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
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.2 Load Combinations, and Allowable Stress Intensities The stress ratios computed for CLTP at nominal frequency and with frequency shifting are listed in Table 9. The stress ratios are grouped according to type (SR-P for maximum membrane and membrane+bending stress, SR-a for alternating stress) and location (away from welds or on a weld). The tabulated nodes are also depicted in Figure 14 (no frequency shift) and Figure 15 (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 display all nodes with SR-a_<5.
For CLTP operation at nominal frequency the minimum stress ratio is identified as a maximum stress, 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 be seen from the high alternating stress ratio at this location (SR-a>16.5 at all frequency shifts).
This is true for all three nodes having the lowest values of SR-P, all having 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 accounted for by identifying the minimum stress ratio at every node, where the minimum is taken over all the frequency shifts 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 by stress type (maximum or alternating) and location (on or away from a weld). The results are summarized in Table 9b and show that the lowest stress ratio, SR-P=1.34, occurs at the same 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 stress ratio, SR-a=2.89 occurs at the common intersection point of the bottom of the inner hood, hood support and base plate (see Figure 15f). Hood supports are also involved in locations 3-5, 10-11 and 15. The next lowest SR-a location involves the lifting rod support brace (Figure 15g) involving locations 2 and 7. The remaining low alternating stress ratio locations occur on: (i) closure plates (locations 9 and 16); (ii) tie bar ends or their immediate vicinity (locations 12 and 14); or (iii) the hoods.
The estimated alternating stress ratio at EPU operation is obtained by scaling the corresponding value at CLTP by the square of the ratio of the steam flow velocities at EPU and CLTP conditions. Since this ratio, (UEPUCLTp)2=l.178 2=1.388, the limiting alternating stress ratio at any frequency shift for EPU is estimated as SR-a=2.89/1.388=2.08. This value qualifies the Unit 2 dryer at EPU conditions with considerable margin. The limiting stress ratio, SR-P, is dominated by the static load and has a weaker dependence on power. When this node is reanalyzed with the MSL signals increased by 1.388, the limiting SR-P reduces to 1.32 at EPU.
In summary, the lowest alternating stress ratio occurs at the base of the inner hood support where it is welded to the middle base plate and vertical vane bank support. Its value, SR-a=2.89 at the -5% frequency shift indicates that stresses are well below allowable levels. The lowest stress ratio associated with a maximum stress is SR-P=1.34 at CLTP. This value is dominated by the static component and is only weakly altered by acoustic loads (it reduces to 1.32 at EPU).
Since acoustic loads scale roughly with the square of the steam flow, the limiting alternating 63 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.2 Load Combinations. and Allowable Stress Intensities The stress ratios computed for CLTP at nominal frequency and with frequency shifting are listed in Table 9. The stress ratios are grouped according to type (SR-P for maximum membrane and membrane+bending stress, SR-a for alternating stress) and location (away from welds or on a weld). The tabulated nodes are also depicted in Figure 14 (no frequency shift) and Figure 15 (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 display all nodes with SR-a:::;;5.
For CLTP operation at nominal frequency the mInImUm stress ratio is identified as a maximum stress, 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 be seen from the high alternating stress ratio at this location (SR-a>16.5 at all frequency shifts).
This is true for all three nodes having the lowest values of SR-P, all having 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 accounted for by identifying the minimum stress ratio at every node, where the minimum is taken over all the frequency shifts 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 by stress type (maximum or alternating) and location (on or away from a weld). The results are summarized in Table 9b and show that the lowest stress ratio, SR-P=1.34, occurs at the same 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 stress ratio, SR-a=2.89 occurs at the common intersection point of the bottom of the inner hood, hood support and base plate (see Figure 15i). Hood supports are also involved in locations 3-5, 10-11 and 15. The next lowest SR-a location involves the lifting rod support brace (Figure 15g) involving locations 2 and 7. The remaining low alternating stress ratio locations occur on: (i) closure plates (locations 9 and 16); (ii) tie bar ends or their immediate vicinity (locations 12 and 14); or (iii) the hoods.
The estimated alternating stress ratio at EPU operation is obtained by scaling the corresponding value at CL TP by the square of the ratio of the steam flow velocities at EPU and CLTP conditions. Since this ratio, (UEPulUcLTPi=1.1782=1.388, the limiting alternating stress ratio at any frequency shift for EPU is estimated as SR-a=2.89/l.388=2.08. This value qualifies the Unit 2 dryer at EPU conditions with considerable margin. The limiting stress ratio, SR-P, is dominated by the static load and has a weaker dependence on power. When this node is reanalyzed with the MSL signals increased by 1.388, the limiting SR-P reduces to 1.32 at EPU.
In summary, the lowest alternating stress ratio occurs at the base of the inner hood support where it is welded to the middle base plate and vertical vane bank support. Its value, SR-a=2.89 at the -5% frequency shift indicates that stresses are well below allowable levels. The lowest stress ratio associated with a maximum stress is SR-P=1.34 at CLTP. This value is dominated by the static component and is only weakly altered by acoustic loads (it reduces to 1.32 at EPU).
Since acoustic loads scale roughly with the square of the steam flow, the limiting alternating 63
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information stress ratio at EPU reduces to 2.08, which given that the applied loads already accourit for all end-to-end biases and uncertainties, still contains ample margin for sustained EPU operation.
64 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information stress ratio at EPU reduces to 2.08, which given that the applied loads already.accourit for all end-to-end biases and Uncertainties, still contains ample margin for sustained EPU operation.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9a. Locations with minimum stress ratios for CLTP conditions with no frequency shift. 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 minimum stress ratio of any type on the structure. Locations are depicted in Figure 14.
Stress Weld Location Location (in.)
node(a)
Stress Intensity (psi)
Stress Ratio Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a SR-P No
- 1. Inner Side 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 4759 5171
<250 3.55
>27
- 3. Support/Seismic Block 10.2 123.8
-9.5 113286 4354 4354 1374 3.88 9.00 SR-a No Middle Hood
-68.9 69.6 41.6 31054 1717 2759 2728 9.19 4.53 SR-P.
Yes' 1; Side Plate-ExtInnerBase Plate 16:3.*I9
- 0 94143'
- 6913,
'09809',
438 1.34" 15.67 it
- 2. Upper Support Ring/Support/Seismic Block
-6.9
-122.3
-9.5 113554 6238 6238 911 1.49 7.54 If
- 3. Tie Bar 49.3 108.1 88 141275 5962 5962 807 1.56 8.51
- 4. Hood Support/Middle Base Plate/Inner 39.9
-59.5 0
101435 5352 5488 1638 1.74 4.19 Backing Bar/Inner Hood
- 5. Inner Side Plate/Inner Base Plate
-2.3
-119 0
99200 4419 7921 511 1.76 13.44
- 6. Closure Plate/Inner Backing Bar Out/Inner 39.9 108.6 0.5 93062 5232 5253 851 1.78 8.07 Backing Bar/Inner Hood
-7. Hood Support/Outer Base Plate/Middle
-71.3 0
0 95428 - 4800 4876 1817 1.94 3.78 Backing Bar
- 8. Side Plate/Top Plate 17.6 119 88 91215 898 7174 1337 1.94 5.14
- 9. Outer Cover Plate/Outer Hood 102.8
-58.1 0
94498 1020
.7053 763 1.98 9.01
- 10. Hood Support/Middle Base Plate/Inner
-39.9 0
0 85723 4684 4849 1842 1.98 3.73 Backing Bar/Inner Hood(6 )
- 11. Thin Vane Bank Plate/Hood Support/Inner 24.1
-59.5 0
85191 4385 4439 772 2.12 8.90 Base Plate.
Notes.
(a)
Node numbers are retained for further reference.
(1-9)
Appropriate stress reduction factor for the welds and modifications listed in Table 7 have been applied. The number refers to the particular location and corresponding stress reduction factor in Table 7.
65 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9a. Locations with minimum stress ratios for CL TP conditions with no frequency shift. 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 minimum stress ratio of any type on the structure. Locations are depicted in Figure 14.
Notes.
(a)
(1-9)
Stress Weld Location Location (in.)
node(a)
Stress Intensity (psi)
Stress Ratio Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a SR-P No
- 1. Inner Side 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 4759 5171
<250 3.55
>27
- 3. Support/Seismic Block 10.2 123.8
-9.5 113286 4354 4354 1374 3.88 9.00 SR-a No Middle Hood
-68.9 69.6 41.6 31054 1717 2759 2728 9.19 4.53
- ,SR-;P. 'Yes' 1; Side Plate ExtllnrierBase Plate,
.,(."
., ;'16:3,, :'119. '
.'~,().
94.143"
'6913,,~'98()9.
.~38', 'i;34~:' IS:§7;
- 2. Upper Support Ring/Support/Seismic Block
-6.9
-122.3
-9.5 113554 6238 6238 911 1.49 7.54 II
- 3. Tie Bar 49.3 108.1 88 141275 5962 5962 807 1.56 8.51
- 4. Hood Support/Middle Base Plate/Inner 39.9
-59.5 0
101435 5352 5488 1638 1.74 4.19 Backing Bar/Inner Hood
- 5. Inner Side Plate/Inner Base Plate
-2.3
-119 0
99200 4419 7921 511 1.76 13.44
- 6. Closure Plate/Inner Backing Bar Out/Inner 39.9 108.6 0.5 93062 5232 5253 851 1.78 8.07 Backing Bar/Inner Hood
-7; Hood Support/Outer Base Plate/Middle
-71.3 0
0 95428* 4800 4876 1817 1.94 3.78 Backing Bar
- 8. Side Plate/Top Plate 17.6 119 88 91215 898 7174 1337 1.94 5.14 9.0uter Cover Plate/Outer Hood.
102.8
-58.1 0
94498 1020
- 7053 763 1.98 9.01
- 10. Hood Support/Middle Base P!ate/lnner
-39.9 0
0 85723 4684 4849 1842 1.98 3.73 Backing Bar/Inner Hood(6)
- 11. Thin Vane Bank Plate/Hood Support/Inner 24.1
-59.5 0
85191 4385 4439 772 2.12 8:90 Base Plate Node numbers are retained for further reference.
Appropriate stress reduction factor for the welds and modifications listed in Table 7 have been applied. Tiienumber refers to the particular location and corresponding s~ess re~uction factor in Table 7.
65
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9a (cont.). Locations with minimum stress ratios for CLTP conditions with no frequency shift. 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 minimum alternating stress ratio on the structure. Locations are depicted in Figure 14.
Stress Weld Location Location (in.
node(a)
Stress Intensity (psi)
Stress Ratio Ratio y
z Pm
-Pm+Pb Salt SR-P SR-a SR-a Yes
- 1. Hood Support/Inner Hood 36.2 0
50.8 99529 975 2316 2290 6.02 3.00 V1
- 2. Hood Support/Inner Hood 39.1 0
23 99515 842 2064 1977 6.75 3.47 if
- 3. Hood Support/Inner Hood 34.3 0
62.7 99535 826 2319 1970 6.01 3.49
- 4. Closure Plate/Middle Hood
-68.7 85.2 42.9 91590 693 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,
- 6. Side Plate/Brace(5)
-79.7 85.2 75.8 103160 1529 2892 1897 4.82 3.62
- 7. Hood Support/inner Hood( 7).
