average impact force from the rightSUPPORT impacts is estimated using the following
equation: 9/21The derivation delineated above is for
symmetric gap configurations only. In cases AMof non-symmetric and one-sided gapconfigurations, the assumption of a symmetric Fr(xo,A½) fr(A,Xo)p(A)dA (12)response prescribed by Eqn.(1) is no longer I.valid. To account for the response Seff,rasymmetry, an offset is introduced into theresponse as illustrated in the following where ef f r is the effective size of the
equation: ~~~~~~~right gap defined above in Eqn. (10); (A) isthe probability density function of
y(t) = + (t) (9) displacement amplitudes. fr(A,xo) is theaverage right impact force over one cycle
where with an amplitude equal to A.y(t) = the assumed pipe displacement in I a eepesda
the direction of the asymmetric I a eepesdagapped support; f(~o (g/w(sn-efr) (3
X0 = the offset of the response; f(~o Krr(sn-efr) (3x(t) = a symmetric displacement about where
the offset. a cos1l(seffr/A);
The physical meaning of offset is thatthe pipe assumes a new position during Seff,r = effective right gap sizedynamic impacts. The of fset s caused bynon-symmetric impact forces. In other words, Kg = Seismic Stop stiffness afterthe unbalanced impact forces from both sides g the right gap closure.generates a net effect to push the pipe to anew position from the original stationaryposition. And the pipe is assumed to vibratesymmetrically about the offset position. P(x0 ) K 11pX4 (14)
To accommodate the new average pipeposition, the gap sizes are redefined as KLin (Kl+Yr)/2 (15)
follows: ~~~where K1 and Kr are the linearized6eff~r ~ 6r-X0 stiffnesses of the two hypothetical
6eff~~~r 6 r~~o (10) symmetrical Stops [12].
Seff,l 61lo
where eff r and eff,l are the effective IK-KI < e Convergedright and left gaps, respectively. Otews Kj 1-). +*
An average unbalanced force can be KLINdefined as U
PREDICTED CALCULATED
F~x0) Fl(XO,½)-Fr(xolAmn) (11) h
where and Fr are average impact forces from the left and right impacts, 5
respectively. Note that they are functionsof the offset Xo and the maximumdisplacement response, A.
PIPE ISPLXCEN[EXT
Fig. 4 Solution Flow Chart and ConvergenceCriterion
9/22
'V.~ ~ ~ ~ ~ ~ ~~~5
9/23
~~~/~~~~~~~44 e
.41~~4
etaA~
- AIR)~A0 (.-
Z- AQ-
AC '~~
-r4 F1:*1J~~'
9/24
2441~~~~~~~-
T = 4(7)~~~~~~~1
'Zn] ~ ~ ~ ~ ~~~~~~~~~2
9/25
Ac~L
Ale,~c~ ~)7
JDt
alt-To,4 47
00000000 Hj r
9/25. 1CL c G)
00 0000 ~~~~-N-N-N0c C> ... c-c.-.>>-.
O O N O O ~ ~ CCDWCD)COWW
m o~~~ ox-,0 0 00 0 00 0 00 0000 000 00 0~~~~~~~~~~~~~~torC
0000000P000000000000 W D
c^ ^ C CDoo CD o oo O NoO O O OiW O CD.
-n~~~r
(0((0(0( ( (0 c) 0(c~00 C>(0(0( 0 C m
N N ~ .NN NN ~ - - - - -ro N3i N 3
N N
-. O C D COc1W.NCDC m O.J C>
- nz
t4 C n-01 . c (0 ~ t C>MNCD 1CO CO
(0 COCOCO)C C> C0 C> C) C) C0COO -4>
0 X
c>c Q >c CO c c 06Qc c>Qc>)c ) 0) p-1 n
COO01 N)JN~c~o o C
C> C: C^ -40)W N M M.) 0 1 W W -C0)W1 " 00 CN)-C
0000 N -0000 N WW0000WWN ((D
D 40 01 CD C -i oh010 - 0 MW(0 N N N (
~~~~~~~~~~ 0~~~~~~~~~~~~~~~m -
:> CaN-4 (0W~~-,mm m
0~ C=, n0C CO:"O M&. 01CO)10CDC.3 N CD 010C0W(0 1N OO )
cn N)W NN MnN CW)NWn WN N~
C,)-- ONC CW OW1 C01CO0OO
C^ C0(0 0 --0 C.) 0)n 01 - 000 CD N) CD 1CD
- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -.0 O- - -1 - - O - C*O
CD
4~~~ CO C> C> to~~~~~~,,ClCO U0)N0WCD1 oN cW
16
SECTION 9/5. REACTOR COOLANT SYSTEM AND CORE INTERNALQUALIFICATION PROCESS
FIG. 9/26 SHOWS AN ELABORATE EVALUATION FLOW DIAGRAM OF SEISMICTESTING OF PWR COOLANT LOOP SYSTEM. SEVERAL KEY COMPARISON OFTEST DATA WITH ANALYSIS RESULTS ARE WORTH NOTING. FIRST, THESTRESS ANALYSIS IS PERFORMED ON THE TEST MODEL TO VERIFY ITSDESIGN ADEQUACY. THEN, THE ADEQUACY OF MODELING SUPPORT STIFFNESSIS SPECIFICALLY EVALUATED, AND THE DAMPING CONSTANT IS ASSESSED.THIS IS FOLLOWED BY THE RESPONSE SPECTRA ANALYSIS USING THE RRSOBTAINED DURING THE TEST AND OBTAINED AT THE MODEL FIXINGPOSITION. THE PROTOTYPE DESIGN ANALYSIS RESULTS FOR ALLAPPLICABLE LOADS ARE THEN ASSEMBLED WITH THE ANALYSIS RESULTS OFTHE TEST MODEL TO COMPLETE THE OVERALL EVALUATION.
IT IS WORTH NOTING THAT AN ANALYSIS OF THE PROTOTYPE DESIGN,USING THE TEST GENERATED DATA (e.g., DAMPING, RESPONSE SPECTRAOUTPUT OR TIME HISTORIES AT THE SUPPORT LOCATIONS) WAS NOT MADEIN THIS PROCESS.
FIG. 9/27 DEPICTS A SERIES OF TEST MODELS USED TO VERIFY COREINTERNALS ANALYSIS RESULTS AND PROVIDE FINAL CONFIRMATORY TESTDATA. PROGRESSIVELY INCREASED DETAIL OF THE CORE INTERNALS WASUSED. HOWEVER, NO SPECIFIC DETAIL WAS PROVIDED FOR THEQUALIFICATION OF THE FUEL ASSEMBLIES, OTHER THEN PRESENTATION OFTHE TEST DATA, INCLUDING THE IMPACT FORCES.
TO THIS END, AND FOR THE PURPOSE OF PROVIDING A SYSTEMATICOVERVIEW OF THE CORE INTERNAL SEISMIC ANALYSIS PROCESS, THEAPPROACH PRESENTED IN FIGS. 9/28 THROUGH 9/41 COULD BE USEFUL.
FIG. 9/28 LISTS SOME HELPFUL HINTS FOR DEVELOPING A GOODVIBRATIONAL MODEL OF FUEL BUNDLE. IT IDENTIFIES THE SPACER GRIDIMPACT TEST DATA BEING A KEY OF THE SOUND DESIGN FOR FUELASSEMBLY.
FIG. 9/29 PRESENTS A REACTOR CORE ANALYSIS PROCESS. AS INDICATEDIN THIS FIGURE, DATA OBTAINED IN THE FUEL ASSEMBLY TESTS AND THESTATIC AND IMPACT TESTS ON SPACER GRIDS ARE PERFORMED FIRST. THETEST DADA ARE THEN USED TO CONSTRUCT THE ANALYTICAL MODEL FOR THEFUEL ASSEMBLY CALCULATION, USING TIME HISTORIES OBTAINED FROM ACOUPLED VESSEL, CORE BARREL AND FUEL ASSEMBLY MODEL. THECALCULATION RESULTS ARE THEN COMBINED WITH THE INFORMATIONAVAILABLE FOR THE FUEL GRID TO DETERMINE THE INTEGRITY OF THEENTIRE FUEL ASSEMBLY.
FIG. 9/30 DISCUSSES THE MODELLING REQUIREMENTS OF THE FUEL RODS.WHICH INDICATED THAT A FUEL ROD MODEL TO INCLUDE THE CLADDING-TO-SPACER GRID CONNECTION BY A ROTARY SPRING OBTAINED FROM A STATICTEST. THE MODEL SHOULD ALSO INCLUDE THE FUEL ROD PRESTRESSESINDUCED BY THE PLENUM SPRING.
17
FIG. 9/31 DEPICTS THE CLAD-TO-SPACER GRID CONNECTION AND THE
SIMPLE CALCULATION MODEL USED TO DETERMINE ITS ROTARY STIFFNESS.
SHOWN IN FIGS. 9/32 AND 9/33 ARE THE COMPARISON OF THE FE MODELSAND TESTS. THEY SHOW STRONG DEPENDENCY OF THE EQUIVALENT BENDINGSTIFFNESS ON THE BOUJNDAR~Y CONDITIONS.
FIG. 9/34 PRESENTS THE FORMULA TO ACCOUNT FOR THE SHEARDEFORMATION OF THE BEAN MODEL, SO AS TO IMPROVE THE CALCULATIONRESULTS.
FIG. 9/35 SHOWS THE BENDING STIFFNESS OBTAINED IN THE FUELASSEMBLY FROM STATIC TESTS. IT SHOWED THAT THE FRICTION INBETWEEN THE FUEL RODS AND SPACER GRIDS CAN BE A STRONG SOURCE OFNONLINEARITY, WHICH NEEDS TO BE ACCOUNTED FOR IN THE ANALYSIS.
FIG. 9/36 SHOWS THE EFFECT OF VARIOUS COMBINATIONS OF BENDING ANDROTARY STIFFNESS OF THE FUEL ASSEMBLY BOUNDARY CONDITIONS. THEYAPPEAR TO BE FAIRLY CONSTANT. A COMPARISON OF THE NATURALFREQUENCIES OF UP TO THE 7TH MODE FOR VARIOUS PLANTS, HOWEVER,SHOWED RATHER SIGNIFICANT DIFFERENCES. IT ALSO SHOWED THAT THEMODELS OF PINED AT BOTH ENDS AND CLAMPED AT BOTH ENDS DISPLAYSIGNIFICANT DIFFERENCES IN HIGHER MODES.
FIG. 9/37 PRESENTS THE DATA OBTAINED FROM THE SPACER GRID IMPACTTESTS. TO ACCOUNT FOR THE NONLINEARITY OF THE ASSEMBLY DURINGIMPACT, IT INTRODUCED A TWO SPRING MODEL WHICH INCLUDES AN IMPACTELEMENT ALONG WITH A VISCOUS DAMPER.
FIG. 9/38 SHOWS A VELOCITY DIAGRAM DURING IMPACT. BOTH IMPACTNO.1 AND NO.2 ON THE SAMPLE GRID DISPLAY FAIRLY CONSTANT VELOCITYBEFORE AND AFTER IMPACT.
FIG. 9/39 COMPARES THE IMPACT FORCES AND OCCURRENCE OF IMPACT FORVARIOUS ASSEMBLIES. IT APPEARS THAT THE INSIDE ASSEMBLIES HAVEMORE IMPACTS BUT LESS FORCES. IT IS THE OUTSIDE ASSEMBLIES WHICHAPPEAR TO EXPERIENCE THE LARGEST IMPACT FORCES BUT THE NUMBER OFSUCH HIGH MAGNITUDE IMPACTS ARE RELATIVELY FEW.
FIG. 9/40 SHOWS A SENSITIVITY STUDY OF THE IMPACT FORCES, WITHRESPECT TO THE MAXIMUM GROUND ACCELERATION, MODAL DAMPING, ANDESTIMATED DURATION OF SEVERE IMPACT.
FINALLY, FIG. 9/41 SHOWS POSSIBLE USE OF THE ENERGY CALCULATEDFROM THE CRITICAL IMPACT VELOCITY, WHERE NO PERMANENT DEFORMATIONOCCURS, AND THE IMPACT MASS AS A "1SOUNDNESS' CRITERION.
