An Effective Method for the Linearization of -
Nodal Stress Components to Apply ASME Criteria
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,
2002e 2% 2 7 9
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SUMMARY
The code of ASME Sec. III prescribes the general rules upon the design of a NSSS (nuclear
steam supply system). The code provides further flexibility to the design of the nuclear
structures by introducing a design by analysis concept. But it still preserves the consewatisms in
design works by imposing strict failure mechanism and controlling material properties in use. A
designer should prove the integrity of a structure under consideration by comparing the stress
intensity, which was driven from the linearization of stress at concerning section, with the
prescribed one. The recent development in computing system has enabled the commercial finite
element programs to be 8 prevailing way to structural analysis field. But only few programs
provide the procedure for stress linearization through the post-processing stage. Therefore, the
simplified method which uses nodal stresses over the concerning section is introduced instead.
But the issues related to the accuracy of nodal stress and the stability of linearized results
according to the number of nodes on a section are raised so far. In this report, an effective
method utilizing the sub-structuring technique is proposed to resolve the inherent problems
emerged from the linearization process using the nodal stress. Since the sub-structuring
technique provides a detail analysis on the concerning section, it affords to increase the
accuracy in stresses and number of node on the section also.
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aQl-s ............................................................... 2 SUhBL4RY ................................................................ 3 4- 21 .................................................................. 4
2 . *q 3 4%l* ...................................................... 9 2.1 AShlEdl 4@ -!SI4 4gq %$ ................................... 9 2.2 %!Is1 $-q& 01-g-a *q 4%* .................................. 11
3 . ?E eqg-& 01%-@ %q 44 ..................................... 14
3.2 735 Egg-& Ol$@ +341 I 4 .................................. 15 4 w3 i3 446 Ol+@ $.q4 gq* 21
1 . A j S ................................................................ 6
3.1 I-DEASE 018@ 735 ..................................... 14
. .............................. 4.1 JZciq 7 ^ d ........................................... 21 4.2 -%-q 44 @q .................................................. 23 4.3 %q4 *%!* ................................................... 26
5 . aE ............................................................... 27 6 . %X%?! ........................................................... 28
% A ANSYSq -%q e%!@ Z!i$ ..................................... 29 -8-1 B 3% -8-qS 01%@ dg@ 84 ............................... 33
<E *3)>
3f 1 SCL& ?iiqS 8 3 T!-?l H l i Z (I-DEAS/ANSYS) .............................. 24 J€ 2 SCL& 7AdsE 834 %-q H1I.Z (I-DEAS/ANSYS) ........................... 24 3E 3 ANSYSq 3% %-q$ 01-8-e +!9@ Z!*q HlX(I-DEAS/ANSYS) ... 24
<=lg +3\>
2 3 1ASME iT8q 4% -8-q4 E%(ag@) .............................................. 7 2 3 2 *%*a -Wl A d s * Srl3 %4 ........................................................ 10 2%? 3 ~ ~ ~ ~ ~ + 2 01-m Wl 4 s ....................................... : ..................... 11 3% 4 "Wl 71s 7R'd .................................................................... 15 Z% 5 I-DEASI Ol%@ 73 EQPl4 34% J;. ............................................ 17 3% 6 CAD 7H4(5?3 a%.) .......................................................................... 17 2% 7 CAD 7fl4(%% %%lo) a71 XF!l ............................................. 18 3% 8 +41*4 $Ql& 7)?l CAD 7"l ........................................... 18 3% 9 wi EYJS~ WE ~ 3 7 - 7 1 4 3 4 e x 5zz ........ 19
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v)
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SBtgq QtSf4 sa84 IIl3Zf4 (Total Stress) (Membrane Stress) (Bending Stress) (Peak Stress)
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1 a, =- t J1'2aidx 112
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,
M * Y a, =- I
( I = $ ) (3)
I Total stress line Node 2
Node 1
I i I I X I I
+ t
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-\
. . . . . . .
