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December 11, I992 To: Dr. Stephen Tumminelli Manager, Engineering Mechanics GPU Nuclear Corporation 1 Upper Pond Road Parsippany, NJ 07054 | |||
==Subject:== | ==Subject:== | ||
Sandbed Local Thinning and Raising the Fixity Height Analyses (Line Items 1 and 2 in Contract # PC-0391407) | |||
==Dear Dr. Tumminelli:== | ==Dear Dr. Tumminelli:== | ||
The attached letter report documents the results of subject analyses. The original purchase order called for the analyses to be conducted on a spherical panel model rather than on the full pie slice model. However, the results are more useful when conducted on the full pie slice model since i n that case no interpretation is required regarding the relationship between the spherical panel results and the pie slice model results. The pie slice model we have used in these studies has the refined mesh in the sandbed region. | |||
The attached letter report documents the results of subject analyses. | A 3.5" PC Disk containing three ANSYS input files (0.636"case, 0.536" case and I foot wall case) is also enclosed with this letter. The detailed calculations have been filed in Chapter 10 of our Design Record File No. 00664. | ||
The original purchase order called for the analyses to be conducted on a spherical panel model rather than on the full pie slice model. However, the results are more useful when conducted on the full pie slice model since | This transmittal completes the scope of work identified in the subject PO. If you have any questions on the above item, please give me a call. | ||
& Structural Analysis Services MaiI Code 747; Phone (408) 925-5029 | Sincerely, I | ||
H.S. Mehta, Principal Engineer Materials Monitoring & Structural Analysis Services MaiI Code 747; Phone (408) 925-5029 | |||
==Attachment:== | ==Attachment:== | ||
Letter Report cc: D.K.Henrie (w/o Attach.) | |||
J.M. Miller (w/o Attach.) | |||
S. Ranganath (w/o Attach.) | |||
HSMOC-57. WP | |||
LETTER REPORT ON ADDITIONAL SAiiDBED REGION ANALYSES 1 .O SCOPE A N D BACKGROUND Structural Analyses of the Oyster Creek drywell assuming a degraded thickness of 0.736 inch in the sandbed region (and sand removed) were documented in GENE Report Numbers 9-3 and 9-4. A separate purchase order was issued (Contract # PC-0391407) to perform additional analyses. The PO listed the additiond analyses under two categories: | |||
# PC-0391407) to perform additional analyses. | |||
The PO listed the additiond analyses under two categories: | |||
Line Item 001 and Line Item 002. This letter report documents the results of these analyses. | Line Item 001 and Line Item 002. This letter report documents the results of these analyses. | ||
The additional analyses are the following: | The additional analyses are the following: | ||
(1) Investigate the effect on the buckling behavior of drywell from postulated local thinning in the sandbed region beyond the uniform projected thickness of 0.736" used in the above mentioned reports (Line Item 001). (2) Determine the change in the drywell buckling margins when the fixity point at tbe bottom of the sandbed is moved upwards by = 1 foot to simulate placement of concrete (Line Item 002). The original PO called for the Line Item 001 analyses to be conducted on a spherical panel. The relative changes in the buckling load factors were to be assumed to be the same for the global pie slice model. However, the mesh refinement activity on the global pie slice model and the availability of work station, | (1) Investigate the effect on the buckling behavior of drywell from postulated local thinning in the sandbed region beyond the uniform projected thickness of 0.736" used in the above mentioned reports (Line Item 001). | ||
The various thicknesses indicated in Figure la were incorporated in the pie slice model by defining new real constants for the elements involved. The buckling analyses conducted as a result of mesh refinement indicated that the refueling loading condition is the governing case from the point of view of ASME Code margins. | (2) Determine the change in the drywell buckling margins when the fixity point at tbe bottom of the sandbed is moved upwards by = 1 foot to simulate placement of concrete (Line Item 002). | ||
Therefore, the stress and buckling analyses were conducted using the refuehg condition loadings. | The original PO called for the Line Item 001 analyses to be conducted on a spherical panel. The relative changes in the buckling load factors were to be assumed to be the same for the global pie slice model. However, the mesh refinement activity on the global pie slice model and the availability of work station, h a s given us the capability to conduct the same analyses on the global pie slice mode1 itself, thus eliminating the uncertainties regarding the correlation between the panel model and the pie dice model. | ||