,531,
9/26
- - ~ ~ ~ ~ ~ ~ ~ S
- m ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~0
EvalutionFlowof Sismi Provin Traesto W rmr oln pSse
F~~q t-t ~~9/27270, 05 ..I~~~~~~~~~~~c20No5grd
yod a-. r~~~~~~~~~~~~2 (2 o.SW
c~ d &d-
U.~ ~ 0 S i0s3
- AdTje Mec
Fig. 9 Comparison between Measurement andSimulated Analysis by FUVIAN4(15z core, S wave vibration, time
Fig. 1 Configuration of PWR, Reactor Core Internals histrical displacement)
byrn 4r
~~~l A.,e~~~~~~~~.d ~~~~~~ ~~~ 4~~~~~ 4 ~~~~~9w *~~~~
F~~~~~~~~~~~~~~~~~~~oo
F- ~Sww ~~~~~~~~~3 000 2 000o 0 0 l0o0 2000 30
MELL in~ac force [1,9 Max ipactforce (La)
Fig. 10 Comparison between Measurement and-F~ ~~~~Simulated Analysis by FUVIAN4
(15x3 core, 1 wave, Max. Impact force)
Fig. 2 Measuring Positions of Vibration Detectorson Proving Test Model (core region) 2
W
3 2 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 3
IC?
[J4L~~~~~~~~~~~~~4~~~~i] ~~~~A~ta input leve (Ratio £ tget s, wave)
Fig. 11 Comparison of S1 Wave SeismicFig. 8 Vibration Analysis Model Response between Proving Model
and Square Model (Relation betweenInput level and mpact force of fuelgrid)
Akiyama, H., et al. SeiSiiC Test and Analysis for PWR Reactor
Core Internals, PVP Vol.182, JlY, 1989.
S -
9/289/29
Core sismic analysis, overall process
A oo vbatonlmoeloffelbudeCholfulfill te ollowig require e.It should:
account or the st TIMtifes propertiesF ofth feassembly;~ ~ ~ oRZNTL)0IO O
- accountfor the ndividua OFibrLatSEinlbhviu f
excit ibation cnain oylo fuelnlcompoentsfuliglhe fqueiny mesreexted shdrn:mat)
- bcsimple inf r t oai betifntsrouedtias sucf the e
mass;~~~~~~~~~
-afeliassembl cotibraonl odfel:nycmpnns
- the spacer grids impact characteristics.
9/30
It is well known that the low amplitude vibrations ofPWR's fuel rods can adequately be represented by abeam model (no shear deformation) with the followingproperties:
'MTe mass per unit length results from both the fuelpellets and the cladding tube.
- Te fuel pellets do not contribute to the rigidity ofthe rod.
-The cladding-to-spacer grid connection is modelledby a rotary spring whose stiffness K 9 can be de-termined by a simple static test (fig. 3). It depends onthe grid spring force and also, heavily, on the dis-tance between the dimples inside the grid cells.
-The fuel rod prestresses induced by the plenum springare considered in the analysis. This longitudinal pre-load introduces a rise in the natural frequencies,which is controlled by the ratio of the preload to theEuler's buckling load of the rod.
9/31CLAD TO SPACER GRID CONNECTION
Spring
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _M o d e l
Dimp~es
M (Nm )__ _ _ __ _ _ _ _ _ _
A F=28 Na F=18N
01 i~~~K =40ONm/mad~ i F=14NF= 1ON
0.4~~~~~~~~~~~~~~~~~~~~~~~
0.3
0.2
.0(10 -3radj0 12 3 1.56
Clad-to-spacer grid connection. Rotary stiffness.
9/3 2
S.- ~ ~ ~ ~ ~ -
/ k~Eprmn
.5-~~~~~~~~~~~~~~3
G, Ty~~~~~~~~~~~E pe!men
element/,/I .F.delde
Mor srpisngisth lag dee1:cyofte0uv
fuel asembly
FL0 PUEL ~~~~~~~~~~~~9/33
W.~:~Meu~rudACERG
(ELL) 44.76
49.3 940Of 2 ~~~~~~~~~~~~~~~49.3053.66
57.9161.50
71.6 moot A ~~~~~~~~~~~~~~~~68.85
15.9 MOOE 5 ~~~~~~~~~~~~~~~79.0079.81
Fuel rod vibrational behaviour. Comparison between F.E. model and experiments. For each mode. the two computefrequencies refer respectively to K# 100 Nm/rad and 200 Nm/rad. The computed mode shapes correspond to K# - 200 Nm/rat
However, if one includes the shear defonnation, which
is much larger with respect to the bending defodrmauon
in case No. than in case No. 2, the agreement of a*
beam model can be considerably improved, provided a
"~rc value is adopted for the shear deformation control
parameter:
i0.l2 to. 15. I
where E stands for the Young's modulus, G is the shear
mnodulus, 9W = k'A is the effective shear area of the
9/35
El 109 kgmm2
Fuel Assembly Equivalent Bending StiffnessF
30..cs
case~~~csef'
10o 2 30 40 5 60
Fuel assembly static tests.
- he equivalent bending stiffness decreases as increases, indicating a softening behaviour oc~.assembly. This expected non-linear effect is leto the fuel assembly design (mainly caused by t;4,' pibetween the fuel rods and the spacer grA ~~
cannot be accounted for in a linear model.this effect seems to be small enough in case- which is close to the in-core boundary cond '!,,b,15
justify the linearity assumption in this case.
lx14 (6 spacer gnids) fuel assembly. Two-beam finite clement model natural frequencies. Parametric study on K. and K#
~~fodC I K. =IO0 Nm/rad K.= 1 0- Nm/rad K. = 1 0' Nm/radK# = 79X 300 K = 179 X300 K = 179 X200Nm/rad aNnm/rad Nm/mad
1 ~~6.33 1.00 6.50 1.00 6.25 1.002 14.62 2.31 14.71 2.26 14.10 1.26
3 ~23.72 3.75 23.84 3.67 22.90 3.664 ~34.34 5.42 34.48 5.30 33.36 5.345 ~50.23 7.94 50.58 7.78 47.21 7.55
6 62.62 9.89 63.20 9.72 61.08 9.77
Natural requencies of PWR-RCC fuel assemblies - Experimental data in air
Mode
I 2 3 4 5 6 7
Pinned at both ends fA/IA: I 4 9 16 25
Clamped at both ends A/IA: 1 2.76 5.4 8.93 13.34
CEA ISX IS A (Hz): 3.7 7.63 .11.67 18.55 24.78 38.31i sp. grid 4J f/f,: 1.0 2.05 3.15 5.01 6.7 9.87
B&W 17 X17 f./IA: 1.0 1.9 3.0 4.1 5.38 sp. grids 5]
Mitsubishi 14 X 14 61 A/If, A: 1.0 2.3 3.6 5.1 6.6
FRAMATOM E 14 X 14 A (Hz): 6.5 13.21 22.05 30.55 _ b 62.16 78.936 sp. grids (7) f I: 1.0 2.03 3.39 4.7 9.56 12.14
K.W.U. 16 X16 f (Hz): 3.0 12.0 20.07 sp. grids 8) A /IA: 1.0 4.0 6.6
'Approximate values estimated from graphs.A fuel rod local mode is missing here.
F (kgpf) assmbty
141 pg0 rid hr awiyhytrti~n
Static compresio test
rod
F cihfe
a.Spacer Grid Representation in the Core Model
400 ®V,
b. Spring and Viscous Damper
f =kx~ci
0.1 Ci OA GA4 v. c
14 X 14 Zhrcaloy spacer grid. Static compression tests. - V0 2 Iv'n
VIV. ~14.14 Zr apce 7Mi
C. Spring and Hysteretic Damper.
(k-hix (i,.c0)
f k - )x w0
.3 ~~~~~~~~~~~~~~~~Impact element.
.
14 X 14 Zircaloy space grid. Impact tests. Restitutioncoefficient and traserse deformation versus impact velocity.
9 38
0.3
N.13
E N,2
_ _ I _ _ _
o
* II V
0 10 20 30 40 50 60
Timne (ins)5 X 5 Zircaloy grid. Velocity diagram during impact.
Comparison of impact No. 2 and impact No. 13 on the samesample grid.
sensitivity analysis
Case Max. Tune steps Impact element Modal Most sevev impactNo. ground (ms) damlpin~g. 9(39
ACC. _ _ _ k A c rF.~ 9do
(g) dri d*2 (N/rn) (N/rn) (Ns/m) (N) (N.m) b (s)
I 0.1 0.5 0.25 2X 107 2X1 06 0.0 0.90.4 0.02 3705 0.312 3.112 0.1 0.5 0.25 1 X10 7 I X 10 0.0 0.904 0.02 2792 0.354 3.113 0.1 0.5 0.25 2X 107 4x 10'I 0.0 0.816 0.02 4200 0.367 3.114 0.1 0.5 0.25 2X 101 6X 10 6 0.0 0.734 0.02 4464 0.383 3.115 0.1 I 0.25 2X 10 7 4X 10 0.0 0.816 0.02 4212 0.369 3.116 0.1 1 0.25 2X10 7 4X 106 0.0 0.816 0.05 3541 0.261 3.127 0.1 I 0.25 2 X10 7 0 3500 0.802a 0.05 3023 0.228 3.128 0.2 1 0.25 2 X16' 0 3500 0.802 0.05 5344 0.714 3.569 0.3 I 0.25 2 X10 7 0 3500 0.802 0.05 6110 0.933 3.74
Impact forces between the spacer grds of the 3rd level (a..=0.2g F~ =10140 N. Ed=2.14 Nm).of occurence
Impact forces (%F..)
1O 20 30 40 50 60 70 80 90 100
assl 24 6 9 6 3 4 I IAssy 1 19 is 4 S 4
Assy2 35 Is 6 3 3Assy 3 20 14 8 3Assy 4 30 15 6 3Assy
Assy6 22 16 8 IAissy 6 24 18 8 2Assy 7 28 17 7 3Assy98 27 1 1 9 4 2A&ssy 9 32 16 7 5 2 Iaffle1 16 24 10 4 6 1 1 1
14 X 14 zircaloy grid (provided with claddings) after
scvcral severe impaCts. Maximum transverse deformations - 15
mmf. The guide tubes remain undamaged.
Ed = 1 F2,,j(k + h).
The energy with which Ed must be compared in order toverify the soundness criterion still has to be found. If we
impose that the impacts remain in the elastic range, twovalues of this energy can be defined, respectively fromthe static and the dynamic tests:(1) The shaded area under the static load diagram (fig.
10) represents the maximum elastic energy. E, thatcan possibly be stored in the spacer grid beforeinstability. Ed Q EJ/2 is therefore a possible crite-dion,
(2) Probably more realistic is the following criterion,defined from the dynamic tests: we have seen
that below a critical impact velocity VO*,no permanent deformation occurs. From V andthe impacting mass, we can define the critical en-ergy:
E = 1MV*2.
The soundness criterion becomes Ed -- E:*/2.
18
SECTION 9/6. ASME SECTION I CODE. DESIGN BY ANALYSIS OF CLASS1 PRESSURE VESSEL
FIG. 9/42 CONTAINS A LIST OF LOADS TO BE INCLUDED IN LOADCOMBINATION FOR THE QUALIFICATION OF PRESSURE VESSEL AND PIPINGSYSTEMS. THE EXACT LOADS TO BE USED WILL DEPEND ON THE PLANTCONDITIONS (e.g., DESIGN, LEVEL A, LEVEL B, LEVEL C, AND LEVEL DCONDITIONS) SPECIFIED IN THE DESIGN REQUIREMENTS. THE LOADCOMBINATION WILL ALSO DEPEND ON THE CLASSIFICATION OF STRESSESDELINEATED IN THE ASME SECTION III CODE. FOR THIS PURPOSE, ABRIEF DISCUSSION OF THE CODE PHILOSOPHY WOULD BE USEFUL.
FIGS. 9/43 THROUGH 9/48 CONTAINS THE DISCUSSION OF THE MAXIMUMSHEAR STRESS THEORY AND STRESS INTENSITIES USED IN THE CODE. THESTRENGTH THEORIES ARE PRESENTED IN FIG. 9/44, AND THE STRESS ANDTHEIR SIGNIFICANCE ARE DISCUSSED IN FIG. 9/45. FIGS. 9/46 AND9/46.1 PRESENT THE DEFINITION AND THE TYPES OF PRIMARY STRESSES.SECONDARY STRESSES AND PEAK STRESSES ARE DISCUSSED IN FIGS. 9/47AND 9/48, RESPECTIVELY.
FIGS. 9/49 AND 9/50 SHOW THE CLASSIFICATION OF STRESS INTENSITIESIN VESSELS FOR SOME TYPICAL CASES.
`HOPPER" DIAGRAMS IN FIGS. 9/51 AND 9/52 SHOW THE REQUIREMENTSFOR THE COMBINATION OF STRESS COMPONENTS AND ALLOWABLE LIMITS OFSTRESS INTENSITIES. A KEY POINT IS THAT FOR LEVEL A AND BLOADING, A FATIGUE EVALUATION TO THE ALLOWABLE STRESS S HAS TOBE MADE.
