ML092020231
| ML092020231 | |
| Person / Time | |
|---|---|
| Site: | Browns Ferry  |
| Issue date: | 06/30/2009 |
| From: | Continuum Dynamics |
| To: | Office of Nuclear Material Safety and Safeguards |
| References | |
| 00053157, TVA-BFN-TS-418 CDI 09-13NP, Rev 0 | |
| Download: ML092020231 (66) | |
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 SR-P_<4, whereas the plots of alternating stress ratios display all nodes with SR-a_*4 or, in some cases, SR-a_<5 as indicated.
For CLTP operation at nominal frequency the minimum alternating stress ratio is SR-a=3.61, and occurs on the weld joining a lower tie bar to the exit flow perforated plate of the inner vane bank. Note that, as explained above in Section 5.1, no stress reduction factor has been applied to this location. If the stress reduction factor of 0.5 developed for this location in [5] were imposed then all locations of this type would disappear from the table. When all frequency shifts are included the minimum alternating stress reduces by 11% to SR-a=3.20 and occurs where the tie bar connecting the outer and middle vane banks lands on the middle hood.
The leading alternating stress locations in Table 9b generally occur on: (i) the lower tie bar/vane bank perforated plate junctions alluded to above; (ii) the bottom of the weld joining the drain channel to the skirt; (iii) the hood/hood support weld, particularly at the bottom where it connects to a base plate; and (iv) the closure plate/hood weld. The 3rd, 4 th, 10th and I Ith nodes in the table correspond to nodes whose computed stresses have been revised to reflect the results from detailed sub-modeling analysis in [26].
The minimum stress ratio due to maximum stress intensity at no frequency shift is SR-P=1.63 and occurs on the middle closure plate connecting to the inner hood; it reduces to 1.53 when all frequency shifts are included. All of these locations lie on welds.
The Tbar/base plate weld is an undersized stitch weld (an undersize weld factor of 2.0 is applied) and experiences a high localized stress at the innermost end of the T-beam. Since the Tbar is a secondary member, it is only necessary to verify that the part remains attached for the dryer lifetime. To this end a part retention analysis is conducted in Appendix A. The stresses reported here presume the condition where the innermost 14.5" of the weld are disconnected.
Full details of the stresses in the connected and disconnected conditions are provided in Appendix A.
Compared to previous stress analysis of the BFN2 steam dryer [6], the addition of the modified tie bars with widened and tapered ends has eliminated virtually all of the high stress areas previously associated with old tie bar bases resulting in stress ratios SR-a>3.20 for the welds on the ends of these tie bars. Moreover replacing the existing outer hood with one that is I in thick and supported by outer channels rather than interior supports results in substantially lower stresses overall. Finally, addition of the half-pipe reinforcement has eliminated all of the previous high stress locations on steam dam/gusset welds that were present without the half-pipe reinforcement.
In summary, the lowest alternating stress ratio occurs where the tie bar connecting the outer and middle vane banks lands on the middle hood. Its value, SR-a=3.20 at the -7.5% frequency shift indicates that stresses are well below allowable levels. The lowest stress ratio associated 63
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information with a maximum stress is SR-P=1.53. This value is dominated by the static component and is only weakly altered by acoustic loads. Since acoustic loads scale roughly with the square of the steam flow, it is reasonable to anticipate that under EPU conditions where the square of the steam flow increases by 35% the limiting stress ratio would reduce from 3.20 to 3.20/1.35=2.37.
This provides ample margin for sustained EPU operation, particularly given that: (i) the applied loads already account for all end-to-end biases and uncertainties; and (ii) no low power noise filtering has been performed.
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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 ype on the structure. Locations are depicted in Figure 14.
Stress Weld Location Location (in.) (a) node(b)
Stress Intensity (psi)
Stress Ratio Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a SR-P No
- 1. USR/Seismic Block/Support Part 122.1
-10
-9.5 147155 7635 7635 1833 2.21 6.74
- 2. USR part/Support/Support Part 7
122.3
-9.5 147263 6406 6406 1207 2.64 10.24
- 3. Middle Closure Plate 33.9 108.4 88.9 6647 5085 5358 809 3.32 15.28 SR-a No
- 1. Mid Plate/Shell Tie Bar 0
-58 88.9 121293 774 3498 2735 7.25 4.52 "SR-P Yes
- 1. TopCover Inner-Hood/Middle-Closure, 31.5 108.4 88.9 128332' 5707 6291 948 163 9.31 Plate/Inner Hood
- 2. Top Cover Middle Hood/Outer Closure
-62.5 85 88.9 130895 4452 4911 2074 2.09 4.26 Plate/Middle Hood
- 3. USR part/Support/Support Part 8.5 122.2
-9.5 147265 3990 3990 570 2.33 12.04
- 4. Middle Base Plate/Tbar(e) 41.8 0
0 133647 3934 4038 1170 2.36 5.87
- 5. Splice Bar/USR Part
-2.2
-119 0
147130 3770 3770 298 2.47 23.03
- 6. Top Cover Inner Hood/Inner Hood
-31.5
-110.1 88.9 130600 3143 3362 501 2.96 13.7
- 7. Hood Support/Vane Bank Thin/Inner Base
-24 0
0 133683 2888 2914 975 3.22 7.04 Plate/Vane Bank Section/Tbar(e)
- 8. Middle Base Plate/Hood Support/Inner Hood 39.8
-59.8 0
128813 2811 2832 1558 3.31 4.41
- 9. Submerged Drain Channel/Skirt(c) 91
-76.7
-100.5 113872 875 4209 1320 3.31 5.2 SR-a Yes
- 1. Mid Bottom Perf Plate (Exit)/Mid Top Perf.
-15
-19.9 62.9 117767 318 2095 1901 6.65 3.61 Plate (Exit)/Tie Bar
- 2. Mid Bottom Perf Plate (Exit)/Mid Top Perf.
-15 39.9 62.9 117818 653 1860 1714 7.49 4.01 Plate (Exit)/Tie Bar
- 3. Submerged Drain Channel/Skirt(c)
-11.5 118.4
-100.5 113791 747 3140 1677 4.44 4.1
- 4. Top Cover Middle Hood/Outer Closure
-62.5 85 88.9 130895 4452 4911 2074 2.09 4.26 Plate/Middle Hood
- 5. Top Cover Middle Hood/Middle Hood/Tie Bar 62.5
-22.2 88.9 129889 1357 2256 1609 6.18 4.27
- 6. Middle Base Plate/Hood Support/Inner Hood(d) 39.8 59.8 0
128553 1623 1708 1579 5.73 4.35
- 7. Middle Base Plate/Hood Support/Inner Hood 39.8
-59.8 0
128813 2811 2832 1558 3.31 4.41 See Table 8a for notes (a)-(e).