38 0
36.9 99522 741 1886 1860 7.39 3.69
- 8. Hood Support/Middle Base Plate/Inner
-39.9 0
0, 85723 4684 4849 1842 1.98 3.73 Backing Bar/Inner Hood( 6 )
- 9. Side Plate/Brace 79.7 85.2 31.2 89646 1447-2182 1820 6.39 3.77 Notes.
(a)
(1-9)
Node numbers are retained for further reference.
Appropriate stress reduction factor for the welds and modifications listed in Table 7 have been applied.
particular location and corresponding stress reduction factor in Table 7.
The number refers-tofthe 66 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9a (cont.). Locations with minimum stress ratios for CLTP conditions with no frequency shift. 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 minimum alternating stress ratio on the structure. Locations are depicted in Figure 14.
Notes.
(a)
(1-9)
Stress Weld
. Location
.. "Location (in.)
node(a)
Stress Intensi~ (psi)
Stress Ratio Ratio "X
y z
Pm
- Pm+Pb Salt SR-P SR-a SR-a Yes
- 1. Hood Support/Inner Hood 36.2 0
50.8 99529 975 2316 2290 6.02 3.00
- 2. Hood Support/Inner Hood 39.1 0
23 99515 842 2064 1977 6.75 3.47
- 3. Hood Support/Inner Hood 34.3 0
62.7 99535 826 2319 1970 6.01 3.49
- 4. Closure Plate/Middle Hood
-68.7 85.2 42.9 91590 69-3 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.
". 6. Side Plate/Brace(5)
-79.7 85.2 75.8 103160 1529 2892 1897 4.82 3.62 7~ Hood Support/Inner Hood(7).
38 0
36.9 99522 741 1886 1860 7.39 3.69
- 8. Hood Support/Middle Base Plate/Inner
-39.9 0
O.
85723 -. 4684 4849
- 1847 1.98 3.73
. Ba~king Bar/Inner Hood(6)
- 9. Side Plate/Brace 79.7 85.2 31.2 89646 1447 2182 1820 6.39 3.77 Node numbers are retained for further reference.
Appropriate stress reduction factor for the welds and modifications listed in Table 7 have been applied. The-number refets*tothe particular location and correspo~ding stress reduction factor in Table 7.
66
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9b. Locations with minimum stress ratios for CLTP conditions with frequency shifts. Stress ratios at every node are recorded as the lowest stress ratio 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 minimum stress ratio of any type on the structure. Locations are depicted in Figure 15.
Stress Weld Location Location (in.)
node(a)
Stress Intensity (psi)
Stress Ratio
% Freq.
Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a Shift SR-P No
- 1. Inner Side Plate 3.1 119 0.5 37229 7490 9003 634 2.26 19.51 10
- 2. Support/Seismic Block 10.2 123.8
-9.5 113286 4829 4829 2019 3.5 6.12 5
- 3. Thin Vane Bank Plate
-15.6
-118.4 0.6 2558 4792 5212 0
3.53 1360 2.5 SR-a No
- 1. Middle Hood
-68.6 69.6 43.7 31149 1717 2953 2914 8.59 4.24 2.5 SR-P Yes
- 1. Side Plate Ext/Inner Base Plate 16.3 119 0
-94143 -
6918 9809 478 1.34 14.38.
5
-2. USR/Support/Seismic Block
-6.9
-122.3
-9.5-113554 6688 6688 1342 1.39 5.12 5
it
- 3. Tie Bar
-49.3
-108.1 88 143795 6077 6077 877 1.53 7.83 5
- 4. Hood Support/Middle Base Plate/Inner.
39.9
-59.5 0
101435 5495 5819 1815 1.69 3.78
-10 Backing Bar/Inner Hood
- 5. Closure Plate/Inner Backing r39.9
-108.6 0.5 84198 5492 5499 1160 1.69 5.92 5
Bar/Inner Backing Bar/Inner Hood
- 6. Inner Side Plate/Inner Base Plate
-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 1.9-4.33 5
- 8. Hood Support/Outer Base
-71.3
- - 0 0
95428 4800 4876 1817 1.94 3.78 0
Plate/Middle Backing Bar
- 9. Outer Cover Plate/Outer Hood 102.8
-58.1 0
94498 1066 7197 910 1.94 7.55 10
- 10. Hood Support/Middle Base 39.9 0
0 88639 4733 4874 1883 1.96 3.65 2.5 Plate/inner Backing Bar/Inner Hood( 6)
- 11. Thin Vane Bank Plate/Hood
- -24.1 59.5 0
99487 4707 4724 1091 1.97 6.3 10 Support/Inner Base P.late
- 12. Hood Support/Outer Cover
-102.8 28.4 0
95267 4451 4533 1942 2.09 3.54 5
Plate/Outer Hood( 7 )
Notes.
(a)
Node numbers are retained for further reference.
(1-9)
Appropriate stress reduction factor for the welds and modifications listed in Table 7 have been applied. The number refers to the particular location and corresponding stress reduction factor in Table 7.
67 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9b. Locations with minimum stress ratios for CLTP conditions with frequency shifts. Stress ratios at every node are recorded as the lowest stress ratio 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 minimum stress ratio of any type on the structure. Locations are depicted in Figure 15.
Notes.
(a)
(1-9)
Stress Weld Location Location (in.)
node(a)
Stress Intensity (psi)
Stress Ratio
% Freq.
Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a Shift SR-P No
- 1. Inner Side Plate 3.1 119 0.5 37229 7490 9003 634 2.26 19.51 10 It It 2: Support/Seismic Block 10.2 123.8
-9.5 113286 4829 4829 2019 3.5 6.12 5
It It
- 3. Thin Vane Bank Plate
-15.6
-118.4 0.6 2558 4792 5212 0
3.53 1360 2.5 SR-a No
- 1. Middle Hood
-68.6 69.6 43.7 31149 1717 2953 2914 8.59 4.24 2.5 SR-P Yes
- 1. Side Plate Ext/Inner Base plate 16.3 119 0
,,941~3, _ 6918 9809 478 1.34 14.38*
5
-2. USR/Support/Seismic Block
-6.9
-122.3
-9.5-113554 6688 6688 1342 1.39 5.12 5
It It
- 3. Tie Bar
-49.3
-108.1 88 143795 6077 6077 877 1.53 7.83 5
It
- 4. Hood Support/Middle Base Plate/Inner, 39.9
-59.5 0
101435 5495 5819 1815 1.69 3.78
-10 Backing Bar/Inner Hood It
- 5. Closure Plate/Inner Backing
- -39.9
-108.6 0.5 84198 5492 5499 1160 1.69 5.92 5
Bar/Inner Backing Bar/Inner Hood
- 6. Inner Side Plate/Inner Base Plate
-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 1.9, 4.33 5
It
- 8. Hood Support/Outer Base
-71.3 0
0 95428 4800 4876 1817 1.94 3.78 0
Plate/Middle Backing Bar It It
- 9. Outer Cover Plate/Outer Hood 102.8
-58.1 0
94498 1066 7197 910 1.94 7.55 10 It
- 10. Hood Support/Middle Base 39.9 0
0 88639 4733 4874 1883 1.96 3.65 2.5 Plate/Inner Backing Bar/Inner H'ood(6)
- 11. Thin Vane Bank Plate/Hood
- -24.1 59.5 0
99487 4707 4724 1091 1.97 6.3 10 Support/Inner Base ~Iate
- 12. Hood Support/Outer Cover
-102.8 28.4 0
95267 4451 4533 1942 2.09 3.54 5
Plate/Outer Hood(7)
Node numbers are retained for further reference.
Appropriate stress reduction factor for the welds and modifications listed in Table 7 have been applied. The number refers to the particular location and corresponding stress reduction factor in Table 7.
67
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9b (cont.). Locations with minimum stress ratios for CLTP conditions with frequency shifts. Stress ratios at every node are recorded as the lowest stress ratio 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). Locations aredepicted in Figure 15.
Stress Weld Location Location (in.
node(a)
Stress Intensity (psi)
Stress Ratio
% Freq.
Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a Shift SR-a Yes
- 1. Hood Support/Middle Base
-39.9 0
0 85723 4695 4849 2378 1.98 2.89
-5 Plate/Inner Backing Bar/Inner Hood( 6)
- 2. Side Plate/Brace(5 )
79.7 85.2 75.8 89649 2002 2884 2343 4.64 2.93 10
- 3. Hood Support/Inner Hood 36.2 0
50.8 99529 975 2316 2290 6.02
-3.00 0
- 4. Hood Support/Middle Base Plate/
-39.9 59.5 0
90468 5397 5524 2277 1.72 3.02
-5 Inner Backing Bar/Inner Hood _ _
- 5. Hood Support/Outer Hood
-96.4
-28.4 66.8 90186 657 2332 2234 5.98 3.07 5
- 6. Hood Reinforcement/Middle Hood
-62.6 101.2 77.9 98277 442 2408 2223 5.79 3.09
-10
- 7. Side Plate/Brace
-79.7
-85.2 31.2 84708 1818 2636 2175 5.11 3.16 2.5
- 8. Outer End Plate/Outer Hood
-97.5
-70 60.8 99212 802 2212 2165 6.30 3.17 5
- 9. Side Plate/Closure Plate/Exit Mid Bottom Perf
-78.5
-85.2 56.5 87780 524 2241 2147 6.22
-3.20-7.5
- 10. Hood Support/Inner Backing Bar/Inner Hood
-39.9 0
1 95620 1943 3082 2100 4.52 3.27
-5
- 11. Hood Support/Inner Hood 34.3 0 62.71 99535 826 2451 2096 5.69 3.28
-10
- 12. Top Plate/Tie Bar
-17.6
-0.5 88 75048 1127 3064 2080 4.55 3.30 2.5
- 13. Top Thick Plate/Side Plate/Exit Top.
-15.6 119 86.5 98451 816 2970 2070 4.70 3.32 2.5 Perf/Inner Side Plate
- 14. Double Side Plate/Top Plate
-54
-54.3 88 85117 587 2323 2032 6.00 3.38 2.5
- 15. Hood Support/Outer Hood( 7 )-
-97.8
-28.4 59 85774 488 2129 2027 6.55 3.39 5
- 16. Closure Plate/Middle Hood 68.7 85.2 42.9 91590 710 2041 2022 6.83 3.40 2.5 (a)
Node numbers. are retained for further reference.
(1-9)
Appropriate stress reduction factor for the welds-and modifications listed in Table 7 have been applied. The number refers to the particular-location and corresponding stress reduction-factor in Table 7.
68 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9b (cont.). Locations with minimum stress ratios for CLTP conditions with frequency shifts. Stress ratios at every node are recorded as the lowest stress ratio 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). Locations are-depicted in Figure 15.