FIG. 9/53 SHOWS SOME BACKGROUND INFORMATION FOR THE FATIGUEEVALUATION. FIGS. 9/54 SHOW THE DESIGN FATIGUE CURVE FORAUSTENITIC STEELS. FIG 9/55 ARE THE EXTENSION TO THE CURVE SHOWNON FIG. 9/54 TO MUCH HIGHER NUMBER OF CYCLES (UP TO 10 TO THE11TH POWER).
THE PROCESS OF FATIGUE CALCULATION, TO ARRIVE AT THE LEVEL OFCUMULATIVE DAMAGE, IS DEPICTED IN FIGS. 9/56 AND 9/57. THELATTER IS DIRECTLY FROM THE CODE.
FIG. 9/58 SHOWS THE STRESS CATEGORIES AND LIMITS OF STRESSINTENSITY FOR LEVEL C SERVICE LIMITS. IT SHOULD BE NOTED THATONLY THE PRIMARY STRESS INTENSITIES NEED BE CONSIDERED AT THISLEVEL. BOTH SECONDARY AND PEAK STRESS INTENSITIES DO NOT HAVE TOBE EVALUATED.
FOR LEVEL D, APPENDIX F IS NORMALLY FOLLOWED. AGAIN, SECONDARYAND PEAK STRESS INTENSITIES NEED NOT BE CONSIDERED. ALSO, LIMITANALYSIS MAY BE USED (FIG. 9/59). THE ALLOWABLE FOR PRIMARYMEMBRANE, BENDING, AND LOCAL MEMBRANE STRESS INTENSITIES ISLIMITED TO TWO THIRDS OF THE LOWER BOUND COLLAPSE LOAD, USING 1.5S. AS THE YIELD STRENGTH.
19
THE USE OF PLASTIC ANALYSIS IS ALSO ACCEPTABLE TO THE CODE (FIG.9/60). THE ALLOWABLE FOR THE COMBINED PRIMARY MEMBRANE PLUSBENDING AND LOCAL MEMBRANE STRESS INTENSITIES IS LIMITED TO TWOTHIRDS OF THE PLASTIC ANALYSIS COLLAPSE LOAD. SECTION II-1430PROVIDES MORE DETAIL.
FIGS. 9/61 AND 9/62 PROVIDE SPECIFIC SECTIONS OF THE APPENDIX FOF THE CODE. APPENDIX F PROVIDES HIGHER ALLOWABLE THAN THESECTION III CODE. FIGS. 9/63 THROUGH 9/65 ALSO PRESENTS THEDESIGN LIMITS FOR CLASS 1 COMPONENT SUPPORTS FOR LEVEL D LOADS.
FOR OTHER THAN LEVEL D LOADS, COMPONENT SUPPORTS NORMALLY FOLLOWSSUBSECTION NF OF THE CODE. THIS IS DISCUSSED IN FIGS. 9/66 AND9/67. FIG. 9/66 ALSO PRESENTED SOME SPECIAL NOTES ON NF,CONCERNING BUCKLING LOADS.
FIG. 9/67 IDENTIFIES THE STRENGTH BASED PLASTIC ANALYSIS CRITERIAFOR SUPPORTS BASED ON SUBSECTION NF AND APPENDIX F.
FIG. 9/68 LISTS THE PROVISIONS TO BE FOLLOWED FOR THEQUALIFICATION OF IN-LINE COMPONENTS, INCLUDING PIPING PRODUCTS(e.g., ELBOWS, INTERSECTIONS, etc.), VESSEL NOZZLE, ATTACHMENTS,AND FLANGED JOINTS.
9/42
LOAD COMBINATIONS
load combinations should identify the most severe combination of theapplicable loads due to:
o Internal fluid weight
o Momentum and pressure
o Deadweight of piping components
o Thermal loads
o Steady state and transient valve operation
o Seismic forces
o Dynamic forces due to rellef.valve discharge
o Pipe break/loss of coolant accident effects
o Any other dynamic load
9/43
Maximum Shear Stress Theory
and Stress Intensities
Defined as one-half of the algebraicdifference between largest andsmallest of the 3 principle stresses
j92-
* Yield predicted when maximumshear stress reaches yield in a tensiletest which is SY,,/2
* Stress Intensity (SI) is defined astwice the maximum shear stress
* Allows for direct comparison with
allowable stress from uniaxial test
b~C)
9/44
Strength Theories
* Stress defined by magnitude anddirections of the 3 principal stresses
* When non-uniaxial, a strengththeory is required for predictingyielding
• Common theories
- Maximum stress theory
- Tresca - maximum shear stress
- Von Mises - distortion energy oroctahedral shear theory
• Tresca. and von Mises better forductile materials
• Class 3 criteria uses maximum stresstheory
* Class 1 and 2 criteria uses Tresca
9/45
Stress Types and Their Significance
* Design by Rule always comparest~asic allowable stress, S. Factorsare applied to expression for non-membrane stresses
* In Design by Analysis, stress limitsare dependant on.
- Location
- Distribution in structure
- Type of loading producing thestress
- Relation to failure mode
* If loads do not decrease withdeformation, stresses are primary
* If loads diminish with deformation,stresses are secondary
* If stresses are a result of a localizedgeometric discontinuity,, stresseSP arepeak (or local)
5J6
9/46
Primary Stresses
* Defined as a stress caused byimposing loadings which arenecessary to satisfy the laws ofequilibrium of external and internalforces and moments
* Basic characteristic is that it is notself-limiting
- Thermal stresses are not primary
* Examples
- Uniaxial tension load fromgravity
- Hoop stress in cylinder frominternal pressure
* If primary stresses exceed the yieldstress by a considerable amount,failure or gross distortion will result
9/46. 1
Primary Stress Types
* General membrane - membranestress across an entire cross sectionof a vessel such that noredistribution of forces can occur
* Local membrane - local increase inmembrane stress from discontinuitywhere forces can redistribute whenlocalized yielding occurs
• Bending - variable component ofthe normal stress (may or may notbe linear)
9/47
Secondary Stresses
* Stress developed by the constraintof adjacent material or self-constraint of the structure
* Basic characteristic is that it is self-limiting; displacement will notcontinue past some point
• Examples
- Thermal stress
- Moments and shears fromchanges in stiffness
• One application of a load whichproduces localized yielding will notcause a failure
* Examples
- Bending stresses at a grossstructural discontinuity
- Thermal stresses
9/48
Peak Stresses
* Incremental stress over and abovethe primary and secondary stresses
* Due to stress concentration effects oflocal structual discontinuities
- Small fillet radii
- Partial penetration welds
- Notch-like effects
* Some thermal stresses
* Basic characteristic is that nonoticeable distortion is produced
* Objectionable only as a possiblesource of fatigue
-515
9/49
TABLE NB-3217-1CLASSIFICATION OF STRESS INTENSITY IN VESSELS FOR SOME TYPICAL CASES'
vem Pt Loain01 of S~sType of Stress aassfictlo
C)ndlc or She& plt remote bu pressue Gae~.aax~ P-qi~erlci d~eI from Ciscntjwa Graient throg lt
ities tcm
or f~g Bdig0 [Note (2)1
Any thed or head Any ection acos External Ad or Ge~naa bemne
aste ssel emm~ or n- avrae acr~ full P.t~n prssr sectionl
External lom or Bendin across Kmimolment section .P
Near nozzle or External loa or Lo emne pcothe opein moment, or ki- Bendin Q
ternal press Peak (fillet or COrne) F
Any location Tempemaure Clifference MembraneQ
between shell ad Bending head
Dsdhedor Crow Interral pressure Membrane P
conical head ~ending
Knuckle or juntion Internal pressure Membrane P, [Note (M)to shell Bending Q
Fiat head Center region internal pressure Membrane P.Bending P.
Junction to shel Internal pressure Membrane P,Bending Q (Note (2)]
Perforated head Typical ligament Pressure Membrane (averaged P-,or el in a uniform through cross section)
pattern Bending (averaged throughwidth of ligament, but Pgradient through plate)
Peak F
Isolated or atypical Pressure MembraneQligament Bending F
Peak F
Nozzle Within the limits of Pressure and external General membrane P.fNB-3227.5) reinforcement loads and moments,
defined by including those Bending (other than pNB-3334 attributable to gross structural
restrained f-e end discontinuity stresses)displacefrets of averaged through
attached piping nozzle thickness________ ________ _______ ________ _____ _ ________ _______ ________ _______ ____ -j _______ ________ _______ ________ ________ _______ ________ _______ ________ _______ ________ ____ __ ________ _______ ________ _______
(r.bke NB-321 7- cntines 0 ". ,.e;
9/50
TABLE 3217-1 (CONro)CLASSIFICATION OF STRESS INTENSITY IN VESSELS FOR SOME TYPICAL CASES'
Vensd pan Locaio Ou~ of S5aes Type of sSs Casfct
Idozl Outi the P ~esr and oxtn~ G nmmrn P.(NB-3227.5) fln~t~of axal she and Stres
reiforcement tor~na lbads otedefined by than those att~lu-N 8-3334 abl to restrained
free end displacementsof attached p~Nn
Presur and ex~aa Membrane p
~od and momentsother than ths Bending p0attiul torestr~e free enddisplacemnt ofattached piping
Pressure and all Membrane pertenal loads BendingQ
and moment Peak F
Nozzle wall Gross structural Local Membrane P,discontinuities Bending Q
Peak F
Differential MembraneQ
expansion t'.IngQPeak F
Cladding Any Differential Membrane Fexpansion Bending F
Any Any Radial temperature Equivalent Qdistribuion linear tress[Note (41 (Note ()]
Nonlinear portion of Fstress distribution
Any Any Any Stress concentrationF(notch effect)
NOTES:(1) Q & Fclassification of stresses refers to other than design condition (Fig. NB-3222-I).(2) If the bending moment at the edge is required to maintain the bending stress in the middle to acceptable limits, the edg bending is
classified as P,. Otherwise, it is classified as Q-(3) Consideration shall also be given to the possibility of wrinkling and excessive defornsation in vessels with a large diameter-thickness ratio.(4) Consider possibility of thermal stress ratchet.(5) Equivalent linear stress if defined as the linear stress distribution which has the same net bending moment as the actual stress distribution.
Fg. NB-3221-1 1995 SECTION I, DIVISION 1 - NB
9/51
Stress _______ _ PrimaryCategoory Genra Membrane Local Membrane Bending
Description (for Average primary Average stress across Component of pri-examples see stress across any solid section. mary stress pro-Table NO- solid se~on. Ex- Considers discon- portional to3217-1) cludes discon- tinuities but not distance from
tinuities and concentrations. centroid of solidconcentrations. Produced only by section. ExcludesProduced only by mechanical loads. discontinuitiesmechanical and concentra-loads. tions. Produced
only by mechan-ical loads.(Note (1]
Symbol P ,P(Note (2)]
Combination of stresscomponents andallowable limits
intensities.
Legend
- Use Design Loads
NOTES:(1) Bending component of primary stress for piping sall be the stress proportional to the distance from
centroid of pipe cross section.(2) The symbols P P and P do not represent single quantities, but rather sets of six quantities
representing the six stress components o,, a,, a, 7%, r,,, and r,
FIG. NB-3221-1 STRESS CATEGORIES AND LIMITS OF STRESS INTENSITYFOR DESIGN CONDITIONS
78
Primary Secondary
Stress General Local Membrane
Category Membrane Membrane Bending Expansion plus Bending Peak
Description (for ex- Average primary Average stress across Component of primary Stresses which result Self-equilibrating (1) Increment added
amples see Table stress across solid any solid section. stress proportional from the constraint stress necessary to to primary or sec-
NB-3217-1) section. Excludes Considers effects of to distance from of free end displace- satisfy continuity of ondary stress by a
effects of discon- discontinuities but centroid of solid ec- ment. Considers structure. Occurs at concentration
inuities and con- not concentrations. tion. Excludes effects of disconti- structural disconti- (notch).
centrations. Pro- Produced by pres- effects of disconti- nuities but not local nuiies. Can be (2) Certain thermal
duced by pressure sure and mechan- nuitiei and conicen- stress concentration caused by pressure, stresses which
and mechanical ical loads, including trations. Produced (not applicable to mechanical loads, or may cause fatigue
loads, inertia earthquake by pressure and vessels), differential thermal but not distortion.
effects. mechanical loads, expansion. Excludesincluding nertia local stressearthquake effects. concentrations.(Note (1]
Symbol Note (2)] P. P. P. QF
Combination of stressI m
components and - --- 0--
allowabie limitsa of stress intensities F
p 3 5 ~ ~~* (Note (3))(Noten -4
Legend
(I Allowable Value PS P +P. a0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I(Note ()]
Calculated Value
…Service Condition Loads [oeW
(Total Stress)
FIG. NB-3222-1 STRESS CATEGORIES AND LIMITS OF STRESS INTENSITY FOR LEVEL A AND LEVEL BSERVICE LIMITS
9/53
Fatigue Background
*Low cycle, strain limited fatigue
- Testing based on strains
- Stresses used in curves for eut
comparison with analysis reut
*Factor of Safety in Design Curves
- 2 on stress
- 20 on cycles
*Not all materials have fatiguecurves
103~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
102~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'
MM--M~~~~~~~~~~~~~~~~~~~I
C,,
10 102 103 10 516
NOTE: ~~~~~~~~~~~~~~Number of cycles, N
E -28.3 X106 psi
FIG. 1-9.2.1 DESIGN FATIGUE CURVE FOR AUSTENITIC STEELS, NICKEL-CHROMIUM-IRONALLOY, NICKEL-IRON-CHROMIUM ALLOY, AND NICKEL-COPPER ALLOY FOR
5, > 28.2 ksi, FOR TEMPERATURES NOT EXCEEDING 800OF(For S, 28.2 ksi, use Fig. 1-9.2.2.)