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9b. Locations with minimum stress ratios at 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.) (a) node(b)
Stress Intensity (psi)
Stress Ratio
% Freq.
Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a Shift SR-P No
- 1. USR/Seismic Block/Support Part 122.1
-10
-9.5 147155 7802 7802 2103 2.17 5.88 7.5
- 2. USR part/Support/Support Part 7
122.3
-9.5 147263 6709 6709 1476 2.52 8.38
-7.5
- 3. Middle Closure Plate 33.9 108.4 88.9 6647 5429 5745 1209 3.11 10.22 5
SR-a No
- 1. Mid Plate 0
-1.7 88.6 23532 342 3685 3256 6.88 3.80
-10
- 2. Mid Plate/Tie Bar 0
-58 88.9 121293 852 3877 2842 6.54 4.35 10 SR-P.
Yes 1.1Tp Cover Inner Hood/Middler 31.5 108.4 88.9 128332 6077 6711
.13706 1.53 6.44.
5
_Closure P1late/Inner Hood
- 2. Top Cover Middle Hood/Outer
-62.5 85 88.9 130895 4531 5080 2120 2.05 4.16 5
Closure Plate/Middle Hood
- 3. Middle Base Plate/Tbar(e) 41.8 0
0 133647 4343 4432 1495 2.14 4.6
-5
- 4. USR part/Support/Support Part 8.5 122.2
-9.5 147265 4148 4148 709 2.24 9.69 7.5
- 5. Splice Bar/USR Part
-2.2
-119 0
147130 3917 3917 417 2.37 16.48 7.5
- 6. Submerged Drain Channel/Skirt 91
-76.7
-98.5 113874 347 4926 1496 2.83 4.59
-7.5
- 7. Top Cover Inner Hood/Inner Hood
-31.5
-110.1 88.9 130600 3258 3478 597 2.85 11.51
-7.5
- 8. Submerged Drain Channel/Skirt(c) 91
-76.7
-100.5 113872 1077 4692 1768 2.97 3.89
-7.5
- 9. Middle Base Plate/Hood 39.8
-59.8 0
128813 3114 3150 1971 2.98 3.48 2.5 Support/Inner Hood I__
r_-.
- 10. Inner Base Plate/Vane Bank Section/Tbar(e)
-17.2 0
0 133679 3046 3061 1085 3.05 6.33
-7.5 See Table 8a for notes (a)-(e).
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9b (cont.). Locations with minimum stress ratios at 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.) (a) node(b)
Stress Intensity (psi)
Stress Ratio
% Freq.
Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a Shift SR-a Yes
- 1. Top Cover Middle Hood/Middle 62.5
-22.2 88.9 129889 1507 2723 2143 5.12 3.20
-7.5 Hood/Tie Bar
- 2. Mid Bottom Perf. Plate (Exit)/Mid Top 15 19.9 62.9 117630 335 2177 2097 6.4 3.28
-2.5 Perf. Plate (Exit)/Tie Bar
- 3. Submerged Drain Channel/Skirt(c)
-11.5 118.4
-100.5 113791 860 3531 2062 3.95 3.33
-10
- 4. Middle Base Plate/Hood Support/Inner Hood(d) 39.8 59.8 0
128553 2108 2195 2035 4.41 3.38 5
- 5. Middle Base Plate/Hood Support/Inner Hood 39.8
-59.8 0
128813 3114 3150 1971 2.98 3.48 2.5
- 6. Mid Bottom Perf. Plate (Exit)/Mid Top
-46 36.4 62.9 118129 586 1961 1905 7.11 3.61 10 Perf. Plate (Exit)/Tie Bar
- 7. Mid Bottom Perf. Plate (Exit)/Mid Top
-46 18.2 62.9 118066 507 2037 1904 6.84 3.61 10 Perf. Plate (Exit)/Tie Bar
- 8. Hood Support/Inner Hood
-35.6
-59.8 38.9 130150 358 1999 1900 6.97 3.61
-7.5
- 9. Mid Bottom Perf. Plate (Exit)/Mid Top
-15 39.9 62.9 117818 687 2134 1896 6.53 3.62
-2.5 Perf. Plate (Exit)/Tie Bar
- 10. Submerged Drain Channel/Skirt(c)
-91
-76.7
-100.5 113764 1072 4438 1883 3.14 3.65 7.5
- 11. Middle Base Plate/Hood Support/Middle Hood(d) 70.8 54.6 0
127334 1745 1970 1869 5.33 3.67 5
- 12. Middle Base Plate/Hood Support/Middle Hood 70.8
-54.6 0
127635 2041 2343 1839 4.55 3.74 7.5
- 13. Mid Plate Support/Mid Plate 0
17 2
123493 266 1849 1821 7.54 3.77
-10
- 14. Top Cover Middle Hood/Outer Closure 62.5 85 88.9 127245 2329 2386-1776 3.99 3.87 5
Plate/Middle Hood
- 15. Middle Closure Plate/Inner Hood
-35.4
-108.4 39.9 130648 612 1904 1746 7.32 3.93
-7.5 See Table 8a for notes (a)-(e).
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 14a. Locations of smallest maximum stress ratios, SR-P<4, at non-welds for nominal CLTP operation. Numbers refers to the enumerated locations for SR-P values at non-welds in Table 9a.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
SR-a m5 4.8 4.6 4.4 4.2 4
Figure 14b. Locations of smallest alternating stress ratios, SR-a_<5, at non-welds for nominal CLTP operation. Number refers to the enumerated locations for SR-a values at non-welds in Table 9a.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information SR-P 3.9 3.6 3.3 3
2.7 2.4 2.1 1.8 1.5 Figure 14c. Locations of smallest maximum stress ratios, SR-P<4, at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 9a.
First view showing locations 1-3 and 6.
70
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 14d. Locations of smallest maximum stress ratios, SR-P_<4, at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 9a.
Second view showing locations 5, 6 and 9.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 14e. Locations of smallest maximum stress ratios, SR-P*4, at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 9a.
Third view showing locations 4 and 7-9.
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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 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. First view showing locations 1, 2, 4 and 5.
73
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 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.
Second view showing locations 3, 6 and 7.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15a.
Locations of minimum stress ratios, SR-P<4, associated with maximum stress intensities 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.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
x SR-a 5
4.9 4.8 4.7 4.6 4.5 4.4 4.3 4.2 4.1 4
3.9 3.8 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 welds in Table 9b.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Z
SR-P 3.9 3.6 3.3 3
2.7 2.4 2.1 1.8 1.5 Figure 15c.
Locations of minimum stress ratios, SR-P_<4, associated with maximum stress intensities 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, 2, 4 and 7.
77
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
tx SR-P 3.9 3.6 3.3 3
2.7 2.4 2.1 1.8 1.5 Figure 15d.
