ML092460596
| ML092460596 | |
| Person / Time | |
|---|---|
| Site: | Nine Mile Point  |
| Issue date: | 08/28/2009 |
| From: | Continuum Dynamics |
| To: | Constellation Energy Group, Nine Mile Point, Office of Nuclear Reactor Regulation |
| References | |
| 7708631, TAC ME1476 CDI Report 09-26NP, Rev 0 | |
| Download: ML092460596 (69) | |
Text
Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information This Document Information Combinations, and Allowable 5.2 Load Combinations. Allowable Stress Intensities .
The stress ratios computed for CLTP at nominal frequency and with frequency shifting are The listed in listed in Table Table 9. 9. The The stress stress ratios ratios are are grouped according according to type (SR-P for maximum membrane and membrane+bending and membrane+bending stress, stress, SR-a for alternating stress) and location (away from welds or on a weld). The tabulated nodes are also depicted in Figure 14 14 (no frequency shift) and Figure 15 15 (all frequency (all frequency shifts included). The plots corresponding to maximum stress intensities depict all nodes with stress ratios less than 4 or 5 as indicated, and the plots of alternating stress ratios SR-a_<5.
display all nodes with SR-a:::;;5.
For CLTP operation at nominal frequency the mInImUm minimum stress ratio is identified as a maximum stress, SR-P=1.34, SR-P=1.34, and is recorded on the bottom of the vertical plate joining the innermost vane banks. However, this location is only weakly responsive to acoustic loads as can can be seen from the high alternating stress ratio at this location (SR-a>16.5 (SR-a>16.5 at all frequency shifts).
This This is is true true for all three nodes having the lowest values of SR-P, all having SR-a>5.1 SR-a>5.1 at all frequency shifts. The minimum alternating stress ratio at zero frequency shift, SR-a=3.00, occurs on the weld connecting the inner hood and hood support.
The effects of frequency shifts can be conservatively conservatively accounted for by identifying the minimum stress ratio at every node, where the minimum is taken over all the frequency shifts considered considered (including the nominal or 0% shift case). The resulting stress ratios are then processed as before to identify the smallest stress ratios anywhere on the structure, categorized categorized by stress type (maximum or alternating) alternating) and location (on or away from a weld). The results are summarized summarized in Table 9b and show that the lowest stress ratio, SR-P=1.34, occurs at the same location location as in the nominal case and retains virtually the same value. Moreover, the next three lowest SR-P locations are the same as in Table 9a. The lowest alternating alternating stress ratio, SR-a=2.89 SR-a=2.89 occurs at the common intersection intersection point of the bottom of the inner hood, hood support and base base plate (see Figure 15i). 15f). Hood supports are also involved in locations 3-5, 10-11 and 15. The next lowest SR-a locationlocation involves the lifting rod support brace (Figure 15g) involving locations locations 2 and 7. The remaining remaining low alternating alternating stress ratio locations locations occur on: (i)(i) closure plates (locations 9 and 16); (ii) (ii) tie bar ends or their immediate vicinity (locations 12 and 14); or (iii) the hoods.
The estimated estimated alternating alternating stress stress ratio at EPU operationoperation is obtained by scaling scaling the corresponding corresponding value at CL CLTPTP by the square of the ratio of the steam steam flow velocities velocities at EPU and CLTP CLTP conditions. Since this ratio, (UEPulUcLTPi=1.1782=1.388, (UEPUCLTp)2=l.178 2=1.388, the limiting alternating stress stress ratio at any frequency shift for EPU is estimated estimated as SR-a=2.89/1.388=2.08.
SR-a=2.89/l.388=2.08. This value value qualifies qualifies the Unit 2 dryer at EPU conditions conditions with considerable considerable margin. The limiting stress ratio, SR-P, is dominated dominated by the static load and has a weaker dependence dependence on power. When When this node is reanalyzed reanalyzed with the MSL signals increased increased by 1.388, 1.388, the limiting SR-P reduces reduces to 1.32 at EPU.
In summary, the lowest alternatingalternating stress ratio occurs occurs at the base of the inner inner hood support where where it is welded welded to the middle middle base base plate and vertical vertical vane vane bank support. Its value, value, SR-a=2.89 SR-a=2.89 at at the the -5%-5% frequency shift shift indicates indicates that stresses stresses are well below below allowable allowable levels. The lowestlowest stress stress ratio associated associated with a maximum stress is SR-P=1.34 stress SR-P=1.34 at CLTP. This value is dominated value dominated by by the static component the static component and and is only weakly weakly altered altered byby acoustic loads (it reduces reduces to 1.32 at EPU).
Since acoustic Since acoustic loads loads scale scale roughly roughly with with the square square of the steam steam flow, the limiting alternating alternating 63
This Document Does Not Contain Continuum Continuum Dynamics, Inc. Proprietary Proprietary Information Information stress ratio at EPU reduces to 2.08, which given that the applied applied loads already .accourit accourit for all end-to-end biases and uncertainties, Uncertainties, still contains ample contains ample margin for sustained EPU operation..
operation
.~' "
~( .
- 1
.. "' .... ../ . *1
-'/ "
. ,i' .*.
64 64
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9a. Locations with minimum stress ratios for CL CLTP TP conditions with no frequency shift. Stress ratios are grouped according to to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates minimum stress ratio of any type on the structure. Locations are depicted in Figure 14.
Stress Stress Weld Location Location (in.) node(a) node(a) Intensity (psi)
Stress Intensity Stress Ratio Ratio x y z Pm Pm+Pb Salt Salt SR-P SR-a SR-P SR-P No No 1. Inner
- 1. Inner Side Side Plate Plate 3.1 119 0.5 37229 7475 8836 460 2.26 26.86
" 2. Thin Vane Bank Plate -15.6 -118.4 0.6 2558
" 2. Thin Vane Bank Plate -15.6 -118.4 0.6 2558 4759 5171 <250 3.55 >27
>27 Support/Seismic Block
- 3. Support/Seismic 10.2 123.8 -9.5 113286 113286 4354 4354 1374 3.88 9.00 SR-a SR-a No No Middle Middle Hood Hood -68.9 69.6 69.6 41.6 31054 31054 1717 2759 2728 9.19 4.53
- ,SR-;P. Yes' 1; Side SR-P. 'Yes' Side Plate Plate- ExtllnrierBase ExtInnerBase PlatePlate, .,(." : ," 16:3.*I9
- '16
- 3, , :'119 . ' .'~ ,().:0 94.143" 6913, ,~'98()9.
94143' '6913, '09809', .~38',
438 'i;34~:'
1.34" IS:§7; 15.67 it 2. Upper Support Ring/Support/Seismic Block -6.9 -122.3
-122.3 -9.5-9.5 113554 6238 6238 1.49
" " 2. Upper Support Ring/Support/Seismic Block -6.9 113554 6238 6238 911 1.49 7.54 If II .. 3. Tie Tie Bar 49.3 108.1 88 141275141275 5962 1.56
" 3. Bar 49.3 108.1 88 5962 807 1.56 8.51
" " 4. Hood
- 4. Hood Support/Middle Support/Middle Base Plate/Inner Plate/Inner 39.9 -59.5
-59.5 101435 5352 0 101435 5488 1638 1.74 4.19 Bar/Inner Hood Backing Bar/Inner
" " 5. Inner Side Plate/Inner Base Plate
- 5. -2.3 -119 0 99200 4419 7921 511 1.76 1.76 13.44 13.44
" " 6. Closure
- 6. Plate/Inner Backing Closure Plate/Inner Backing Bar Bar Out/Inner Out/Inner 39.9 108.6 39.9 108.6 0.5 93062 5232 5253 851 1.78 8.07 Backing Bar/Inner HoodHood
" " -7. Hood
-7; Hood Support/Outer Support/Outer Base Base Plate/Middle Plate/Middle -71.3 0 0 95428 - 4800 95428* 4876 1817 1.94 3.78 Backing Bar
".. .." 8. Side Plate/Top Plate 17.6 17.6 119 88 91215 898 7174 1337 1.94 5.14
" " "" 9. Outer Cover 9.0uter Cover Plate/Outer Plate/Outer Hood.
Hood 102.8 102.8 -58.1
-58.1 00 94498 1020 .7053
- 7053 763 1.98 9.01
" ." 10. Hood
- 10. Support/Middle Base Hood Support/Middle Base P!ate/lnner Plate/Inner -39.9 0 0 85723 4684 4849 1842 1.98 1.98 3.73 Hood( 6 )
Backing Bar/Inner Hood(6) -
" " 11. Thin
- 11. Thin Vane Vane Bank Plate/Hood Support/Inner Bank Plate/Hood Support/Inner 24.1 -59.5 0 85191 4385 4439 772 2.12 8.90 8:90 Base Plate.
Plate Notes. ,.
(a)
(a) Node numbers are retained for further reference. reference.
(1-9) Appropriate (1-9) Appropriate stress reduction factor for the welds stress reduction welds and modifications modifications listed in Table Table 7 have have been applied. The number refers to the Tiienumber particular location and corresponding corresponding stress s~ess reduction re~uction factor in in Table 7.
65 65
This Document Does Not Contain Contain Continuum Dynamics, Inc. Proprietary Information Information Table 9a (cont.). Locations with minimum stress ratios for CLTP conditions with no frequency frequency shift. Stress ratios are grouped grouped according according to stress type (maximum - SR-P; or alternating alternating - SR-a) and location (away (away from a weld or at a weld). Bold text indicates minimum alternating alternating stress ratio on the structure. Locations are depicted in Figure 14. 14.
Stress Weld . Location ,. . . "Location Location (in.