The center of the thinned area was located close to the calculated maximum displacement point in the refueling condition buckling analyses with uniform thickness of 0.736 inch. Figure lb shows the location of the thinned area in the pie slice model. 2.1 0.536 Inch Thickness Case Figures 2 through 5 show the membrane meridional and circumferential stress distributions from the refueling condition loads. As expected, the tensile circumferentia1 stress (Sx in element coordinate system) and the compressive meridional stress (Sy in element coordinate system) magnitudes in the thinned region are larger than those at the other edge of the model where the thickness is 0.736 inch. However, this is a local effect and the average meridional | All of the results reported in this report are based on the pie slice model with a refined mesh in the sandbed region. | ||
'stress and the average circumferential stress is not expected to change significantly. | 2.0 LINEITEM001 Figure la shows the local thickness reductions modeled in the pie slice model. A locally thinned region of = 6"x12" is modeled. The thickness of this region is 0.636" in one | ||
Figures 6 and 7 show the first buckling mode with the symmetric boundary conditions at both the edges of the model (sym-sym). This mode is clearly associated with the thinned region. The load factor value is 5.562. The second mode with the same boundiry conditions is also associated with the thinned region. Figure 8 shows the buckled shape. The load factor value is 5.872. Next, buckling analyses were conducted with the symmetric boundary conditions specified at the thinned edge and the asymmetric boundary conditions at the other edge (sym-asym). | |||
The load factor of the first mode for this case was 5.58. Figure 9 shows the buckling mode shape. It is clearly associated with the thinned region. Figure 10 shows the buckled mode shape with asymmetric boundary conditions at the both edges (asym-asym). | case and 0.536" in the other case, The transition to the sandbed projected thickness of 0.736" occurs over a distance of 12" (4elements). | ||
As expected, the load factor for this case is considerably higher (7.037). | The various thicknesses indicated in Figure la were incorporated in the pie slice model by defining new real constants for the elements involved. The buckling analyses conducted as a result of mesh refinement indicated that the refueling loading condition is the governing case from the point of view of ASME Code margins. Therefore, the stress and buckling analyses were conducted using the refuehg condition loadings. The center of the thinned area was located close to the calculated maximum displacement point in the refueling condition buckling analyses with uniform thickness of 0.736 inch. Figure lb shows the location of the thinned area in the pie slice model. | ||
Thus, the load factor value of 5.562 is the Iowest value obtained. | 2.1 0.536 Inch Thickness Case Figures 2 through 5 show the membrane meridional and circumferential stress distributions from the refueling condition loads. As expected, the tensile circumferentia1 stress (Sx in element coordinate system) and the compressive meridional stress (Sy in element coordinate system) magnitudes in the thinned region are larger than those at the other edge of the model where the thickness is 0.736 inch. However, this is a local effect and the average meridional 'stress and the average circumferential stress is not expected to change significantly. | ||
The load factor for the same loading case (refueling condition) with a uniform thickness of 0.736'' was 6.141. Thus, the load factor is predicted to change from 6.141 to 5.562 with the postulated thinning to 0.536". 2.2 0.636 Inch Thickness Case Figures 11 through 14 show the membrane meridional and circumferential stress distributions from the refueling condition loads. As expected, the tensile circurnferentiat stress (Sx in element coordinate system) and the compressive meridional stress (Sy in element coordinate system) magnitudes in the thinned region are larger than those at the other edge of the model where the thickness is 0.736 inch. However, this is a Iocal effect and the average meridional stress and the average circumferential stress is not expected to change significantly, Figures 15 and 16 show the first buckling mode with the symmetric boundary conditions at both the edges of the model (sym-sym). | Figures 6 and 7 show the first buckling mode with the symmetric boundary conditions at both the edges of the model (sym-sym). This mode is clearly associated with the thinned region. The load factor value is 5.562. The second mode with the same boundiry conditions is also associated with the thinned region. Figure 8 shows the buckled shape. | ||