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A , = h - ( T ) , Y2 + Y 2 A 2 = h . ( y ) , , , & = h . ( Y n + Yn+l ) ( 6 )
b-a where, h =- 2 2 i52 n -+-+Cy, Y1 Ym+l
(8)
= :( hi - y i + g hi-, . y, ) where, hi = Length of i th Element i=2
* JIJ
n
s W
n
4
4
W
n
2
W
n
n
L
4 c
0
3J
- ti-
ti $J - I
&-
+ =mn
I
El I 5- &-
k' u
ti- *TCJ
b I
;t b- -.- c
tc1
b'
22
--
- n-
b" v
b'
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,
Create Part 1 I I
COPY Original Part
Initial Mesh I Sub-Region
Model Creation I
F.E. Solution
I r i 2 Y - J Sub-Region
Solution
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I L
I
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I A x
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~
37
0.005% 0.017%
0.018%
0.000% 0.018% 0 .m 0.005% 0.017% 0 .ooo9b
Remark
i
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1.0XlO'
8.0~10'
6.0~10' 0 Q
e 4.0~10' t: 2 3j 2.0~10'
0.0
-2.0~10'
4.0~10'
6.0xlO' -
4.0x106 - h Q
v) v)
2.0xro6 - 2 65 0.0 -
-2.ox10' - -4.OxlO' -
- /-- /
--c- sx ---*----SY
- -A- sz
- --- .@zT---."m--. -m - m-. -.
-
// - * A -
-. -..___ 0 ------.--__
-. -. -. --e-.-- ----- ..-. ---
--. --. ''-0 ..-
%* -. I-..
I . I . I , t , I 1 . 1
4 t , l , ' , t , 1 , 1 , 1
1 2 3 4 5 6 7
Node Location (n36-1-1841 -n846+1845-n848-n847-n37)
2% 16 sCL& 334 -%q ?$E (Sxy, Syz, Szx)
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1 . G Hollinger & J. Hechmer, *‘ Xhree Dimensional Srress Criteria-Summary PVRC Project’’,
Journal of Pressure Vessel Technology, V01.122,2000
2. European Commission Joint Research Center,
EPERC, 1999
T.P. Pastor & J. Hechmer, “ASME Task Group Report in the Priniary Stress”, Journal of
Pressure Vessel Technology, Vol. 119, 1997
J.L. Hechmer & GL. Hollinger, “30 Stress Criteria Guidelines for Application ”, WRC
Bulletin 429, 1998.
M.L.James, GM. Smith & J.C. Wolford, “Applied Numerical Metho& for Digita!
Computation”, 1993
ANSYS, Inc., “ANSYS User h Manual”, 200 1
SDRC, “I-DEAS User S Manual”, 2001
“The Design by Analysis Manual”,
3.
4.
5.
6.
7.
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LOADSTEP 1 SUBSTEP= 1
TILIE= 1.oooO LOADCASE= 0
THE F U U K G X.Y.Z STRESSES ARE Ih: GLOBAL CO0RDIh;ZTEs.
** MELIBRAKE **
s)( SY sz SXY SYZ SU
0.7915Ei-07 -0.2447EM7 0.993GEi-08 0.3431EtO7 0.1768Ei-05 -0.110GEM7