Table 1-9.1 Contains Tabulated Values and a Formula for Accurate Interpolation of This Curve
APPENDIX I FIg. I-9.2
24 t ft--- 1 ~~~~~~~~~~~~Curve A
'i18Curve 1
106 i Curve C
106 107 los 109~~10 1010 1011
NOTE: Number of cycles, NE 28.3 X 106 psi
Criteria for the Use of the Curves in This Figure[Notes (1)-(5)J
Elastic Analysis of Material Elastic Analysis ofOther Than Welds and Welds and Adjacent
Curve Adjacent Base Metal Base Metal
A (P + Pb+Q)~. •27.2 ksi
B (P + %b + ). > 27.2 ksi and 1W, + + Q)Q_, 27.2 ksiS. is corrected for applied mean stress
C (PL+ P,,+ Q)~> 27.2 ksi (P,.+ PS+ Q)~ 27.2 ksi
NOTES:(1) Range applies to the individual quantities P,, P,, and Q and applies to the set of cycles under
consideration.(2) Thermal bending stresses resulting from axial and radial gradients are excluded from Q.(3) Curve A is also to be used with inelastic analysis with S, = %/ A e E, where A , is the total effective
strain range.(4) The maximum effect of retained mean stress is included in Curve C.(5) The adjacent base metal is defined as three wall thicknesses from the center line of the weld.
FIG. -9.2.2 DESIGN FATIGUE CURVES FOR AUSTENITIC STEELS, NICKEL-CHROMIUM-RONALLOY, NICKEL-IRON-CHROMIUM ALLOY, AND NICKEL-COPPER ALLOY FOR
S < 28.2 ksi, FOR TEMPERATURES NOT EXCEEDING 800'F(For S. > 28.2 ksi, use Fig. 1-9.2.1.)
Table 1-9.2.2 Contains Tabulated Values for Accurate Interpolation of This Curve
9/56
Cumulative Damage
*Methodology- Designate how many cydles each stress
cycle will have. Call these nj, n 2 11, etc.Consideration should be given forsuperpositioning of the stress cycles.
- For each type of stress cycle, calculateSalt based on whether the principal
stress directions change or not- For each type of stress cycle, use the
fatigue curves to determine themaximum number of repetitions whichwould be allowed if this type of cyclewas acting alone. Call these NI, N 2, N 3 ,etc.
- For each stress cycle, calculate theusgefactors, Ul U2 U3 etc. where U,
n 1 /NI, etc.
- Calculate the cumulative usage factor,U =U + U 2 +U 3 , + ... ; this cumulativeusage factor must not exceed 1.0
9/57
Cwuuative Damage. If there are two or moretypes of stress cycle which produce significant strssstheir cumulative effect shall be evaluated as stipulatedin Steps 1 through 6 below.
Step 1: Designate the specified number of times eachtyp of stress cycle of types 1, 2,3, .. .,n, will be repeated during the life of thecomponent as ni, n2, n3, . . ., n,,, respectively.
NOTE: In determining n %2 n3, --- n consideration shall begiven to the superposition of cycles of various origins which producea1 total stress difference range greater than the sumes difference rangesof the individual cycles. For exa~mple, if one type of stress cycleproduces 1000 cycles of a strs difference variation fm zero to+60,000 psi and another type of strs cycle produces, 10,000 cyclesof a stress difference vaiation from zero to -50,000 psi, the two typesof cycle to be considered are defined by the following paramneters:
(a) for type 1 cycle, n 1000 and S, = (60,000 + 50,000)12=55,000 psi;(b) for type 2 cycle, fl2 =9000 and S 2 = (50,000 + 0)12
25,000 psi.
Step 2: For each type of stress cycle, determinethe alternating stress intensity S by theprocedures of NB-3216.1 or NB-3216.2above. Call these quantities S , S 2.
Salt 3 ... ,pSlt#
Step 3: For each value S , Salt2, St 3, ... , ffuse the applicable design fatigue curve todetermine the maximum number of repeti-tions which would be allowable if this typeof cycle were the only one acting. Call thesevalues NI, N2, Nt3 , . .. , N..
Step 4: For each type of stress cycle, calculate theusage factors U, U2, U3, . . ., U,,, fromU, = n (IN, U2 =n2fIN 2, U3 =n3 IN3,1],=nfl/N..
Step 5: Calculite the cumulative usage factor U from
U= U1+U2 +U3+. .+ U.Step 6: The cumulative usage factor U shall not
exceed 1.0.
Primary Notes (1) and (6) Secondary
[Notes (1) and ()
Stress Category General Membrane Local Membrane Bending Membrane pus Bending Peak Notes (1) and (]
Description (for examples Average primary stress Average stress across any Component of primary Self-equilibrating stress (1) incremnent added tose Table NB-3217-1) across solid section. Ex- solid section. Considers stress proportional to necessary to satisfy con- primary or secondary
cludes discontinulties and discontinuiies but not distance from centroid of tinuitY of structure. Occurs stress by a concentrationconcentrations. Produced concentrations. Produced solid section. Excludes at structural discon- (oc)only by mechanical loads, only by mechanical loads. discontinuitles and concen- tinuities. Can be caue by (2) Certain thermal stresses
trations. Produced only by mechanical load or by which may cause fatiguemechanical loads, differential thermal expan- but not distortion of
sion. Excludes local stress vessel shape.____ ____ ____ ____ ____ ____ concentration. _ _ _ _ _ _ _ _ _ _ _ _ _ _
Symbol ~P. P, p% FSyotl NB-3213.6 and NB-3213.8 NB-3213.10 NO-3213.7 and NB-3213.9 NB-3213.11
(Note (1~~~~~ (Note 3 NB-3213.8
Combination of stress I
components andallowable limits of I
______________________stress intensitiesI * * ~~~~~~~~~~~~~~~~~~~~ElasticElastic :analysis
astic ~~1.85, analysis : .5 NB-3224.1:
00 ~ ~ ~ ~ ~~ ~~anlss* 1.5, N B-3224.2 NB3-3224.2:C5 NB-3224 ~~~~~~~~~~~~~~~~~or 0
L~~~~~~~~ ~~~or Limit I
- - - -- - - -- - - -L yiiit anasis -Evaluation not required L -Evaluation not required
\ N -324.3; (Note (4)* ~~ [Note (4)] Triaxial
I *~~~~~ 4.8S stresses
N B-3224.3(Note (]
NOTES:(1) The symbols P P, P, Q, and F do not represent single quantities, but rather sets of six quantities representing the six stress components a.,, o.,, a.,,
iR, T , and r,.
(2) For configurations where compressive stresses occur, the stress limits shall be revised to take into account critical buckling stresses NB-3211(c)].(3) The limits shown are for stresses resulting from pressure in combination with other mechanical loads. For ferritic materials, the P. elastic analysis limits
for pressure loadings alone shall be equal to the greater of 1.15. or 0.95,(4) C, the collapse load calculated on the basis of the lower bound theorem of limit analysis and yield strength values specified in Soction II, Part D,
Subpart 2. Table Y-1(5) The triaxial stresses represent the algebraic sum of the three primary principal stresses (a, + ., + a.,) for the combination of stress components. 0(61 For piping. aternative requirements are provided n NB.3224.7.
Use the greater of the values specified.
FIG. NB-3224-1 STRESS CATEGORIES AND LIMITS OF STRESS INTENSITY FOR LEVEL C SERVICE LIMITS
9/599/60
NB-3228 Applications of Plastic Analysis
The following subparagraphs provide guidance in theapplication of plastic analysis and some relaxation ofthe basic ss limits which are allowed if plasticanalysis is ud
NB-3228.1 Limit Analysis. The limits on General NB-3228.3 Plastic Analysis. Plastic analysis is aMembrane Stress Intensity (N13-3221.1), Lccal. Mem- method of structural analysis by which the structuralbrane Stress Intensity (NB-3221 .2), and Primary Mem- behavior under given loads is computed by consideringbrane Plus Primary Bending Stress Intensity (NB- the actual material stress-strain relationship and ss3221.3) need not be satisfied at a specific location if redistribution, and it may include either stain hardeningit can be shown by limit analysis that the specified or change in geometry, or both.loadings do not exceed two-thirds of the lower bound The limits of General Membrane Stress Intensitycollapse load. The yield strength to be used in these (N1B-3221 .1), Local Membrane Stress Intensity (NB-calculations i 1.5Sm. The use of 1.5S., for the yield 3221.2), and Primary Membrane Plus Primary Bendingstrength of those materials of Section II, Part D, Subpart Stress Intensity (NB-3221 .3) need not be satisfied at1, Tables 2A and 2 to which Note (2) of the Table a specific location if it can be shown that the specifiedis applicable may result in small permanent strains loadings do not exceed two-thirds of the plastic analysisduring the first few cycles of loading. If these strains collapse load determined by application of II-1430 toare not acceptable, the yield strength to be used shall a load-deflection or load-strain relationship obtainedbe reduced according to the strain limiting factors of by plastic analysis. When this rule is used, the effectsSection II, Part D, Subpart 2, Table Y-2. When two- of plastic strain concentrations in localized areas ofthirds of the lower bound collapse load is used, the the structure, such as the points where hinges form,effects of plastic strain concentrations in localized areas must be considered. The effects of the concentrationsof the structure such as the points where hinges form of strain on the fatigue behavior, ratcheting behavior,must be considered. The effects of these concentrations or buckling behavior of the structure must be consideredof strain on the fatigue behavior, ratcheting behavior, in the design. The design shall satisfy the minimumor buckling behavior of the structure must be considered wall thickness requirements.in the design. The design shall satisfy the minimumwall thickness requirements.
F-1322.2 APPENDIX F F-1331.5
9/61for dynamic amplification of structural response, bath F-1331 Criteria for Componentsin the component and in the system. F-1331.1 Elastic Analysis
F-1322.3 Material Behavior (a) The general primary membrane stress intensity(a) The mechanical and physical properties shall be P,, shall not exceed the lesser of 2.4S, and 0. 7S. for
taken from Appendix at the actual temperature of materials included in Table I- .2, or 0.7S. for materialsthe material. The allowable stresses shall be based on included in Table -1. 1.material properties given in Appendix at temperature. (b) The local primary membrane stress intensity PL
If S., values at temperature are not tabulated in Ap- shall not exceed 150% of the limit for general primnarypendix I,' the value used shall be included and justified membrane stress intensity P..in the Design Report. (c) The primary membrane (general or local) plus
(b) The stress and strain allowables given in this primary bending stress intensity P. ± Pb shall beAppendix are based on an engineering stress-strain limited in accordance with one of the following pro-curve. If another type of stress-strain curve (e.g., true visions:stress-strain or Kirchoff stress-strain) is used, the re- (1) stress intensity PL + Pb shall not exceed 1 50%suits from the analysis or the allowables given in this of the limit for general primary membrane stress in-Appendix shall be appropriately transformed. tensity Pm;
(c) When performing plastic analysis, the stress- (2) static or equivalent static loads shall not x-strain curve used shall be included and justified in the ceed 90% of the limit analysis collapse load using aDesign Report. It is permissible to adjust the stress- yield stress which is the lesser of 2.3Sm and 0.7S., orstrain curve to include strain rate effects resulting from 100% of the plastic analysis collapse load or test col-dynamic behavior. However, the allowables shall be lapse load (-1321.6).selected in accordance with (a) above. (d) The average primary shear stress across a section
(d) The yield criteria and associated flow rule used loaded in pure shear shall not exceed 0.42S,,.in the inelastic analysis may be either those associated F-1331.2 Interaction Method. As an alternative towith the maximum shear stress theory (Tresca) or the the requirements of F- 1331.1 above, acceptability ofstrain energy distortion theory (Von Mises). individual members of components may be demon-
F-1322.4 Geometric Nonllnearities. Geometric non- strated using the interaction method. Procedures forlinearities may be produced by relatively large defor- interaction method analysis are given in A-9000. Themations and/or rotations and by gaps between parts allowable stress S&, shall not exceed the lesser of 2.4Smof the structure. Analyses performed for derivation of and 0. 7S..loads and for evaluation of acceptability of components F.1331.3 Bearing Stresses. Except for pinned andand component supports shall consider geometric non- bolted joints, bearing stresses need not be evaluatedlinearities if appropriate. for loads for which Level D Service Limits are spec-
F-1322.5 Strain and/or Deformation Limits. In ad- ified.dition to the limits given in this Appendix, the strain F-1331.4 Stress Limits for Bolts. Bolts shall be eval-or deformation limits (if any) provided in the Design uated in accordance with the rules of F- 1335.Specification shall be satisfied.