This mode is clearly associated with the thinned region. The load factor value is 5.91. Next, buckling analysis was conducted with the symmetric boundary conditions specified at the thinned edge and the asymmetric boundary conditions at the other edge. | The load factor value is 5.872. | ||
The load factor of the first mode for this case was 5.945. Figure 17 shows the buckling mode shape. It is clearly associated with the thinned region. Based on the results of 0.536" case, the load factor for asym- | Next, buckling analyses were conducted with the symmetric boundary conditions specified at the thinned edge and the asymmetric boundary conditions at the other edge (sym-asym). | ||
The load factor for the same loading case (refueling condition) with a uniform thickness of 0.736" was 6.141. Thus, the load factor is predicted to change from 6.141 to 5.91 with the postulated thinning to 0.636". , 2.3 Summary The load factors for the postulated 0.536" and 0.636" thinning cases are 5.562 and 5.91, respectively. | The load factor of the first mode for this case was 5.58. Figure 9 shows the buckling mode shape. It is clearly associated with the thinned region. Figure 10 shows the buckled mode shape with asymmetric boundary conditions at the both edges (asym-asym). As expected, the load factor for this case is considerably higher (7.037). | ||
These values can be compared to 6.141 obtained for the case with a uniform sandbed thickness of 0.736 inch. | |||
Thus, the load factor value of 5.562 is the Iowest value obtained. The load factor for the same loading case (refueling condition) with a uniform thickness of 0.736'' was 6.141. | |||
Thus, the load factor is predicted to change from 6.141 to 5.562 with the postulated thinning to 0.536". | |||
2.2 0.636 Inch Thickness Case Figures 11 through 14 show the membrane meridional and circumferential stress distributions from the refueling condition loads. As expected, the tensile circurnferentiat stress (Sx in element coordinate system) and the compressive meridional stress (Sy in element coordinate system) magnitudes in the thinned region are larger than those at the other edge of the model where the thickness is 0.736 inch. However, this is a Iocal effect and the average meridional stress and the average circumferential stress is not expected to change significantly, Figures 15 and 16 show the first buckling mode with the symmetric boundary conditions at both the edges of the model (sym-sym). This mode is clearly associated with the thinned region. The load factor value is 5.91. | |||
Next, buckling analysis was conducted with the symmetric boundary conditions specified at the thinned edge and the asymmetric boundary conditions at the other edge. The load factor of the first mode for this case was 5.945. Figure 17 shows the buckling mode shape. It is clearly associated with the thinned region. Based on the results of 0.536" case, the load factor for asym-asymcase is expected to be considerably higher. | |||
Thus, the load factor value of 5.91 is the Iowest value obtained. The load factor for the same loading case (refueling condition) with a uniform thickness of 0.736" was 6.141. | |||
Thus, the load factor is predicted to change from 6.141 to 5.91 with the postulated thinning to 0.636". , | |||
2.3 Summary The load factors for the postulated 0.536" and 0.636" thinning cases are 5.562 and 5.91, respectively. These values can be compared to 6.141 obtained for the case with a uniform sandbed thickness of 0.736 inch. | |||
The objective of this task was to determine the change in the drywell buckling margins when the fixity point at the bottom of the sandbed is moved upwards by = 1 foot to simulate placement of concrete. The elements in the sandbed region are approximately 3-inch square. Thus the nodes associated with the bottom four row of elements (nodes 1027 through 1271, Figure 18) were fixed in all directions. | The objective of this task was to determine the change in the drywell buckling margins when the fixity point at the bottom of the sandbed is moved upwards by = 1 foot to simulate placement of concrete. The elements in the sandbed region are approximately 3-inch square. Thus the nodes associated with the bottom four row of elements (nodes 1027 through 1271, Figure 18) were fixed in all directions. | ||