Locations of minimum stress ratios, SR-P*4, associated with maximum stress intensities 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 5-8.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Y z SR-P 3.9 3.6 3.3 3
2.7 2.4 2.1 1.8 1.5 Figure 15e.
Locations of minimum stress ratios, SR-P<4, associated with maximum stress intensities 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 3, 6 and 8-10.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Yz f-x SR-a 5
4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 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 shows locations 1, 2, 14 and 15.
80
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 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. Second view showing locations 1, 6, 7, 9, 13 and 14.
81
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 9i SR-a 5
4.8 4.6 4.4 4.2 4
3.8 3.6 3.4 3.2 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. Third view showing locations 3, 5, 8, 10, 12 and 15.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information x
SR-a 5
4.8 4.6 4A4 4.2 4
3.8 3.6 3.4 3.2 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. Fourth view showing locations 4, 10 and 11.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.3 Frequency Content 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 (On)=k=1 where &(iOk) is the complex stress harmonic at frequency, 0ok. 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 X(w) 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 X(0N) (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 first, second, fourth and fifth locations having the lowest alternating stress ratios (at a weld) in Table 9b, together with the limiting node at EPU in Table lOb. These nodes are:
Node 129889 - this node has the lowest alternating stress ratio and is located on the weld where the tie bar connecting the middle and outer vane banks lands on the middle hood. The associated PSDs are shown in Figure 16a.
Node 117630- located at end of the lower tie bar connecting to the exit perforated plate of the inner vane bank. The associated PSDs are shown in Figure 16b.
Node 113791 - located at bottom of the skirt/drain channel weld. The associated PSDs are shown in Figure 16c.
Node 128553 - located at the middle base plate/inner hood/hood support junction. The associated PSDs are shown in Figure 16d.
Node 130895 - located on the weld joining the middle hood, its top cover plate and the outer closure plate. This node appears as the limiting node at EPU when all frequency shifts are considered. The associated PSDs are shown in Figure 16e.
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 percomponent.
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.
For the limiting stress location, the dominant frequency peak is centered at 79.6 Hz. Since it occurs at the -7.5% shift, the corresponding frequency in 'the non-shifted signal is 85.6 Hz.
84
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Comparing the shifted and non-shifted stress PSDs (and accumulative PSDs) it is clear that peaks (or step increases) are shifted and amplified. This is indicative of a strong peak in the load signal being applied to the structure. This is in contrast to the case when stress peaks increase but do not shift which is indicative of a broad spectrum load with less pronounced peaks being imposed upon the structure. The next location (node 117630) manifests a dominant response at 62.6 Hz (65.9 Hz in the unshifted signal). This is close to the 57.9 Hz peak (64.3 Hz in the unshifted signal) in the third location (node 113791) and 67.1 Hz (63.9 Hz unshifted) in the fourth location (node 128553) and also aligns closely with the second highest peak in the limiting stress location. All of these (unshifted) signals are in the 60-70 Hz range where the signal bias and uncertainty have been increased.
The fourth and fifth locations also exhibit a strong peak at 116.7 Hz (111.1 Hz unshifted) (for the fifth node 130895 this is the dominant peak). This is in the 109-113 Hz range where the onset of SRV resonance is anticipated so one expects these peaks to become more pronounced in the EPU response as is confirmed in Section 6. In all cases the accumulative stress PSDs are nearly flat above 150 Hz (a slight slope is evident which is characteristic of the background noise that has been left in the signals) suggesting that the signals at high frequencies are not significant stresses contributors.
Specifically, no significant FIV sources appear present at these higher frequencies.
85
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 129889, c (00.
N d
C,)
0~
G)
-5EE 0
N I
(0 0~
0a) 0~
a) 350 300 250 200 150 100 50 0
10 104 1000 10 0.1 0.01 No shft 0
50 100 150 200 Frequency [ Hz ]
Node 129889, az 250 No shff 9
9 t
f!1 0
50 100 150 200 250 Frequency [ Hz ]
Figure 16a. Accumulative PSD and PSD curves of the rzz stress response at node 129889.
86
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 117630, a cn E~
E 300 250 200 150 100 No shift
-2.5% shift 50 0
0 50 100 150 200 250 Frequency [ Hz ]
Node 117630, ar 10 5 104 N
(n a-0ci) 0~
C,)
C,)
C)
C')
Noshff 1000 100 10 f
9 0.1 0ý01 0
50 100 150 200 250 Frequency [ Hz ]
Figure 16b. Accumulative PSD and PSD of the azz stress response at node 117630.
87
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 113791, a U)
Q.
E E
500 400 300 200 100 0
No0shift 0
50 100 150 200 250 Frequency [ Hz ]
Node 113791, aYY 106 101 10e NM CD Q-U) 1000 100 "9!
10 I*
No shift
-10%shf A
20 150 200 1
0.1 0.01 0
50 100 250 Frequency [ Hz ]
Figure 16c. Accumulative PSD and PSD of the (yy stress response at node 113791.
88
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 128553, a
()
E E
500 400 300 200 100 0 Noshift 0
50 100 150 200 250 Frequency [ Hz ]
Node 128553, a 10 5 104 9
0)
(/)
1000 100
+5%shj 9
10 0.1 0.01 0
50 100 1 50 200 250 Frequency [ Hz ]
Figure 16d. Accumulative PSD and PSD of the Txx stress response at node 128553.
89
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 130895, cyx C,,
cc E
350 300 250 200 150 100 50 0
10O l0O 1000 100 10 L+5% shift 0
50 100 150 200 250 Frequency [ Hz]
Node 130895, a 9e No shift
+51Y. shift Jý 0e J iq A
1 0.1 0.01 0
50 100 150 200 250 Frequency [ Hz ]
Figure 16e. Accumulative PSD and PSD of the
,,xx stress response at node 130895.
90
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 6. Results at Predicted EPU Using Bump Up Factors
[(3 (3)))
91
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 6.1 Load Combinations and Allowable Stress Intensities at EPU (3)))
92
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 10a. Locations with minimum stress ratios for estimated EPU 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 17.
Stress Weld Location Location (in.) (a) node(b)
Stress Intensity (psi)
Stress Ratio Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a SR-P No
- 1. USR/Seismic Block/Support Part 122.1
-10
-9.5 147155 8309 8309 2562 2.03 4.83
- 2. USR part/Support/Support Part 7
122.3
-9.5 147263 6776 6776 1634 2.49 7.56
- 3. Middle Closure Plate
-33.9
-108.4 88.9 7323 5475 5692 1198 3.09 10.32 SR-a No
- 1. Mid PlateTie Bar 0
-58 88.9 121293 976 5427 4804 4.67 2.57
- 2. Mid Plate/Tie Bar 0
-3.2 88.9 130877 758 4276 3538 5.93 3.49
- 3. USR/Seismic Block/Support Part 122.1
-10
-9.5 147155 8309 8309 2562 2.03 4.83 SR:P Yes
-1. Top Cover InnierHOod/Middle Closure '
31.5
'i08.4
-88.9 128332".6.i39. *-:6718'4 -:1427, 1.51.:;6.19
ýPlaite/Inner'Hood
~--:-~'.'