SI s2 s3 SIhT W\'
0.9938EtO8 0.893GEM7 -0.3482Ei-07 0.1029E4.09 0.9725EM8
** BEh'DIKG ** I=Ih'SIDE C=CEhTER O=OUTSIDE
SX SY SZ SXY SYZ SSZ
I -0.WGEi-07 0.6859EM7 -0.2738Ei-08 0.3308E+OG -0.1360E+07 -0.2361EM7
c O.Oo0 O.OO0 O.OO0 0.0o0 0.W 0.W
0 0.8066EM7 -0.6859EM7 0.2738Ei-08 -0.3308EtOG 0.1360EtO7 0.23GlEM7
SI s2 s3 SIhT Wl'
I 0.6925Ei-07 -0.7798Ei-07 -0.2772Ei-08 0.3464E+08 0.3011EiQ8
c o.Oo0 0.W O.OO0 0.W 0.000
0 0.2772EtO8 0.7798EM7 -0.6925EM7 0.34G4E08 0.3011Ei-08
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** NElIBRAK'E PLUS BEhDIKG ** I=II\'SIDE CICEhTER O=OCITSIDE
sx ss sz SXY SYZ sxz I -0.1516E+06 .0.441lE+O7 0.7198E+08 0.3762Ei-07 -0.1342Ei-07 -0.3467Ei-07
C 0.7915Ei-07 -0.2447Ei-07 0.9936EtO8 0.343lEtO7 0.1768Ei-05 -0.1106Ei-07
0 0.1598EtO8 -0.9306Ei-07 0.1267EtO9 0.3101Ei-07 0.1378Ei-07 0.1255Ei-07
s1 52 s3 SIhT WI' I 0.7218Ei-08 0.6405Ei-07 -0.2346Ei-07 0.7453Ei-08 0.7056Ei-08
C 0.9938Ei-08 0.8936Ei-07 -0.3482Ei-07 0.1029E+09 0.9725Ei-08
0 0.1268E-W 0.1634Ei-08 -0.9691Ei-07 0.1365EtO9 0.1255EtO9
** PEAK ** I=IKSIDE C=CEhTER WXrrsIDE
sx SY sz SXY SYZ SXZ
I -0.3502E06 -0.1915Ei-07 -0.2070EtO6 -0.3044EM6 -0.1795Ei-07 -0.3567E+QG
C 0.3467E06 0.1918Ei-07 0.19518+06 0.3045EtO6 0.1794Ei-07 0.3556E06
0 -0.3432EtO6 -0.1921Ei-07 -0.1832E+06 -0.304GBtOG -0.1793EtO7 -0.354GE+06
Sl s2 s3 SI~T~) SEQP
I 0.9421E06 -0.2933EtO6 -0.3 12 1EtO7 0.4063EtO7 0.3607Ei-07
C 0.3 119Ei-07 0.2899E06 -0.949 1Em 0.4068Et07 0.361 1Et07
0 0.9562EtO6 -0.2866Em -0.31 17E+07 0.4073EtO7 0.3615EM7
** TOTAL ** I=II\'SIDE C=CEKXR O=OUTSIDE
SX SS sz SXY SYZ SXZ
I -0.sO18EtO6 0.2497Ei-07 0.7177Ei-08 0.3458Ei-07 -0.3137Ei-07 -0.3824Ei-07
C 0.8261EW7 -0.5298EtO6 0.9956E+08 0.3736Ei-07 0.1812Ei-07 -0.7505E+O6
0 0.1564Ei-08 -0.1123Ei-08 0.1266E-W 0.279GEi-07 -0.4 158EtO6 0.9002E+06
s1 s2 s3 SIhT SEQY mlP I 0.7213EW 0.4437EtO7 -0.2802EN7 0.7494EtO8 0.7159Et08 O.OO0
C 0.996OEtO8 0.9634Ei-07 -0.194 lEi-07 0,1015E-W 0.9627Ek8
0 0.1266EtO9 0.1592Ei-08 -0.1152EM8 0.1381E~N 0.1266EtO9 0. OOO
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I
PRIAT LIAXARIZED SIRE!S THROUGH A SECTIoh: D E F I A ! BY PATH= SCL DSYS= 0
***** Posrl LIh’EARIZED STRESS LISTIKG +****
IKSIDEE;ODE= 36 ocrrSIDEKoDE= 37
L o m m 1 suBsIEP= I
T I E = 1.oooO LOAD CASE= 0
THE FOLLOWING X.Y.2 STRESSES ARE IK GLOBAL COORDIRATES.