(in.) node(a) node(a) Stress Intensi~
Intensity (psi) Stress Ratio Ratio Ratio "X y z Pm *Pm+Pb
-Pm+Pb Salt Salt SR-P SR-a SR-a Yes 1. Hood Support/Inner Support/Inner Hood 36.2 0 50.8 99529 975 2316 2290 6.02 3.00 "V1 2. Hood Support/Inner Hood Hood 39.1 39.1 00 23 99515 842 2064 1977 1977 6.75 3.47
" 2. Hood Support/Inner
" if 3. Hood Support/Inner Hood 34.3 00 62.7 62.7 99535 826 2319 1970 6.01 3.49
" 3. Hood Support/Inner Hood 34.3
" ".. 4. Closure Plate/Middle
- 4. Closure Plate/Middle Hood Hood -68.7
-68.7 85.2 85.2 42.9 91590 91590 69-3 693 1963 1963 1936 7.10 3.55
. 5. Hood Support/Middle Hood -68.7 54.3 "42.9 99140 554 1968 1902 7.09 3.61, 1902 .7.09
" " 5. Hood Support/Middle Hood -68.7 54.3 "42.9 99140 554 1968 3.61.
" " . *6.
- 6. Side Plate/Brace(5) -79.7 85.2 75.8 103160 103160 1529 2892 1897 1897 4.82 3.62
".. " 7~ Hood Support/inner
- 7. Support/Inner Hood(7).7 Hood( ). -. 38 38 00 36.9 36.9 99522 99522 741 741 1886 1886 1860 1860 7.39 3.69 7.39 3.69
" " Support/Middle Base Plate/Inner
- 8. Hood Support/Middle Plate/Inner -39.9 0 0, O. 85723- . 4684 4849 1842
- 1847 1.98 1.98 . . 3.73
. Ba~king
.-..... 6 -_-_.
__ Backing Bar/Inner Hood(6))
Bar/Inner Hood(
" " 9. Side Plate/Brace 79.7 85.2 31.2 89646 89646 1447-1447 2182 1820 6.39 3.77 Notes.
(a) Node numbers are retained retained for further reference. - , . .
(1-9)
(1-9) Appropriate stress reduction reduction factor for the welds and modifications modifications listed in Table 7 have been been applied. The-number The number refets*tothe refers-tofthe particular particular location and correspo~ding corresponding stress reduction factor in Table 7.
66
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Information Table Table 9b. Locations with with minimum minimum stress ratios for CLTP conditions conditions with frequency frequency shifts. Stress ratios at every node are recorded as the lowest stress ratio identified identified during the frequency shifts. Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates indicates minimum stress ratio of any type on the structure. Locations are depicted in Figure 15.
Stress Weld Location Location (in.)
Location (in.) node(a) node(a) Stress Intensity Stress Intensity (psi) Stress Ratio % Freq.
Ratio x y z Pm Pm+Pb Salt Salt SR-P SR-a Shift SR-P No 1. Inner Side Plate
- 1. 3.1 119 119 0.5 37229 7490 9003 634 2.26 19.51 19.51 10 10 It .. It.. 2. Support/Seismic Block 2: Support/Seismic Block .. 10.2 10.2 123.8 123.8 -9.5
-9.5 113286 4829 2019 3.5 6.12 6.12
-- 113286 4829 4829 5 It It
- 3. Thin Vane Bank Plate -15.6 -118.4 0.6 2558 4792 5212 0 3.53 1360 2.5 2.5 SR-a No 1. Middle Hood
- 1. ,-
-68.6 69.6 43.7 31149 1717 2953 2914 8.59 4.24 2.5 2.5 SR-P SR-P Yes 1. Side Plate Ext/Inner Ext/Inner Base platePlate 16.3 119 0 -94143 -,
,,941~3 _6918 9809 478 1.34 14.38.
14.38* 5
" ." -2. USR/Support/Seismic USR/Support/Seismic Block -6.9 -122.3 -9.5- 113554 6688 6688 1342 1.39 1.39 5.12 5 It it It 3.
- 3. Tie Tie Bar Bar -49.3
-49.3 -108.1
-108.1 88 88 143795 6077 143795 6077 6077 877 1.53 1.53 7.83 5
" It
- 4. Hood Support/Middle Support/Middle Base Plate/Inner, Plate/Inner. 39.9 -59.5 0 101435 5495 5819 1815 1.69 1.69 3.78 3.78 -10
-10 Backing Bar/Inner Hood
" It
- 5. Closure Plate/Inner Plate/Inner Backing Backing r39.9
- -39.9 -108.6 0.5 84198 5492 5499 1160 1.69 1.69 5.92 .
5.92 5 Bar/Inner Backing Bar/Inner Hood Hood
" " Plate/Inner Base Plate
- 6. Inner Side Plate/Inner -2.3 -119 0 99200 4464 8176 793 1.71 8.66 5
" " 7. Side Plate/Top Plate 17.6 119 88 91215 920 7332 1585 1585 1.9-1.9, 4.33 5
" It
- 8. Hood Support/Outer Support/Outer Base -71.3
-71.3 - - 0 0 95428 4800 4876 1817 1817 1.94 1.94 3.78 0 Plate/Middle Plate/Middle Backing Bar Bar -
It It
- 9. Outer
- 9. Outer Cover Plate/Outer Hood 102.8 -58.1
-58.1 0 94498 .. 1066 7197 910 1.94 1.94 7.55 10
" It
- 10. Hood
- 10. Hood Support/Middle Support/Middle Base 39.9 0 00 88639 4733 88639 4874 1883 1883 1.96 3.65 2.5 2.5 6
.. Plate/Inner Backing Bar/Inner Plate/inner H'ood(6))
Bar/Inner Hood(
" " 11. Thin Vane Bank Plate/Hood
- 11. - -24.1 59.5 0 99487 4707 4724 4724 1091 1091 1.97 6.3 10 Support/Inner Base ~Iate Support/Inner P.late
". ". 12. Hood
- 12. Hood Support/Outer Cover Support/Outer Cover -102.8
-102.8 28.4 28.4 00 95267 95267 4451 4451 4533 4533 1942 1942 2.09 3.54 5 7
Hood(7))
Plate/Outer Hood(
Notes.
(a) Node numbers are retained for further reference.
(1-9) Appropriate stress reduction factor for the welds and modifications (1-9) Appropriate modifications listed in Table 7 have been applied. The number refers to the particular location and corresponding corresponding stress reduction reduction factor in Table 7.
67 67
Document Does This Document Does NotNot Contain Contain Continuum Dynamics, Inc. Proprietary Continuum Dynamics, Proprietary Information Information Table Table 9b (cont.).(cont.). Locations Locations with with minimum minimum stress stress ratios for CLTP CLTP conditions conditions with frequencyfrequency shifts. Stress ratios ratios at every every node are recorded as recorded as the the lowest lowest stress stress ratio identified identified during during the!the' frequency frequency shifts. _StressStress ratios are are grouped grouped according according to stress stress type (maximum (maximum
-- SR-P; SR-P; or alternating alternating - SR-a) and location location (away (away fromfrom a weld weld or at a weld).
weld). Locations Locations aredepicted are-depicted in in Figure 15.15.
Stress Stress Weld Location Location Location (in.
Location (in.) node(a) Stress Stress Intensity Intensity (psi) Stress Stress Ratio % Freq.
Ratio "-
x y z Pm Pm+Pb Pm+Pb Salt Salt SR-P SR-P SR-a SR-a Shift SR-a Yes Yes 1.
- 1. Hood Support/Middle Support/Middle Base -39.9 00 0 85723 85723 4695 4849 2378 1.98 1.98 2.89 -5 6 -
tiDod(6))
Plate/Inner Backing Plate/Inner Bar/Inner Hood(
Backing Bar/Inner
." ." 2. Side Plate/Brace( 5 ) 79.7 79.7 85.2 85.2 75.8 75.8 89649 2002 2002 2884 2884 2343 2343 4.64 2.93 2.93 10 10 2: Side Plate/Brace(5)
. ~,
" " - 3. Hood
- 3. Hood Support/Inner Support/Inner Hood - 36.2 36.2 0 50.8 ,9952999529 975 2316 2290 2290 6.02 ,3.00,
-3.00 00
" " 4. Hood Hood Support/Middle Support/Middle Base Plate/Plate/ -39.9
-39.9 59.5 59.5 0 90468 5397 5524 2277 2277 1.72 1.72 3.02 -5 Inner Backing Backing Bar/Inner Bar/Inner Hood Hood,_ -_
" .. .." 5.
- 5. Hood Hood Support/Outer Support/Outer HoodHood -96.4 -28.4 ,96.866.8 90186 657 657 2332 2234 2234 5.98 3.07 5
" .. .." 6. Hood Reinforcement/Middle Reinforcement/Middle Hood -62.6 101.2 77.9 98277 442 2408 2223 5.79 3.09 -10
-10
" " 7. Side Plate/Brace -79.7 -85.2 31.2 84708 1818 2636 2175 5.11 5~11 3.16 2.5 2.5
" .. .." 8.
- 8. Outer End Plate/Outer Hood -97.5 -70 60.8 99212 802 2212 2165 2165 6.30 3.17 5
.." .." 9. Plate/Exit Mid Bottom
- 9. Side Plate/Closure Plate/Exit Bottom Perf -78.5 -85.2 56.5 87780 524 524 2241 2147 2147 6.22 -3.20
-3.20- 7.5 7.5
"" ."" 10. Hood Hood Support/Inner Support/Inner Backing Backing Bar/Inner Hood -39.9 0 1 95620 1943 3082 2100 2100 4.52 3.27 -5
" " 11.