- 2. Top Cover Middle Hood/Outer Closure
-62.5 85 88.9 130895 6003 6480 3464 1.55 2.55 Plate/Middle Hood
- 3. Middle Base Plate/Tbar(e) 41.8 0
0 133647 4453 4567 1653 2.09 4.16
- 4. USR part/Support/Support Part 8.5 122.2
-9.5 147265 4103 4103 774 2.27 8.87
- 5. Splice Bar/USR Part
-2.2
-119 0
147130 3878 3878 405 2.4 16.97
- 6. Middle Base Plate/Hood Support/Inner Hood 39.8
-59.8 0
128813 3833 3834 2480 2.43 2.77
- 7. Hood Support/Thin Vane Bank/Inner Base
-24 0
0 133683 3403 3430 1444 2.73 4.76 Plate/Vane Bank Section/Tbar(e)
- 8. Top Cover Inner Hood/Inner Hood
-31.5
-110.1 88.9 130600 3390 3644 805 2.74 8.54
- 9. Submerged Drain Channel /Skirt(c) 91
-76.7
-100.5 113872 1091 4838 1887 2.88 3.64
- 10. Middle Base Plate/Thin Vane Bank/Vane 86
-28.7 0
115276 727 4707 1709 2.96 4.02 Bank Section
- 11. Submerged Drain Channel/Skirt 91
-76.7
-98.5 113874 352 4550 1214 3.06 5.66 See Table 8a for notes (a)-(e).
93
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 10a (cont.). Locations with minimum stress ratios for estimated EPU 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 17.
Stress Weld Location Location (in.) (a) node(b)
Stress Intensity (psi)
Stress Ratio Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a SR-a Yes
- 1. Top Cover Middle Hood/Outer Closure
-62.5 85 88.9 130895 6003 6480 3464 1.55 2.55 Plate/Middle Hood
- 2. Mid Bottom Perf Plate (Exit)/Mid Top Perf.
-15
-19.9 62.9 117767 423 2847 2624 4.9 2.62 Plate (Exit)/Tie Bar
- 3. Middle Base Plate/Hood Support/Middle Hood(d) 70.8 54.6 0
127334 2451 2646 2586 3.79 2.66
. 4. Middle Base Plate/Hood Support/Inner Hood(d) 39.8 59.8 0
128553 2615 2772 2561 3.55 2.68
- 5. Hood Support/Middle Hood
-67.1 54.6 36.6 131019 246 2669 2556 5.22 2.69
- 6. Gusset Pad Thin/Top Cover Outer Hood/Top
-91.5 57.5 88.9 113537 364 3175 2492 4.39 2.76 Reinforcement
- 7. Middle Base Plate/Hood Support/Inner Hood 39.8
-59.8 0
128813 3833 3834 2480 2.43 2.77
- 8. Middle Base Plate/Hood Support/Middle Hood 70.8
-54.6 0
127635 2843 2911 2357 3.27 2.91
- 9. Mid Bottom Perf Plate (Exit)/Mid Top Perf.
-15 39.9 62.9 117818 725 2484 2346 5.61 2.93 Plate (Exit)/Tie Bar
- 10. Submerged Drain Channel /Skirt(c)
-11.5 118.4
-100.5 113791 1077 3858 2321 3.61 2.96
- 11. Top Cover Middle Hood/Middle Hood/Shell Tie Bar 62.5
-22.2 88.9 129889 1664 2948 2280 4.73 3.01
- 12. Mid Bottom Perf Plate (Exit)/Mid Top Perf.
-46
-18.2 62.9 118079 364 2129 2107 6.55 3.26 Plate (Exit)/Tie Bar See Table 8a for notes (a)-(e).
94
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 10b. Locations with minimum stress ratios at estimated EPU 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 18.
Stress Weld Location Location (in.) (a) node(b)
Stress Intensity (psi)
Stress Ratio
% Freq.
Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a Shift SR-P No
- 1. USR/Seismic Block/Support Part 122.1
-10
-9.5 147155 8490 8490 2843 1.99 4.35 7.5
- 2. USR part/Support/Support Part 7
122.3
-9.5 147263 7201 7201 1992 2.35 6.21
-7.5
- 3. Middle Closure Plate 33.9 108.4 88.9 6647 6111 6461 1926 2.77 6.42 5
SR-a No
- 1. Mid Plate/Tie Bar 0
-58 88.9 121293 1056 5427 4804 4.67 2.57 0
it
- 2. Mid Plate 0
-1.7 88.6 23532 398 4869 4401 5.21 2.81
-10
- 3. Inner Hood
-35.8
-81.9 38.2 49770 334 3165 3076 8.01 4.02
-7.5 SR-P Yes
- 1. Top Cover Inner-Hood/Middle :
31.5.108.4 88.9 128332 6832.-7422 2197 i136.
4.02 5.
Closure Plate/Inner Hood;-
- 2. Top Cover Middle Hood/Outer
-62.5 85 88.9 130895 6468 6862 4054 1.44 2.18 5
Closure Plate/Middle Hood
- 3. Middle Base Plate/Tbar(e) 41.8 0
0 133647 4928 5024 2031 1.89 3.38
-5
- 4. USR part/Support/Support Part 8.5 122.2
-9.5 147265 4316 4316 964 2.15 7.13 10
- 5. Middle Base Plate/Hood Support/Inner Hood 39.8
-59.8 0
128813 4151 4191 3046 2.24 2.25 2.5
- 6. Splice Bar/USR Part
-2.2
-119 0
147130 4071 4071 566 2.28 12.13 7.5
- 7. Submerged Drain Channel/Skirt 91
-76.7
-98.5 113874 417 5504 2014 2.53 3.41
-7.5
- 8. Inner Base Plate/Vane Bank Section/Tbar(e) 21.8 0
0 117782 3662 3682 1979 2.54 3.47 5
- 9. Submerged Drain Channel/Skirt(c) 91
-76.7
-100.5 113872 1330 5460 2570 2.55 2.67 5
- 10. Top Cover Inner Hood/Inner Hood
-31.5
-110.1 88.9 130600 3544 3772 915 2.62 7.51 2.5
- 11. Middle Base Plate/Vane Bank 86
-28.7 0
115276 766 5105 2083 2.73 3.3
-5 Thin/Vane Bank Section
- 12. Middle Base Plate/Hood Support/Inner Hood(d)
-39.8 59.8 0
129842 3353 3555 2360 2.77 2.91
-5
- 13. Middle Base Plate/Hood Support/Middle Hood 70.8
-54.6 0
127635 3092 3151 2788 3.01 2.46
-2.5 See Table 8a for notes (a)-(e).