F-133 1.5 Requirements for Compressive Loads.Components subjected to compressive loads shall be
F-1330 ACCEPTANC CRITERIA USINGevaluated against buckling limits. Maximum compres-F-1330 EACETACE CITE IAA USING sive load (or stress) shall be limited to a value estab-
ELASTIC SYSTEM ANALYSIS lished by (a), (b), or (c) below.The acceptance criteria in this Section shall be ap- (a) Two-thirds of the value of buckling load (or
plied when elastic system analysis is used to determine stress) determined by one of the methods given below:loads on components and component supports. These (1) comprehensive analysis which considers ef-criteria are subject to the restrictions on methods of fects such as geometric imperfections, deformationsevaluation stated in F- 1322. due to existing loading conditions, nonlineari ties, large
deformations, residual stresses, and inertial forces; or
'In addition to Appendix 1, Tables [.3.0, S values are also available (2) tests of physical models under conditions ofin Code Cases covering new or additional materials for components restraint and loading the same as those to which theand their supports. configuration is expected to be subjected;
561
F-1331.5 1989 SECTION III, DIVISION 1 - APPENDICES F-1334
(b) a value equal to 1 50% of the limit established F-1332.7 Load Rating. As an alternative to the re-by the rules of NB-3 133, except that the pressure is quirements of F-l332.1 through F-1332.6 ab~platepermitted to be 250% of the given value when the and shell type component supports may be qualifiedovality is limited to 1% or less; or to Service Level D Limits using the procedure for load
(c) a value determined in accordance with the pro- rating (NF-3282). The load rating for Level D Servicecedures contained in a Code Case for metal contain- Loadings shall be determined by the following equa-ment shell buckling design methods using a factor of tion:safety of 1.34.
load rating = TL X 0.7s S.
F-1332 Criteria for Plate and Shell Type whereComponent Supports TL = support test load equal to or less than the load
under which the component support fails toThe criteria presented in this paragraph pertain to perform its specified support function, lb
primary stresses only. Stresses resulting from con- S,= tensile strength of the support material at tern-straint of free end displacement and anchor point perature, ksimotion (NF.3121. 12 and NF-3121. 13) shall be con- S =, tensile strength of the support material at testsidered primary stresses in the evaluation. Neither peak temperature, ksistresses nor stresses resulting from thermal expansion butwithin the component support need be evaluated.
F-1332.1 Primary Membrane Stress Intensity. The . -
general primary membrane stress intensity Pm is lim-S,ited to the greater of .2s, and .5S, but may not
-exceed 0.7S.
F-1332.2 Primary Membrane Plus Bending Stress F..1333 Criteria for Component StandardIntensity. The general primary membrane plus pri- Supportsmary bending stress intensity, P, + P&, shall be limited Criteria in F-1332 or F-1334 shall be applied ac-in accordance with one of the following provisions: cording to whether component standard supports are
(a) 150% of the limit for general primary stress plate and shell or linear type supports.intensity Pm; or
(b) static or equivalent static loads shall not exceed90% of the limit analysis collapse load (F- 1321.6) usinga yield strength which is the lesser of 1. 2S, and 0.7SU, F-1334 Criteria for Linear Type Componentor 100% of the plastic analysis collapse load or test Suppotcollapse load (F- 1 321.6).
The criteria presented in this paragraph pertain toF-1332.3 Bearing Stress. Except for pinned and primary stresses only. Stresses resulting from con-
bolted joints, bearing stresses need not be evaluated straint of free end displacement and anchor point mo-for loads for which Level D Service Limits are spec- tion (NF-3121.12 or NF-3121.13) shall be consideredified. primary stresses in the evaluation.
F-133.4 Pre Sear.The aerag priary hear Neither peak stresses nor stresses resulting fromacross a Pec reo Soaedr Thpue averagehaprimaryeshear thermal expansion within the component support need
across, eto oddi uesersalntece be evaluated.0.42S~~~~~~~~~~. ~~Unless otherwise specified, the allowable stresses
F-1332.5 Requirements for Compressive Stresses. presented (NF-3 320) for Level A Service ConditionPlate and shell type component supports subject to may be increased using the following factors: thecompressive stresses shall be evaluated in accordance smaller of 2 or .167SJ S, if S. > 1. 2S,or1.4 ifS,,with the rules of F-1331.5(a). • 1 .2S,, where S, is the yield strength, ksi, and S. is
the ultimate tensile strength, ksi, both at temperature.F-1332.6 Stress Limits for Bolts. Bolts shall be eval- In addition, members must be checked for local and
uated in accordance with the rules of F-1335. general instability.
562
9/63
F.1334.1 APPENDIX F F-1334.4
F-1334.1 Stresses in Tension. The tensile stress on (KL\ 1 the net section, except at pin holes and in the through- X= -
plate- thickness direction, shall not exceed the lesser of ~ r~
l.2Sand .7S4 E= modulus of elasticity, psi
F-1334.2 Stresses in Shear. The shear stress on the K= effective length factorgross section shall not exceed the lesser of 0. 72Sy and L = unbraced length, in.0.42SU. Gross section shall be determined in accor- r= radius of gyration, in.dance with NB-3322.1(b). (2) For nonstress-relieved heavy structural shapes
(web or flange thickness greater than in.) or forF.1334.3 Axial Compression. Maximum load in ax- nonstress-relieved built-up members using universal
ially loaded compression members shall be limited in mill plate, the following rules shall be applied:accordance with either (a) or () below.
(a) Two-thirds of the buckling load, as determined For 0 < < 1by one of the following methods:
(1) comprehensive stability analysis which con- p _1 - A2 /4siders effects such as large deformations, deformations - 1.1+07X+08) due to existing loading conditions, material nonilin- P .11+07k+08)2-08kearities, local buckling, out-of-straightness and other For 1 < X A 2tolerances, load eccentricity, end conditions, residualstresses and inertia loads (for dynamic loading); or p I - X
2 /4(2) testing of a full-scale prototype under condi- = 18
tions of support and loading the same as those to which 18the actual compression member is expected to be sub- For > ,2jected;
(b) the maximum allowable load for ferritic steelsp shall be determined in accordance with the following = .8)
provided that the initial out-of-straightness does not p .8,
exceed 1/1000 of the unsupported length. Effects ofdeformations due to existing loads shall also be con-sidered. F-1334.4 Combined Axial Tension and Bending
(1) Except as noted in (2) below, the following (a) For members subject to both axial tension andrules shall be applied: bending stresses, the following equation shall be sat-
isfied:For 0 < <
P _ I-X2 /4 ~~~~~~~~~~~.+ fb. + y<
P,- 1. 11 + 0. 50X + 0.17X2-0.28X
3lFb b
For 1< A .~~~~~~~~ whereFo 1 V 2 F,,= smaller of .2S, or .7S,ksi
7?5T For -members qualifying as compact sections un-P =2 (1-X/)der criteria of NF-3 322. 1(d)(1), the maximum bending
(1 -24)stress shall be given by:
For > XF = fSy
P_ 2 where
P,~ 3)2 f= plastic shape factor for the cross section(c) If members do not meet the compact section
where requirements, they shall be designed using one of twoP= maximum allowable load, lb methods below to determine Eb for use in the equationP,= SA,, lb above.AS= area of gross section, in. 2 (1) Allowable values for Fb given in NF-
F-1334.4 1989 SECTION M, DIVISION 1 - APPENDICES F-L33
3322.1 (d)(2) may be increased by a factor of 1.11 (to F-1334.10 Bearing Stresses. Except for pM~h#andmaintain a nominal factor of safety of 1.5 against in- bolted joints, bearing stresses need not be evaluatedstability). for loads for which Level D Service Limits are spec-
(2) Rigorous analysis of member stability may be ified.used to determine critical bending stress. A factor ofsafety of 1.5 shall be used in determining allowabledesign bending sess F-1335 Requirements for Bolted Joints
(a) The requirements provided in this Section shallF-1334.S Combined Axial Compression and Bend- be applied to components and component supports.
ing. Members subject to combined axial compression Threaded structural fasteners used in core supportand bending shall satisfy Eqs. (20), (21), and (22) of structures shall be evaluated using the rules of F- 1440.NF-3322. l(eXl) with allowable stresses defined as fol- (b) Allowable stresses for bolts are given in thelows, paragraphs below. These allowable stresses are only
(a) F. = P/Ag where P shall be determined in accor- applicable if the bolt stresses are calculated using elasticdance with F-1334.3. methods.
(b) The value of F', shall be taken as:F-1335.1 Allowable Tensile Stress. The average ten-
W2E sile stress computed on the basis of the available tensilel,= .30(K4/lrb)2 stress area shall not exceed the smaller of 0.7S. and
S, When high strength bolts or threaded parts havingwith terms as defined in NF-3313.1. an ultimate strength greater than 100 ksi at operating
(c) Fb shall be determined using F-1334.4(b) or (c) temperature are used in component applications, theas appropriate. maximum value of the stress at the periphery of the
bolt cross section resulting from direct tension plusF-1334.6 Collapse Load Analysis. As an alternative bending and excluding stress concentrations shall not
to the requirements in F- 1334.4 above, acceptability exceed S,,. The bolt load shall be the sum of the externalof linear type component supports may be established load and any bolt tension resulting from prying actionusing one of the methods given below: produced by deformation of the connected parts.
(a) using lower bound limit analysis given in NF. F-1335.2 Allowable Shear Stress3340, static or equivalent static loads shall not exceed (a) For bearing type joints, the average bolt shear90% of the limit analysis collapse load using a yield stress expressed in terms of available shear stress areastress which is the greater of .2 S, and .5Sr, but not shall not exceed the smaller of 0.42SU and 0.6S,larger than 0.7S,,; (b) Friction type joints shall be evaluated using the
(b) 100% of the plastic analysis collapse load; or rules of NF-3324.6(a)(3)(b).(c) 100% of the test collapse load (F-1321.6).
F-1335.3 Combined Tensile and Shear StressF-1334.7 Interaction Method. As an alternative to (a) Bolts subjected to combined shear and tension
the requirements of F-1334.1 through F-1334.5 above, in bearing type joints shall be so proportioned that theacceptability for individual structural members of in- shear and the tensile stresses satisfy the following equa-ear type component supports may be demonstrated tion:using the interaction method. Procedures for interac-tion method analysis are given in A~90. The allow- + Nable stress S0, shall not exceed the greater of 1.2S, andFb 2 F 2
1.5S, but not larger than 0.7S,.where
F-1334.8 Load Rating. As an alternative to the re- f= computed tensile stress, ksiquirements of F- 1334.1 through F- 13 34.5 above, linear f,= computed shear stress, ksitype component supports may be qualified to Service Fb= allowable tensile stress at temperature perLevel D Limits using load rating criteria given in F- 13 35. , ksiF-1332.7. Fb= allowable shear stress at temperature per
F-1335.2(a), ksiF-1334.9 Stress Limits for Bolts. Bolts shall be eval- (b) In friction type joints, the joint clamping force
uated in accordance with the rules of F-1335. will be reduced by any direct tension load on the joint.
564
STRESS UMETS FOR CLASS 1 SUPPORTS 9/65
DESIGN LIMITS
* PATE AND SHELL TYPE SUPPORTS
GENERAL PRIMARY MEMBRANE STRESS INTENSITY DERIVED
FROM AVERAGING (PRIOR TO THE DETERMINAllON OF THE
STRESS INTENSITY VALUES ACROSS THE THICNESOF A
SECTION FOR THE SPECIFIED DESIGN MECHANICAL LOADS
SHALL BE LESS THAN Sm.
PRIMARY MEMBRANE PLUS PRIMARY BENDING STRESS
INTENSITY DERIVED FROM THE HIGHEST VALUE ACROSS THE
THICKNESS FOR THE SPECIFIED DESIGN MECHANICAL LOADS
SHALL BE LESS TH-AN 1.55m.
FOR BEARING LOADS AND SUPPORT SECTIONS LOADED IN
SHEAR, SUBSECTION NF-3223 APPLIES.