The buckling analyses conducted as a result of mesh refinement indicated that the refueling loading condition is the governing case from the point of view of ASME Code margins. Therefore, the stress and buckling analyses were conducted using the refueling condition loadings. | The buckling analyses conducted as a result of mesh refinement indicated that the refueling loading condition is the governing case from the point of view of ASME Code margins. Therefore, the stress and buckling analyses were conducted using the refueling condition loadings. Figure 19 through 22 show the membrane meridional and circumferential stress distributions from the refueling condition loads. Figure 23 shows the Caicuiated average values of meridional and circumferential stresses that are used in the buckling margin evaluation. | ||
Figure 19 through 22 show the membrane meridional and circumferential stress distributions from the refueling condition loads. Figure 23 shows the Caicuiated average values of meridional and circumferential stresses that are used in the buckling margin evaluation. | Figure 24 shows the first buckling mode with sym-syrn boundary conditions. The load factor for this mode is 6.739. The load factor with asym-sym boundary conditions is 6.887 and the mode shape shown in Figure 25. It is clear that the sym-sym boundary condition gives the least load factor. Figure 26 shows the buckling margin calculation. It is seen that the buckling margin is 5.3% compared to 0% margin in the base case calculation. | ||
Figure 24 shows the first buckling mode with sym-syrn boundary conditions. | To summarize, the load factor changes to 6.739 for the refueling condition when the fixity point at the bottom of the sandbed is moved upwards by 1 foot. This results in an excess margin of 5.3% above that required by the Code. | ||
The load factor for this mode is 6.739. The load factor with asym-sym boundary conditions is 6.887 and the mode shape shown in Figure 25. It is clear that the sym-sym boundary condition gives the least load factor. Figure 26 shows the buckling margin calculation. | |||
It is seen that the buckling margin is 5.3% compared to 0% margin in the base case calculation. | ... | ||
To summarize, the load factor changes to 6.739 for the refueling condition when the fixity point at the bottom of the sandbed is moved upwards by margin of 5.3% above that required by the Code. 1 | . . I . | ||
... . .I . ....... .-. .. .. . ........ . | ....... . - . . . . | ||
. . .. | |||
. | |||
. . . . . . . . ._.I . .- | |||
:> | |||
. . . | |||
AMSYS 4.4A1 DEC 9 1992 17:41:51 POST1 STRESS STEP=l ITER-1 MIDOL (EAVG) | |||
ELEM CS OMX = n . z z z n 5 SMN 1-3561 SMX = 7 6 1 4 XV =1 YV - 0 . 8 OIST-718.786 XF 1313.031 ZF 439.498 ANGZ- -9 0 CEMTROID HIDDEN | |||
-3561 | |||
-2319 m -1078 iEEI 163.887 1406 2647 388 9 5131 6372 7614 OYSTER CREEK DW AWtALYSIS - -2LL-L OCRFTHl (NO SAND, REFUELING) | |||
AMSYS 4.4A1 DEC 9 1992 17;43:35 POST1 STRESS STEP=l LTER=1 SX (AVG) | |||
MIDDLE ELEM CS Dt4X - 0 . 2 2 2 7 1 5 SMW --3561 SMX = 7 6 1 4 HV -1 2v =-1 aDIST*121.539 3XF 046.39 | |||
'YF =-1.382 5 2 ~ -382.857 APBCZ--SO CENTROID H I D D E N I | |||
-3561 | |||
-2319 | |||
-1078 163.887 1406 2647 34389 OYSTER CREEK MJ ANALYSIS - OCRFTHl (MO !WOgD, REFUELING) | |||
v C | |||
z b | |||
c I | |||
c L* | |||
p: | |||
c c | |||
t | |||
LBWZ-OEOP-212s-S6E9-LLSL-09fU-E8'66- | |||
, | |||
, | |||
EO-39LZ'O EO-32BL'O- | |||
~ ~ 1 0o 868200'0- m 9 S 6 E Q Q .0 = | |||
~1:OSOO'O-zf0900'0-N 3 Q U I H llIOpllQ133 Q 6 =ZDNV | |||
- | |||
2 2 i e 5 9 = fZcr | |||
$ S 6 U 9 P W O - JAo fStr'ti2- 4XP | |||
$00'Dlt=,LSI0a 1-5 A2 T= AX S V O Q | |||
* f l = XMS z L 0 9 0 0 | |||
* 0 - = NWS | |||
& t 0 9 0 O ' O = x#a 1tlQOW a xn 295'S=13VSa T=831I T=d3IS SS3241S TlSOd UT: f s : 9 2661: 01: 330 T W ' P SASNQ | |||
ANSYS 4.4A1 DEC 1 0 1992 a:io:a4 POST1 STRESS STEP-1 ITER=Z | |||
~ ~ ~ ~ ~ 5 . 8 7 2 UX D MODAL DMX | |||
* 0 . 0 0 6 4 3 . 4 SMld - - 0 . 0 0 6 4 1 4 SMX =0.0[12261 xv =l ZY =-1 | |||
*DfST=lLO.004 | |||
@XF -29.455 | |||
@YF 10.4609SQ | |||
@ZF =365.922 ANGZI-90 CENTROID H I D D E N | |||
-a. 006ai4 | |||
- a . 00545 | |||
-0.004486 | |||
-a. 0 0 3 ~ 2 2 | |||
-0.0112558 | |||
-0.001598 | |||
-0.630E-03 0.333-03 0.001297 a . ao22si ecRf o w 3 9 5 OYSTER CREEK DRYWELL ANALYSIS - (NO SAND, REFUELING) | |||
289F.00 Q TS200'0 s | |||
AMSYS 4.4Al DEC 10 1992 l0:12:22 POST1 S T R E S S STEP-1 ITER31 FACT-7.037 ux D NODAL DMX 1 0 . 0 0 3 4 9 2 SWN --0.0021188 SMX =u. 002164 xv -1 zv =-l | |||
*DIST=IlO.OOQ | |||
*XF 029.455 aYF PO. 460954 ZF a365.922 | |||
- | |||
ANCZ- 9 0 CENTROID H I D D E N | |||
-0.0021388 | |||
-0.001615 | |||
-0.0011113 | |||
-0.670E-03 | |||