95
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 10b (cont.). Locations with minimum stress ratios at estimated EPU 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 18.
Stress Weld Location Location (in.) (a) node(b)
Stress Intensity (psi)
Stress Ratio
% Freq.
Ratio x
y z
Pm Pm+Pb Salt SR-P SR-a Shift SR-a Yes
- 1. Top Cover Middle Hood/Outer Closure
-62.5 85 88.9 130895 5031 5337 3153 1.85 2.18 5
Plate/Middle Hood
- 2. Middle Base Plate/Hood Support/Inner Hood(d) 39.8 59.8 0
128553 3262 3349 3144 2.85 2.18 5
- 3. Hood Support/Middle Hood
-66.6 54.6 38.9 131020 278 3251 3120 4.29 2.20
-2.5
- 4. Gusset Pad Thin/Top Cover Outer Hood/Top Reinforcement 91.5
-57.5 88.9 122251 348 3774 3101 3.69 2.21 5
- 5. Middle Base Plate/Hood Support/Inner Hood 39.8
-59.8 0
128813 4151 4191 3046 2.24 2.25 5
- 6. Top Cover Middle Hood/Middle Hood/Tie Bar 62.5
-22.2 88.9 129889 1888 3537 2968 3.94 2.31
-7.5
- 7. Mid Bottom Perf Plate (Exit)/Mid Top Perf.
15 19.9 62.9 117630 416 2923 2847 4.77 2.41
-2.5 Plate (Exit)/Tie Bar
- 8. Middle Base Plate/Hood Support/Middle Hood(d) 70.8 54.6 0
127334 2695 2957 2844 3.45 2.41 5
- 9. Mid Bottom Perf Plate (Exit)/Mid Top Perf.
-46 18.2 62.9 118066 633 2921 2843 4.77 2.42 10 Plate (Exit)/Tie Bar
- 10. Middle Base Plate/Hood Support/Middle Hood 70.8
-54.6 0
127635 3092 3151 2788 3.01 2.46 7.5
- 11. Submerged Drain Channel/Skirt(c)
-11.5 118.4
-100.5 113791 1170 4379 2780 3.18 2.47
-10
- 12. Mid Bottom Perf Plate (Exit)/Mid Top Perf.
77
-66.9 62.9 118529 1043 2830 2717 4.93 2.53 5
Plate (Exit)/Tie Bar
- 13. Mid Bottom Perf Plate (Exit)/Mid Top Perf.
-46 36.4 62.9 118129 759 2708 2624 5.15 2.62 10 Plate (Exit)/Tie Bar
- 14. Submerged Drain Channel/Skirt(c)
-91
-76.7
-100.5 113764 1330 5129 2619 2.72 2.62 7.5
- 15. Hood Support/Inner Hood
-35.6
-59.8 38.9 130150 443 2662 2566 5.24 2.68
-7.5
- 16. Mid Bottom Perf Plate (Exit)/Mid Top Perf.
-15 39.9 62.9 117818 771 2821 2556 4.94 2.69
-2.5 Plate (Exit)/Tie Bar
- 17. Hood Support/Inner Hood
-39.7
-59.8 18.8 130120 899 2718 2516 5.13 2.73
-5 See Table 8a for notes (a)-(e).
96
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 17a. Locations of smallest maximum stress ratios, SR-P<4, at non-welds for nominal EPU operation. Numbers refers to the enumerated locations for SR-P values at non-welds in Table 10a.
97
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 17b. Locations of smallest alternating stress ratios, SR-a<5, at non-welds for nominal EPU operation. Numbers refers to the enumerated locations for SR-a values at non-welds in Table 1Oa.
98
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Fz XA~
Y SR-P 3.9 3.6 3.3 3
2.7 2.4 2.1 1.8 1.5 Figure 17c. Locations of smallest maximum stress ratios, SR-P<4, at welds for nominal EPU operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 10a.
First view showing locations 1, 2, 4 and 8.
99
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 17d. Locations of smallest maximum stress ratios, SR-P<4, at welds for nominal EPU operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 10a.
Second view showing locations 5, 8, 9 and 11.
100
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Y z SR-P 3.9 3.6 3.3 3
2.7 2.4 2.1 1.8 1.5 Figure 17e. Locations of smallest maximum stress ratios, SR-P<4, at welds for nominal EPU operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 10a.
Second view showing locations 3, 6, 7 and 9-11.
101
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 177f. Locations of minimum alternating stress ratios, SR-a<<5, at welds for nominal EPU operation. Numbers refer to the enumerated locations for SR-a values at welds in Table 1 Oa.
First view showing locations 1, 2, 6, 9, 11 and 12.
102
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Y
SR-a 4.9 4.7 4.5 4.3 4.1 3.9 3.7 3.5 3.3 3.1 2.9 2.7 2.5 Figure 17g. Locations of minimum alternating stress ratios, SR-a_<5, at welds for nominal EPU operation. Numbers refer to the enumerated locations for SR-a values at welds in Table 1 Oa.
Second view showing locations 3-5 and 10.
103
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information x
Y SR-a 4.9 4.7 4.5 4.3 4.1 3.9 3.7 3.5 3.3 3.1 2.9 2.7 2.5 Figure 17h. Locations of minimum alternating stress ratios, SR-a*<5, at welds for nominal EPU operation. Numbers refer to the enumerated locations for SR-a values at welds in Table 10a.
Third view showing locations 7 and 8.
104
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information SR-P 4
3.8 3.6 3.4 3.2 3
2.8 2.6 2.4 2.2 2
Figure 18a.
Locations of minimum stress ratios, SR-P<4, associated with maximum stress intensities at non-welds for EPU 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 10b.
105
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information SR-a 4.9 4.7 4.5 4.3 4.1 3.9 3.7 3.5 3.3 3.1 2.9 2.7 2.5 Figure 18b.
Locations of smallest alternating stress ratios, SR-a_<5, at non-welds for EPU 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-a values at non-welds in Table 10b.
106
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 3.9 3.7 3.5 3.3 3.1 2.9 2.5 2.3 2.1 1.9 1.7 1.3 Figure 18c.
Locations of minimum stress ratios, SR-P<4, associated with maximum stress intensities at welds for EPU 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 10b. This view shows locations 1, 2, 4 and 10.
107
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
Yi' i
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 18d.
Locations of minimum stress ratios, SR-P_<4, associated with maximum stress intensities at welds for EPU 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 lOb. This view shows locations 6, 7, 9 and 10.
108
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 18e.