** hEME3RAKE **
sx SI’ SZ SXI SYZ SXZ
0.74 13EtO7 -0.5204EtO7 0.9250E4-08 0.1349E+07 0.6655E+06 0.1562EtO7
s1 s2 s3 SIN SEQV
0.925484-08 0.7525EtO7 -0.5349Ei-07 0.9789EtO8 0.92 13EtO8
** BEADIKG ** I=IKSIDE C=CEI\TER O=OUTSIDE
SX SY SZ SXY SYZ SXZ
I -0.1910E+07 0.233 1EW8 -0.2280E+08 0.2246EiQ7 0.3118E+o(i -0.2187EtOG
c o.OO0 O.OO0 O.OO0 O.OO0 O.OO0 O.OO0
0 0.1910EtO7 -0 .23 lE+O8 0.2280EtO8 -0.2246EM7 -0.3 l18EtO6 0.2 187E+O6
s1 s2 s3 SIAT SEQV
I 0.255oE+o8 -0.2O91E.CO7 -0.2280E+O8 0.483OEi.08 0.4 197Et08
c o.OO0 0 .Ooo 0 .OO0 O.OO0 O.OO0
0 0.2280EtO8 0.2O91EtO7 -0.255OE+O8 0.48Wi-O8 0.4197Ei-08
*+ IIE!WE PLUS BEh’DIh’C ** I=IISIDE C=CEKl’ER MTSIDE
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SX SY sz SXY SYZ SXZ
I 0.5503Ei-07 0.2011EW8 0.6971Ei-08 0.3594EM7 0.9773EtO6 0.1343Ei-07
C 0.7413EtO7 -0.520hEM7 0.925OEi-08 0.1349Ei-07 0.6655E+o6 0.1562EtO7
0 0.9324Ei-07 -0.305lEi-08 0.1153Ei-09 -0.8966Em 0.3537EiQ6 0.1780Ei-07
s1 s2 s3 SIhT SEQV
I 0.6976Ei-08 0.2O91Ei-08 0.4648Ei-07 0.651lEM8 0.5869Ei-08
C 0.92548408 0.7525EM7 -0.5349Ei-07 0.9789EW 0.92 13Ei-08
0 0.1153Ei-09 0.9314EM7 -0.3054Ei-08 0.1459EW 0.1306E+09
** PEAK ** I=IKSIDE c=cmm WWTSIDE
sx SY si! SXY SYZ SXZ
I -0.2859Ei-07 -0.5197Ei-07 -0.2343Ei-07 -0.2 14 1EM7 0.6453Ei-07 0.2236EM7
C 0,167 1Ei-07 0.2 128EM7 0.2259EW7 0.5569Em -0.3060Ei-07 -0.9876Ei-06
0 -0.3824Ei-07 -0.3314EM7 -0.6692Et07 -0.8683EM5 0.5786Ei-07 0.1714Ei-07
s1 s2 s3 SIhT a\' I 0,287lEtO7 -0.1796Ei-07 -0.1147Ei-08 0.1435Ei-08 0.l267EM8
C 0.5563Ei-07 0.1397EM7 -0.9032EtO6 0. 6466EM7 0.5677Ei-07
0 0.12 13EM7 -0.3739EM7 -0.1130Ei-08 0.1252Em 0.1092EM8
** TOTAL ** I=Ih'SIDE C=CEh'TER O=OUTSIDE
SX SY SZ SKY SYZ SXZ
I 0,2644EM7 0.1491E08 0.6736EM8 0.1454EM7 Q .7430Ei-07 0.3579Ei-07
C 0.9084Ei-07 -0.3076Ei-07 0.9476Ei-08 0.1906Et07 -0.2394Ei-07 0,5739E+06
0 0.54998+07 -0.3383Ei-08 0.1086E+09 -0.9835E4-06 0.6140Ei-07 0.3494Et07
s1 s2 s3 SIAT mi' mlr I 0.6861EM8 0.1395E4-08 0.2354Ei-07 0.6625EM8 0.6128Ei-08 O.OO0
C 0.9482E+O8 0.9375Ei-07 -0.3429Ei-07 0.9825EM8 0.9252Ei-08
0 0.1090EtO9 0.5417Ei-07 -0.3412EtO8 0.1431EW 0.128OEW9 O.OO0
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n := 7 number of nodes on concerned SCL
a :=
0.25) integration factors -1 -1 1 1
-0.25 7 7 0 6 7
5.98
7.88
6.92
10.3
8.01
pa:=(0.5 1 1 1 1 1 0 . 5 )
Case .- Sxx ( x E6)
a:=
1.36
0.647
-0.683 membrane := - paba bending := -1 64p.a)
n - 1 n - 1 -1.26
-2.28
pa-a 6 4 P - 4 membrane := - bending := -1 - n - 1 n - 1
membrane = ( 7.1933 ) bending = ( -1.795 )
Case:Syy ( x E7)
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Case : Szz ( x E7)
a :=
7.64 8.46
9.36 10.5 10.7
Case: Sxy
' 1.45 2.10 3.85 1.05
-0.04 16 0.506
\ -0.984
a :=
paaa membrane := -
n - 1
membrane = ( 9.2467 )
( x E61
pa-a membrane := -
n - 1
Case : Syz ( x E6)
a :=
' 7.43 ' 3.42
-2.68
-3.1 1 -2.1 1 2.26 6.14 ,
membrane = ( 1.2829 )