- -0.198E-03 0.274E-03 0.747E-03 0.001219 0.0016g1 Q.QO2164 OYSTER CREEK DW AWALYSLS - OCRFOSM (NO SAND, REFUELING) | |||
AMSYS 4.4Al DEC 10 1992 8:18:30 POST1 STRESS STEP-1 ITER=l SX (AVG) | |||
MIDDLE E L E M CS DMX P O . 222456 SWN --3554 SMX a 6 9 5 0 DIST~718.786 HF =303.03i 2F = C 3 9 . 4 9 8 AMCZn-SO 1 CENTROID HIDDERI | |||
-3554 | |||
-2387 | |||
-1220 809 1114 2281 n 3448 U | |||
4615 5783 | |||
! 6950 1 OYSTER CREEK DEl AfMaLYSIS = OCRFOGS ~ N > & d . REFUELING) | |||
8btrE U 1822 BITT m 608'2s- IE OZZT-f8EZ-PSSE- | |||
ANSYS 4.4A1 D E C i a 1992 8:18:45 POST1 STRESS STEP-l ITER-1 SY (AUG) | |||
MIDDLE E L E M CS OMX =0.222456 SHN 9 - 8 7 6 7 SHX - 6 9 4 . 6 5 3 HV =1 YV =-0.8 DIST-718.786 XF -303.031 ZF ~639.498 AMGZ=-911 CENTROID H I D O E N | |||
-a767 | |||
-7716 | |||
-6664 | |||
-5613 | |||
-4562 | |||
-3511 | |||
-2459 L | |||
WSTER CREEK DW BMALYSIS - OCWFOGS (IMO SAND, REFUELING) | |||
6SbZ-TIS&- | |||
Z9SP-ETSS-9999-91Lf-6918- | |||
ANSYS 4.4A1 DEC 10 1392 10 :37 :5 6 POST1 STRESS STEP=l ITER=1 FACT-5.91 ux 0 NODAL OMX - 0 . 0 0 5 1 7 5 SHN -0.oasi74 SMX - 0 . 0 0 3 2 6 xv =I zv =.I-1 | |||
*DIST=100.004 | |||
*XF -29.455 | |||
*YF = O . 46O¶54 | |||
*ZF ~365.922 | |||
- | |||
AMGZ- 9 0 CEMTROID HIDDEN | |||
-0.00Sl.74 | |||
-0.004237 | |||
-0.01133 | |||
-0.002362 | |||
- -0.001425 | |||
-0.4aa~-03 0 - 449E-03 0.001386 0.002323 0.00326 | |||
..OYTER CREEK D R W E L L AQjalYSIS - OCRFOGBSS (NO SAND, REFUELING) | |||
i ANSYS 4.4Al DEC 7 1992 12 :44: 31 POST1 STRESS STEP=l ITERa.1 SX (AW) | |||
MIDDLE ELEM CS D#X =0.211959 SPON --3547 SMX -6041 | |||
-+9 | |||
# | |||
xv =1 P YV -0 .a C DIST1718.786 XF -3113.031. | |||
F ZF t639.498 AMCZ-- 9 0 3 CENTROID H I D O E M | |||
-3547 | |||
-2482 | |||
-1416 | |||
-350.884 714.437 1980 2845 O W V E R CREEK DRYWELL ANALYSIS - OYCRlS (NO SAND, REFUELIWG) | |||
AMSYS 4 . 4 A 1 DEC 7 1992 1 2 :33: 33 POST1 STRESS STEPml ITER= 1 SX (AVG) | |||
MIDDLE E L E M cs DMX -0.211959 SMN a - 3 5 4 7 SM% =6041 xv =I LV =-I | |||
*DIST-121-539 c. | |||
*XF 046.39 V F a-1.382 | |||
*ZF -3132.as7 | |||
- | |||
ANCZm 9 0 4 | |||
0 CENTROID H I D D E N | |||
-3547 | |||
-2482 | |||
-1416 | |||
-350.884 | |||
- | |||
714.437 1780 284s 3910 4976 6041 I OYSTER CREEK O R Y W L L A W L V S I S = OYCRlS (NO WPQD, REFUELING) I | |||
TbT2- U O'EIE-6f OP- m 6PQS-8109-L869-BStiL- | |||
AMSYS 4.4A1 DEC 7 1992 12 : 3 4 : 18 POST1 STRESS STEP-1 ITER=l SY (AVG) | |||
MIDDLE ELEM CS RWX -0.211959 SMM -.-7956 SMX 5 7 6 6 . 9 5 3 xv -1 zv =-I | |||
* D I S T = 1 2 1 - 539 " | |||
*XF ~46.39 0 | |||
\ | |||
*YF 0-1.382 | |||
@ZF ~ 3 8 2 . 8 5 7 ANCZ--90 CENTROID H I D D E N | |||
-7956 | |||
-6987 | |||
-6018 | |||
-5049 | |||
-4079 | |||
-3110 n -2141 | |||
-1172 | |||
* -202.3U1 766.953 OYSTER CREEK DRYWELL A M L Y S I S - OYCRlS I N 0 SAND. REFUELING1 | |||
APPLIED MERIDIONAL AH0 CIRCUHFEREHllAL STRESSES - REFUELING CCNOlTION ONE FOOT IMCREASE !N FIXITY CASE; STRESS RUN: 0CRFRLSB.CUT AVERAGE APPLIED MERIDIONAL STRESS: | |||
The average meridional s t r e s s is defined as the average stress across the e l e v a t i o n inctuding nodes 1419 through 1467. Stresses a t nodes 1419 and 1467 are weighted only one h a l f as nuch as the ather nodes because they Lie on the edge o f the mcdeLed l/lOth section o f the drywelt and thus represent only 1/2 o f the area represented by t h e other nodes. | |||
# of Nodes X | |||
# of Meridional Meridional Nodes Nodes Stress ( k s i ) Stress (ksi) | |||
..--. .................... ............... | |||
1419-1667 1 -7.726 -7.726 | |||
- | |||
1 423 1 663 2 -7.?38 -15.476 1427-1659 2 -7.760 -15.520 1431 | |||
* 1455 2 -7.682 -15.364 3435.145 1 2 s7.394 -14.788 7439- 1447 2 -7.011 -16.028 1443 1 -6.831 -6.834 | |||
_____ ---I. ............... | |||
Total: 12 -89.736 12 | |||
............... | |||
Average H e r i d i o n e l Stress: -7.478 tksi) | |||
AVE3AGE APPLIED CIRCUMFERENTIAL STRESS: | |||
The c i r c m f e r e n t i a l s t r e s s i s averaged along the v e r t i c a l l i n e frem node 1223 t o ncde 2058. | |||
# of Nodes X | |||
# of C i rcumferentiel Modes Nodes Stress ( k s i ) | |||
_ _ _ .--.-- _ | |||
1223 0 0.000 1419 1 0.505 1615 1 4.165 1811 1 5.866 2058 1 5.024 | |||
..... ............... | |||
Total: 4 15-54 4 | |||
............... | |||
Average C i r c u n f e r e n t i a l Stress: 3.W (ksi) | |||
OCRFSTOL.UK1 | |||
ANSYS 4.4A1 DEC 8 1992 6:15:38 POST1 STRESS STEP= 1 I TER= 1 FACT=6.739 ux D NQDGL DMX =0.003681 SMN =-0,00368 SMX =0.001848 xv =t zu =-I | |||
~DZST=l10,004 wXF =29.455 | |||
*YF =O .46O954 wZF =365,922 ANGZ=-F)O CENTROID HIDOEN | |||
-0 00368 | |||
-0.003065 | |||
-0 ,a02451 | |||
- | |||
-0.00 1837 | |||
-0.00 1223 | |||