Locations of minimum stress ratios, SR-P<4, associated with maximum stress intensities at welds for EPU 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 lOb. This view shows locations 3, 5, 8, 9, 11 and 13.
109
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information SR-P m
3.9 3.7 3.5 3.3 3.1 2.9 2.7 2.5 z
2.3 1.3 Figure 18f.
Locations of minimum stress ratios, SR-P<4, associated with maximum stress intensities at welds for EPU 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 I Ob. This view shows locations 7, 9 and 12.
110
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information v
Oda--
V.
-S 0 W S
MAN MR-4V IF3z 3ts 3M 3-*
3z:
2M 2~
4 2N-2zok Figure 1g. Locaion fmnmmatraigsrs ais Ra<,a ed o
P prto with freqencyzshitsThreoddsrsraiatandistemnmmvleaknvral freqencyshits.
umbes rfer o te enmeraed ocatons orR-a aluSSa ed i al 10b Tisviw sow lcaion 14,6,9, 3End16 111
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 18h. Locations of minimum alternating stress ratios, SR-a_<4, at welds for EPU 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 lOb. This view shows locations 1,4, 6, 7 and 12.
112
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 18i. Locations of minimum alternating stress ratios, SR-a_<4, at welds for EPU 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 lOb. This view shows locations 2, 3, 8 and 14.
113
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 04.
L.
WOM a
as8 a2.
04w4 JV4 PM2.2 Figur 18j oction of mnimu altrnatng stess atio, SRa<4 OtWelsfrEUNprto wihfrqecysifs hercrde stes rati atand stemnimmvlu ae oe 1~ '0.
of i 2z e h w 1oai n 5,1,1,1 n07 114
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 6.2 Frequency Content at EPU The same nodes whose frequency content was examined in Section 5.3 are considered here.
At EPU these nodes reappear in Table 10b as the first or limiting (node 130895), second (node 128553), sixth (node 129889), seventh (node 117630) and twelfth (node 113791) entries in the list of lowest alternating stress ratio locations. The stress PSDs and accumulative stress PSDs are reported in Figure 19 in the same order as in Section 5.3 to facilitate comparison between the plots at CLTP and EPU.
After one accounts for the overall velocity ratio-based scaling of 1.35 (which corresponds to 2
a factor of 1.35 =1.82 scaling in PSDs) the stress PSDs and accumulative PSDs at CLTP and EPU conditions are very similar. This is clearly the case for the first node 129889 which was limiting at CLTP. Moreover, its alternating stress ratio at EPU is SR-a=2.31 which is close to the value expected from scaling the CLTP value, SR-a=3.20/1.35=2.37. Similar observations hold for the second and third nodes. For the fifth node 130895 which is limiting at EPU, the curves at CLTP and EPU are still similar, but the increase over the 109-113 Hz range is higher than the velocity ratio scaling, 1.35. This is because the bump-up factor and the associated bias and uncertainty are higher in this range. Hence the increase in the peak in the stress PSD is also higher. This is ultimately reflected in the change in stress ratio from SR-a=4.16 at CLTP to SR-a=2. 18 at EPU which corresponds to an increase in alternating stress intensity of 91% rather than the 35% increase resulting from a pure velocity-based scaling. For the fourth node 128553 located on the inner hood/hood support/base plate junction, the stress increase from CLTP to EPU is 55%. This is consistent with a location (such as this one - Figure 19d) with significant stress contributions from both inside and outside the 100-120 Hz frequency range, the latter receiving a 35% increase in the stress contribution and the former obtaining a higher increase. A summary of these observations and the relative stress intensity changes between CLTP and EPU is given in Table 11.
Table 11. Comparison of CLTP and EPU alternating stress ratios at selected locations.
Location Node SR-a (CLTP Freq. Shift (%)
Stress Change CLTP EPU CLTP EPU
- 1. Top Cover Middle Hood/Middle 129889 3.2 2.31
-7.5
-7.5 39%
Hood/Tie Bar
- 2. Mid Bottom Perf. Plate (Exit)/Mid Top 117630 3.28 2.41
-2.5
-2.5 36%
Perf. Plate (Exit)/Tie Bar
- 3. Submerged Drain Channel/Skirt 113791 3.33 2.47
-10
-10 35%
- 4. Middle Base Plate/Hood Support/Inner Hood 128553 3.38 2.18
+5
+5 55%
- 5. Top Cover Middle Hood/Outer Closure 130895 4.16 2.18
+5
+5 91%
Plate/Middle Hood 115
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 129889, az 500 C',
lid (U
a-E E
400 300 200 100 0
No shift
-7.5% s1hift 0
50 100 150 200 250 Frequency [Hz]
Node 129889, a 10 5 104 X
0)
CO) 1000 j..
<'F 100 10 1
0.1 0No sh2ft
-7.5% shift 200 250 0.01 0
50 100 150 Frequency [ Hz ]
Figure 19a. Accumulative PSD and PSD of the azz stress response at node 129889 at EPU.
116
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 117630, az
-C, (D
E E
400 350 300 250 200 150 100 No shift 50 0
0 50 100 150 200 250 Frequency [ Hz ]
Node 117630, a 106 105 10, N~o shffJ N
U)
(L 1000 100 10
~flj "0',S 1
0.1 0.01 0
50 100 150 200 250 Frequency [ Hz ]
Figure 19b. Accumulative PSD and PSD of the cyz stress response at node 117630 at EPU.
117
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 113791, a Cc)
M~
E 700 600 500 400 300 200 100 0
r No shift
-10% sh]ift 0
50 100 150 200 250 Frequency [ Hz ]
Node 113791, a 106 105 104 9
No shfft I 1
-10% shift N
Cl) 0-E,
.9 0
1000
.9 0
100 10 4
0.1 0.01 0
50 100 150 200 250 Frequency [ Hz ]
Figure 19c. Accumulative PSD and PSD of the (Y stress response at node 113791 at EPU.
118
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 128553, c 700 C,,
0q E
E 600 500 400 300 200 100 0
No shift 0
50 100 150 200 250 Frequency [ Hz]
Node 128553, a 106 10o5 1 04
[
o hft]
ci)
U) 1000 100 e
10 1
0.1 0.01 0
50 100 150 200 250 Frequency [ Hz ]
Figure 19d. Accumulative PSD and PSD of the Yxx stress response at node 128553 at EPU.
119
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 130895, a a.
E 600 500 400 300 200 100 0
No shift
+5% shift 0
50 100 150 200 250 Frequency [ Hz]
Node 130895, c,xx 106 105 104 9 Noshif N
0)
C,)
U) w 1000 1 ý
'," 1 141 1, V, [ 'o"J 0
100 V
10 0.1 0.01 0
50 100 150 200 250 Frequency [ Hz ]
Figure 19e. Accumulative PSD and PSD of the Yxx stress response at node 130895 at EPU.