- 11. Hood Hood Support/Inner Support/Inner Hood , 34.3 62.7., -, 99535 0 62.71 826 826 2451 2451 2096 2096 5.69 5.69 3.28 -10
" " 12. Top Plate/Tie Plate/Tie Bar -17.6
-17.6 -0.5 88 75048 1127 3064 3064 2080 2080 4.55 3.30 3.30 2.5 2.5
" " 13.
- 13. Top Thick Plate/Side Plate/Exit Plate/Exit Top . -15.6 119 86.5 98451 816 2970 2070 2070 4.70 3.32 3.32 2.5 2.5 Perf/Inner Perf/Inner Side Side Plate " _ -_-
".. .." 14.
- 14. Double Side Plate/Top Double Side Plate/Top Plate Plate -54
-54 -54.3 88 88 85117 85117, 587 587 2323 2323 2032 2032 6.00 6.00 3.38 3.38 2.5 2.5
"" "" 15. Hood Support/Outer Hood( 7 Hood(7))- -97.8 -28.4 59 85774 85774 488 2129 2027 6.55 6.55 3.39 5..
".. _ -"... 16. Closure Plate/Middle Plate/Middle Hood ....,-
68.7
-68.7 85.2 '42.942.9 91590 710 2041 2022 6.83 3.40 3.40 2.5 2.5
((a) a) Node numbers, numbers.are retained retained for further reference.
reference.
(1-9)
(1-9) Appropriate stress reduction factor for the welds welds-and modifications modifications listed in Table 7 have been applied. The number refers to the particular-location and corresponding particular-location corresponding stress reduction reduction-factor in Table 7, 7. ' '
68
Contain Continuum Dynamics, This Document Does Not Contain Dynamics, Inc. Proprietary Information Information 5
4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 3
2.8 2.6 2.4 2.2 Figure 14a. Locations Locations of nodes with stress ratios, SR-P<5, associated ratios, SR-P::;5, associated with a maximum stress stress at at non-welds for non-welds for nominal CLTP operation. Numbers refers refers to the enumerated enumerated locations for SR-P values values at non-welds non-welds in Table Table 9a.
69 69
Contain Continuum This Document Does Not Contain Proprietary Information Dynamics, Inc. Proprietary Continuum Dynamics, Information x
Y'vi/
SR-a 5
4.9 4.8 4.7 4.6 4.5 SR-a:::;S, at non-welds for Figure 14b. Locations of smallest alternating stress ratios, SR-a<5, nominal for nominal CLTP operation. Numbers refer to the enumerated locations for SR-a values at non-welds in values at non-welds in Table 9a.
70
Document Does Not Contain Continuum Dynamics, Inc.
This Document Inc. Proprietary Proprietary Information Information z
A y SR-P 3.9 3.9 3.7 3.7 3.5 3.5 3.3 3.3 3.1 2.9 2.7 2.5 2.5 2.3 2.1 2.1 1.9 1.9 1.7 1.7 1.5 1.5 1.3 Figure 14c.
14c. Locations Locations of smallest ratios, SR-P<4A smallest stress ratios, SR-Ps4, associated associated with maximum stresses stresses at operation. Numbers refer to the enumerated welds for nominal CLTP operation. locations for SR-P values enumerated locations values at welds in Table 9a. This view shows locations 1, 3, 6, 8 and 9.
locations 1,3,6,8 9.
71
Continuum Dynamics, Inc. Proprietary Information This Document Does Not Contain Continuum
[] zz k X SR-P 3.9 3.7 3.5 3.3 3.1 2.9 2.7 2.7 2.5 2.3 2.1 1.9 1.9 1.7 1.7 1.5 1.5 1.3 1.3 Locations of minimum stress ratios, SR-P~4, Figure 14d. Locations associated with maximum stresses at SR-P_<4, associated welds for nominal CLTP operation. Numbers CLTP operation. Numbers refer to the enumerated locations for SR-P values enumerated locations values at welds in Table 9a. This view shows locations locations 2, 3, 5, 8 and 9.
2,3,5,8 72 72
This Document Does This Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information y
X ~
3.9 3.7 3.5 3.3 3.1 2.9 2.7 2.5 2.3 2.1 1.9 1.7 1.5 1.3 Figure Figure 14e.
14e. Locations Locations of minimum minimum stress ratios, ratios, SR-P<4, SR-P:::;4, associated associated with maximum maximum stresses at welds welds for nominal nominal CLTP CLTP operation. Numbers Numbers refer refer to the enumerated enumerated locations locations for SR-P SR-P values values at at welds in Table Table 9a. This view shows locations shows locations 4, 7, 10 and 1 73 73
Contain Continuum Document Does Not Contain This Document This Continuum Dynamics, Inc. Proprietary Dynamics, Inc. Proprietary Information Information SR-a 5
4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 3
SR-a<5, at welds for nominal CLTP Locations of minimum alternating stress ratios, SR-as5, Figure 14f. Locations enumerated locations for SR-a values at welds in Table 9a.
operation. Numbers refer to the enumerated Locations 1-5, 7 and 88 are shown.
74
This Document Does Not Contain Continuum Continuum Dynamics, Inc. Proprietary Proprietary Information zz x~
x SR-a 5
4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 3
Figure 14g. Locations of minimum alternating stress ratios, SR SR-a_<5,
-a:s;5, at welds for nominal CL CLTP TP operation. Numbers operation. Numbers refer to the enumerated enumerated locations locations for SR-a values at welds in Table 9a.
4, 6 and 9 are shown.
Locations 4,6 75
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
x~ y 5
4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 3
2.8 2.6 2.4 2.2 ratios, SR-P<5, Figure 15a. Locations of minimum stress ratios, SR-P~5 , associated with maximum maximum stresses at non-welds TP operation with frequency shifts.
CLTP non-welds for CL recorded stress ratio is the minimum shifts. The recorded value taken over all frequency shifts.
value shifts. The The numbers enumerated location for SR-P numbers refers to the enumerated non-welds in Table 9b.
values at non-welds 76 76
This Document Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information Figure 15b. Locations Locations of minimum alternating stress ratios, SR-a<5, SR-a~5, at non-welds for CLTP CLTP operation operation with frequency shifts. The recorded recorded stress ratio at a node is the minimum value taken over all frequency shifts. Numbers Numbers refer to the enumerated enumerated locations locations for SR-a values at non-welds in Table 9b.
77
Proprietary Information This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
[] z SR-P 3.9 3.9 3.7 3.7 3.5 3.3 3.3 3.1
- 3. 1 2.9 2.7 2.5 2.5 2.3 2.3 2.1 2.1 1.9 1.9 1.7 1.7 1.5 1.5 1.3 1.3 Figure 15c. SR-P<4, associated with maximum 15c. Locations of minimum stress ratios, SR-P:::;4, maximum stresses at CLTP operation with frequency shifts. The recorded stress ratio at a node is the welds for CLTP enumerated locations for Numbers refer to the enumerated minimum value taken over all frequency shifts. Numbers 1, 3, 7 and 9.
SR-P values at welds in Table 9b. This view shows locations 1,3, 78
This Document Does Not Contain Continuum Dynamics,Dynamics, Inc. Proprietary Information SR-P 3.9 3.7 3.7 12 3.5 3.3 3.1 3.1 2.9 2.7 2.5 5 2.3 2.1 2.1 2 1.9 1.9 1.7 1.7 1.5 1.5 1.3 Figure Figure 15d. Locations of minimum stress l5d. Locations stress ratios, SR SR-P(4,
-P:S;4, associated associated with with maximum maximum stresses stresses at welds for CLTP CLTP operation frequency shifts operation with frequency shifts.. The The recorded recorded stress ratio ratio at aa node node is the the minimum minimum value taken over all frequency frequency shifts. Numbers Numbers refer to the enumerated enumerated locations locations for SR-P values values at welds in Table Table 9b. This This view shows locations 2, 3, 5-7 shows locations 5-7 and and 12.
12.
79 79
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Information x
3.9 3.7 3.5 2.9 3.3 2.7 3.1 2.9 2.7 2.1 2.5 2.3 2.1 1.9 1.7 1.5 1.3 SR-P~4 , at welds for CLTP operation with Figure 15e. Locations of minimum stress ratios, SR-P<4, frequency shifts. The recorded stress ratio at a node is the minimum value taken over all frequency shifts. Numbers refer to the enumerated locations for SR-P values at welds in Table 9b. This view from below shows locations 4, 5 and 8-12.
locations 4,5 80 80
This Document Document Does Not Contain Continuum Continuum Dynamics, Dynamics, Inc. Proprietary Proprietary Information Information SR-a 5
4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 3
2.8 Figure 15f.
15f. Locations of minimum alternating stress ratios, ratios, SR-a:::;5, SR-a<<5, at welds for CLTP operation shifts. The recorded stress ratio at a node is the operation with frequency shifts. the minimum value taken over all frequency shifts.
frequency shifts. Numbers refer to the enumerated enumerated locations locations for SR-a values at welds in in Table 9b. This Table 9b. This view from below below shows locations 1, 1, 3, 4, 10 and 11 all on hood welds.
81
Proprietary Information This Document Does Not Contain Continuum Dynamics, Inc. Proprietary z
x Y SR-a 5
4.8 4.8 4.6 4.4 4.2 4
3.8 3.8 3.6 3.4 3.2 3
2.8 2.8 SR-a<5, at welds for CLTP alternating stress ratios, SR-a:::;5, Figure 15g. Locations of minimum alternating frequency operation with frequency shifts. The recorded stress ratio at a node is the minimum value taken enumerated locations for SR-a values at welds in over all frequency shifts. Numbers refer to the enumerated in Table 9b. This view shows locations 2 and 12-14.
Table 12-14.
82
Contain Continuum Dynamics, Inc. Proprietary Information This Document Does Not Contain Information SR-a .