* LINEAR SUPPORTS
SUBSECTION NF-3322 APPLIES.
SERVICE LEVEL A THROUGH D SERVICE LIMITS
*USE THE ALLOWABLE STRESS INTENSITY VALUESMULTIPLIED BY THE APPROPRIATE FACTOR SHOWN INTABLES NF-3522(b)-1, NF-3523(b)-1, NF7-3622(b)-1, AND NF-3623 (b)-i.
9/66
SPECIAL NOTES ON NF
FOR PLATE AND SHELL TYPE OF SUPPORTS, THE
ALLOWABLE BUCKUING STRESS IS UIMITED TO 1/2 OF THE
CRITICAL BUCKUING STRESS (NF-3522(b)-1) FOR SERVICE
LEVELS A, By AND C LOADINGS.
FOR LINEAR TYPE OF SUPPORTS, THE ALLOWABLE
BUCKLING STRESS FOR ANY MEMBER S LIMITED TO 2/3 OF
THE CRITICAL BUCKLNG LOAD (NF-3523(b)-1) FOR SERVICE
LEVELS A, B, AND C LOADINGS.
BOTH TABLES NF-3522-(b)-1 AND NF-3523(b)-1 REFER TO
APPENDIX F FOR SERVICE LEVEL D CONDITION FOR STRESS
LIMITS.
9/67
STRAIN BASED PLASTIC ANALYSIS CRITERIA
Support
1. ASME Section 1II, Subsection NF
Tables 3523(b) - and 3623 (b) -1 Refer toAppendix F Service Level D for Stress Limits.
2. ASME Section it, Appendix F
Plate and Shell Type Component Supports
F-i1332.2 - 90% of Limit Analysis Collapse Load(Yield Strength < 1.2Sy, or 0.7Su),
or,
1 00% Plastic Analysis or TestCollapse Load
Linear Type Component Supports
F-i1334 - Level A Limit in NF-3320 Increasesby 2for Level Dif Su> .2 Sy
Use A-9000 for Interaction with1.2Sy or 0.7 Su as Allowable
F-i 334.6 - 1 00% of the Plastic Analysis Collapse Load
WZJ
9/68
QAUFCAT~O OF IN-UNE COMPONENTS
*PIPING PRODUCT
PIPE BENDS, ELBOWS, INTERSECTIONS, MITERS, CLOSURES,FLANGES, REDUCERS, ATTACHMENTS, MADE ACCORDING TO NB-3132
+ MEET NB-365 USING APPROPRIATE STRESS INDICES OR STRESSINTENSIFICATION FACTORS GIVEN IN NB3-3632-1
INTERSECTIONS - BRANCH CONNECTIONS
+ REINFORCEMENT CALCULATIONS BASED ON NB-3643
*VESSEL NOZZLE
APPLY NOZZLE LOADS OBTAINED THROUGH PIPING SYSTEMANALYSIS AND CONDUCT FINITE ELEMENT ANALYSIS OF THEVESSEL NOZZLE
USE THE LIMITS SPECIFIED IN TABLE NB-3217-1 IN ACCORDANCEWITH THE REQUIREMENTS OF SUBSECTION NB3-3227.5
*ATTACHMENTS
STRESS INTENSIFICATION FACTOR NOT PROVIDED IN THE CODE
CODE CASE N-122 PROVIDES STRESS INDICES AND DESIGNPROCEDURES FOR CLASS ATTACHMENTS
*FLANGED JOINTS
REQUIREMENTS GIVEN IN SUBSECTION NB-3658
+ BOLTING: MEET NB-3232
+ FLANGES: MEET NB3-361 2.1
+ PIPE TO FLANGE WELDS: MEET NB-3652, NB-3653, AND NB-3654 USING APPROPRIATE STRESS INDICES FROM TABLE NB-3681 (a)-1.
20
SECTION 9/7. ASME SECTION III CODE. DESIGN BY ANALYSIS OF CLASS1 PIPING
FOR PIPING ANALYSIS, THE CLASSIFICATION OF STRESS INTENSITY ISSHOWN IN FIG. 9/69.
SPECIFIC FORMULAS ARE PROVIDED FOR BY THE CODE FOR PIPING. THEEQUATIONS ARE DESCRIBED IN FIGS. 9/70 THROUGH 9/74.
FIG. 9/75 PROVIDES A SUMMARY OF THE EQUATIONS LISTED IN THE ABOVEMENTIONED FIGURES FOR PIPING.
IT SHOULD BE NOTED THAT EQUATION FOR PRIMARY STRESS INTENSITY(EQU. (9)) IS THE KEY EQUATION TO BE FOLLOWED FOR DESIGN, ANDLEVELS B, C, AND D ANALYSES. EQUATION (9) IS NOT SPECIFICALLYREQUIRED FOR LEVEL A CONDITION. SOME PLANTS HAVE SPECIFICREQUIREMENTS FOR USING EQU. (9) IN THE DESIGN SPECIFICATION,HOWEVER.
FIG. 9/75 ALSO IDENTIFIES APP. F AS AN ALTERNATIVE FOR THE LEVELD LOADS.
FIG. 9/76 PROVIDES TWO ILLUSTRATIONS FOR THE CONSIDERATION OFCYCLICAL LOADINGS AND STRESS RANGES.
NB-3000 - DESIGN Table NB-3217-2
9/69
TABLE NB-3217-2CLASSIFICATION OF STRESS INTENSITY IN PIPING, TYPICAL CASES
DiscontinuitiesConsidered
Piping Componen Locations Origin of Stress Classification Gross Local
Pipe or tube, elbows, and Any, except crotch Internal pressure P-, No Noreducers. Intersections regions of intersections P, and Q Yes Noand branch F Yes Yesconnections, except incrotch regions
Sustained mechanical loads, P* No Noincluding weight P, and Q Yes No
Nonreversing Dynamic Loads F Yes Yes
Expansion P. Yes NoF Yes Yes
Axial thermal gradient Q Yes NoF Yes Yes
Reversing Dynamic Loads [Note (2)]
Intersections, including In crotch region Internal pressure, sustained P, and Q (Note (] Yes Notees and branch mechanical loads, expansion F Yes Yesconnections and nonreversing dynamic loads
Axial thermal gradient QYes NoF Yes Yes
Reversing Dynamic Loads (Note (2)]
Bolts and flanges Any Internal pressure, gasket P. No Nocompression, and bolt load Q Yes No
F Yes Yes
Thermal gradient Q Yes NoF Yes Yes
Expansion P~, Yes NoF Yes Yes
Any Any Nonlinear radial thermal gradient F Yes yes
Linear radial thermal gradient F Yes No
Anchor point motions, including QYes Nothose resulting from earthquake
NOTES:(1) Analysis is not required when reinforced in accordance with NB-3643.(2) The stress intensity resulting from this loading has special requirements which must be satisfied. For evel Service Limits these
are provided in NB-3223(b)(2) and for level Service Limits in NB-32281.
77
NB-36513 1995 SECTON RII, DIVISION 1 - NB NB-3653.1
(b) Attachments shall meet the requirements of loading, to any other load set which followsg'iiame.NB-3135. It is the range of pressure, temperature, and moment
(c) Figure NB-4433- 1 shows some typical types of between two load sets which is to be used in theattachment welds (NB3-4430). calculations. For example, one of the load sets to be
included is that corresponding to zero pressure, zero
NB-3652 Consideration of Design Conditions moment, and room temperature. Equation (10) shall besatisfied for all pairs of load sets:
The primary stress intensity limit is satisfied if therequirement of Eq. (9) is met: S ClP 0,D0,+C D, .+CE
PD. D,, 21 21
2t 21 q XIT.- abTb 1 3S hS. (10)
Bwher prmretrs nicsfrth pcfi rd (b) If for one or more pairs of load sets Eq. (10)uctB=pimr undrinesigai o thepecficrod is not met, the piping product may still be satisfactory,uc ouder dimestteroi n. (1-360 ) provided that the conditions of NB-3653.6 are met or
I= moment of inertia, in.4 (NB3-3683) provided that the requirements of NB-3200 are satisfied.Miresultant moment due to a combination of (c) The nomenclature used in Eq. (10) is defined as
Design Mechanical Loads, iA.b. All Design follows:Mechanical Loads, and combinations thereof Cl, C2, C3 =secondary stress indices for the specificshall be provided in the Design Specifica- component under investigation (NB-tion. In the combination of loads, all direc- 3680)tional moment components in the same D,,,1 , S,= as defined for Eq. (9)direction shall be combined before determin- d0(d6 ) = inside diameter on side a(b) of a grossing the resultant moment (i.e., resultant mo- structural discontinuity or material dis-ments from different load sets shall not be continuity, in.used in calculating the moment M,). f th Eb= average modulus of elasticity of the twomethod of analysis for earthquake or other sides of a gross structural discontinuitydynamic loads is such that only magnitudes or material discontinuity at room temper-without relative algebraic signs are obtained, ature, psi (Section II, Part D, Subpartthe most conservative combination shall be 2, Tables TM)assumed. i= resultant range of moment which occurs
P =Design Pressure, psi when the system goes from one service.= allowable design stress intensity value, psi la e oaohr n-b evc od
(Section II, Part D, Subpart 1, Tables 2A and combinations thereof shall be pro-and 2) vided in the Design Specification. In the
= nominal wall thickness of product, in. combination of moments from load sets,(NB3-3683) all directional moment components in
the same direction shall be combinedbefore determining the resultant moment
NB-3653 Consideration of Level A Service (i.e., resultant moments from differentLimits load sets shall not be used in calculating
NB-3653.1 Satisfaction of Primary Plus Secondary the moment range M1). Weight effectsStress Intensity Range need not be considered in determining the
(a) This calculation is based upon the effect of loading range since they are noncyclic inchanges which occur in mechanical or thermal loadings character. If the method of analysis iswhich take place as the system goes from one load such that only magnitudes without rela-set, such as pressure, temperature, moment, and force tive algebraic signs are obtained, the
most conservative combination shall be
23 For piping products, such as tees and branch connections, the assumed. If a combination includes re-second term of Eqs. (9), (10), and (11), narnely that containing Mb versing dynamic loads, M, shall be either:is to be calculated as referred to in NB.3683.1(d). (1) the resultant range of moment due
1so
G l
NB-36531 NB-3000 - DESIGN N41-3653.
to the combination of all loads consider- I AT, 1 I = absolute value of the range of th4Xier~-ing one-half the range of the reversing ature difference between the temperaturedynamic loads; or (2) the resultant range of the outside surface T,, and the tempera-of moment due to the full range of the ture of the inside surface T of the pipingreversing dynamic loads alone, which- product assuming moment generatingever is greater. equivalent linear temperature distribu-
P, = range of service pressure, psi tion, FT8(Tb) =range of average temperature on side For a quantitative definition of Ti 1 I and AT2 I
a(b) of gross structural discontinuity or see NB-3653.2(b) below. All other terms are as definedmaterial discontinuity, F. For generally for Eq. (1 0).cylindrical shapes, the averaging of T (b) Quantitative Definitions of AT, 1 I and AT 2 .(NB-3653.2) shall be over a distance of
,7.for T and over a distance of The following nomenclature is used:for Tfr ~~~~~~~T = value of T(y) at inside surface, F
dt, for T, ~~~~~~~~= -t/2)ta,(tb,) average wall thickness through the T. = value of Tny) at outside surface, F
length 4 d ('1 t,3 in. A trial and = t(/2)error solution for t and b may be nec- T7(y), Tk (y) = temperature, as a function of radial posi-essary. tion, for load set j and load set kc respec-
cr.(ab) =coefficient of thermal expansion on side tively. 'Fa(b) of a gross structural discontinuity T(y ) = temperature distribution range from con-or material discontinuity, at room temper- dition j to condition k, 'ature, 1 /'F. (Section HI, Part D, Subpart = Tky - {Y)2, Tables TE) t = thickness of the wall of the pipe or
NB-3653.2 Satisfactio of Peak S~ Intensityelement, in.Rnge6 2Stsacino ekStesItniyy radial position in the wall, measured
()For every pair of load sets (N13-3653), calculate positive outward fom the midthickness( aue uigE.(l:position (-t12 y t/2), in.
S~~, values using Eq. (11): Then the temperature distribution range T(y) may be
P.D))0 D thought of as being composed of three parts:Sp KC 1- +K 2 C2 -m, (1) a constant value:
2t 21
I ~~~~~~~~~~~~~~~~~~~1It)Tyd+ ~ K3Ea AT 1 i-K3 C3Ej, T=lIt T2 d
2(1 - v)
* I aj.T - abTb + - Ea AT2 1I (1 1) which is the average value through the thickness. T- v may be used in determining free thermal expansions.