-0,609E-03 0.567E-05 0,620E-03 0.001 234 0.001848 OYSTER CREEK ORYWELL ANALYSIS - ocrfs-s (NO SAND, REFUELING) | |||
004 | |||
-0 | |||
-0. | |||
-0 | |||
-0. | |||
-0. | |||
-0 | |||
ANSYS 4.4A1 DEC | ANSYS 4.4A1 DEC 9 1992 I1 :35 :17 P O S T l STRESS STEP-I. | ||
ITER=1 FACT-6.887 ux D NODAL DMX = O I O O ! i 1 3 6 SMN = - 0 . 0 0 5 1 3 4 St4X = O . 0 0 3 2 4 4 xv -1 zv --1 3DIST=110.004 W F -29.455 , | |||
4 V F = O . 46O954 . | |||
-0. | i 92F -365.922 | ||
-0. | - | ||
- | M G Z = 90 CENTROID H I O D E W " | ||
-0.005134 | |||
- a . 004203 | |||
-0.003273 | |||
-0.002342 | |||
-a. o a m i i | |||
-1.480E-03 0.451E-03 0.001382 O.OO2313 | |||
: a. 003244 | |||
CALCUUTION OF ALLOWABLE BUCKLING STRESSES - REFUELING CASE, NO SAND ONE FOOT INCREASE IN FIXITY CASE; STRESS RUN OCRFRLSB.OUT, BUCKLING RUN 0YCRSBBK.OUT LOAD ITEM PAHAMETER UNITS VALUE FACTOR I----- ................................................ ------- ------- ------ | |||
*** DRYWELL GEOMETRY AND MATERIALS 1 Sphere Radius, R (in.) 420 2 Sphere Thickness, t (in.) 0.736 3 Material Yield Strength, Sy (ksi) 38 4 Material Modulus of Elasticity, E (ksi) 29600 5 Factor of Safety, FS - 2 | |||
*** BUCKLING ANALYSIS RESULTS 6 Theoretical Elastic Instability Stress, Ste (ksi) 50.394 6.739 | |||
+** STRESS ANALYSIS RESULTS 7 Applied Meridional Compressive Stress, sm (ksi) 7.478 8 Applied Circumferential Tensile Stress, Sc (ksi) 3.885 | |||
*** CAPACITY REDUCTION FACTOR CALCULATION 4 | |||
9 Capacity Reduction Factor, ALPHAi - 0.207 10 Circumferential S t r e s s Equivalent Pressure, Peq (psi) 13.616 11 X I Parameter, X= (Peq/4E) ( d / t ) 2 ... 0.075 12 Delta C (From Figure - ) - 0.064 13 Modified Capacity Reduction Factor, ALPHA,i,mod - 0.313 14 Reduced Elastic Instability S t r e s s , Se (ksi) 15.753 2.107 | |||
*** PLASTICITY REDUCTION FACTOR CALCULATION 15 Y i e l d Stress Ratio, DELTA=Se/Sy - 0.415 16 Plasticity Reduction Factor, N U i - 1.000 17 Inelastic Instability Stress, Si. = N U i x S e (ksi) 15.753 2.107 | |||
*** ALLOWABLE COMPRESSIVE STRESS CALCULATION 18 Allowable Compressive Stress, Sal1 = S i / F S (ksi) 7.877 1.053 19 Compressive Stress Margin, M=(Sall/Sm -1) x 100% (%I 5.3 k | |||
REFNSND2 .WK1}} | |||
------- ------- ------ *** DRYWELL GEOMETRY AND MATERIALS 1 Sphere Radius, R 2 Sphere Thickness, t 3 Material Yield Strength, Sy 4 Material Modulus of Elasticity, E 5 Factor of Safety, FS | |||
-1) x 100% (%I 5.3 |
Revision as of 10:02, 23 November 2019
ML070600381 | |
Person / Time | |
---|---|
Site: | Oyster Creek |
Issue date: | 12/11/1992 |
From: | Mehta H General Electric Co |
To: | Tumminelli S GPU Nuclear Corp, Office of Nuclear Reactor Regulation, NRC/OGC, NRC Region 1 |
References | |
PC-0391407 | |
Download: ML070600381 (32) | |
Text
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December 11, I992 To: Dr. Stephen Tumminelli Manager, Engineering Mechanics GPU Nuclear Corporation 1 Upper Pond Road Parsippany, NJ 07054
Subject:
Sandbed Local Thinning and Raising the Fixity Height Analyses (Line Items 1 and 2 in Contract # PC-0391407)
Dear Dr. Tumminelli:
The attached letter report documents the results of subject analyses. The original purchase order called for the analyses to be conducted on a spherical panel model rather than on the full pie slice model. However, the results are more useful when conducted on the full pie slice model since i n that case no interpretation is required regarding the relationship between the spherical panel results and the pie slice model results. The pie slice model we have used in these studies has the refined mesh in the sandbed region.
A 3.5" PC Disk containing three ANSYS input files (0.636"case, 0.536" case and I foot wall case) is also enclosed with this letter. The detailed calculations have been filed in Chapter 10 of our Design Record File No. 00664.
This transmittal completes the scope of work identified in the subject PO. If you have any questions on the above item, please give me a call.
Sincerely, I
H.S. Mehta, Principal Engineer Materials Monitoring & Structural Analysis Services MaiI Code 747; Phone (408) 925-5029
Attachment:
Letter Report cc: D.K.Henrie (w/o Attach.)
J.M. Miller (w/o Attach.)
S. Ranganath (w/o Attach.)
HSMOC-57. WP
LETTER REPORT ON ADDITIONAL SAiiDBED REGION ANALYSES 1 .O SCOPE A N D BACKGROUND Structural Analyses of the Oyster Creek drywell assuming a degraded thickness of 0.736 inch in the sandbed region (and sand removed) were documented in GENE Report Numbers 9-3 and 9-4. A separate purchase order was issued (Contract # PC-0391407) to perform additional analyses. The PO listed the additiond analyses under two categories:
Line Item 001 and Line Item 002. This letter report documents the results of these analyses.