5 4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 3
2.8 Figure 15h.
15h. Locations of minimum minimum alternating stress ratios, SR-a<5, SR-a:::;5, at welds for CLTP CLTP operation operation with with frequency shifts. The recorded recorded stress ratio at a node is the minimum value taken taken over all frequency shifts. Numbers over all frequency shifts. Numbers refer to the enumerated enumerated locations locations for SR-a values at welds in Table Table 9b. Close-up Close-up view showing locations locations 5, 6, 12 and 14-16.
14-16.
83
This Document Document Does NotNot Contain Contain Continuum Continuum Dynamics, Dynamics, Inc. Proprietary Proprietary Information Information SR-a 5
4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 3
2.8 Figure 15i.
lSi. Locations of minimum minimum alternating alternating stress ratios, SR-aS;5, SR-a<5, at welds for CLTP operation with frequency shifts. The recorded stress ratio at a node is the minimum value taken operation over all frequency shifts. Numbers refer to the enumerated frequency shifts. enumerated locations for SR-a values at welds in Table 9b. Close-up locations 5, Close-up view around locations 5, 7-9 and 15.
84 84
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information 5.3 Frequency Content and and Filtering Filtering of of the Stress Signals.
Signals The. frequency contribution to the stresses can be investigated by examining the power The, power spectral density (PSD) curves and accumulative PSDs for selected nodes having lowalte~ating spectraL low alternating stress ratios.
stress ratios. TheThe accumulative accumulative PSDs are computed directly from the Fourier coefficients as Z~~~~Y*n) (O)2 where &(rok)
C(ok) is the complex stress harmonic at frequency, rok. ok. Accumulative 'PSD PSD plots areare the frequency coinponent~
useful for determining the"frequency components an4freq~ency and frequency ranges that make the largest contributions to the fluctuating stress. Unlike PSD' PSD plots, no "binning" or smoothing of of frequency components frequency components is needed to obtain obtain smooth curves. $teep Steep step-like rises in L(ro)
Z(co) indicate the presence of the ,presence of aa strong component component at a discrete frequency whereas gradual increases increases in the curve curve imply significant content over a broader frequency fre,quency range. From Parsival's theorem, equality between equalio/ Y((oN) (whereN between L(roN) (where N is the total number.of frequency components) numbero.ffr~queIl.~y components) and the RMS of of the stress the stress. signal signal in the time,time domain is established.
The selected The selected nodes nodes are are the the ones having the ones having the lowest alternating stress ratios (at a weld) in Table 9b. These are:
Node 85723 -- located Node 85723 located on the inner hood/hood support/middlesupport/middle base plate junction. The associated PSDs are shown in Figure 16a.
Node 89649 Node 89649 -- located located on the lifting rod brace/vane bank end plate connection. The associated PSDs are shown in Figure 16b.
Node 99529 Node 99529 -- located located on on the weld weld joining joining the inner hood and hood support. The associated PSDs are shown in Figure 16c.
PSDs Node Node 99212 99212 -- located located on on the the weld weld joining joining thethe outer hood and its end plate. The associated PSDs are shown in Figure 16d.
Node Node 87780 87780 -- located located on the weld joining joining the closure plate to the outer closure plate plate to the outer vane vane bank. The associated associated PSDs are shown in Figure Figure 16e.
These are the nodes labeled These labeled 1-3, 1-3, 8 and 9 in Table 9b and accompanying accompanying Figure 15f-i.15f-i.
In In each case, since each case, since there there are six stress components components and up to three different different section section locations for shells for (the top, shells (the top, mid mid andand bottom surfaces), there is a total of 18 bottom surfaces), 18 stress histories per component.
- Moreover, Moreover, at at junctions junctions there are at least two components components that meet at the junction. The particular particular stress component that is plotted stress component that is plotted is chosen is chosen as follows. First, the component component and section section location location (top/mid/bottom) is (top/midlbottom) is taken taken as as the the one one that that hashas the the highest highest alternating alternating stress. This narrows narrows the selection to selection to six six components.
components. Of Of these, the the component component having the highest highest Root Root Mean Mean Square (RMS)
(RMS) is selected.
selected.
The The first first node node (85723),
(85723), is dominated by is dominated by aa broad broad peak peak centered centered at 7171 Hz. TheThe frequency frequency shifted curves do not differ significantly from shifted curves do not differ significantly from the non-shifted the non-shifted results. Judging Judging from the PSD PSD curves, it appears that in the curves, it appears that in the non-shifted case case there are two peaks peaks about about 71 Hz, with one - the 85 85
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information '
Proprietary Information lower frequency one - being dominant. When the signal is ,shifted, shifted, the forcing on the lower lower,.,
frequency mode is reduced and that on the higher frequency frequency mode increases.
increases. Interestingly, the combined combined effect is to effectively effectiviely shift, the peak frequency upward upward even though the 'signal: signal is shifted 'downward (as is clear by comparing some of the other peaks). This is effect effect is readily explainable explainable in the context of the complex multi-modalITlUlti-modal system being considered here. Frequency, Frequency*
shifting has a more pronounced pronounced effect on node 89649 which has dominant frequencies at 13.4 Hz, 19.6 Hz and 136 Hz. The lower frequency peaks grow, but do not shift significantly with the + +10%10% frequency shift. The higher frequencyfrequency peak, peak appears to shift and attenuate with the frequency shift in the signal. The third node is dominated dominated by a 45.4 Hz peak. This dominance appears to be spatially localized localized meaning that the number of locations locations on the dryer dryer where this is the .the;dominant dominant frequency, are few. However, few., Howe:v~r, the same frequency peak shows up in the limiting location 85723 'which also involves the inner hood suggesting location at node 85723 suggesting that the inner "
hood isisrespon~ive' acoustiC signals ~t
- responsiveto acoustic at this frequency. The stress response at node n6de. 99212 is also characterized characterized by a single dominant dominant the' dominant peak, this time at a frequency'between the'dominant frequency 'between '
69 and 771i Hz. This frequency characterizes most 'of the surface frequency char'acterizesmost surface on bn the outer panels of the outer "
elD the MSL C/D side. Finally for node 87780, the dominant stress contributions occur at -
hood on the'MSL frequenCies; , Without frequency shifting the dominant frequency isi80~0 higher frequencies. is 180.0 Hz which which coincides coincides with a multiple of electrical electrical noise (60 Hz - note however:
however, that the electrical electrical noise is' is .
filtered). At the +7.5% +7.5% shift the dominant frequency is at 184.5 Hz which corresponds corresponds to' to 171.6 Hz in the original non-shifted non-shifted signal.
' **** 1 i,
'1','
86 86
This Document Does Not Contain Continuum Continuum Dynamics, Dynamics, Inc. Proprietary Proprietary Information Information Node 85723, a- a.zz 400 400 350 Ir * ** ....... .. .
350
'iii a.
H 300 L. .,
a- f 6 :
en 250 a.. i
.~
Q) i -- n
- e- o no shift shift iii
- s 200 t- I **_.*****
... .... -5%
.5% shift Stijl E
E E
- J 150 '
150
~ 100 50 0 i l
0 50 100 100 150 200 250 Frequency [Hz)
Frequency [ Hz]
Node 85723, a-a zz 10l 104 no shift
-5% shift
~
N 1000 .j
.~
CO 100 100 o
en 1
0.
a..
co, I/)
10
~
to I en 1
I I
0.1 0.1 I 0.01 0.001 o0 50 100 150 150 200 200 250 250 Frequency [ Hz ]
Frequency [Hz)
Figure 16a. Accumulative Accumulative PSD and PSD curves of the az:z cyzz stress response at node 85723.
87 87
Continuum Dynamics, Inc.
Document Does Not Contain Continuum This Document Information Inc, Proprietary Information Node 89649, cr Node ayy yy 600
'iii 0.
500 ~ ...
~
6 (J) 400 I-C,,
a..
Q)
.~
(D -no no shift shift m 300 **'"""-_ ** +10%0 sshift hi]ft "5
E E
- l 0 200
~
100 100 0
0 50 100 150 200 250 Hz ]
Frequency ((Hz]
Node 89649, cr a yy
- - . - no shift 105 Zo +10% shift shift N
J:
N-
'iii 1000 1000 a.
0.
A Cl CO (J) a..
a-(/)
(/) 10 10
-~
O-( J) 0.1 0.001 0.001 L 0o 50 100 150 150 200 250
[ Hz ]
Frequency [Hz]
ayy Accumulative PSD and PSD of the cr Figure 16b. Accumulative response at node 89649.
yy stress response 88 88
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 99529, CJ o"YY yy 400 350 I-
'iii Cl.
V.J 300 L 6CJ) a.. 250 -
Q)
(1l 200 I-O%Shift 0%ssift I E
E I I
E E
- ) 150 .. ....-1
()
()
c{
100 50 0
0 50 100 150 200 250 250 Frequency [ Hz]
Frequency [Hz]
Node 99529, o Node CJ yy yy 5
10 N
N
'1~O%shift 10% 10ift) I I
~
.~
0~ 1000 oCJ) 0 a..
Co iZ 0) 10
~
U5 0.1 0.1 0.001 ------_. ~
0o 50 50 100 150 200 200 250 Frequency Frequency ((HzHz ]1 Figure Figure 16c.
16c. Accumulative Accumulative PSD and PSD of the the cyy cryy stress stress response atat node node 99529.
99529.
89
Document Does Not Contain Continuum Dynamics, This Document Dynamics, Inc. Proprietary Information Information Node 99212, CJ a yy yy 300
- r. .....
~ ........-....- . . .....-.. -.-.. -................
-.~ - ........-;;-.
. 1
'ea.