Also, the values of T determined (for the same pairof load sets) or two locations a and b on either side
NOTE: This simplified analysis s intende to provide a value of of a gross continuity may be used for T and T inS, thatervatively estiates he surof P+P+ P +Q +F Eq.(0an(1)as required in Fig. NB-3222-1. Es 1)ad( )
(2) a linear portion, with zero average value, hay-The nomenclature used in Eq. (1 1) is defined as follows: ing variation given by:
Ear= modulus of elasticity (E) times the meancoefficient of thermal expansion (a) both 1
at room temperature, psil'F V = (12/1t 2) JyT(y)dyK,, K2 , K3 = local stress indices for the specific corn- 1
ponent under investigation (NB-3680)I AT 2 = absolute value of the range for that por- (3) a nonlinear portion with a zero average value
tion of the nonlinear thermal gradient and a zero first moment with respect to the mid-through the wall thickness not included thickness. This decomposition of T(y) into three partsin AT1 as shown below, F is ilustrated in Fig. NB-3653.2(b)-1. The value of AT,
151
NB1-3453.2 1995 SECTION mI, DIVISION 1 - NB NB-3653.6
9/72Outside T
surface\ T 0 ~1 2
Midthickcness it.-T;K j7Inside - ..- vT1
surface
FIG. NB-3653.2(b)-1 DECOMPOSITION OF TEMPERATURE DISTRIBUTION RANGE
to be used in Eq. (11) is the variation V of the linear S= 2D' 0 s3.(2portion: S=C 2 1~sS~.(2
4AT1 =v whereMl= same as M, in Eq. (10), except that it includes
only moments due to thermal expansion andThe value of AT2 to be used in Eq. (11) is as follows: thermal anchor movements, in.-b
S=nominal value of expansion stress, psi(b) The requirements of NB-3653.7 shall be met,
AT 2 = max. (IT - TI- /21AT 11, i~ - T - 4214T 11, 0) and, having satisfied those requirements, the primaryplus secondary membrane plus bending stress intensity,excluding thermal bending and thermal expansion
NB-3653.3 Alternating Strs Intensity. The alter- stresses, shall be <3S,. This requirement is satisfiednating stress intensity S~t is equal to one-half the value by meeting Eq. (13) below:of Sp, (S.,,=Sp/2) calculated in Eq. (11) above.
clP.D_ D^ M C3ENB1-3653.4 Use of Design Fatigue Curve. Enter the C1 '2I+C 3~
applicable design fatigue curve, Figs. 1-9.0, on the (13)ordinate using S = S, and find the corresponding x aT - abTbi :53Snumber of cycles on the abscissa. If the service cyclebeing considered is the only one that produces significantfluctuating stresses, this is the allowable number of wherecycles. C 3 = values in Table NB-3681(a)-1
Mi= as defined in NB-3652 and all other variablesNB-3653,5 Cumulative Damage. The cumulative are as defined in NB-3653
damage shall be evaluated in accordance with NB- (c) If these conditions are met, the value of Sd shall3222.4{e)(5). If N is greater than the maximum number be calculated by Eq. (14):of cycles defined on the applicable design fatigue curve,the value of nNi may be taken as zero. K P(4
NB-3653.6 Simplified Elastic-Plastic Discontinuity 2Analysis. If Eq. (10) cannot be satisfied for all pairsof load sets, the alternative analysis described below wheremay still permit qualifying the component under NB- K,= 1.0 for S,, : 3,3650. Only those pairs of load sets which do not satisfy = 1.0 + [(1 - n)/n(m 1)I(Sj,3Sm. - 1), for 3 SmEq. (10) need be considered. <Sn, < 3mSm
(a) Equation (12) shall be met: = l1/n, for S, z. 3mSm
152
NB..3653.6 ~~~~~~~~~NB-3000 - DESIGN NIB-3655.3
mn, n= material parameters given in Table NB- Mi which result in the maximum calculated stress. The3228.5(b)-1 allowable stress to be used for this condition
Sdt= alternating stress intensity, psi but not greater than .S.r In addition, the proceduresS.= primary plus secondary stress intensity value for analyzing Service Loadings for which Level B
calculated in Eq. (10), NB-3653.1, psi Service imits are designated are the same as thoseSp,= peak stress intensity value calculated by Eq. given in NB-3653 for Level A Service imits.
(11), (NB-3653.2), psiSyyilsteghvlepstknaaerefudSk for all load sets shall be calculated in accordance teyietregth ransien atde avseraflidnwith NB-3653.3 or Eq. (14). Using the alternating strsesrtreo h rnsetudrcosdrtointensity values calculated by the above procedures, (b) For Service Loadings for which Level B Servicedetermine the cumulative usage factor in accordance Limits are designated which include reversing dynamicwith NB-3653.4 and NB-3653.5. The cumulative usage loads that are not required to be combined with nonre-factor shall not exceed 1.0. versing dynamic loads, the requirements of NB-3653
NB-3653.7 Thermal Stress Ratchet. When the limits for Level A Service Limits shall be met. In addition,of Eq. (10) are exceeded and before the rules of Eq. any deflection limits prescribed by the Design Specifica-(13) of NB-3653.6 can be utilized, the value of the tion must be satisfied.range of AT, cannot exceed that calculated as follows:
AdT1 range -- -S NB-3655 Consideration or Level C Service0.7 Ea limits
NB-3655.1 Permissible Pressure. When Level Cwhere Service Limits [NCA-2142.4(b)(3) and NB-31 13(b)1 are
C4 = 1.1 for ferritic: material specified, the permissible pressure shall not exceed the= 1.3 for austenitic material pressure P's, calculated in accordance with Eq. (3) of
E& = as defined for Eq. (1 1), psi/ 0 F NB-3641.1, by more than 50%.P = maximum pressure for the set of conditions un-
der consideration, psi NB-3655.2 Analysis of Piping Components. ForSy= yield strength value, psi, taken at average fluid Service Loadings for which Level C Service Limits
temperature of the transient under consideration INCA-2142.4(bX3) and NB-3113(b)] are designated,x = (PDO, 12t) ( Sy,) the requirements of (a) or (b) below shall apply.y= 3.33, 2.00, 1.20, and 0.80 for x = 0.3, 0.5, 0.7, (a) For Service Loadings for which Level C Service
and 0.8, respectively limits are designated which do not include reversingdynamic loads or have reversing dynamic loads com-bined with nonreversing dynamic loads, the conditions
NB-3654 Consideration of Level B Service of Eq. (9) of NB-3652 shall be met using ServiceLlmits Level C coincident pressure P and moments Mi which
NB-3654.1 Permissible Pressure. For Level B Ser- result in the maximum calculated stress. The allowablevice Limits 1NCA-2142.4{bX2)], the permissible pres- stress to be used for this condition is 2.25S, but notsure shall not exceed the pressure Pf., calculated in greater than I1.8Sy.accordance with Eq. (3) of NB-3641.1, by more (b) For Service Loadings for which Level C Servicethan 10%. limits are designated which include reversing dynamic
loads that are not required to be combined with nonre-NB-3654.2 Analysis of Piping Components. For versing dynamic loads, the requirements of NB-3656(b)
Service Loadings for which Level B Service Limits shall be satisfied using the allowable stress in NB-are designated, the requirements of (a) or (b) below 3656(bX2), 70% of the allowable stress in NB-shall apply. 3656(bX3), and 70% of the allowable loads in NB-
(a) For Service Loadings for which Level B Service 3656(.X4).limits are designated which do not include reversingdynamic loads (NB-3622.2) or have reversing dynamic NB-3655.3 Deforms,' Jon Limits. Any deformation orloads combined with nonreversing dynamic loads (NB- deflection limits prescribed by the Design Specifications3622.4), the conditions of Eq. (9) shall be met using shall be considered with respect to Level C ServiceService evel B coincident pressure P and moments Limits.
153
NB-3656 1995 SECTION III, DIVISION 1 - NB NB-3656
NB-3656 Consideration of Level D) Service spectrum analysis as defined in ApedxN-Limits 1226, except the spectrum peak broadening
If the Design Specifications specify any Service value Aft in N-1226-3 shall not be less thanLoading for which Level D Limits are designated 15% and, in place of the damping values for
[NCA-242.2(X4)j, he reuiremets of(a), (), orboth large and small diameter piping systems in[(c below2(bha )I tpple reurmnso a,() rTable N- 1230-1 for Operating Basis Earthquake() ow Shallc aly frwic.evlDSevc and Safe Shutdown Earthquake, a value of 5(im)tFore Sevicne odi fo which noilee v ersice shall be used. The ground motion design input
Limitsiareodesignatedewhichrdongotyincludeoreversm- for generating the floor response spectrum tobda ih lo reven reversig ldsi load reuie be used in the linear elastic analysis shall meetbnd with nnreversin dynaic aplasyh. rqie the requirements of Appendix N- 121 1(a) and N-
me (1) and(2 prisbelowsu shall ply. ed2. 1211(1b). Moments and forces may be computed(1e thepsbe pressure shallulte incotdexcee 2.0h using a methodology other than prescribed
ties the prssrePNcacuatd641ccrdnc1wt above if the alternate methodology is demon-Ec.(3) ofe nditions1 oEq 9ofN-6 salstrated to produce results which envelope the
(2)et The londi tins o e (9)d fo tBhis5 shaio prescribed methodology results. In the combina-be3. me., he alo aer t be0 usdfrthscnto tion of loads, all directional moment compo-is) 3.0 pipiutngt gariedo marerthand2.0gnate nents in the same direction shall be combinedP-N.) Fouiig -o fb icae frome mateia einat before determining the resultant moment. If the
P-o 1n ii tho P-No 9s i abl D Section iits~ method of analysis is such that only magnitudeDr designited toic Dinclu50 ifrevelsn dyServic ts without algebraic signs is obtained, the mostthare intried hic inle bndt reversingdyailos conservative combination shall be assumed.tha ar oarqur toh e coirmbned wi 1thoreversing the pressure occurring coincident with the re-dynami salasphp rqielnyo.()trog 5 versing dynamic load
belo shal pply.ur ocrigciidnwthhe(4) The range of the resultant moment M~m and(1)rthqae rotesureocring oinen wih nt the amplitude of the longitudinal force FAM resulting
earthquake oreothe revsuen. yeladn hl o from the anchor motions due to earthquake and otherexcee the Desinedestress detwigtlang reversing type dynamic loading shall not exceed the
shall not exceed the following: floig
DOB2 - Mw~r0.5 S., MAN DO
21 C2 < S121
whereMW= resultant moment due to weight effects (NB-
3623)(3) The stress due to weight and inertial loadingFA
due to reversing dynamic loads in combination with - < S2the Level D coincident pressure shall not exceed the ANfollowing:
PD DO DO whereB, + B2 - ME s 4.5 S,, AM = cross-sectional area of metal in the piping corn-
2t 21 ponent wallS, = SA,
where (5) Piping displacemnents shall satisfy Design Spec-ME= the amplitude of the resultant moment due to ification limitations.
the inertial loading from the earthquake, other (c) As an alternative to NB-3656(a) and (b), thereversing type dynamic events and weight. rules contained in Appendix F may be used in evaluatingEarthquake and other reversing dynamic loads these service loadings independently of all other Designshall be computed from a linear elastic response and Service Loadings.
154
9/75
LEVEL CONSIDERATION EQUATIONS LOALELIMTS
DESIGN PRIMARY SI (9) 1.5 S.
A PRIMARY PLUS SECONDARY (10) 3.0 .SI RANGE; IF NOTSATISFIED, CONTINUE ASFOLLOWS:
SIMPLIFIED ELASTIC- (12) 3.0 .PLASTIC DISCONTINUITYANALYSIS FOR RESULTANTMOMENT RANGE OF THERMALEXPANSION & THERMAL SAM
THERMAL RACHET NB 3653.7CONDITION
FOR THOSE LOAD SETS NOT (13) 3.0 .SATISFYING EQ (10)
FIND PEAK STRESS (11)INTENSITY RANGE
FIND ALTERNATING (14)STRESS RANGE S,
CHECK FOR CUMULATIVE FATIGUE LESS THAN 1 FOR PLANT LIFE
B LEVEL B COINCIDENT (9) 1. 8 S OR 1. 5 yPRESSURE P & MOMENTS M,
c LEVEL C COINCIDENT (9) 2.S. OR 1.8 S.PRESSURE P & MOMENTS ,
D LEVEL D COINCIDENT (9) OR 3. 0 S. OR 2. 0 SYPRESSURE P & MOMENTS NI APP. F
9/76CONSIDERATION OF CYCLICAL LOADINGS
AND STRESS RANGES
MODE NO.1 CC
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.'