120
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 7. Conclusions A frequency-based steam dryer stress analysis has been used to calculate high stress locations and calculated / allowable stress ratios for the Browns Ferry 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 BFN2 steam dryer is presented. The CLTP loads obtained in a separate acoustic circuit model [2, 3, 8], including end-to-end bias and uncertainty for both the ACM 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 resulting stress histories were analyzed to obtain maximum and alternating stresses, at all nodes for comparison against allowable levels.
For added conservatism, no low power noise filtering is attempted in the current analysis.
The stresses resulting from the application of CLTP loads to the steam dryer are tabulated in Table 9 of this report. The minimum alternating stress ratio at nominal operation is SR-a=3.61 and the minimum alternating stress ratio taken over all frequency shifts is SR-a=3.20. The stress ratios corresponding to maximum stresses are SR-P=1.63 at nominal operation and 1.53 when all frequency shifts are considered. The results show that the new tie-bars with widened and tapered ends, and the thicker I in'hood with external channel reinforcements replacing the interior hood supports result in significantly lower stresses.
On the basis of these CLTP plant loads, the dynamic analysis of the steam dryer shows that the combined acoustic, hydrodynamic, and gravity loads produces the following minimum stress ratios.
Frequency Shift Minimum Stress Ratio at CLTP Max. Stress, Alternating Stress, SR-P SR-a 0% (nominal) 1.63 3.61
-10%
1.65 3.29
-7.5%
1.59 3.20
-5%
1.61 3.48
-2.5%
1.62 3.28
+2.5%
1.59 3.48
+5%
1.53 3.38
+7.5%
1.56 3.62
+10%
1.57 3.46 All shifts 1.53 - 1.65 3.20-3.62 Limiting 1.53 3.20 EPU stresses are estimated using two methods. The first scales the CLTP stresses by the square of the steam flow velocity ratio, (UEPU/UCLTP)--=1.35. The second method utilizes the bump up factors developed in [4] over the 100-120 Hz frequency interval and the velocity scaling (1.35) at all other frequencies.
The limiting stress ratios using these methods are 121
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information summarized for each frequency shift in the table below. The limiting alternating stress ratios at any frequency shift are: 2.37 with velocity scaling (Method 1) and 2.18 when bump up factors are used over the 100-120 Hz range (Method 2). In all cases the alternating stress ratio remains above 2.0, thus qualifying the steam dryer for EPU operation with regard to stress evaluation.
Frequency Shift Method I Method 2 Alt. Stress, Max. Stress, Alt. Stress, SR-a SR-P SR-a 0% (nominal) 2.68 1.51 2.55
-10%
2.44 1.56 2.44
-7.5%
2.37 1.49 2.31
-5%
2.57 1.51 2.44
-2.5%
2.43 1.50 2.20
+2.5%
2.58 1.47 2.27
+5%
2.50 1.36 2.18
+7.5%
2.68 1.45 2.35
+10%
2.57 1.47 2.42 All shifts 2.37-2.68 1.36 - 1.56 2.18 - 2.55 Limiting 2.37 1.36 2.18 122
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 8. References
- 1.
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), November.
- 2.
Continuum Dynamics, Inc. (2008), Acoustic and Low Frequency Hydrodynamic Loads at CLTP Power Level on Browns Ferry Nuclear Unit 2 Steam Dryer to 250 Hz with Noise Removed, Rev. 1, C.D.I. Report No.08-05P (Proprietary).
- 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), Flow-Induced Vibration in the Main Steam Lines at Browns Ferry Nuclear Units I and 2, With and Without Acoustic Side Branches, and Resulting Steam Dryer Loads, C.D.I. Report No.08-14P (Proprietary).
- 5.
Continuum Dynamics, Inc. (2009), Stress Assessment of Browns Ferry Nuclear Unit I Steam Dryer with Tie-Bar Modifications, Rev. 3, C.D.I. Report No.08-15P (Proprietary),
March.
- 6.
Continuum Dynamics, Inc. (2008), Stress Assessment of Browns Ferry Nuclear Unit 2 Steam Dryer, Rev. 1, C.D.I. Report No.08-07P (Proprietary).
- 7.
Continuum Dynamics, Inc. (2008), Stress Assessments of Browns Ferry Nuclear Unit 2 Steam Dryer with Tie Bar and Hood Modifications, Rev. 0, C.D.I. Report No.08-16P (Proprietary).
- 8.
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).
- 9.
Structural Integrity Associates, Inc. (2006), Main Steam Line 100% CLTP Strain Data Transmission, SIA Letter Report No. GSZ-06-017.
- 10.
ANSYS URL: http://www.ansys.com, ANSYS Release 10.0 Complete User's Manual Set.
- 11.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Appendix A. Part Retention Analysis of the T-Beam Introduction The lowest stress ratio calculated for the BFN2 steam dryer involves the T-bar connected to the base plates along the centerline of the dryer. The connection consists of staggered stitch welds. These welds are undersized since the weld leg is 1/44" whereas both the T-bar and base plates are '/2" thick. For this reason an undersize weld factor of 2.0 must be applied to the stresses in addition to the weld factor of 1.8 (i.e., the calculated nominal stresses are multiplied by 3.6) to obtain the limiting stress in the weld for comparison to the allowable stress levels.
The T-bar is not a primary structural member. While a definitive statement regarding its purpose cannot be documented, it appears to have been added to facilitate transportation and assembly of the two steam dryer halves. This assertion is supported by the observations that it is not continuous (hence the appearance of a stress concentration at its inboard ends) and it is connected to the base plates by an undersized stitch weld. Moreover, its removal in the finite element model does not produce any significant stress change elsewhere in the steam dryer.
Nevertheless, although it is a secondary structural member, it cannot simply be dismissed on this basis since it still experiences high stresses and there is potential for fatigue cracking of the stitch weld. In this case the primary consideration is to ensure that the member remains attached to the steam dryer and this consideration is addressed here. Finally, it is important to point out that access to the T-beam is difficult and any remedial work to the high stress locations (e.g., by additional weld reinforcement or T-bar removal) would be costly and undesirable since it would necessarily take place in a confined underwater workspace under hazardous high radiation conditions.
The highest stress in the T-bar occurs at its end nearest the center (viewed from above) of the dryer. The dominant frequency in the stress response is at 58.1 Hz. This peak occurs at the
-10% frequency shift meaning that the signal exciting this response is at 64.55 Hz which is in the 60-70 Hz frequency interval where the ACM bias and uncertainty have been increased.