The additional analyses are the following:
(1) Investigate the effect on the buckling behavior of drywell from postulated local thinning in the sandbed region beyond the uniform projected thickness of 0.736" used in the above mentioned reports (Line Item 001).
(2) Determine the change in the drywell buckling margins when the fixity point at tbe bottom of the sandbed is moved upwards by = 1 foot to simulate placement of concrete (Line Item 002).
The original PO called for the Line Item 001 analyses to be conducted on a spherical panel. The relative changes in the buckling load factors were to be assumed to be the same for the global pie slice model. However, the mesh refinement activity on the global pie slice model and the availability of work station, h a s given us the capability to conduct the same analyses on the global pie slice mode1 itself, thus eliminating the uncertainties regarding the correlation between the panel model and the pie dice model.
All of the results reported in this report are based on the pie slice model with a refined mesh in the sandbed region.
2.0 LINEITEM001 Figure la shows the local thickness reductions modeled in the pie slice model. A locally thinned region of = 6"x12" is modeled. The thickness of this region is 0.636" in one
case and 0.536" in the other case, The transition to the sandbed projected thickness of 0.736" occurs over a distance of 12" (4elements).
The various thicknesses indicated in Figure la were incorporated in the pie slice model by defining new real constants for the elements involved. The buckling analyses conducted as a result of mesh refinement indicated that the refueling loading condition is the governing case from the point of view of ASME Code margins. Therefore, the stress and buckling analyses were conducted using the refuehg condition loadings. The center of the thinned area was located close to the calculated maximum displacement point in the refueling condition buckling analyses with uniform thickness of 0.736 inch. Figure lb shows the location of the thinned area in the pie slice model.
2.1 0.536 Inch Thickness Case Figures 2 through 5 show the membrane meridional and circumferential stress distributions from the refueling condition loads. As expected, the tensile circumferentia1 stress (Sx in element coordinate system) and the compressive meridional stress (Sy in element coordinate system) magnitudes in the thinned region are larger than those at the other edge of the model where the thickness is 0.736 inch. However, this is a local effect and the average meridional 'stress and the average circumferential stress is not expected to change significantly.
Figures 6 and 7 show the first buckling mode with the symmetric boundary conditions at both the edges of the model (sym-sym). This mode is clearly associated with the thinned region. The load factor value is 5.562. The second mode with the same boundiry conditions is also associated with the thinned region. Figure 8 shows the buckled shape.
The load factor value is 5.872.
Next, buckling analyses were conducted with the symmetric boundary conditions specified at the thinned edge and the asymmetric boundary conditions at the other edge (sym-asym).
The load factor of the first mode for this case was 5.58. Figure 9 shows the buckling mode shape. It is clearly associated with the thinned region. Figure 10 shows the buckled mode shape with asymmetric boundary conditions at the both edges (asym-asym). As expected, the load factor for this case is considerably higher (7.037).
Thus, the load factor value of 5.562 is the Iowest value obtained. The load factor for the same loading case (refueling condition) with a uniform thickness of 0.736 was 6.141.
Thus, the load factor is predicted to change from 6.141 to 5.562 with the postulated thinning to 0.536".
2.2 0.636 Inch Thickness Case Figures 11 through 14 show the membrane meridional and circumferential stress distributions from the refueling condition loads. As expected, the tensile circurnferentiat stress (Sx in element coordinate system) and the compressive meridional stress (Sy in element coordinate system) magnitudes in the thinned region are larger than those at the other edge of the model where the thickness is 0.736 inch. However, this is a Iocal effect and the average meridional stress and the average circumferential stress is not expected to change significantly, Figures 15 and 16 show the first buckling mode with the symmetric boundary conditions at both the edges of the model (sym-sym). This mode is clearly associated with the thinned region. The load factor value is 5.91.
Next, buckling analysis was conducted with the symmetric boundary conditions specified at the thinned edge and the asymmetric boundary conditions at the other edge. The load factor of the first mode for this case was 5.945. Figure 17 shows the buckling mode shape. It is clearly associated with the thinned region. Based on the results of 0.536" case, the load factor for asym-asymcase is expected to be considerably higher.
Thus, the load factor value of 5.91 is the Iowest value obtained. The load factor for the same loading case (refueling condition) with a uniform thickness of 0.736" was 6.141.
Thus, the load factor is predicted to change from 6.141 to 5.91 with the postulated thinning to 0.636". ,
2.3 Summary The load factors for the postulated 0.536" and 0.636" thinning cases are 5.562 and 5.91, respectively. These values can be compared to 6.141 obtained for the case with a uniform sandbed thickness of 0.736 inch.
The objective of this task was to determine the change in the drywell buckling margins when the fixity point at the bottom of the sandbed is moved upwards by = 1 foot to simulate placement of concrete. The elements in the sandbed region are approximately 3-inch square. Thus the nodes associated with the bottom four row of elements (nodes 1027 through 1271, Figure 18) were fixed in all directions.
The buckling analyses conducted as a result of mesh refinement indicated that the refueling loading condition is the governing case from the point of view of ASME Code margins. Therefore, the stress and buckling analyses were conducted using the refueling condition loadings. Figure 19 through 22 show the membrane meridional and circumferential stress distributions from the refueling condition loads. Figure 23 shows the Caicuiated average values of meridional and circumferential stresses that are used in the buckling margin evaluation.