Stress Weld Location Location (in.)
node(a)
Stress Intensity (psi)
Stress Ratio
% Freq.
Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a Shift SR-a Yes
- 1. Hood Support/Middle Base
-39.9 0
0 85723 4695 4849 2378 1.98 2.89
-5 Plate/Inner Backing Bar/Inner tiDod(6) 2: Side Plate/Brace(5) 79.7 85.2 75.8 89649 2002 2884 2343 4.64 2.93 10
. ~,
- 3. Hood Support/Inner Hood -
36.2 0
50.8,99529 975 2316 2290 6.02
,3.00, 0
- 4. Hood Support/Middle Base Plate/
-39.9 59.5 0
90468 5397 5524 2277 1.72 3.02
-5 Inner Backing Bar/Inner Hood, -
- 5. Hood Support/Outer Hood
-96.4
-28.4,96.8 90186 657 2332 2234 5.98 3.07 5
- 6. Hood Reinforcement/Middle Hood
-62.6 101.2 77.9 98277 442 2408 2223 5.79 3.09
-10
- 7. Side Plate/Brace
-79.7
-85.2 31.2 84708 1818 2636 2175 5~11 3.16 2.5
- 8. Outer End Plate/Outer Hood
-97.5
-70 60.8 99212 802 2212 2165 6.30 3.17 5
- 9. Side Plate/Closure Plate/Exit Mid Bottom Perf
-78.5
-85.2 56.5 87780 524 2241 2147 6.22 -3.20 7.5
- 10. Hood Support/Inner Backing Bar/Inner Hood
-39.9 0
1 95620 1943 3082 2100 4.52 3.27
-5
- 11. Hood Support/Inner Hood
, 34.3 0
62.7., -, 99535 826 2451 2096 5.69 3.28
-10
- 12. Top Plate/Tie Bar
-17.6
-0.5 88 75048 1127 3064 2080 4.55 3.30 2.5
- 13. Top Thick Plate/Side Plate/Exit Top
-15.6 119 86.5 98451 816 2970 2070 4.70 3.32 2.5 Perf/Inner Side Plate
- 14. Double Side Plate/Top Plate
-54
-54.3 88
- 85117, 587 2323 2032 6.00 3.38 2.5
- 15. Hood Support/Outer Hood(7)
-97.8
-28.4 59 85774 488 2129 2027 6.55 3.39 5..
- 16. Closure Plate/Middle Hood
-68.7 85.2 '42.9 91590 710 2041 2022 6.83 3.40 2.5
( a)
Node numbers, are retained for further reference.
(1-9)
Appropriate stress reduction factor for the welds and modifications listed in Table 7 have been applied. The number refers to the particular-location and corresponding stress reduction factor in Table 7, 68
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 14a. Locations of nodes with stress ratios, SR-P<5, associated with a maximum stress at non-welds for nominal CLTP operation. Numbers refers to the enumerated locations for SR-P values at non-welds in Table 9a.
69 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary 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 of nodes with stress ratios, SR-P::;5, associated with a maximum stress at non-welds for nominal CLTP operation. Numbers refers to the enumerated locations for SR-P values at non-welds in Table 9a.
69
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 14b. Locations of smallest alternating stress ratios, SR-a<5, at non-welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-a values at non-welds in Table 9a.
70 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Y'vi/
SR-a 5
4.9 4.8 4.7 4.6 4.5 x
Figure 14b. Locations of smallest alternating stress ratios, SR-a:::;S, at non-welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-a values at non-welds in Table 9a.
70
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information SR-P 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 Figure 1 4c. Locations of smallest stress ratios, SR-P<4A associated with maximum stresses at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 9a. This view shows locations 1, 3, 6, 8 and 9.
71 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z A y 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 14c. Locations of smallest stress ratios, SR-Ps4, associated with maximum stresses at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 9a. This view shows locations 1,3,6,8 and 9.
71
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
[]
z SR-P 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 14d. Locations of minimum stress ratios, SR-P_<4, associated with maximum stresses at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 9a. This view shows locations 2, 3, 5, 8 and 9.
72 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
k X SR-P 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 14d. Locations of minimum stress ratios, SR-P~4, associated with maximum stresses at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 9a. This view shows locations 2,3,5,8 and 9.
72
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 14e. Locations of minimum stress ratios, SR-P<4, associated with maximum stresses at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 9a. This view shows locations 4, 7, 10 and 1 73 This Document Does Not Contain Continuum Dynamics, Inc. 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 14e. Locations of minimum stress ratios, SR-P:::;4, associated with maximum stresses at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 9a. This view shows locations 4, 7, 10 and 1 73
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 14f. Locations of minimum alternating stress ratios, SR-a<5, at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-a values at welds in Table 9a.
Locations 1-5, 7 and 8 are shown.
74 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information SR-a 5
4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 3
Figure 14f. Locations of minimum alternating stress ratios, SR-as5, at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-a values at welds in Table 9a.
Locations 1-5, 7 and 8 are shown.
74
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
x Figure 14g. Locations of minimum alternating stress ratios, SR-a_<5, at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-a values at welds in Table 9a.
Locations 4, 6 and 9 are shown.
75 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
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 -a:s;5, at welds for nominal CL TP operation. Numbers refer to the enumerated locations for SR-a values at welds in Table 9a.
Locations 4,6 and 9 are shown.
75
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15a. Locations of minimum stress ratios, SR-P<5, associated with maximum stresses at non-welds for CLTP operation with frequency shifts. The recorded stress ratio is the minimum value taken over all frequency shifts. The numbers refers to the enumerated location for SR-P values at non-welds in Table 9b.
76 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 Figure 15a. Locations of minimum stress ratios, SR-P~5, associated with maximum stresses at non-welds for CL TP operation with frequency shifts. The recorded stress ratio is the minimum value taken over all frequency shifts. The numbers refers to the enumerated location for SR-P values at non-welds in Table 9b.
76
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15b. Locations of minimum alternating stress ratios, SR-a<5, at non-welds for CLTP operation with 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-a values at non-welds in Table 9b.
77 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15b. Locations of minimum alternating stress ratios, SR-a~5, at non-welds for CLTP operation with 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-a values at non-welds in Table 9b.
77
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
[]
z SR-P 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 15c. Locations of minimum stress ratios, SR-P<4, associated with maximum stresses at welds for CLTP operation with 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 shows locations 1, 3, 7 and 9.
78 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information SR-P 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 15c. Locations of minimum stress ratios, SR-P:::;4, associated with maximum stresses at welds for CL TP operation with 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 shows locations 1,3, 7 and 9.
78
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information SR-P 3.9 3.7 12 3.5 3.3 3.1 2.9 2.7 2.5 5
2.3 2.1 2
1.9 1.7 1.5 Figure 15d. Locations of minimum stress ratios, SR-P(4, associated with maximum stresses at welds for CLTP operation with 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 shows locations 2, 3, 5-7 and 12.
79 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 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 l5d. Locations of minimum stress ratios, SR -P:S;4, associated with maximum stresses at welds for CL TP operation with 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 shows locations 2, 3, 5-7 and 12.
79
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information x
2.9 2.7 2.1 1.9 Figure 15e. Locations of minimum stress ratios, SR-P<4, at welds for CLTP operation with 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.
80 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 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 15e. Locations of minimum stress ratios, SR-P~4, at welds for CLTP operation with 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.
80
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15f.
Locations of minimum alternating stress ratios, SR-a<<5, at welds for CLTP operation with 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-a values at welds in Table 9b. This view from below shows locations 1, 3, 4, 10 and 11 all on hood welds.
81 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary 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.
Locations of minimum alternating stress ratios, SR-a:::;5, at welds for CLTP operation with 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-a values at welds in Table 9b. This view from below shows locations 1, 3, 4, 10 and 11 all on hood welds.
81
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
x Y
SR-a 5
4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 32.8 Figure 15g.
Locations of minimum alternating stress ratios, SR-a<5, at welds for CLTP operation with 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-a values at welds in Table 9b. This view shows locations 2 and 12-14.
82 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary 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 15g.
Locations of minimum alternating stress ratios, SR-a:::;5, at welds for CLTP operation with 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-a values at welds in Table 9b. This view shows locations 2 and 12-14.
82
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15h.
Locations of minimum alternating stress ratios, SR-a<5, at welds for CLTP operation with 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-a values at welds in Table 9b. Close-up view showing locations 5, 6, 12 and 14-16.
83 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary 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.
Locations of minimum alternating stress ratios, SR-a:::;5, at welds for CLTP operation with 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-a values at welds in Table 9b. Close-up view showing locations 5, 6, 12 and 14-16.
83
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15i.
Locations of minimum alternating stress ratios, SR-a<5, at welds for CLTP operation with 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-a values at welds in Table 9b. Close-up view around locations 5, 7-9 and 15.
84 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary 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 lSi.
Locations of minimum alternating stress ratios, SR-aS;5, at welds for CLTP operation with 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-a values at welds in Table 9b. Close-up view around locations 5, 7-9 and 15.
84
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.3 Frequency Content and Filtering of the Stress Signals The. frequency contribution to the stresses can be investigated by examining the power spectral density (PSD) curves and accumulative PSDs for selected nodes having low alternating stress ratios. The accumulative PSDs are computed directly from the Fourier coefficients as Z~~~~Y*n)
(O)2 where C(ok) is the complex stress harmonic at frequency, ok. Accumulative PSD plots are useful for determining the frequency components and frequency ranges that make the largest contributions to the fluctuating stress.
Unlike PSD plots, no "binning" or smoothing of frequency components is needed to obtain smooth curves. Steep step-like rises in Z(co) indicate the presence of a strong component at a discrete frequency whereas gradual increases in the curve imply significant content over a broader frequency range.
From Parsival's theorem, equality between Y((oN) (where N is the total number.of frequency components) and the RMS of the stress. signal in the time domain is established.
The selected nodes are the ones having the lowest alternating stress ratios (at a weld) in Table 9b. These are:
Node 85723 - located on the inner hood/hood support/middle base plate junction. The associated PSDs are shown in Figure 16a.
Node 89649 - located on the lifting rod brace/vane bank end plate connection.
The associated PSDs are shown in Figure 16b.
Node 99529 - located on the weld joining the inner hood and hood support. The associated PSDs are shown in Figure 16c.
Node 99212 - located on the weld joining the outer hood and its end plate. The associated PSDs are shown in Figure 16d.
Node 87780 - located on the weld joining the closure plate to the outer closure plate to the outer vane bank. The associated PSDs are shown in Figure 16e.
These are the nodes labeled 1-3, 8 and 9 in Table 9b and accompanying Figure 15f-i.
In each case, since there are six stress components and up to three different section locations for shells (the top, mid and bottom surfaces), there is a total of 18 stress histories per component.
Moreover, at junctions there are at least two components that meet at the junction. The particular stress component that is plotted is chosen as follows. First, the component and section location (top/mid/bottom) is taken as the one that has the highest alternating stress. This narrows the selection to six components. Of these, the component having the highest Root Mean Square (RMS) is selected.