W n
- a. 250
!f
. j C,,I ci
(/)
200 , ~ ~~--.----.--~~--.----.--~.--
0-.=_
Q)
> .--.- no shift (13 150 I ********* +5% shift
-*--noshift E
E E
E
- l 8 100 1100
~
50 ...... .. ... ...... ,.i j ... J I
0 0 50 100 150 150 200 250 Frequency ((Hz] Hz]
Node 99212, CJ cr yy yy 1015 10 1 1044 10 I
no shift I r no shift I
N 1000 1000
+5% shift I
N
--'en J:
a a.
100 I
(/)
0-C,) 10 III III
~
(/) I
...*.*. -1 0.1 0.01 0.01 0.001 0.001 0 50 100 100 150 200 250 Frequency [Hz]
Frequency [ Hz ]
Accumulative PSD and PSD of the cr Figure 16d. Accumulative yy stress response at node 99212.
ayy 90
This This Document Document Does Not Not Contain Contain Continuum Continuum Dynamics, Dynamics, Inc. Inc. Proprietary Proprietary Information Information Node Node 87780, 87780, a a xx 400 400 350 350 l. .
r
- r. *. :. .* _* *_* . ******1
. f ... . ..-
'iii IZ a.
300 300 '- .. . ........
"""-no no
. shift ... !
V.;J d(/)
c:i
- + +77,5%
.5% sh]f shift i CO, a..
Q) 250 250 I
.,> 200 III 200 E
E E
- J 150 150 L 8
<< I 100 100
..*.*-' . ........ . .... .. ..K ..
50 0
0 50 100 150 200 200 250 Frequency [Hz] [ Hz]
Node 87780 a xx 1 - -
hift no o shift 1055 7.50 shift N
N
- r:r A
F' CR,
'iii
- a. 1000 1000 00.
(/)
a..
II)
II) 10
- Q)
( /)
--.-4 0.1 0.1 0.001 I _
o0 50 100 150 150 200 250 Frequency [Hz]
Frequency [ Hz ]
Figure 16e. Accumulative Accumulative PSD and PSD of the acxx xx stress response at node 87780.
91
This Document Document Does Not Contain Contain Continuum Dynamics, Dynamics, Inc. Proprietary Information
- 6. Conclusions A frequency-based frequency-based steam dryer stress analysis has been used to calculate calculate high stress locations and calculated calculated / allowable stress ratios for the Nine Mile Point Unit 2 steam dryer at CLTP load conditions using plant measurement measurement data. A detailed description of the frequency-based frequency-based methodology methodology and the finite fmite element element model for the NMP Unit 2 steam dryer is presented.
presented. The CLCLTP TP loads obtained in a separate acoustic circuit model [4] including acoustic uncertainty for both the ACM [4] and FEA including end-to-end bias and uncertainty were applied applied to a finite element element model of the steam dryer consisting mainly of the ANSYS Shell 63 elements, brick continuum elements elemepts and beam elements.
The measured measured CLTP loads are applied without filtering of low power data. The resulting stress histories were analyzed analyzed to obtain maximum and alternating stresses at all nodes for comparison comparison against against allowable levels. These results are tabulated in Table 9 of this report. The minimum alternating alternating stress ratio at nominal operation is SR-a=3.00 SR-a=3.00 and the minimum alternating stress ratio taken over all frequency shifts is SR-a=2.89.
SR-a==2.89. The stress ratio associated with maximum stress intensities varies weakly with frequency shift and assumes a minimum value of SR-P=1.34 SR-P=1.34 both with and without frequency shifting.
Since flow-induced acoustic resonances resonances are not anticipated in the steam dryer, the alternating stress ratios at EPU operation operation can be obtained by scaling the CLTP values by the steam flow velocity squared,.
Under this approach, the limiting alternating stress ratio becomes SR-a=2.89/1.388=2.08. For the node becomes SR-a=2.89/1.388=2.08.
with the limiting maximum stress ratios at CLTP, the correspondingcorresponding limiting value at EPU is SR-P=1.32.
SR-P=1.32. Given that the alternating stress ratio SR-a obtainedobtained at EPU remains above 2.08 at all frequency shifts together with the comparatively comparatively small dependence dependence of SR-P upon acoustic acoustic loads, the Unit 2 dryer is expected expected to qualify at EPU conditions.
Frequency Shift Frequency Minimum Stress Ratio at CL CLTP TP Min. Alt. Stress Max. Stress, Alternating Alternating Stress, Ratio (SR-a)
SR-P SR-a at EPU atEPU 0% (nominal) 1.34 1.34 3.00 3.00 2.16
-10%
-10% 1.36 3.09 2.23
-7.5%
-7.5% 1.36 1.36 3.07 2.21
-5%
-5% 1.36 1.36 2.89 2.08
-2.5%
-2.5% 1.36 1.36 3.27 2.36
+2.5%
+2.5% 1.36 2.93 2.11
+5%
+5% 1.34 2.97 2.14
+7.5%
+7.5% 1.35 1.35 3.07 3.07 2.21 2.21
+10%
+10% 1.35 1.35 2.93 2.11 All shifts 1.34--1.36 1.34 1.36 2.89- 3.27 2.89- 3.27 2.08-2.36 2.08-2.36 Limiting Limitin2 1.34 2.89 2.08 92 92
This Document Does Not Contain Continuum Dynamics, Dynamics, Inc. Proprietary Proprietary Information Information References
- 7. References
- 1. EPRI (2008), BWRVIP-194: BWR BWR Vessel andandInternals Internals Project: Methodologiesfor Project: Methodologiesfor Demonstrating Demonstrating Steam DryerDryerIntegrity Integrity for for Power Uprate, Palo Alto, CA: 2008. 1016578.
- 2. ASME Boiler and Pressure ASME Boiler PressureVessel Code, Code,Section III, III, Subsection Subsection NG (2007).
(2007).
3.
- 3. Continuum Dynamics, Inc. (2005), Methodology to Determine Continuum Determine Unsteady Unsteady Pressure Pressure Loading Loading on Components in Reactor Components Reactor Steam Domes (Rev. (Rev. 6),
6), C.D.I.
C.D.1. Report Report No. 04-09 (Proprietary).
- 4. Continuum Dynamics, Inc. (2008), Acoustic and and Low Frequency Frequency Hydrodynamic Hydrodynamic Loads at at CLTP PowerLevel Power Level on Nine Mile PointPoint Unit Unit 2 Steam Dryer Dryer to 250 Hz, Hz, Rev. 2, C.D.I. Report No.08-08P 08-08P (Proprietary).
- 5. Continuum Continuum Dynamics, Inc. (2007), Methodology to Predict PredictFull Full Scale Steam Dryer Dryer Loads from from In-Pl~~t In-PlantMeasurements, Measurements, with the Inclusion Inclusion of a Low Frequency FrequencyHydrodynamic Hydrodynamic Contribution, Contribution, C.D.I. Report Report No.07-09P (Proprietary).
(Proprietary).
- 6. Structural Integrity Associates, Inc. (2009), Nine Mile Point Unit 2 Steam Dryer Point Unit ClosurePlates Dryer Closure Plates Analysis Results, SIA Letter Report No. 0900895.401 0900895.401 Revision 0, August 21. 21.
- 7. Structural Integrity Associates, Inc. (2008), Nine Mile Point Unit 2 Main Point Unit Main Steam Line Strain Gage Strain Gage DataReduction, Data Reduction, SIA Calculation Calculation Package No. NMP-26Q-302.
NMP-26Q-302.
- 8. ANSYS ANSYS URL: http://www.ansys.com, ANSYS Release 10.
http://www.ansys.com.ANSYSRelease 10.00 Complete User's User's Manual Manual Set.
- 9. Continuum Dynamics, Inc. (2007), Response to NRC Request Continuum Dynamics, Request/orfor Additional Additional Information Information on the Hope Creek Generating Hope GeneratingStation, Station, Extended Power Power Uprate, Uprate,RAIRAJ No. 14.110.
- 10. Continuum Dynamics, Inc. (2008), Stress Assessment of Hope Continuum Dynamics, Hope Creek Creek Unit I1 Steam Dryer Dryer Based on Revision 4 Loads Model, Model, Rev. 4, C.D.I. Report No.07-17P (Proprietary).
11.
- 11. Press, W.H.,
W.R., et aI.,
al., Numerical NumericalRecipes. 2 ed. 1992: Cambridge Cambridge University Press.
- 12. Structural Integrity Associates, Associates, Inc. (2008), Flaw Evaluation and Vibration Flaw Evaluation VibrationAssessment of the Mile Point Nine Mile Point Unit Unit 2 Steam Dryer Dryer for Extended PowerPower Uprate Uprate Operating Conditions, Report Operating Conditions, No. 0801273.401.
0801273.401.
- 13. Dynamics, Inc. (2008), Stress Assessment ofBrowns Ferry Continuum Dynamics, FerryNuclear Nuclear Unit Unit 1I Steam Steam Dryer,Rev. 0, C.D.I.
Dryer, C.D.1. Report No.08-06P (Proprietary).
- 14. O'Donnell, W.J.,
W.J., Effective Elastic Constants For Elastic Constants For the Bending of Thin Perforated Perforated Plates Plates With Triangularand Triangular and Square Square Penetration Patterns.ASME Journal of Engineering Penetration Patterns. Engineering for Industry, 1973.
1973.
95: p. 121-128.
- 15. de Santo, D.F., Added MassMass and and Hydrodynamic HydrodynamicDamping Dampingof Perforated PerforatedPlates Plates Vibrating VibratingIn Water.
Water. Journal Journal of Pressure Vessel Technology, 1981. 103: p. 175-182.
Technology, 1981.
- 16. Idel'chik, I E. and E. Fried, Flow Flow Resistance, Design Guidefor Resistance, a Design Guide for Engineers.
Engineers. 1989, Washington Washington D.C.: Taylor & & Francis. pg. 260.