Examination of the unit solutions at 58.1 Hz indicates the following explanation for the high stress location. At this frequency, the vane banks experience a rocking motion. Because the vane banks are connected by tie-bars at the top, all vane banks tend to rock in unison. The rocking motion imparts a small rotation at the vane bank bases. Moreover, because the dryer supports are at 40, 940, 1840 and 2740 azimuths rather than the preferred (from a load distribution perspective) 00, 900, 180' and 270', the rocking motions are accompanied by asymmetric vertical displacements of the vane bank bases as well as small rocking about the x-axis (the x-axis coincides with the T-bar/cover plate weld). These displacements (highly amplified for visibility) are shown in Figure 20. The inner base plates conform to the vane bank motion. The resulting deflection shape is the one that matches the same sign rotation angles of the vane bank bases and thus has two extrema (a maximum and minimum) in the deflection. The T-bar is very stiff in bending; ona cross-sectional basis the second area moment associated with vertical bending is at least two orders of magnitude higher than the inner base plate. The connection between the T-bar and inner base plate constrains the natural displacement of the base plate and produces a locally high stress which is resolved primarily at the end of the T-bar.
Examination of Figure 20 suggests that if the stitch weld were to be removed from the T-bar tip all the way to the innermost vane bank then the secondary stresses induced in the T-bar and base plates would be substantially relieved. This conclusion is inferred by noting the following.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information First, the hot spot at the T-bar end would no longer be present, since the local weld no longer transfers any load between the T-bar and base plate. In this configuration, the T-bar is free to remain straight and the inner base plate is free to deform to match the vane bank base rotations.
Second, the T-bar stresses in the portion of beam between the inner and outer vane banks are relatively low because the beam is essentially straight. Finally, the high T-bar stresses occurring at the base of the inner vane bank would diminish since the T-bar no longer experiences a significant root moment. The root moment results from distributed loading on the T-bar by the connected base plates. With the weld disconnected, the base plates no longer load the T-bar and the root moment is much smaller.
Figure 20. Unit solution deflection at 58.1 Hz. Note that deflections are amplified for visibility.
The dryer is "sliced" through the center plane (the xz-plane corresponding to y=O) to reveal the deflections of the T-bar.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Analysis In order to verify this assertion, unit solutions were regenerated with the T-bar disconnected from the inner base plate inboard from the innermost vane banks. This simulates the situation where the stitch weld is severed from the T-bar tip to the innermost vane bank.
To limit calculation effort, unit solutions were only calculated over the 39.9 Hz to 70.4 Hz frequency range. This adequately covers the frequency range containing the dominant contributions to the T-bar stresses. Note too that for the given T-bar cross-section the cantilever frequency of the first mode is 286 Hz which is above the frequency range of acoustic forcing. This indicates that dynamic amplification of stresses due to acoustic excitation of the T-bar cantilever mode is small. Disconnecting nodes does not alter the FEA mesh. Hence, existing unit solutions for the BFN2 dryer in this frequency range can be exchanged with the ones corresponding to the partially disconnected T-bar. Once the unit solutions are exchanged the remaining stress analysis proceeds in the same manner as the standard frequency-based stress analysis by combining the MSL signals with the unit solution stresses.
Stresses are calculated for all nodes residing on the T-bar/base plate connection. For the nodes on the T-bar weld, the limiting alternating stress ratios at any frequency shift are SR-a=4.16 at CLTP and SR-a=2.72 at EPU (note that these values reflect the undersize weld factor of 2.0). Both of these alternating stress ratios occur at the common junction between the inner hood, middle base plate, hood support and T-bar. These stress ratio values confirm that if the stitch weld on the T-bar inboard of the inner vane bank were to fail, then the stress on the remaining weld is below the allowable levels and the T-bar remains joined to the steam dryer.
Table 12 and Table 13 list the nodes on T-bar weld having alternating stress ratio, SR-a<4.5 at CLTP and SR-a<3.0 at EPU. Only two nodes satisfy any of these conditions: the limiting node and its reflected image across the x=0 plane. In each case, the limiting stress occurs in the base plate.
At the original high stress locations (see Table 14) involving the T-bar, (nodes 133672 and its mirror image 121720) the smallest alternating stress ratios are SR-a=7.22 at CLTP and SR-a=4.34 at EPU. These corresponding values for the fully connected case (i.e., no stitch weld cracks) were 2.51 and 1.86 respectively.
At the node corresponding to the root of the disconnected weld the limiting alternating stress ratios are SR-a=6.31 at CLTP and SR-a=4.21 at EPU, both well above the fatigue endurance limits and the target levels (i.e., 2.7 at CLTP and 2.0 at EPU).
Based on these results it is concluded that if the stitch weld at the high stress location were to fail, then the disconnection would either: (i) terminate at one of the stitch welds between the T-bar end and the innermost vane bank or (ii) proceed all the way to the innermost vane bank. In the latter case, the analysis of the full steam dryer with the T-bar disconnected from the inner base plate inboard of the inner vane bank, shows that the alternating stress ratios along the
-remainder of the T-bar welds are above the target levels. Hence no fatigue-induced cracking of the remaining weld will occur and the T-bar remains attached to the steam dryer structure.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 12. List of T-bar weld nodes having alternating stress ratio, SR-a<4.5 at CLTP. The terms in parentheses provide the corresponding values when the T-bar is fully connected.
Location Node x
y z
SR-a Freq. Shift I[%]
Middle Base Plate/Hood 133648 39.75 0.0 0.0 4.40 (4.38) 5 Support/Inner Hood/Tbar 133690
-39.75 0.0 0.0 4.16 (4.25) 5 Table 13. List of T-bar weld nodes having alternating stress ratio, SR-a<3.0 at EPU. The terms in parentheses provide the corresponding values when the T-bar is fully connected.
Location Node x
y z
SR-a Freq. Shift I[%]
Middle Base Plate/Hood 133648 39.75 0.0 0.0 2.72 (2.79) 5 Support/Inner Hood/Tbar 133690
-39.75 0.0 0.0 2.75 (2.80) 5 Table 14. List of selected T-bar weld locations comparing the stress ratios before and after disconnection. The terms in parentheses provide the corresponding values when the T-bar is fully connected.
Location Node x
y z SR-a SR-a CLTP EPU Inner Base Plate/Tbar 121720 0.75 0
0 7.95 (2.76) 4.34 (2.04) 133672
-0.75 0
0 7.22 (2.51) 4.38 (1.86) 119640 12.625 0
0 7.80 (7.81) 5.21 (5.23) 133677
-12.625 0
0 7.48 (8.68) 5.48 (5.95)
Thin Vane Bank/Inner Base Plate/Vane 117775 15 0
0 6.50 (4.91) 4.21 (3.49)
Bank Section/Tbar 133678
-15 0
0 6.31 (4.61) 4.33 (3.42)
Inner Base Plate/Vane Bank Section/Tbar 131391 17.25 0
0 10.22 (6.14) 6.34 (4.06) 133679
-17.25 0
0 9.20(6.33) 6.70 (4.18) 128