The first node (85723), is dominated by a broad peak centered at 71 Hz. The frequency shifted curves do not differ significantly from the non-shifted results. Judging from the PSD curves, it appears that in the non-shifted case there are two peaks about 71 Hz, with one - the 85 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.3 Frequency Content and Filtering of the Stress Signals.
The, frequency contribution to the stresses can be investigated by examining the power spectraL density (PSD) curves and accumulative PSDs for selected nodes having lowalte~ating stress ratios. The accumulative PSDs are computed directly from the Fourier coefficients as where &(rok) is the complex stress harmonic at frequency, rok. Accumulative 'PSD plots are useful for determining the"frequency coinponent~ an4freq~ency ranges that make the largest contributions to the fluctuating stress.
Unlike PSD' plots, no "binning" or smoothing of frequency components is needed to obtain smooth curves. $teep step-like rises in L(ro) indicate the,presence of a strong component at a discrete frequency whereas gradual increases in the curve imply significant content over a broader fre,quency range.
From Parsival's theorem, equalio/ between L(roN) (whereN is the total numbero.ffr~queIl.~y components) and the RMS of the stress signal in the time, domain is established.
The selected nodes are the ones having the lowest alternating stress ratios (at a weld) in Table 9b. These are:
Node 85723 - located on the inner hood/hood support/middle base plate junction. The associated PSDs are shown in Figure 16a.
Node 89649 - located on the lifting rod brace/vane bank end plate connection.
The associated PSDs are shown in Figure 16b.
Node 99529 - located on the weld joining the inner hood and hood support. The associated PSDs are shown in Figure 16c.
Node 99212 - located on the weld joining the outer hood and its end plate. The associated PSDs are shown in Figure 16d.
Node 87780 - located on the weld joining the closure plate to the outer closure plate to the outer vane bank. The associated PSDs are shown in Figure 16e.
These are the nodes labeled 1-3, 8 and 9 in Table 9b and accompanying Figure 15f-i.
In each case, since there are six stress components and up to three different section locations for shells (the top, mid and bottom surfaces), there is a total of 18 stress histories per component.
Moreover, at junctions there are at least two components that meet at the junction. The particular stress component that is plotted is chosen as follows. First, the component and section location (top/midlbottom) is taken as the one that has the highest alternating stress. This narrows the selection to six components. Of these, the component having the highest Root Mean Square (RMS) is selected.
The first node (85723), is dominated by a broad peak centered at 71 Hz. The frequency shifted curves do not differ significantly from the non-shifted results. Judging from the PSD curves, it appears that in the non-shifted case there are two peaks about 71 Hz, with one - the 85
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information lower frequency one - being dominant. When the signal is shifted, the forcing on the lower,.,
frequency mode is reduced and that on the higher frequency mode increases. Interestingly, the combined effect is to effectiviely shift, the peak frequency upward even though the signal is shifted 'downward (as is clear by comparing some of the other peaks). This is effect is readily explainable in the context of the complex multi-modal system being considered here. Frequency, shifting has a more 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% frequency shift. The higher frequency peak, appears to shift and attenuate with the frequency shift in the signal.
The third node is dominated by a 45.4 Hz peak. This dominance appears to be spatially localized meaning that the number of locations on the dryer where this is.the dominant frequency, are few. However, the same frequency peak shows up in the limiting location at node 85723 'which also involves the inner hood suggesting that the inner hood is *responsive to acoustic signals at this frequency. The stress response at node 99212 is also characterized by a single dominant the' dominant peak, this time at a frequency 'between 69 and 71 Hz. This frequency characterizes most 'of the surface on the outer panels of the outer hood on the MSL C/D side. Finally for node 87780, the dominant stress contributions occur at higher frequencies.
Without frequency shifting the dominant frequency is 180.0 Hz which coincides with a multiple of electrical noise (60 Hz - note however, that the electrical noise is filtered).
At the +7.5% shift the dominant frequency is at 184.5 Hz which corresponds to' 171.6 Hz in the original non-shifted signal.
86 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information '
lower frequency one - being dominant. When the signal is,shifted, the forcing on the lower ',. '
frequency mode is reduced and that on the higher frequency mode increases. Interestingly, the combined effect is to effectively shift, the peak frequency upward even though the 'signal: is shifted 'downward (as is clear by comparing some of the other peaks). This is effect is readily explainable in the context of the complex ITlUlti-modal system being considered here. Frequency*
shifting has a more 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 + 1 0% frequency shift. The higher frequency peak appears to shift and attenuate with the frequency shift in the signal.
The third node is dominated by a 45.4 Hz peak.
This dominance appears to be spatially localized meaning that the number of locations on the dryer where this is the ;dominant frequency, are few., Howe:v~r, the same frequency peak shows up in the limiting location at node 85723 'which also involves the inner hood suggesting that the inner "
hood isrespon~ive' to acoustiC signals ~t this frequency. The stress response at n6de. 99212 is also characterized by a single dominant the'dominant peak, this time at a frequency'between '
69 and 7 i Hz. This frequency char'acterizesmost 'of the surface bn the outer panels of the outer "
hood on the'MSL elD side. Finally for node 87780, the dominant stress contributions occur at -
higher frequenCies;, Without frequency shifting the dominant frequency isi80~0 Hz which coincides with a multiple of electrical noise (60 Hz - note however: that the electrical noise is'.
filtered).
At the +7.5% shift the dominant frequency is at 184.5 Hz which corresponds to 171.6 Hz in the original non-shifted signal.
'1','
86
' **** 1 i,
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 85723, a.
a-E E
400 350 300 250 200 150 100
-- e-no shift
.5% Stijl 50 0
0 50 100 150 200 Frequency [ Hz]
Node 85723, a 250 10l 104 no shift
-5% shift N
CO 0.
co, to 1000 100 10 1
1 0.1 0.01 0.001 0
150 200 50 100 250 Frequency [ Hz ]
Figure 16a. Accumulative PSD and PSD curves of the cyzz stress response at node 85723.
87 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 400 I
350 r * **..........
'iii
- a.
H 6
en a..
Q)
.~
iii
- s E
E
- J
~
300 L.
250 200 t-150 '
~
1000
.~
o en 100 a..
10 I/)
~
I en I
I 0.1 I 0.01 0.001 o 50 f :
i i I !
Node 85723, a-zz 100 150 Frequency [Hz)
Node 85723, a-zz 100 150 Frequency [Hz)
-no shift
- _ ***** -5% shift i
200 200 l
250
.j 250 Figure 16a. Accumulative PSD and PSD curves of the az:z stress response at node 85723.
87
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 89649, ayy C,,
(D EE 600 500 400 no shift s
0 hi]ft 300 200 100 0
0 50 100 150 200 Frequency [ Hz ]
Node 89649, a 250 Zo shift a.
CO a-O-
1000 A
10 0.1 200 0.001 L
0 150 50 100 250 Frequency [ Hz ]
Figure 16b. Accumulative PSD and PSD of the ayy stress response at node 89649.
88 This Document Does Not Contain Continuum Dynamics, Inc, Proprietary Information 600
'iii 500
- 0.
~
6 400 (J) a..
Q)
.~ -
300 m
"5 E E
- l 0
200
~
100 0
105 N
J:
N-
'iii 1000
- 0.
Cl (J) a..
(/)
(/)
10
~ -
(J) 0.1 0.001
~...
I-0 50 o
50 Node 89649, cr yy 100 150 Frequency [Hz]
Node 89649, cr yy 100 150 Frequency [Hz]
-no shift
- '"""-_ ** + 1 0% shift 200
--.- no shift
+10% shift 200 250 250 Figure 16b. Accumulative PSD and PSD of the cryy stress response at node 89649.
88
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 99529, o"YY EE 400 350 300 250 200 150 100 0%ssift 50 0
0 50 100 150 200 250 10 5
N I
0~
0 Co 0) 1000 Frequency [ Hz]
Node 99529, o yy 10% 10ift) 100 150 200 10 0.1 0.001 0
50 250 Frequency [ Hz ]
Figure 16c. Accumulative PSD and PSD of the cyy stress response at node 99529.
89 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
'iii Cl.
V.J 6
CJ) a..
Q) >
(1l :;
E E
- )
()
()
c{
N I
~
400 350 300 250 200 150 100 50 0
.~
1000 o
CJ) a..
iZ 10
~
U5 0.1 0.001 I -
L 0
o 50 Node 99529, CJ yy I-O%Shift I 100 150 Frequency [Hz]
Node 99529, CJ yy 200
'1 ~O%shift I
_. ~
I I
...... -1 250 50 100 200 250 Frequency [Hz 1 Figure 16c. Accumulative PSD and PSD of the cryy stress response at node 99529.
89
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 99212, ayy a.
C,,I
.=_
EE 300 250 200 150 f.....
I -*--noshift 1100 50 0
0 50 100 150 200 250 Frequency [ Hz]
Node 99212, cr yy 101 104 C,)
I no shift 1000 100 10 I
150 0.1 0.01 0.001 200 0
50 100 250 Frequency [ Hz ]
Figure 16d. Accumulative PSD and PSD of the ayy stress response at node 99212.
90 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 300
'en 250
- a.
W ci 200,
(/)
0-Q) >
150 (13 :;
E E
- l 8 100
~
105 104 N
1000 J: --
N 'en a.
100 a
(/)
0-10 III III
~
(/)
0.1 0.01 0.001 0
Node 99212, CJ yy r..... -.... ~........ -.... -... -.~..... -... -.-... -...... -........ -;;--..... 1 j
~ ~~--.----.--~~--.----.--~.--
i j
.--.- no shift
- +5% shift
... J I
50 50 100 150 Frequency [Hz]
Node 99212, CJ yy 1
100 150 Frequency [Hz]
200
no shift r
+5% shift 200 250 I
I I
I
...*.*. -1 250 Figure 16d. Accumulative PSD and PSD of the cryy stress response at node 99212.
90
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 87780, a 400 350 IZ d
CO, E
E 300 no shift
.+7,5% sh]f 250 200 150 100 K
50 0
0 50 100 150 Frequency [ Hz]
Node 87780 a 200 250 10 5 0
o hift Nr CR, 0.
A 1000 10 F'
0.1 0.001 150 0
50 100 200 250 Frequency [ Hz ]
Figure 16e. Accumulative PSD and PSD of the cxx stress response at node 87780.
91 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 400 l...
350
'iii
- a.
V.;J 300 '-..
c:i
(/)
250 a..
Q)
III 200 E
L E
150
- J 8 I
100 50 0
0 105 N :r:
'iii 1000
- a.
0
(/)
a..
II)
II)
Q)... -
(/)
0.1 0.001 o r
50 50 Node 87780, a xx
. """-no shift
- +7.5% shift 100 150 Frequency [Hz]
Node 87780 a
-- no shift 7.50 shift 100 xx 1 -
I _
150 Frequency [Hz]
r
.. *..:...**_***_**.. ******1
. f i
I 200 200 250
--.-4 250 Figure 16e. Accumulative PSD and PSD of the axx stress response at node 87780.