pa.a membrane := -
n - 1
membrane = ( 0.7608 )
64p.a) bending := -1 - n - 1
bending = ( -2.4 )
6 - ( P 4 bending := - 1 n - 1
bending = ( 1.7884 )
64P.d bending := -1 +
n - 1
bending = ( 0.6142 )
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Case .- Szx ( x E61
a :=
I 0.196 I -1.02 0.952
pa-a 64p.a) membrane := - bending := -1 - n - 1 n - 1
I t::: J membrane = ( 1.4272 ) bending = ( -0.1968 )
I
For membrane comDonent
ma :=
7.193 - lo6 1.2829- 1 O6 1.4272.1 O6
1.2829. lo6 -0.5268. lo7
1.4272. lo6 7.61. lo5 9.2467. lo7
7.61 - lo5
v := eigenvalgma)
max := v3 - v1
max = 9.79 x 10 7
For bendinp comDonent
ba :=
-0.1795.1 O7 1.7884. lo6 1.9683-10’
1.7884*106 2.7487. lo7 6.14. lo5 1.9683.10’ 6.14 lo5 -2.4 10 7
v := eigenvalgba)
rnax := v2 - v3
-5.403 x lo6
( 9.25 107
(-1.903 x lo6
(-2.401 x lo7
7 max= 5.161 x 10
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For membrane olus bending
a. At outside
mba := ma + ba
I 5.398 x lo6 3.071 x lo6 1.624 x lo6 3.071 x lo6 2.222 x lo7 1.375 x lo6 1.624 x lo6 1.375 x lo6 6.847 x lo7
v := eigenvalqmba)
max := v3 - vl
max = 6.373 x 10 7
b. At inside
mba := ma - ba
4.826~ lo6
[ 6.855~ 1:l v = 2.27~ 10
1 8.988 x lo6 -5.055 x lo5 1.23 x lo6 -5.055 x lo5 -3.276 x lo7 1.47 x lo5
1.23 x lo6 1.47 x lo5 1.165 x lo8
-3.276~ lo7 v := eigenvalgmba)
max := v3 -.VI
max= 1.492 x 10 8
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I
BIBLIOGRAPHIC INFORMATION SHEET
Performing Org.
Report No.
Sponsoring Org.
Report No. Standard Report No. INIS Subject Code
I I KAERLflX-2057/2002 I
Publication Place Taejeon Publisher KAERI Publication Year
Page 36 Ill. & Tab. Yes Size
An Effective Method for the Linearization of I Title /Subtitle
2002
A4
Nodal Stress Components to Apply ASME Criteria
Project Manager and
Department Tae-Wan Kim (Advanced Reactor System Development)
Classified
Researcher and ~~ -7
Open ( o ) restricted( ) Report Type Technical Report - Class Document
~~ ~
Suhn Choi. Keun-Bae Park, Moon-Hee Chang
Subject Keywords Linearization of Stress, Sub-structuring Method, I-DEAS, ANSYS
Sponsoring org. I I Contract~o. I Abstract 1
The code of ASME Sec. III prescribes the general rules upon the design of a NSSS (nuclea
steam supply system). The code provides further flexibility to the design of the nuclear structures b]
introducing a design by analysis concept. But it still preserves the conservatisms in design works b
imposing strict failure mechanism and controlling material properties in use. A designer should prove thc
integrity of a structure under consideration by comparing the stress intensity, which was driven from thl
linearization of stress at concerning section, with the prescribed one. The recent development ii
computing system has enabled the commercial finite element programs to be a prevailing way tl
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