- 17. Continuum Dynamics, (2007), Dynamics 0/
Dynamics, Inc. (2007), ofBWR BWR Steam DryerDryer Components, Components, C.D.I. Report No.07-11P.
No.07-11P.
- 18. U.S. Nuclear Regulatory Comprehensive Vibration Regulatory Commission (2007), Comprehensive Vibration Assessment Programfor Programfor Reactor Internals During Preoperational and Initial Startup Reactor Internals During Preoperational and Initial Startup Testing, Testing, Regulatory Guide 1.20, March.
- 19. Weld Research Council (1998),
(1998), Fatigue Fatigue Strength Strength Reduction and StressStress Concentration ConcentrationFactors Factors For For Welds In Pressure Pressure Vessels and Piping, and Piping, WRC Bulletin Bulletin 432.
- 20. Pilkey, W.D., Peterson's Stress Concentration Peterson's Stress ConcentrationFactors, Factors, 2nd ed. ed 1997, New York: John Wiley.
pg. 139.
pg.139.
21.
- 21. Lawrence, F.V., N.-J. Ho, Lawrence, Ro, and P.K. Mazumdar, Predicting Predicting the Fatigue FatigueResistance Resistance of Welds. Ann.
Rev. Mater. Sci., 1981.
1981. 11: p. 401-425.
401-425.
- 22. General Electric (GE) Nuclear Nuclear Energy, Supplement 1 I to Service Information Information Letter (SIL) 644, 644, "B WR/3 Steam Dryer HBWRl3 Dryer Failure, Failure,"" September September 5. 2003.
5.2003.
93
This Document Document Does Not Contain Continuum Dynamics, Inc. ProprietaryProprietary Information Information
- 23. Tecplot, Inc. (2004), URL: http://www.tecplot.com.*Documentation:
http://www.tecplot.com, Documentation: Tecplot User's User's Manual Manual Version Version 10 Tecplot, Tecplot, Inc., October.
- 24. GE Nuclear Nuclear Energy (2006), Browns Ferry Ferry Nuclear Nuclear Plant Units 1,2, Plant Units 1, 2, and 3 Steam Dryer Dryer Stress, Stress, Dynamic, and Dynamic, andFatigue Fatigue Analysis for EPU Analysisfor EPUConditions, Conditions, GE-NE-0000-0053-7413-R4-NP.
GE-NE-0000-0053-7413-R4-NP.
- 25. Structural Integrity Integrity Associates, mc.
Iic. (2008), Shell and and Solid Sub-Model Finite Finite Element Stress Comparison, Comparison, Rev. 2, Calculation Calculation Package, 0006982.301, Oct.
0006982.301, OC,t. 17.
- 26. Continuum Continuum Dynamics, Inc. (2008), Stress Assessment of Browns Ferry (2008), Stress FerryNuclear Unit 2 Steam Nuclear Unit Steam Dryerwith Outer Dryer OuterHood and Tie-Bar Tie-Bar Reinforcements, Reinforcements, Rev. 0, C.D.I. Report No.08-20P (Proprietary),
(Proprietary) *
- 27. Structural Integrity ComparisonStudy of Integrity Associates, Inc. (2008), Comparison ofSubstructure and Submodel Substructure and Analysis using ANSYS, Calculation usingANSYS, Calculation Package, Package, 0006982.304, December.
- 28. Continuum Continuum Dynamics, Inc. (2009), Response to NRC Round 23 RAI RAJ EMCB 2011162 201/162part part c, January.
- 29. Continuum Dynamics, Inc. (2009), Compendium Continuum Compendium ofNine Mile Point Point Unit Unit 2 Steam Dryer DryerSub-Models Away From
, ModelsAway From Closure Closure Plates PlatesC.D.l C.D.I. Technical Technical Note No.09-16P (Proprietary), August.
- 30. Continuum Dynamics, Inc. (2008), Response to NRC RAIEMCB RAI EMCB 172, June. '
94
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Appendix A Sub-modeling and Modification of Closure Plates
((
(3)))
95 95
This Document Proprietary Information Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 9,438 8 ,0896 6.7415 5.3932 4.0449 2,6966 1.3483 oMin 0,000 10,000 20.000 (In)
I 5.000 15 .000 shape (f=128.45 Figure 17: Second mode shape unmodified closure plates (f=128.45 Hz) of unmodified 96 96
This Document This Document Does Does Not Not Contain Contain Continuum Continuum Dynamics, Dynamics, Inc.
Inc. Proprietary Proprietary Information Information 1
SQT.DTIcM NCDAL SOWTICN NOJAL STEP=-I STEP=l SUB =1 SOB FRED=259.55 FRE.CF259.55 USUM USUM RSYS=o RSYS=O
=17.218 DMX =17 .218 SEPC=27.778 SEPC=27.778 SMX =17.218 SMX 0o 3.826 3.826 '77.652
.652 11.478 11.478 15.305 15.305 1.913 1.913 5.739 5.739 9.565 13.391 13.391 17.218 17.218 Figure 18: Fundamental Figure 18: Fundamental mode mode shape shape (f=259.6 (f=259.6 Hz)
Hz) of modified modified closure plate.
plate.
97 97
This Document Does This Document DoesNot Contain Continuum Not Contain Dynamics, Inc.
Continuum Dynamics, ProprietaryInformation Inc. Proprietary Information
((
(3)))
98
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information
((
(3)))
The sub-modeled sub-modeled locations locations together with the calculated calculated stress reduction factors are given in Table
- 10. For each location depictions depictions of the shell and solid element-based element-based sub-models sub-models are given together with the applied loads/moments and resulting stresses. This is followed by a summary summary of the linearization linearization paths and the limiting linearized linearized stresses. The calculation of the stress reduction reduction factor concludes concludes the presentation presentation for each location.
Table 10. List of sub-model sub-model locations Location x y z node Stress reduction reduction factor Top Thick Plate/Side Plate/Side Plate/Closure Plate/Closure 47.1 -108.6 88 101175 101175 0.62 0.62 Plate/Top Plate Closure Plate/Middle Hood Closure PlatelMiddle -63.8 85.2 72.5 91605 0.71 Closure Plate/Inner Hood Closure PlatelInner Hood 28.8 -108.6 87 95172 0.86 0.86 Side Plate/Closure Plate/Exit Top -47.1 108.6 74.5 100327 0.88 0.88 Perf/Exit Mid Top Perf Perf Note: The side plate/closure plate/closure plate connection involving plate connection involving nodes 101175 and 100327 100327 is reinforced reinforced on the interior side with a 0.25" weld. The hood/closure hood/closure plate weld involving nodes 91605 and 95172 is reinforced on the interior side with a 0.125" 0.125" weld.
99 99
This Document Contain Continuum Dynamics, Inc. Proprietary Information Document Does Not Contain Information
((
((
(3)))
sub-modeled locations The sub-modeled locations together with the calculated calculated stress reduction factors are given in Table
- 10. For each location location depictions of the shell and solid element-based element-based sub-models are given together with the applied loads/moments loads/moments and resulting resulting stresses. This is followed by a summary of the linearization linearization paths and the limiting linearized stresses.
stresses. The calculation calculation of the stress reduction reduction factor concludes the presentation for each location.
concludes Table 10. List of sub-model sub-model locations Location x y z node Stress reduction reduction factor Top Thick Plate/Side Plate/Closure 47.1 -108.6
-108.6 88 101175 0.62 Plate/Top Plate Closure Plate/Middle PlatelMiddle Hood -63.8 85.2 72.5 91605 0.71 Closure Platellnner Plate/Inner Hood 28.8 -108.6
-108.6 87 95172 0.86 Side Plate/Closure Plate/Exit PlatelExit Top -47.1 108.6 74.5 100327 0.88 PerfiExit Mid Top Perf Perf/Exit Perf Note: The side plate/closure plate/closure plate connection involving nodes 101175 and 100327 is reinforced on the interior side with a 0.25" weld. The hood/closure plate weld involving nodes 91605 and 95172 is reinforced on the interior interior side with a 0.125" 0.125" weld.
99 99
This Document Document DoesDoes Not Contain Contain Continuum Dynamics, Inc.
Continuum Dynamics, Inc. Proprietary Proprietary Information Information Sub Sub model model Node Node 101175 101175 The sub-model for this node The sub-model located at the top of the vertical node located vertical weld joining closure plate joining the closure plate to the vane bank vane bank shown is shown in Figure 19a Figure 19a and involves involves five different components.
different components. The extracted forces extracted forces are shown shown in in Figure 19b.
19b. The shell sub-model stress The shell distribution is shown in stress distribution in Figure Figure 19c 19c with with aa maximum maximum (i.e. , the maximum taken over all (i.e., components and all components and surfaces bottom and middle) surfaces - top, bottom middle) stress intensity intensity stress at the stress location of 3362 the location 3362 psi.
psi. The The corresponding together with mesh sub-model together corresponding solid sub-model details and mesh details and the stress distribution resulting stress resulting when the same loadsloads used in the shell sub-model applied, are sub-model are applied, are shown shown in Figure Figure 20. 20. Finally, the stress Finally, the stress intensity linearization paths and corresponding intensity linearization linearized stresses corresponding linearized stresses extracted extracted from the solid model are shown solid model shown in Figure 21 and tabulatedtabulated in Table Table 11.11. The limiting sub-model is 2088 psi. Comparing this value against linearized stress in the solid sub-model linearized against the one obtained in the shell yields the stress reduction sub-model (3362 psi) yields shell sub-model reduction factor: 2088/3362 2088/3362 == 0.62.