91
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 6. Conclusions A frequency-based steam dryer stress analysis has been used to calculate high stress locations and calculated / allowable stress ratios for the Nine Mile Point Unit 2 steam dryer at CLTP load conditions using plant measurement data. A detailed description of the frequency-based methodology and the finite element model for the NMP Unit 2 steam dryer is presented. The CLTP loads obtained in a separate acoustic circuit model [4] including end-to-end bias and uncertainty for both the ACM [4] and FEA were applied to a finite element model of the steam dryer consisting mainly of the ANSYS Shell 63 elements, brick continuum elements and beam elements.
The measured CLTP loads are applied without filtering of low power data. The resulting stress histories were analyzed to obtain maximum and alternating stresses at all nodes for comparison against allowable levels. These results are tabulated in Table 9 of this report. The minimum alternating stress ratio at nominal operation is SR-a=3.00 and the minimum alternating stress ratio taken over all frequency shifts is 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 both with and without frequency shifting.
Since flow-induced acoustic resonances are not anticipated in the steam dryer, the alternating stress ratios at EPU 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 with the limiting maximum stress ratios at CLTP, the corresponding limiting value at EPU is SR-P=1.32. Given that the alternating stress ratio SR-a obtained at EPU remains above 2.08 at all frequency shifts together with the comparatively small dependence of SR-P upon acoustic loads, the Unit 2 dryer is expected to qualify at EPU conditions.
Frequency Shift Minimum Stress Ratio at CLTP Min. Alt. Stress Max. Stress, Alternating Stress, Ratio (SR-a)
SR-P SR-a at EPU 0% (nominal) 1.34 3.00 2.16
-10%
1.36 3.09 2.23
-7.5%
1.36 3.07 2.21
-5%
1.36 2.89 2.08
-2.5%
1.36 3.27 2.36
+2.5%
1.36 2.93 2.11
+5%
1.34 2.97 2.14
+7.5%
1.35 3.07 2.21
+10%
1.35 2.93 2.11 All shifts 1.34-1.36 2.89-3.27 2.08-2.36 Limiting 1.34 2.89 2.08 92 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 6. Conclusions A frequency-based steam dryer stress analysis has been used to calculate high stress locations and calculated / allowable stress ratios for the Nine Mile Point Unit 2 steam dryer at CLTP load conditions using plant measurement data. A detailed description of the frequency-based methodology and the fmite element model for the NMP Unit 2 steam dryer is presented. The CL TP loads obtained in a separate acoustic circuit model [4] including end-to-end bias and uncertainty for both the ACM [4] and FEA were applied to a finite element model of the steam dryer consisting mainly of the ANSYS Shell 63 elements, brick continuum elemepts and beam elements.
The measured CLTP loads are applied without filtering of low power data. The resulting stress histories were analyzed to obtain maximum and alternating stresses at all nodes for comparison against allowable levels. These results are tabulated in Table 9 of this report. The minimum alternating stress ratio at nominal operation is SR-a=3.00 and the minimum alternating stress ratio taken over all frequency shifts is 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 both with and without frequency shifting.
Since flow-induced acoustic resonances are not anticipated in the steam dryer, the alternating stress ratios at EPU 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 with the limiting maximum stress ratios at CLTP, the corresponding limiting value at EPU is SR-P=1.32. Given that the alternating stress ratio SR-a obtained at EPU remains above 2.08 at all frequency shifts together with the comparatively small dependence of SR-P upon acoustic loads, the Unit 2 dryer is expected to qualify at EPU conditions.
Frequency Shift Minimum Stress Ratio at CL TP Min. Alt. Stress Max. Stress, Alternating Stress, Ratio (SR-a)
SR-P SR-a atEPU 0% (nominal) 1.34 3.00 2.16
-10%
1.36 3.09 2.23
-7.5%
1.36 3.07 2.21
-5%
1.36 2.89 2.08
-2.5%
1.36 3.27 2.36
+2.5%
1.36 2.93 2.11
+5%
1.34 2.97 2.14
+7.5%
1.35 3.07 2.21
+10%
1.35 2.93 2.11 All shifts 1.34 -1.36 2.89-3.27 2.08-2.36 Limitin2 1.34 2.89 2.08 92
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 7. References
- 1.
EPRI (2008), BWRVIP-194: BWR Vessel and Internals Project: Methodologies for Demonstrating Steam Dryer Integrity for Power Uprate, Palo Alto, CA: 2008. 1016578.
- 2.
ASME Boiler and Pressure Vessel Code,Section III, Subsection NG (2007).
- 3.
Continuum Dynamics, Inc. (2005), Methodology to Determine Unsteady Pressure Loading on Components in Reactor Steam Domes (Rev. 6), C.D.I. Report No. 04-09 (Proprietary).
- 4.
Continuum Dynamics, Inc. (2008), Acoustic and Low Frequency Hydrodynamic Loads at CLTP Power Level on Nine Mile Point Unit 2 Steam Dryer to 250 Hz, Rev. 2, C.D.I. Report No.08-08P (Proprietary).
- 5.
Continuum Dynamics, Inc. (2007), Methodology to Predict Full Scale Steam Dryer Loads from In-Plant Measurements, with the Inclusion of a Low Frequency Hydrodynamic Contribution, C.D.I. Report No.07-09P (Proprietary).
- 6.
Structural Integrity Associates, Inc. (2009), Nine Mile Point Unit 2 Steam Dryer Closure Plates Analysis Results, SIA Letter Report No. 0900895.401 Revision 0, August 21.
- 7.
Structural Integrity Associates, Inc. (2008), Nine Mile Point Unit 2 Main Steam Line Strain Gage Data Reduction, SIA Calculation Package No. NMP-26Q-302.
- 8.
ANSYS URL: http://www.ansys.com, ANSYS Release 10. 0 Complete User's Manual Set.
- 9.
Continuum Dynamics, Inc. (2007), Response to NRC Request for Additional Information on the Hope Creek Generating Station, Extended Power Uprate, RAI No. 14.110.
- 10.
Continuum Dynamics, Inc. (2008), Stress Assessment of Hope Creek Unit I Steam Dryer Based on Revision 4 Loads Model, Rev. 4, C.D.I. Report No.07-17P (Proprietary).
- 11.
Press, W.H., et al., Numerical Recipes. 2 ed. 1992: Cambridge University Press.
- 12.
Structural Integrity Associates, Inc. (2008), Flaw Evaluation and Vibration Assessment of the Nine Mile Point Unit 2 Steam Dryer for Extended Power Uprate Operating Conditions, Report No. 0801273.401.
- 13.
Continuum Dynamics, Inc. (2008), Stress Assessment of Browns Ferry Nuclear Unit I Steam Dryer, Rev. 0, C.D.I. Report No.08-06P (Proprietary).
- 14.
O'Donnell, W.J., Effective Elastic Constants For the Bending of Thin Perforated Plates With Triangular and Square Penetration Patterns. ASME Journal of Engineering for Industry, 1973.
95: p. 121-128.
- 15.
de Santo, D.F., Added Mass and Hydrodynamic Damping of Perforated Plates Vibrating In Water. Journal of Pressure Vessel Technology, 1981. 103: p. 175-182.
- 16.
Idel'chik, I E. and E. Fried, Flow Resistance, a Design Guide for Engineers. 1989, Washington D.C.: Taylor & Francis. pg. 260.
- 17.
Continuum Dynamics, Inc. (2007), Dynamics ofBWR Steam Dryer Components, C.D.I. Report No.07-11P.
- 18.
U.S. Nuclear Regulatory Commission (2007), Comprehensive Vibration Assessment Program for Reactor Internals During Preoperational and Initial Startup Testing, Regulatory Guide 1.20, March.
- 19.
Weld Research Council (1998), Fatigue Strength Reduction and Stress Concentration Factors For Welds In Pressure Vessels and Piping, WRC Bulletin 432.
- 20.
Pilkey, W.D., Peterson's Stress Concentration Factors, 2nd ed. 1997, New York: John Wiley.
pg. 139.
- 21.
Lawrence, F.V., N.-J. Ho, and P.K. Mazumdar, Predicting the Fatigue Resistance of Welds. Ann.
Rev. Mater. Sci., 1981. 11: p. 401-425.
- 22.
General Electric (GE) Nuclear Energy, Supplement I to Service Information Letter (SIL) 644, "B WR/3 Steam Dryer Failure, " September 5. 2003.
93 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 7. References
- 1.
EPRI (2008), BWRVIP-194: BWR Vessel and Internals Project: Methodologiesfor Demonstrating Steam Dryer Integrity for Power Uprate, Palo Alto, CA: 2008. 1016578.
- 2.
ASME Boiler and Pressure Vessel Code,Section III, Subsection NG (2007).
- 3.
Continuum Dynamics, Inc. (2005), Methodology to Determine Unsteady Pressure Loading on Components in Reactor Steam Domes (Rev. 6), C.D.1. Report No. 04-09 (Proprietary).
- 4.
Continuum Dynamics, Inc. (2008), Acoustic and Low Frequency Hydrodynamic Loads at CLTP Power Level on Nine Mile Point Unit 2 Steam Dryer to 250 Hz, Rev. 2, C.D.I. Report No.08-08P (Proprietary).
- 5.
Continuum Dynamics, Inc. (2007), Methodology to Predict Full Scale Steam Dryer Loads from In-Pl~~t Measurements, with the Inclusion of a Low Frequency Hydrodynamic Contribution, C.D.I. Report No.07-09P (Proprietary).
- 6.
Structural Integrity Associates, Inc. (2009), Nine Mile Point Unit 2 Steam Dryer Closure Plates Analysis Results, SIA Letter Report No. 0900895.401 Revision 0, August 21.
- 7.
Structural Integrity Associates, Inc. (2008), Nine Mile Point Unit 2 Main Steam Line Strain Gage Data Reduction, SIA Calculation Package No. NMP-26Q-302.
- 8.
ANSYS URL: http://www.ansys.com.ANSYSRelease 10.0 Complete User's Manual Set.
- 9.
Continuum Dynamics, Inc. (2007), Response to NRC Request/or Additional Information on the Hope Creek Generating Station, Extended Power Uprate, RAJ No. 14.110.
- 10.
Continuum Dynamics, Inc. (2008), Stress Assessment of Hope Creek Unit 1 Steam Dryer Based on Revision 4 Loads Model, Rev. 4, C.D.I. Report No.07-17P (Proprietary).
- 11.
Press, W.R., et aI., Numerical Recipes. 2 ed. 1992: Cambridge University Press.
- 12.
Structural Integrity Associates, Inc. (2008), Flaw Evaluation and Vibration Assessment of the Nine Mile Point Unit 2 Steam Dryer for Extended Power Uprate Operating Conditions, Report No. 0801273.401.
- 13.
Continuum Dynamics, Inc. (2008), Stress Assessment of Browns Ferry Nuclear Unit 1 Steam Dryer, Rev. 0, C.D.1. Report No.08-06P (Proprietary).