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THERMALMODE NO. 2
c~ 2Ql
21
SECTION 9/8. ASME SECTION III CODE. DESIGN BY ANALYSIS OFREACTOR CORE INTERNALS
FIG. 9/77 SHOW THE CONTROL ROD ASSEMBLIES, WHILE FIG. 9/78 SHOWSTHE W LOWER CORE SUPPORT ASSEMBLY. FIG. 9/79 PROVIDES KEYFACTS ON THE REACTOR INTERNALS. IT IDENTIFIES SUBSECTION NG ASTHE CODE TO BE GENERALLY FOLLOWED SINCE 1973. THE USE OF AISCCODE IS ALSO PERMISSIBLE.
FIG. 9/80 SHOWS THAT SUBSECTION NG ACCOUNTS FOR COMBINED LOADSFROM MECHANICAL LOADS AND OTHER DESIGN LOADS SUCH AS SEISMIC ANDLOCA.
IN ADDITION TO SUBSECTION NG, NRC ALSO PROVIDES GUIDELINES (9/81)IN SRP SECTION 3.9.3 THROUGH 3.9.5 AND SECTION 4.2. REGULATORYGUIDES 1.124 AND 1.130 PROVIDE GUIDELINES FOR SUPPORT DESIGN.
FIG. 9/82 PRESENTS SOME KEY POINTS MENTIONED IN NG. ITSPECIFICALLY IDENTIFIED THE WELD OF GREATER OR LESS THAN 2t ASTHE BOUNDARY BETWEEN NB AND NG.
FIG. 9/83 PROVIDES ADDITIONAL DISCUSSION OF CORE SUPPORTS.
FIG. 9/84 SHOWS CLASSIFICATION OF STRESS INTENSITIES FOR SOME
TYPICAL CASES.
FIG. 9/85 IDENTIFIES THE IMPACT FORCES, EARTHQUAKE, AND VIBRATIONBEING LOADS WHICH MUST BE CONSIDERED.
FIGS. 9/86 AND 9/87 ARE THE HOPPER DIAGRAMS FOR LEVELS A AND B,AND LEVEL C CONDITIONS, RESPECTIVELY. AGAIN, FATIGUECALCULATIONS ARE TO BE MADE FOR LEVELS A AND B SECONDARY AND PEAKSTRESS INTENSITIES. FOR LEVEL C LOADS, NO EVALUATION ISNECESSARY FOR SECONDARY AND PEAK STRESS INTENSITIES.
FOR THREADED FASTENERS, THE ALLOWABLE VALUE OF STRESS INTENSITYIS GIVEN BY A THIRD HOPPER DIAGRAM (NG-3230) (FIG. 9/88). ONLYPEAK STRESS INTENSITIES NEED BE INCLUDED IN THE FATIGUEEVALUATION.
FINALLY, FIG. 9/89 SUMMARIZES THE REQUIREMENTS OF NG-3200, DESIGNBY ANALYSIS FOR THE CORE DESIGN.
CONTROL ROD ASSEMBLIES 9/77
Elevation and plan Cross-section views
of two Westinghouse full-length controlrod and guide tube assemblies, one fullywithdrawn and one inserted.
Control roddrive mechanism
Drive rodassembly Upper support
plate
Internals support
Full length l.ebrelcontrol rod
assembly inGudpltthe withdrawnGidplt
position
Guide tube assembly
Guide plate
assembly Upper core plate
assembly inserted
PWR CORE SUPPORTS
9/78
Core barrel flange
Core barrelNozzle
Upper core plateguide pins ____
Former
Neutron shield plate
______ - - Irradiationspecimen basket
Radial support key
Core support plate(flow holes not
Upper tie plate Instrumentation
Lower tie pt Energy absorber
assembly
Westinghouse lower core support assembly,
9/79
REACTOR INTERNALS
*Components are welded, bolted, screwed,or pinned
*Upper core support structure is removablefor refueling
*Reactor internals designed and analyzedto AS ME Code Section III 1, Division 1,Subsection NG as of 1973.
U.S. PWR design predated Subsection NGexcept for a handful of plants
*Using Subsection NG for internalstructures (other than core supports) is -amatter of interpretation. Also possible touse AISC Code for internal structures as acheaper alternative (AISC cannot handleLOCA)
REACTOR INTERNALS 9/80
*Subsection NG is roughly the same asSubsection NB with some philosophicaldifferences
a) There are no leakage concerns for NGb) Structural loadings from adjacent
structures must be defined in NGc) Usually there are no nozzle concerns in
NG
*Subsection NG has weld quality andfatigue factors for various weld types
*Subsection NG accounts for combinedloads from:
a) Pressure diff erentials due to coolant flowb) Weight of the structurec) Superimposed loads from other
components-md) Earthquake (or seismic) loads
e) Vibratory loadsf) Preloadsg) Thermal loads (steady state and
transients)-~h) Loss of coolant accident loads (LOCA)
*NG ties in with Section Xi IWG
9/81
REACTOR INTERNALS
U.S. NRIC requirements and guidelines
given in the following:
SRP 3.9.3 Core support structures
SRP 3.9.4 Control rod driven systems
SRP 3.9.5 Pressure vessel internals
SRP 4.2 Fuel system design
Regulatory Guide 1.124 Linearcomponents supports
Regulatory Guide 1.130 Plate/shellsupports
9/82
CORE SUPPORT STRUCTURES -ARTICLE NG
* Goal of Code evaluation is to preventplastic collapse, ductile rupture,progressive distortion, fatigue failure andbrittle fracture
• Core support Structures provide directsupport or restraint of the core [fuel andblanket assemblies] (NG-1 120)
*Non-core support structures can betreated using NG as an option (NG-1 120)
*Most severe loads are abnormal loadconditions usually
*Design ties in with hydraulic design
*Boundry between core supports aid
reactor pressure vessel (NG-1 131)
weld < 2t from vessel NB
weld > 2t from vessel NG
9/83
PWR CORE SUPPORTS
*A vertical secondary core support islocated under bottom support casting tolimit core drop (severe accident)
-.. Core supports and secondary coresupports do not transmit load directly tothe bottom of the pressure vessel
*Core supports are not welde d to bottom ofpressure vessel
NG-3000 - DESIGN Table NG-3217-1
9/84
TABLE NG-3217-1CLASSIFICATION OF STRESS INTENSITIES FOR SOME TYPICAL CASES
DiscontinuityCore Support Origin of Classifi-
Stnscture Location Stress Type of Stress cation Gross local
Cylindrical or Shell plate remote Pressure difference General membraneP, No ospherical sheA from discontinuities Gradient through plate P o N
thickness Q Yes No
Axial thermal Membrane Q Yes No___________________ gradient Bending Q Yes No
Junction with head Pressure Membrane Q Yes Noor flange difference Bending Q Yes No
Any sheld or head Any section across External load or General membrane averagedentire shell moment, or pres- across full section. P. No No
sure difference Stress component per-pendicular to cross section
External load or Bending across full section.moment Stress component perpen- P. No No
dicular to cross section.
Near nozzle or other External load or Membrane Q Yes Noopening moment, or pres- Bending Q Yes No
sure difference Peak (fillet or corner) F Yes yes
Any location Temp. difference be- Membrane Q Yes Notween shell and Bending Q Yes No-head
Dished head or Crown Pressure difference General membrane P- No Noconical Bending P. No No
Knuckle of junc- Pressure difference Membrane Q(1) Yes Notion to shell Bending Q Yes No
Flat head Center region Pressure difference General membrane P., No No_______ _______ ____ __ _______ _______ Bending P& No No
Junction to shell Pressure difference Membrane Q Yes NoBending Q Yes No
Perforated head Typical ligament in Pressure difference General membrane (avg. P. No Noor shel a uniform pattern or external load through cross section)
Bending (avg. through width of P6 No Noligament, but gradient
C ~~~~~~~~~~~~~~~~~~~through plate)Peak F No Yes
Isolated or atypical Pressure difference Membrane Q Yes Noligament Bending F Yes Yes
Peak F Yes Yes
(Table NG-321 7-1 continues on nert page;
49
9/85
CORE SUPPORT STRUCTURES - NG-3100GENERAL DESIGN
*Design mechanical loads from DesignSpecification. Also must consider(NG-31 12):
a) impact forcesb) earthquakec) vibration
*Stress intensity values from Section II,Part D, Subpart 1 (NG-3112)
*Service loadings for Level A, B,9 C, & Dfrom design specification are used onstructure (NG-31 13)
*Corrosion, erosion, abrasion must beconsidered (NG-3120)
*Irradiation effects should be considered(NG-31 20)
HOPPER niar..iRAM NG
NG-3000 - DESIGN Fig. NG-3221-1
9/86
Z R
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51
HOPPER DIAGRAM NG
NG-3000 - DESIGN Fig. NG-3224-19/87
Primary Stresses Secondary Stresses Peak
Stress Membrane, P. Bending, P. Membrane and Stresses.Category [Notes (1). (2), and (3)1 (Notes (1), (2), and (3) Bending. 0_
Level C
(Note (4)1 Elastic Elastic1 ~~m ~analysis .25 analysis
I Note (5)l (Note ()1
Limanalysis Evaluation not Evaluationanalysis ~~~~analysis required not
(Note (6)) [Note (611 required
or o
Plastic ~~~~~~PlasticPnlasis.5, analysisNaltse I7]1Notes (7)
(Note (7)) ~~~and (8)1
or O5~
£ O.S~e Test o(Note (9)) O.6L Test
or 1Note (g)]
S tress-ratio Stress-ratioanalysis SE analysis
INote (10)1 1Note (10)l
NOTES:(11 The symbols P P, 0, and F do not represent single quantities, but rather sets of six quantities representing the six
stress components a,,. a-,. -,. T6., T.. and ,..
(2) For configurations where compressive stresses occur, the stress limits shall be revised to take into account criticalbuckling stresses (NG-3224.2).
(3) When loads are transiently applied, consideration should be given to the use of dynamic load amplification and possiblechange in modulus of elasticity.
(4) Where deformation is of concern in a structure, the deformation shall be limited to two-thirds the value given in DesignSpecifications fr level C Service limits.
(5) The triaxial stresses represent the algebraic sum of the three primary principal stresses ( + o'2 + a3 ) for thecombination of stress components. Where uniform tension loading is present. triaxial stresses should be limited to6S..
(6) L4 lower bound limit load with yield point equal to 1.5 S (where S is the value of allowable stress intensity attemperature as contained in Tables 2A and 2. Section II. Part 0, Subpart 1. The lower bound limit load is here definedas tha t produced from the analysis of an ideally plastic (nonstrain-hardening) material wvhere deformations increasewith no further increase in applied load. The lower bound load is one in which the material everywhere satisfiesequilibrium and nowhere exceeds the defined material yield strength using either a shear theory or a strain energy ofdistortion theory to relate multiaxial yielding to the uniaxial case.
(7) Elastic-plastic evaluated nominal primary stress. Strain hardening of the material may be used for the actual monotonicstress-strain curve at the temperature of loading or any approximation to the actual stress-strain curve which every-where has a lower stress for the same strain as the actual monotonic curve may be used. Either the shear or strainenergy of distortion flow rule shall be used to account for multiaxial effects.
(8) S. = ultimate strength at temperature. Multiaxiality effect on the ultimate strength shall be considered.(9) L. is defined in NG.3224-1(e).
(1 0) Stress ratio is a method of plastic analysis which uses the stress ratio combinations [combination of stresses thatconsider the ratio of the actual stress to the allowable plastic or elastic stress. NG3-3224-1(d)I to compute the maximumload strain-hardening material can' carry.
FIG. NG-3224-1 STRESS CATEGORIES AND LIMITS OF STRESS INTENSITIES FOR SERVICE LEVEL C
57
HOPPER DIAGRAM NGFlig. NG-3232-1 1992 SECTION UI, DIVISION NG
9/88
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(b -0 E c z E E
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4P ca c > COc C,4 CA C14 E Ek7 E:5 r-e ccM, 1,4 C? clIrDF- JC2DE on cr c� z z 0c 5 eEC� -.� = z z
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toJ-- z�: Wm zc c
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62
9/89
CORE SUPPORT STRUCTURES - NG-3200DESIGN BY ANALYSIS
*Fatigue analysis is required if temperaturedifference between two adjacent pointsexceeds (SaI2Eo) or if full range ofmechanical loads exceeds Sa (NG-3216)
*Procedure for computing alternatingstress intensity factor (NG-321 6) is thesame as NB
Extreme ranges of stress differences (forcomplete cycle) are determined. Thealternating stress is half the value of thelargest stress difference (range) (absolutevalue).
*Stress categories for core barrel sides andend plates are given in Table NG-3217-1
*Aillowable value of stress intensity isgiven by Hopper Diagram for Levels A andB conditions (NG-3222 and NG-3223)
*Limit analysis acid testing are alternativesto stress intensity limits
C, ~