Top plate, 0.25" Vane bank ]
Vane bank side plate, side 0.375" plate, 0.375" Closure plate, 0.125" Closure plate, 0.125" Thick plate, 0.5"
[Perforated plate, 0.078" '
Perforated plate, 0.078" z
_ _-====:5 0.000 1.000 2.000 (in) :;
Figure 19a. Shell sub-model node 101175.
100 100
This Document Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information Force 9 Time:: 1. s Time 12110/2008 10:12 AM 12/1012008 AM
- Force:
Force: 14.684 Ibflbf
- Force 2: 2.5432 Ibf Ibf
- Force 3: 60.4081bf 60.408 Ibf
- Force 4: lbf 4: 29.682 Ibf
- Force 5: 6.6215 Ibf Ibf
- Force 6: 25.379 Ibf Ibf
- Force 7: 2.0671 Ibf Ibf
- Force 8: 8: 41.024 Ibf 41 .0241bf
- Force Force 9:9: 5.7018 5.7018 Ibf Ibf
___~~==2S 0.000 . qoO (in) 2.000 (in) 1.000 1.000 Moment Moment 9 Time: 1. s LU I 12l 012008 1013 12/10/2008 10:13 AM AM
- Moment: 6.5096 Ibf-inlbf-in
- Moment 2: 8.1909 IbV'in 2: 8.1909Ibf-in
- Moment Moment 3: 5.6901 Ibf*in lbf'in
- Moment Moment 4: 6.7147 Ibf-in Ibfin
- Moment Moment 5:3.8973 lbflin 5: 3.8973 Ibf-in
- Moment Moment 6: 6: 6.1644e-003 6.1644e-003 lbf in Ibf*in
- Moment Moment 7: 8.9112e-002 8.9112e-002 IbfinIbfin
- Moment 8: 2.4226 Ibfinr M Moment 9:0.14082 Ibfi
____===22.000 0.000 S
.qOO (in) 1.000 1.000 Figure 19b. Forces and moments.
101
This Document Document Does Contain Continuum Dynamics, Does Not Contain Information Proprietary Information Dynamics, Inc. Proprietary
"~'. ~ ,",I*~"':r-.
I '.
")I)f:,,\-
Stress Intensity stress Intensity L.i \. -'J'LL. ,\..2.-
Stress Intensity Type: Stress Type: ToplBottom Intensity-- Top/Bottom If,"'i.
~/~
Unit: psi Unit: psi Time: 11 Time:
1211012008 10:39 12/10/2008 10:39 AM AM 20311 Max 20311 Max 3500 3150 3150 2800 2800 2450 2450 2100 2100 1750 1750
.M 1400 1400 N
1050 1050 700 700 350 11.75 Min 11.75 Min o0 4,X
.iii___-====25.~00 (in) 1.000 1.000 19c. Shell sub-model stress contours. Stress intensity: 3362 psi.
Figure 19c.
102 102
This Document This Document Does Not Contain Continuum Dynamics, Inc. Inc. Proprietary Proprietary Information Information Proposed additional weld 0.000 O.OjOO"__ C==2S 1.000 1 .000 2.000 (in)
- 000 (in)
I 0 .000 0.000 22.000
.000 (In)
(In)
I 1.000 1 .000 Figure 20a. Solid model geometry.
103
This Document This Does Not Document Does Not Contain Dynamics, Inc.
Continuum Dynamics, Contain Continuum Proprietary Information Inc. Proprietary Information Figure 20b.
Figure Mesh overview.
20b. Mesh 748,327 nodes, parameters: 748,327 overview. Mesh parameters: 176,028 elements.
nodes, 176,028 elements.
104 104
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information NODAL SOLUTION STEP=1 STEP=l SUB =1 TIME=1 TIME=l SINT (AVG)
(AVG)
DMX DMX ==.012723
. 012723 SMN =.605642 SMX = . 166E+07
=.166E+07 1200 2400 2400 600 1800 1800 3000 3 000 AN Figure 20c.
20c. Stress intensity contours (total) in solid sub-model.
105
Continuum Dynamics, Inc.
This Document Does Not Contain Continuum Information Proprietary Information Inc. Proprietary AN Figure 21.
- 21. Linearization Linearization paths for sub-model node 101175.
101175.
11.. Linearized Table 11 Linearized stresses along the linearization linearization paths shown in Figure 21.
21.
Path Membrane + bendin Membrane bending linearized linearized stress intensi intensity, psi SI AB 1605 AC 710 710 AD 689 AF 492 BE 2088 106
This Document Does Not Contain Dynamics, Inc. Proprietary Contain Continuum Dynamics, Proprietary Information Information Sub model node 91605.
91605.
The sub-model sub-model for this node located located on the weld connecting connecting the closure plate to the hood is shown in Figure 22a and involves two different components components - the hood and closure plate. The extracted forces are shown in Figure 22b.
22b. The shell sub-model stress distribution is shown in Figure 22c with a maximum maximum (i.e., the maximum taken over all components components and surfaces - top, bottom and middle) stress intensity stress at the location of 3176 psi. The stresses in the comers are neither singularities singularities nor due to constraint constraint forces (they arise regardless of where the model is supported). When the sub-model mesh is refined these stresses do not grow. InsteadInstead they essentially essentially retain their coarse level values but extend over a smaller range (i.e.,
(i.e. , over one element). A mathematical explanation for this behavior indicates mathematical explanation that the localized localized stress is due to the local imbalance (due to discretization discretization error) in the applied shear loads. Thus to equilibrate loads. equilibrate the applied applied in-plane stresses on the edges a jump in element stress is required.
The same behavior generally occurs when non-equal shear stresses are applied near the comer. comer.
The solid sub-model, mesh and stresses are shown in Figure 23 and, the stress intensity linearization linearization paths and corresponding corresponding linearized stresses extracted from the solid model are shown in Figure 24 and tabulated in Table 12.12. The limiting linearized stress in the solid sub-model sub-model is 2254 psi, which, which, when compared compared against the one obtained in the shell sub-model (3176 psi) yields the stress reduction factor:
2254/3176 2254/3176 = = 0.71.
107 107
Information This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information L
IHood,0.125" Ho,0.125"~
Closure plate, 0.125" z
,,1. x o.oiioo 3.000 (in) 0.000_ _ _ _====3J.~00(in) 1.500 1.500 Figure 22a. Shell sub-model node 91605.
108 108
This Document Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information Force 7 Time 1. s Time:
1211012008 2:52 PM PM
- Force:
Force: 8.2261 IbfIbf
- Force Force 2:
2:22.492 22.492 1
- Force 3:18.258 Ibf
- Force 4: 51.111 Ibf
- Force 5: 43.361 Ibf
- Force 6:3.1687 Force 6: 3.1687 Ibf Ibf
- Force 7: 46.837 Ibf Ibf z
0.000 I 3.000 (in)
(in)
I 1.500 Moment 7 t Time: 1. s Time:
12110/2008 2:52 1211012008 2:52 PM PM
- Moment: 3.8738 Ibfjn
- Moment Moment 2:6341 2: 6.3414
- Moment 8.55141bf1 Moment 3: 8.5514
- Moment 4: 3.6938 IbfVi
- Moment 5:12.605 Ibf-i
- Moment 6:11.556 Ibf.
- Moment 7: 8.7125 8.7125 1bf z
0.000 3.000 3.000 (in) y -:} "
I 1.500 1.500 Figure 22b. Forces Forces and moments.
109 109
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
'.1 r.";>" )< .
\ ~ ".~ ~.'~.J' .\..,'
! "1 L-l Stress Intensity stress Intensity L 1 L..l._ "'
, .", * .') I ~,
..::"t.-_
Type Stress Intensity Type:: stress Intensity-Top,
- To t"Jj"jL Unit: psi Unit:
Time: 1 1211012008 2:56 PM 12/10/2008 6854.3 Max 6854.JMax 3500 3150 2800 2450 2100 1750 1400 1050 700 Min 51.895 Min
- 0o z
4.. . v Y~ "
contours. Stress intensity: 3176 psi.
Shell sub-model stress contours.
Figure 22c. Shell 110 110
This Document Does Not Contain Contain Continuum Dynamics, Inc. Proprietary Information Proprietary Information Proposed additional weld I !Proposed additional weld F 1.500 Figure 23a. Solid model geometry.
111 111
Proprietary Information This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Figure 23b. Mesh overview.
112 112
This Document Does Not Contain Continuum Continuum Dynamics, Inc. Proprietary Proprietary Information Information NODAL SOLUTION AN J\N STEP=l STEP=1 SUB =1 TIME=l TIME=1 SINT SINT (AVG)
(AVG)
DMX =.00998 DMX SMN =14.524 SMN SMX =5788 SMX 14.524 1298 1298 3863 5146 656.013 1939 1939 3222 4505 5788 NODAL SOLUTION STEP=l SUB =1 TIME=l SINT (AVG)
DMX =.0 0998 SMN =17.52 SMX =4327 Figure 23c. Stress intensity contours contours (total) in solid sub-model. Part of structure structure is removed in the lower figure to show internal stress distribution.
113 113
This Document Document Does Not Contain Continuum Dynamics, Dynamics, Inc. Proprietary Proprietary Information Information ELEMENT S PATH Figure 24.
- 24. Linearization paths for sub-model node 91605 91605..
Table Linearized stresses along the linearization paths shown in Figure 24.
Table 12. Linearized Path Membrane + bending bendin linearized linearized stress intensity, intensi psi S1 A1-B1 AI-Bl 2254 2254 Al-Cl AI-Cl 1891 Al-DI AI-D l 1261 A1-F1 AI-Fl 822 Cl-El CI-El 1899 A2-B2 2170 A2-C2 1154 1154 A2-D2 1160 1160 A2-F2 867 C2-E2 930 B1-B2 BI-B2 2139 2139 114 114
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model node 95172.