- 14.
O'Donnell, W.J., Effective Elastic Constants For the Bending of Thin Perforated Plates With Triangular and Square Penetration Patterns. ASME Journal of Engineering for Industry, 1973.
95: p. 121-128.
- 15.
de Santo, D.F., Added Mass and Hydrodynamic Damping of Perforated Plates Vibrating In Water. Journal of Pressure Vessel Technology, 1981. 103: p. 175-182.
- 16.
Idel'chik, I E. and E. Fried, Flow Resistance, a Design Guidefor Engineers. 1989, Washington D.C.: Taylor & Francis. pg. 260.
- 17.
Continuum Dynamics, Inc. (2007), Dynamics 0/ BWR Steam Dryer Components, C.D.I. Report No.07-11P.
- 18.
U.S. Nuclear Regulatory Commission (2007), Comprehensive Vibration Assessment Programfor Reactor Internals During Preoperational and Initial Startup Testing, Regulatory Guide 1.20, March.
- 19.
Weld Research Council (1998), Fatigue Strength Reduction and Stress Concentration Factors For Welds In Pressure Vessels and Piping, WRC Bulletin 432.
- 20.
Pilkey, W.D., Peterson's Stress Concentration Factors, 2nd ed 1997, New York: John Wiley.
pg.139.
- 21.
Lawrence, F.V., N.-J. Ro, and P.K. Mazumdar, Predicting the Fatigue Resistance of Welds. Ann.
Rev. Mater. Sci., 1981. 11: p. 401-425.
- 22.
General Electric (GE) Nuclear Energy, Supplement 1 to Service Information Letter (SIL) 644, HBWRl3 Steam Dryer Failure," September 5.2003.
93
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 23.
Tecplot, Inc. (2004), URL: http://www.tecplot.com, Documentation: Tecplot User's Manual Version 10 Tecplot, Inc., October.
- 24.
GE Nuclear Energy (2006), Browns Ferry Nuclear Plant Units 1, 2, and 3 Steam Dryer Stress, Dynamic, and Fatigue Analysis for EPU Conditions, GE-NE-0000-0053-7413-R4-NP.
- 25.
Structural Integrity Associates, Iic. (2008), Shell and Solid Sub-Model Finite Element Stress Comparison, Rev. 2, Calculation Package, 0006982.301, Oct. 17.
- 26.
Continuum Dynamics, Inc. (2008), Stress Assessment of Browns Ferry Nuclear Unit 2 Steam Dryer with Outer Hood and Tie-Bar Reinforcements, Rev. 0, C.D.I. Report No.08-20P (Proprietary),
- 27.
Structural Integrity Associates, Inc. (2008), Comparison Study of Substructure and Submodel Analysis using ANSYS, Calculation Package, 0006982.304, December.
- 28.
Continuum Dynamics, Inc. (2009), Response to NRC Round 23 RAI EMCB 201/162 part c, January.
- 29.
Continuum Dynamics, Inc. (2009), Compendium of Nine Mile Point Unit 2 Steam Dryer Sub-Models Away From Closure Plates C.D.I. Technical Note No.09-16P (Proprietary), August.
- 30.
Continuum Dynamics, Inc. (2008), Response to NRC RAIEMCB 172, June.
94 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 23.
Tecplot, Inc. (2004), URL: http://www.tecplot.com.*Documentation: Tecplot User's Manual Version 10 Tecplot, Inc., October.
- 24.
GE Nuclear Energy (2006), Browns Ferry Nuclear Plant Units 1,2, and 3 Steam Dryer Stress, Dynamic, and Fatigue Analysisfor EPU Conditions, GE-NE-0000-0053-7413-R4-NP.
- 25.
Structural Integrity Associates, mc. (2008), Shell and Solid Sub-Model Finite Element Stress Comparison, Rev. 2, Calculation Package, 0006982.301, OC,t. 17.
- 26.
Continuum Dynamics, Inc. (2008), Stress Assessment of Browns Ferry Nuclear Unit 2 Steam Dryer with Outer Hood and Tie-Bar Reinforcements, Rev. 0, C.D.I. Report No.08-20P (Proprietary) *
- 27.
Structural Integrity Associates, Inc. (2008), Comparison Study of Substructure and Submodel Analysis usingANSYS, Calculation Package, 0006982.304, December.
- 28.
Continuum Dynamics, Inc. (2009), Response to NRC Round 23 RAJ EMCB 2011162 part c, January.
- 29.
Continuum Dynamics, Inc. (2009), Compendium of Nine Mile Point Unit 2 Steam Dryer Sub-
, ModelsAway From Closure Plates C.D.l Technical Note No.09-16P (Proprietary), August.
- 30.
Continuum Dynamics, Inc. (2008), Response to NRC 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
((
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Appendix A Sub-modeling and Modification of Closure Plates 95
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 17: Second mode shape (f=128.45 Hz) of unmodified closure plates 96 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 9,438 8,0896 6.7415 5.3932 4.0449 2,6966 1.3483 o Min 0,000 10,000 5.000 Figure 17: Second mode shape (f=128.45 Hz) of unmodified closure plates 96 15.000 20.000 (In)
I
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NCDAL SQT.DTIcM STEP=-I SUB =1 FRED=259.55 USUM RSYS=o DMX =17.218 SEPC=27.778 SMX =17.218 0
3.826 7.652 11.478 15.305 1.913 5.739 9.565 13.391 17.218 Figure 18: Fundamental mode shape (f=259.6 Hz) of modified closure plate.
97 1
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NOJAL SOWTICN STEP=l SOB =1 FRE.CF259.55 USUM RSYS=O DMX =17.218 SEPC=27.778 SMX =17.218 o
3.826
'7.652 11.478 15.305 1.913 5.739 9.565 13.391 17.218 Figure 18: Fundamental mode shape (f=259.6 Hz) of modified closure plate.
97
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information (3)))
98 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
((
98
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information (3)))
The sub-modeled locations together with the calculated stress reduction factors are given in Table
- 10. For each location depictions of the shell and solid element-based sub-models are given together with the applied loads/moments and resulting stresses.
This is followed by a summary of the linearization paths and the limiting linearized stresses. The calculation of the stress reduction factor concludes the presentation for each location.
Table 10. List of sub-model locations Location x
y z
node Stress reduction factor Top Thick Plate/Side Plate/Closure 47.1
-108.6 88 101175 0.62 Plate/Top Plate Closure Plate/Middle Hood
-63.8 85.2 72.5 91605 0.71 Closure Plate/Inner Hood 28.8
-108.6 87 95172 0.86 Side Plate/Closure Plate/Exit Top
-47.1 108.6 74.5 100327 0.88 Perf/Exit Mid Top Perf Note: The side 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 side with a 0.125" weld.
99 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
((
The sub-modeled locations together with the calculated stress reduction factors are given in Table
- 10. For each location depictions of the shell and solid element-based sub-models are given together with the applied loads/moments and resulting stresses.
This is followed by a summary of the linearization paths and the limiting linearized stresses. The calculation of the stress reduction factor concludes the presentation for each location.
Table 10. List of sub-model locations Location x
y z
node Stress reduction factor Top Thick Plate/Side Plate/Closure 47.1
-108.6 88 101175 0.62 Plate/Top Plate Closure PlatelMiddle Hood
-63.8 85.2 72.5 91605 0.71 Closure PlatelInner Hood 28.8
-108.6 87 95172 0.86 Side Plate/Closure Plate/Exit Top
-47.1 108.6 74.5 100327 0.88 Perf/Exit Mid Top Perf Note: The side 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 side with a 0.125" weld.
99
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
((
(3)))
The sub-modeled locations together with the calculated stress reduction factors are given in Table
- 10. For each location depictions of the shell and solid element-based sub-models are given together with the applied loads/moments and resulting stresses.
This is followed by a summary of the linearization paths and the limiting linearized stresses. The calculation of the stress reduction factor concludes the presentation for each location.
Table 10. List of sub-model locations Location x
y z
node Stress reduction factor Top Thick Plate/Side Plate/Closure 47.1
-108.6 88 101175 0.62 Plate/Top Plate Closure Plate/Middle Hood
-63.8 85.2 72.5 91605 0.71 Closure Plate/Inner Hood 28.8
-108.6 87 95172 0.86 Side Plate/Closure Plate/Exit Top
-47.1 108.6 74.5 100327 0.88 PerfiExit Mid Top Perf Note: The side 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 side with a 0.125" weld.
99 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
((
The sub-modeled locations together with the calculated stress reduction factors are given in Table
- 10. For each location depictions of the shell and solid element-based sub-models are given together with the applied loads/moments and resulting stresses.
This is followed by a summary of the linearization paths and the limiting linearized stresses. The calculation of the stress reduction factor concludes the presentation for each location.
Table 10. List of sub-model locations Location x
y z
node Stress reduction factor Top Thick Plate/Side Plate/Closure 47.1
-108.6 88 101175 0.62 Plate/Top Plate Closure PlatelMiddle Hood
-63.8 85.2 72.5 91605 0.71 Closure Platellnner Hood 28.8
-108.6 87 95172 0.86 Side Plate/Closure PlatelExit Top
-47.1 108.6 74.5 100327 0.88 Perf/Exit Mid Top Perf Note: The side 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 side with a 0.125" weld.
99
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model Node 101175 The sub-model for this node located at the top of the vertical weld joining the closure plate to the vane bank is shown in Figure 19a and involves five different components. The extracted forces are shown in Figure 19b. The shell sub-model stress distribution is shown in Figure 19c with a maximum (i.e., the maximum taken over all components and surfaces - top, bottom and middle) stress intensity stress at the location of 3362 psi. The corresponding solid sub-model together with mesh details and the stress distribution resulting when the same loads used in the shell sub-model are applied, are shown in Figure 20.
Finally, the stress intensity linearization paths and corresponding linearized stresses extracted from the solid model are shown in Figure 21 and tabulated in Table 11.
The limiting linearized stress in the solid sub-model is 2088 psi. Comparing this value against the one obtained in the shell sub-model (3362 psi) yields the stress reduction factor: 2088/3362 = 0.62.
Vane bank
]
side plate, 0.375" Closure plate, 0.125" Thick plate, 0.5"
[Perforated plate, 0.078" 0.000 2.000 (in) 1.000 Figure 19a. Shell sub-model node 101175.
100 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model Node 101175 The sub-model for this node located at the top of the vertical weld joining the closure plate to the vane bank is shown in Figure 19a and involves five different components. The extracted forces are shown in Figure 19b. The shell sub-model stress distribution is shown in Figure 19c with a maximum (i.e., the maximum taken over all components and surfaces - top, bottom and middle) stress intensity stress at the location of 3362 psi. The corresponding solid sub-model together with mesh details and the stress distribution resulting when the same loads used in the shell sub-model are applied, are shown in Figure 20.
Finally, the stress intensity linearization paths and corresponding linearized stresses extracted from the solid model are shown in Figure 21 and tabulated in Table 11.
The limiting linearized stress in the solid sub-model is 2088 psi. Comparing this value against the one obtained in the shell sub-model (3362 psi) yields the stress reduction factor: 2088/3362 = 0.62.
Top plate, 0.25" Vane bank side plate, 0.375" Closure plate, 0.125" Perforated plate, 0.078" z
0.000 __ -====:5 1.000 Figure 19a. Shell sub-model node 101175.
100
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 9 Time: 1. s 12110/2008 10:12 AM
- Force: 14.684 lbf
- Force 2: 2.5432 Ibf
- Force 3: 60.408 Ibf
- Force 4: 29.682 lbf
- Force 5: 6.6215 Ibf
- Force 6: 25.379 Ibf
- Force 7: 2.0671 Ibf
- Force 8: 41.024 Ibf
- Force 9: 5.7018 Ibf 0.000 2.000 (in) 1.000 Moment 9 Time: 1. s 12l 012008 10:13 AM LU I
- Moment: 6.5096 lbf-in
- Moment 2: 8.1909 IbV'in
- Moment 3: 5.6901 lbf'in
- Moment 4: 6.7147 Ibfin
- Moment 5:3.8973 lbflin
- Moment 6: 6.1644e-003 lbf in
- Moment 7: 8.9112e-002 Ibfin
- Moment 8: 2.4226 Ibfinr M Moment 9:0.14082 Ibfi 0.000 2.000 (in) 1.000 Figure 19b. Forces and moments.
101 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 9 Time: 1. s 12/1012008 10:12 AM Force: 14.684 Ibf Force 2: 2.5432 Ibf Force 3: 60.4081bf Force 4: 29.682 Ibf Force 5: 6.6215 Ibf Force 6: 25.379 Ibf Force 7: 2.0671 Ibf Force 8: 41.0241bf Force 9: 5.7018 Ibf Moment 9 Time: 1. s 12/10/2008 1013 AM Moment: 6.5096 Ibf-in Moment 2: 8.1909Ibf-in Moment 3: 5.6901 Ibf*in Moment 4: 6.7147 Ibf-in Moment 5: 3.8973 Ibf-in Moment 6: 6.1644e-003 Ibf*in Moment 7: 8.9112e-002 Ibfin Figure 19b. Forces and moments.
___ ~~==2S
. qoO (in) 1.000
____===2S.qOO (in) 1.000 101
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Stress Intensity Type: Stress Intensity-ToplBottom Unit: psi Time: 1 1211012008 10:39 AM N.M 20311 Max 3500 3150 2800 2450 2100 1750 1400 1050 700 350 11.75 Min 0
4,X 1.000 Figure 19c. Shell sub-model stress contours. Stress intensity: 3362 psi.
102 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information stress Intensity Type: Stress Intensity - Top/Bottom Unit: psi Time: 1 12/10/2008 10:39 AM 20311 Max 3500 3150 2800 2450 2100 1750 1400 1050 700 350 11.75 Min o
.iii ___
-====25
. ~00 (in) 1.000 Figure 19c. Shell sub-model stress contours. Stress intensity: 3362 psi.
102 I
~ '. I*~"':r-. I)f: -
"~'.,", "),,\\
L.i \\.. -'J'LL.,\\..2.-
If,"'i.
~/~
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Proposed additional weld 0.000 2.000 (in) 1.000 0.000 2.000 (In) 1.000 Figure 20a. Solid model geometry.
103 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 20a. Solid model geometry.
O.OjOO" __ C==2S
- 000 (in)
I 1.000 0.000 1.000 103 2.000 (In)
I Proposed additional weld
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 20b. Mesh overview. Mesh parameters: 748,327 nodes, 176,028 elements.
104 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 20b. Mesh overview. Mesh parameters: 748,327 nodes, 176,028 elements.
104
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NODAL SOLUTION STEP=1 SUB =1 TIME=1 SINT (AVG)
DMX =.012723 SMN =.605642 SMX =.166E+07 2400 1800 3000 AN Figure 20c. Stress intensity contours (total) in solid sub-model.
105 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NODAL SOLUTION STEP=l SUB =1 TIME=l SINT (AVG)
DMX =. 012723 SMN =.605642 SMX =. 166E+07 1200 600 1800 Figure 20c. Stress intensity contours (total) in solid sub-model.
105 2400 3000
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 21. Linearization paths for sub-model node 101175.
Table 11. Linearized stresses along the linearization paths shown in Figure 21.
Path Membrane + bending linearized stress intensity, psi AB 1605 AC 710 AD 689 AF 492 BE 2088 106 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information AN Figure 21. Linearization paths for sub-model node 101175.
Table 11. Linearized stresses along the linearization paths shown in Figure 21.
Path Membrane + bendin linearized stress intensi SI AB 1605 AC 710 AD 689 AF 492 BE 2088 106
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model node 91605.
The sub-model for this node located on the weld connecting the closure plate to the hood is shown in Figure 22a and involves two different components - the hood and closure plate. The extracted forces are shown in Figure 22b. The shell sub-model stress distribution is shown in Figure 22c with a maximum (i.e., the maximum taken over all components and surfaces - top, bottom and middle) stress intensity stress at the location of 3176 psi. The stresses in the comers are neither singularities nor due to constraint forces (they arise regardless of where the model is supported). When the sub-model mesh is refined these stresses do not grow. Instead they essentially retain their coarse level values but extend over a smaller range (i.e., over one element). A mathematical explanation for this behavior indicates that the localized stress is due to the local imbalance (due to discretization error) in the applied shear loads. Thus to equilibrate the 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.
The solid sub-model, mesh and stresses are shown in Figure 23 and, the stress intensity linearization paths and corresponding linearized stresses extracted from the solid model are shown in Figure 24 and tabulated in Table 12. The limiting linearized stress in the solid sub-model is 2254 psi, which, when compared against the one obtained in the shell sub-model (3176 psi) yields the stress reduction factor:
2254/3176 = 0.71.
107 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model node 91605.
The sub-model for this node located on the weld connecting the closure plate to the hood is shown in Figure 22a and involves two different components - the hood and closure plate. The extracted forces are shown in Figure 22b. The shell sub-model stress distribution is shown in Figure 22c with a maximum (i.e., the maximum taken over all components and surfaces - top, bottom and middle) stress intensity stress at the location of 3176 psi. The stresses in the comers are neither singularities nor due to constraint forces (they arise regardless of where the model is supported). When the sub-model mesh is refined these stresses do not grow. Instead they essentially retain their coarse level values but extend over a smaller range (i.e., over one element). A mathematical explanation for this behavior indicates that the localized stress is due to the local imbalance (due to discretization error) in the applied shear loads. Thus to equilibrate the 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.
The solid sub-model, mesh and stresses are shown in Figure 23 and, the stress intensity linearization paths and corresponding linearized stresses extracted from the solid model are shown in Figure 24 and tabulated in Table 12. The limiting linearized stress in the solid sub-model is 2254 psi, which, when compared against the one obtained in the shell sub-model (3176 psi) yields the stress reduction factor:
2254/3176 = 0.71.
107
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information L
I Ho,0.125"~
Closure plate, 0.125" z
,,1.
x 0.000 3.000 (in) 1.500 Figure 22a. Shell sub-model node 91605.
108 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Hood,0.125" Closure plate, 0.125" o.oiioo ____
====3J.~00(in) 1.500 Figure 22a. Shell sub-model node 91605.
108
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 7 Time: 1. s 1211012008 2:52 PM
- Force: 8.2261 Ibf
- Force 2:22.492 1
- Force 3:18.258 Ibf
- Force 4: 51.111 Ibf
- Force 5: 43.361 Ibf
- Force 6:3.1687 Ibf
- Force 7: 46.837 Ibf Moment 7 Time: 1. s 12110/2008 2:52 PM
- Moment: 3.8738 Ibfjn
- Moment 2:6341
- Moment 3: 8.5514 1bf1
- Moment 4: 3.6938 IbfVi
- Moment 5:12.605 Ibf-i
- Moment 6:11.556 Ibf.
- Moment 7: 8.7125 1bf Figure 22b. Forces and moments.
0.000 I
3.000 (in) 1.500 t
0.000 3.000 (in) 1.500 109 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 7 Time 1. s 1211012008 2:52 PM Force: 8.2261 Ibf Force 2: 22.492 Force 5: 43.361 Ibf Force 6: 3.1687 Ibf Force 7: 46.837 Ibf Moment 7 Time: 1. s 1211012008 2:52 PM Moment: 3.8738 Moment 2: 6.3414 Moment 3: 8.5514 Moment 7: 8.7125 Figure 22b. Forces and moments.
0.000 0.000 1.500 1.500 109 3.000 (in)
I 3.000 (in)
I z
z
-:}
y
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Stress Intensity Type: Stress Intensity-Top, Unit: psi Time: 1 1211012008 2:56 PM 6854.3 Max 3500 3150 2800 2450 2100 1750 1400 1050 700 51.895 Min
- 0 4.
Figure 22c. Shell sub-model stress contours. Stress intensity: 3176 psi.
110 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information stress Intensity Type: stress Intensity - To Unit: psi Time: 1 12/10/2008 2:56 PM 6854.JMax 3500 3150 2800 2450 2100 1750 1400 1050 700 51.895 Min o
Figure 22c. Shell sub-model stress contours. Stress intensity: 3176 psi.
110
! 1
'.1 r.";>" )<.
"1 \\
~.' ~.J'.\\..,'
,.", * ~
.~.')
I ~,
L L-l L..l._ "'
..::"t.-_
t"Jj"jL z
v Y~ "
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Proposed additional weld I
F Figure 23a. Solid model geometry.
111 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Proposed additional weld 1.500 Figure 23a. Solid model geometry.
111
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 23b. Mesh overview.
112 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 23b. Mesh overview.
112
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NODAL SOLUTION STEP=1 SUB =1 TIME=1 SINT (AVG)
DMX =.00998 SMN =14.524 SMX =5788 AN 3863 5146 3222 4505 5788 14.524 1298 656.013 1939 Figure 23c. Stress intensity contours (total) in solid sub-model. Part of structure is removed in the lower figure to show internal stress distribution.
113 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NODAL SOLUTION STEP=l SUB =1 TIME=l SINT (AVG)
DMX =.00998 SMN =14.524 SMX =5788 14.524 1298 656.013 1939 NODAL SOLUTION STEP=l SUB =1 TIME=l SINT (AVG)
DMX =.00998 SMN =17.52 SMX =4327 J\\N 3222 4505 5788 Figure 23c. Stress intensity contours (total) in solid sub-model. Part of structure is removed in the lower figure to show internal stress distribution.
113
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 24. Linearization paths for sub-model node 91605.
Table 12. Linearized stresses along the linearization paths shown in Figure 24.
Path Membrane + bending linearized stress intensity, psi A1-B1 2254 Al-Cl 1891 Al-DI 1261 A1-F1 822 Cl-El 1899 A2-B2 2170 A2-C2 1154 A2-D2 1160 A2-F2 867 C2-E2 930 B1-B2 2139 114 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information ELEMENTS PATH Figure 24. Linearization paths for sub-model node 91605.