Sub The sub-model for this node located at the top of the weld connecting the closure plate to the curved hood is shown in Figure 25a and again involves only two distinct components - the curved hood and closure plate. The extracted forces are shown in Figure 25b and the shell sub-model stress distribution is shown in Figure 25c with a maximum (i.e., (i.e., the maximum taken over all components and surfaces - top, bottom and middle) stress intensity stress at the location of 3198 psi. The solid sub-model, mesh and stresses are shown in Figure 26 and, the stress intensity linearization paths on the original and added weld are shown in Figure 27. The corresponding corresponding linearized stresses extracted from the solid model are tabulated in Table 13. 13. The limiting linearized linearized stress in the solid sub-model sub-model is 2762 psi. The corresponding value in the shell sub-model is 3198 psi so that the stress reduction factor is 2762/3198 =
corresponding 0.86.
- 2 7~9 Hood,0.125" I Hood,0125" Closure plate, 0.125" I Closure I
plate, 0.125" k_
I 0.000 o.o1lloo_ _ _ _-=====3j 1.500 1.500 3.000
.~00 (in)
(in) ;"v Figure Figure 25a. Shell sub-model sub-model node node 95172.
115 115
This Document Does Not Contain Continuum Continuum Dynamics, Inc. Proprietary Information Proprietary Information Force 6 Time: 1. s Time:
121 012008 10:33 PM 1211012008 PM
- Force:
Force: 4.3941 Ibflbf
- Force 2:13.957 Ibf 2: 13.957 Ibf
- 3:13.152 Force 3: lbf 13.152 Ibf
- Force 4: 5.8579 Force lbf 5.8579 Ibf
- Force 5:12.614 Force 5: lbf 12.614 Ibf Force 6:
- Force Ibf 1 9.54 Ibf 6:19.54 z
0.000 I 1.500 1.500 3.000 (in)
I ~Y Moment Moment 6 -i
.4<~
Time: 1. s 1211012008 10:33 PM 1211012008 PM
- Moment: 3.3253 Ibf-in lbfin
- Moment 2: 2:6.7324 lbf in 6.7324 Ibf-in
[ Moment 3: 38.492 Ibf*in lbf in
- Moment 4: 4: 4.9806 lbfln Ibf-In Moment 5:12.813
- Moment Ibf in 5: 12.813 Ibf*in Moment 6:2.5859
[ Moment Ibf in 6: 2.5859 Ibf-in z
0.000 1.500 3.000 (in)
I ~Y Figure 25b. Forces and moments.
116 116
This Document Does Not Contain Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information Intensity Stress Intensity Type: Stress Intensity Intensity -- Top/Bottom TopfBottom Unit: psi Time:: 1I Time 1211012008 10:42 PM 12/10/2008 PM 3200 3198 MaxMax 2880 2560 2240 1920 1600 1280 960 960 wl 640 640 320 39.598 MinMin o0 z
Figure 25c.
25c. Shell sub-model stress contours. Stress intensity: 3198 psi.
psi.
117 117
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Information Proposed additional weld I 0.000 V 3.000 (in) 3.000 (in)
I 1.500 1.500
' - -_ _ ,800 (in) 0:..:.:;
,< ~\
y Figure 26a. Solid model geometry.
118 118
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 26b. Solid mesh.
119 119
Proprietary Information This Document Does Not Contain Continuum Dynamics, Inc. Proprietary This 26c. Stress intensity contours (total) in solid sub-model.
Figure 26c.
120 120
Document Does This Document Does Not Contain Contain Continuum Dynamics, Dynamics, Inc.
Inc. Proprietary Proprietary Information Information Figure Figure 27a. Linearization Linearization paths at the original weld for sub-model node 95172.
121 121
Does Not Contain Document Does This Document Information Contain Continuum Dynamics, Inc. Proprietary Information Linearization paths at the additional weld for sub-model node 95172.
Figure 27b. Linearization 122 122
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Information Table 13.
- 13. Linearized Linearized stresses along the linearization linearization paths shown shown in Figure 27.
Path Membrane + bending linearized Membrane linearized stress intensity, psi AB 1910 1910 AC 2437 AD 1696 AE 2421 AF 639 639 Al-BI AI-Bl 2002 Al-Cl AI-Cl 2689 Al-DI AI-Dl 1837 1837 Al-El AI-El 2696 Al-Fl AI-Fl 1598 C-C1 C-Cl 2762 123 123
This This Document Document Does Does Not Contain Continuum Dynamics, Inc.
Continuum Dynamics, Inc. Proprietary Proprietary Information Information model node 100327.
Sub model 100327.
The final sub-model sub-model involving involving the closure closure plate vertical weld plate is for aa node on the vertical weld connecting connecting the closure plate closure plate to the vane bank. It is located 13.5 inches below located 13.5 inches below the the top of the of the weld. The The shell element-element-based sub-model is shown in Figure 28a and based sub-model and involves involves four components.
components. The extracted extracted forces are are shown shown in Figure 28b 28b and the shell sub-model stress distribution is shown sub-model stress shown in Figure 28c 28c with aa maximum stressstress intensity intensity stress at the the location of 2744 of 2744 psi. The The solid sub-model, mesh mesh and stresses stresses are shown in Figure Figure 29 and, intensity linearization and, the stress intensity linearization paths depicted depicted in Figure Figure 30. The extracted extracted linearized linearized stresses stresses are tabulated in Table are tabulated Table 1414 and and show a limiting linearized stress in the limiting linearized the solid sub-model sub-model of of 2406 2406 psi. The reduction factor is 2406/2744 == 0.88.
stress reduction Geometry Geometry 12/11/2008 12/1112008 9:32 AMAM M1 Side plate, 0.375" Side plate, 0.375" I Closure plate, 0.125" Perforated plate, 0.078" I Perforated plate, 0.078" Perforated plate, 0.078" I Perforated plate, 0.078" Z
o.o.oo 0.000___-====3:j 1.500
. ~00 (in) 3.000 (in) tý IX, Figure 28a. Shell sub-model node 100327. 100327.
124 124
This Document Does Not Contain Continuum Continuum Dynamics, Dynamics, Inc. Proprietary Information Information Force 10 Time:: 1. s Time 1211112008 121111200B 9:44 AM AM
- Force:
Force: 2.6676 Ibf Ibf
- Force 2: 2: 9.5592 Ibf Ibf Force 3:4.0199 Force 3: 4.01 9B Ibf Ibf Force 4:
Force 4: 7.6292 IbV Ibf Force 5:14.618 5: 14.61 B IbV Ibf Force 6: 5.0388 IbV 6: 5.03BB Ibf Force Force 7:7: 3.16B51bf 3.1685 IbfI
- Force Force B:8: B.960B 8.9608 IVb Ibf Force 9: 9.0228 IbI 9: 9.022B Ibf
- Force 10 10: 2.967 2.9671bf IV z
0.000 3.000 (in)
(in) 1 1.500 Moment 10 Moment Time:
Time : 1. s 12/112008 9:44 AM 121111200B AM
- Moment: 2.7487 Ibflin 2.74B7 Ibfin
- Moment 2: 2: 4.111 4.1118B Ibfin Ibflin
- Moment 3: 2.8888 Ibf-in 3: 2.BBBB Ibf-in
- Moment 4: 59596 lbfin
- Moment 5: 22.463 Ibf'in
- Moment 6: 6: 5.067 lb
- Moment 7: 7:1.2317 1.2317 E Moment B:: 0.742441 0.74244 bfbi Moment Moment 9: 9:0.41921 0.41921 Ibf.I 1
Moment 110: 0: 1.7222 Ib 1 z
0.000 (in) 3.000 (in) L x 1
1.500 1.500 Figure 28b. Forces and moments.
125 125
This Document Does Not Contain Continuum Dynamics, Information Dynamics, Inc. Proprietary Information Stress stress Intensity J Type: Stress Intensity- ToplBottom Intensity - Top/Bottom Unit: psi Time: 1I AM 12111/2008 9:51 AM 12/11/2008 3000 Max 2743.7 Max 2500 2250 2000 1750 1750 1500 1500 1250 1000 1000 750 750 500 250 25.701 Min Min
-- 0o z
Z 0.000 1.500 I
(in) 3.000 (in) J-'
)*__'11 1 Y
Figure 28c. Shell sub-model contours. Stress intensity: 2744 psi.
sub-model stress contours.
126 126
This Document Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information z
1III
_ _II:=~2j.oOO(in) 1.000 I
A
,{ t
~y Proposed additional weld Proposed additional weld z
t .,.I Y 1 .500 "-x Figure 29a. Solid model geometry.
127 127
Inc. Proprietary Information This Document Does Not Contain Continuum Dynamics, Inc. Information Figure 29b. Solid mesh. Mesh parameters:
parameters: 567369 nodes, 133680 133680 elements.
128 128
This Document Does Not Contain Contain Continuum Dynamics, Inc.
Inc. Proprietary Proprietary Information Information NODAL SOLUTION J\N STEP=1 STEP=l SUB =1 SUB =1 TIME=1 TIME=l SINT SINT (AVG)
(AVG)
DMX =.004133
= . 004133 SMN =1.847 SMX =6458 0 1200 2400 600 1800 3000 3000 Figure 29c. Stress intensity intensity contours (total) in solid sub-model. Parts of the structure removed to show show internal internal stress distribution (bottom).
129 129
Continuum Dynamics, Inc. Proprietary This Document Does Not Contain Continuum Information Proprietary Information Figure 30. Linearization Linearization paths at the additional weld for sub-model node 100327.
Linearized stresses along the linearization paths shown in Figure 30.
Table 14. Linearized Path Membrane + bending Membrane bending linearized stress intensity, psi AB 1589 1589 AC 439 439 AD 724 724 BE 2406 AF 488 130 130