Table 12. Linearized stresses along the linearization paths shown in Figure 24.
Path Membrane + bendin linearized stress intensi S1 AI-Bl 2254 AI-Cl 1891 AI-Dl 1261 AI-Fl 822 CI-El 1899 A2-B2 2170 A2-C2 1154 A2-D2 1160 A2-F2 867 C2-E2 930 BI-B2 2139 114
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model node 95172.
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., 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 linearized stresses extracted from the solid model are tabulated in Table 13.
The limiting linearized stress in the solid 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 0.86.
- 2 7~9 I Hood,0125" I Closure plate, 0.125" k_
I 0.000 3.000 (in) 1.500 Figure 25a. Shell sub-model node 95172.
115 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model node 95172.
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., 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 linearized stresses extracted from the solid model are tabulated in Table 13.
The limiting linearized stress in the solid 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 =
0.86.
Hood,0.125" Closure plate, 0.125" I
o.o1lloo ____
-=====3j
.~00 (in)
- "v 1.500 Figure 25a. Shell sub-model node 95172.
115
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 6 Time: 1. s 121 012008 10:33 PM
- Force: 4.3941 lbf
- Force 2:13.957 Ibf
- Force 3:13.152 lbf
- Force 4: 5.8579 lbf
- Force 5:12.614 lbf
- Force 6:19.54 Ibf Moment 6 Time: 1. s 1211012008 10:33 PM
- Moment: 3.3253 lbfin
- Moment 2:6.7324 lbf in
[
Moment 3: 38.492 lbf in
- Moment 4: 4.9806 lbfln
- Moment 5:12.813 Ibf in
[
Moment 6:2.5859 Ibf in Figure 25b. Forces and moments.
0.000 I
3.000 (in) 1.500
-i
.4<~
0.000 3.000 (in) 1.500 116 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 6 Time: 1. s 1211012008 10:33 PM Force: 4.3941 Ibf Force 2: 13.957 Ibf Force 3: 13.152 Ibf Force 4: 5.8579 Ibf Force 5: 12.614 Ibf Force 6: 1 9.54 Ibf Moment 6 Time: 1. s 1211012008 10:33 PM Moment: 3.3253 Ibf-in Moment 2: 6.7324 Ibf-in Moment 3: 38.492 Ibf*in Moment 4: 4.9806 Ibf-In Moment 5: 12.813 Ibf*in Moment 6: 2.5859 Ibf-in Figure 25b. Forces and moments.
0.000 0.000 1.500 1.500 116 3.000 (in)
I 3.000 (in)
I z
~ Y z
~ Y
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Stress Intensity Type: Stress Intensity - TopfBottom Unit: psi Time: I 1211012008 10:42 PM 3200 3198 Max 2880 2560 2240 1920 1600 1280 960 640 320 39.598 Min 0
wl Figure 25c. Shell sub-model stress contours. Stress intensity: 3198 psi.
117 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Stress Intensity Type: Stress Intensity - Top/Bottom Unit: psi Time: 1 12/10/2008 10:42 PM 3200 3198 Max 2880 2560 2240 1920 1600 1280 960 640 320 39.598 Min o
z Figure 25c. Shell sub-model stress contours. Stress intensity: 3198 psi.
117
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Proposed additional weld I 0.000 V
3.000 (in) 1.500 Figure 26a. Solid model geometry.
118 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 0.000 Figure 26a. Solid model geometry.
1.500 3.000 (in)
I 0:..:.:;,800 (in) 118 Proposed additional weld
,<~
,--. \\
y
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 26b. Solid mesh.
119 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 26b. Solid mesh.
119
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 26c. Stress intensity contours (total) in solid sub-model.
120 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 26c. Stress intensity contours (total) in solid sub-model.
120
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 27a. Linearization paths at the original weld for sub-model node 95172.
121 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 27a. Linearization paths at the original weld for sub-model node 95172.
121
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 27b. Linearization paths at the additional weld for sub-model node 95172.
122 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 27b. Linearization paths at the additional weld for sub-model node 95172.
122
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 13. Linearized stresses along the linearization paths shown in Figure 27.
Path Membrane + bending linearized stress intensity, psi AB 1910 AC 2437 AD 1696 AE 2421 AF 639 Al-BI 2002 Al-Cl 2689 Al-DI 1837 Al-El 2696 Al-Fl 1598 C-C1 2762 123 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 13. Linearized stresses along the linearization paths shown in Figure 27.
Path Membrane + bending linearized stress intensity, psi AB 1910 AC 2437 AD 1696 AE 2421 AF 639 AI-Bl 2002 AI-Cl 2689 AI-Dl 1837 AI-El 2696 AI-Fl 1598 C-Cl 2762 123
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model node 100327.
The final sub-model involving the closure plate is for a node on the vertical weld connecting the closure plate to the vane bank. It is located 13.5 inches below the top of the weld. The shell element-based sub-model is shown in Figure 28a and involves four components. The extracted forces are shown in Figure 28b and the shell sub-model stress distribution is shown in Figure 28c with a maximum stress intensity stress at the location of 2744 psi. The solid sub-model, mesh and stresses are shown in Figure 29 and, the stress intensity linearization paths depicted in Figure 30. The extracted linearized stresses are tabulated in Table 14 and show a limiting linearized stress in the solid sub-model of 2406 psi. The stress reduction factor is 2406/2744 = 0.88.
Geometry 12/1112008 9:32 AM M1 Side plate, 0.375" I Closure plate, 0.125" I Perforated plate, 0.078" I Perforated plate, 0.078" Z
tý IX, 0.000 3.000 (in) 1.500 Figure 28a. Shell sub-model node 100327.
124 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model node 100327.
The final sub-model involving the closure plate is for a node on the vertical weld connecting the closure plate to the vane bank. It is located 13.5 inches below the top of the weld. The shell element-based sub-model is shown in Figure 28a and involves four components. The extracted forces are shown in Figure 28b and the shell sub-model stress distribution is shown in Figure 28c with a maximum stress intensity stress at the location of 2744 psi. The solid sub-model, mesh and stresses are shown in Figure 29 and, the stress intensity linearization paths depicted in Figure 30. The extracted linearized stresses are tabulated in Table 14 and show a limiting linearized stress in the solid sub-model of 2406 psi. The stress reduction factor is 2406/2744 = 0.88.
Geometry 12/11/2008 9:32 AM Side plate, 0.375" Perforated plate, 0.078" Perforated plate, 0.078" o.o.oo ___
-====3:j
. ~00 (in) 1.500 Figure 28a. Shell sub-model node 100327.
124
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 10 Time: 1. s 1211112008 9:44 AM
- Force: 2.6676 Ibf
- Force 2: 9.5592 Ibf Force 3:4.0199 Ibf Force 4: 7.6292 IbV Force 5:14.618 IbV Force 6: 5.0388 IbV Force 7: 3.1685 IbfI
- Force 8: 8.9608 IVb Force 9: 9.0228 IbI
- Force 10: 2.967 IV 0.000 3.000 (in) 1.500 Moment 10 Time: 1. s 12/112008 9:44 AM
- Moment: 2.7487 Ibflin
- Moment 2: 4.1118 Ibflin
- Moment 3: 2.8888 Ibf-in
- Moment 4: 59596 lbfin
- Moment 5: 22.463 Ibf'in
- Moment 6: 5.067 lb
- Moment 7:1.2317 E Moment : 0.74244 bfbi Moment 9:0.41921 Ibf.I Moment 10: 1.7222 Ib 0.000 3.000 (in)
L x
1.500 Figure 28b. Forces and moments.
125 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 10 Time: 1. s 121111200B 9:44 AM Force: 2.6676 Ibf Force 2: 9.5592 Ibf Force 3: 4.01 9B Ibf Force 4: 7.6292 Ibf Force 5: 14.61 B Ibf Force 6: 5.03BB Ibf Force 7: 3.16B51bf Force B: B.960B Ibf Force 9: 9.022B Ibf Force 10 2.9671bf Moment 10 Time: 1. s 121111200B 9:44 AM Moment: 2.74B7 Ibfin Moment 2: 4.111 B Ibfin Moment 3: 2.BBBB Ibf-in Moment 6: 5.067 Moment 7: 1.2317 Moment B: 0.742441 Moment 9: 0.41921 1 Moment 1 0: 1.7222 1 0.000 0.000 Figure 28b. Forces and moments.
1.500 1.500 125 3.000 (in) 1 3.000 (in) 1 z
z
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Stress Intensity Type: Stress Intensity-ToplBottom Unit: psi Time: I 12111/2008 9:51 AM 3000 2743.7 Max 2500 2250 2000 1750 1500 1250 1000 750 500 250 25.701 Min
--0 J
z
)*__'11 Y
0.000 3.000 (in) 1.500 Figure 28c. Shell sub-model stress contours. Stress intensity: 2744 psi.
126 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information stress Intensity Type: Stress Intensity - Top/Bottom Unit: psi Time: 1 12/11/2008 9:51 AM 3000 2743.7 Max 2500 2250 2000 1750 1500 1250 1000 750 500 250 25.701 Min o
0.000 1.500 3.000 (in)
I Z J- '1 Figure 28c. Shell sub-model stress contours. Stress intensity: 2744 psi.
126
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information A
Proposed additional weld Figure 29a. Solid model geometry.
127 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 1III __
II:=~2j
.oOO(in)
I 1.000 1.500 Figure 29a. Solid model geometry.
127 z
,{
t
~ y Proposed additional weld z t.,.I Y
"-x
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 29b. Solid mesh. Mesh parameters: 567369 nodes, 133680 elements.
128 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 29b. Solid mesh. Mesh parameters: 567369 nodes, 133680 elements.
128
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NODAL SOLUTION STEP=1 SUB =1 TIME=1 SINT (AVG)
DMX =.004133 SMN =1.847 SMX =6458 0
1200 2400 600 1800 3000 Figure 29c. Stress intensity contours (total) in solid sub-model. Parts of the structure removed to show internal stress distribution (bottom).
129 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NODAL SOLUTION STEP=l SUB =1 TIME=l SINT (AVG)
DMX =. 004133 SMN =1.847 SMX =6458 600 J\\N 2400 1800 3000 Figure 29c. Stress intensity contours (total) in solid sub-model. Parts of the structure removed to show internal stress distribution (bottom).
129
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 30. Linearization paths at the additional weld for sub-model node 100327.
Table 14. Linearized stresses along the linearization paths shown in Figure 30.
Path Membrane + bending linearized stress intensity, psi AB 1589 AC 439 AD 724 BE 2406 AF 488 130 This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 30. Linearization paths at the additional weld for sub-model node 100327.
Table 14. Linearized stresses along the linearization paths shown in Figure 30.
Path Membrane + bending linearized stress intensity, psi AB 1589 AC 439 AD 724 BE 2406 AF 488 130