Figure 24 shows the first buckling mode with sym-syrn boundary conditions. The load factor for this mode is 6.739. The load factor with asym-sym boundary conditions is 6.887 and the mode shape shown in Figure 25. It is clear that the sym-sym boundary condition gives the least load factor. Figure 26 shows the buckling margin calculation. It is seen that the buckling margin is 5.3% compared to 0% margin in the base case calculation.
To summarize, the load factor changes to 6.739 for the refueling condition when the fixity point at the bottom of the sandbed is moved upwards by 1 foot. This results in an excess margin of 5.3% above that required by the Code.
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. . .
AMSYS 4.4A1 DEC 9 1992 17:41:51 POST1 STRESS STEP=l ITER-1 MIDOL (EAVG)
ELEM CS OMX = n . z z z n 5 SMN 1-3561 SMX = 7 6 1 4 XV =1 YV - 0 . 8 OIST-718.786 XF 1313.031 ZF 439.498 ANGZ- -9 0 CEMTROID HIDDEN
-3561
-2319 m -1078 iEEI 163.887 1406 2647 388 9 5131 6372 7614 OYSTER CREEK DW AWtALYSIS - -2LL-L OCRFTHl (NO SAND, REFUELING)
AMSYS 4.4A1 DEC 9 1992 17;43:35 POST1 STRESS STEP=l LTER=1 SX (AVG)
MIDDLE ELEM CS Dt4X - 0 . 2 2 2 7 1 5 SMW --3561 SMX = 7 6 1 4 HV -1 2v =-1 aDIST*121.539 3XF 046.39
'YF =-1.382 5 2 ~ -382.857 APBCZ--SO CENTROID H I D D E N I
-3561
-2319
-1078 163.887 1406 2647 34389 OYSTER CREEK MJ ANALYSIS - OCRFTHl (MO !WOgD, REFUELING)
v C
z b
c I
c L*
p:
c c
t
LBWZ-OEOP-212s-S6E9-LLSL-09fU-E8'66-
,
,
EO-39LZ'O EO-32BL'O-
~ ~ 1 0o 868200'0- m 9 S 6 E Q Q .0 =
~1:OSOO'O-zf0900'0-N 3 Q U I H llIOpllQ133 Q 6 =ZDNV
-
2 2 i e 5 9 = fZcr
$ S 6 U 9 P W O - JAo fStr'ti2- 4XP
$00'Dlt=,LSI0a 1-5 A2 T= AX S V O Q
- f l = XMS z L 0 9 0 0
- 0 - = NWS
& t 0 9 0 O ' O = x#a 1tlQOW a xn 295'S=13VSa T=831I T=d3IS SS3241S TlSOd UT: f s : 9 2661: 01: 330 T W ' P SASNQ
ANSYS 4.4A1 DEC 1 0 1992 a:io:a4 POST1 STRESS STEP-1 ITER=Z
~ ~ ~ ~ ~ 5 . 8 7 2 UX D MODAL DMX
- 0 . 0 0 6 4 3 . 4 SMld - - 0 . 0 0 6 4 1 4 SMX =0.0[12261 xv =l ZY =-1
- DfST=lLO.004
@XF -29.455
@YF 10.4609SQ
@ZF =365.922 ANGZI-90 CENTROID H I D D E N
-a. 006ai4
- a . 00545
-0.004486
-a. 0 0 3 ~ 2 2
-0.0112558
-0.001598
-0.630E-03 0.333-03 0.001297 a . ao22si ecRf o w 3 9 5 OYSTER CREEK DRYWELL ANALYSIS - (NO SAND, REFUELING)
289F.00 Q TS200'0 s
AMSYS 4.4Al DEC 10 1992 l0:12:22 POST1 S T R E S S STEP-1 ITER31 FACT-7.037 ux D NODAL DMX 1 0 . 0 0 3 4 9 2 SWN --0.0021188 SMX =u. 002164 xv -1 zv =-l
- DIST=IlO.OOQ
- XF 029.455 aYF PO. 460954 ZF a365.922
-
ANCZ- 9 0 CENTROID H I D D E N
-0.0021388
-0.001615
-0.0011113
-0.670E-03
- -0.198E-03 0.274E-03 0.747E-03 0.001219 0.0016g1 Q.QO2164 OYSTER CREEK DW AWALYSLS - OCRFOSM (NO SAND, REFUELING)
AMSYS 4.4Al DEC 10 1992 8:18:30 POST1 STRESS STEP-1 ITER=l SX (AVG)
MIDDLE E L E M CS DMX P O . 222456 SWN --3554 SMX a 6 9 5 0 DIST~718.786 HF =303.03i 2F = C 3 9 . 4 9 8 AMCZn-SO 1 CENTROID HIDDERI
-3554
-2387
-1220 809 1114 2281 n 3448 U
4615 5783
! 6950 1 OYSTER CREEK DEl AfMaLYSIS = OCRFOGS ~ N > & d . REFUELING)
8btrE U 1822 BITT m 608'2s- IE OZZT-f8EZ-PSSE-
ANSYS 4.4A1 D E C i a 1992 8:18:45 POST1 STRESS STEP-l ITER-1 SY (AUG)
MIDDLE E L E M CS OMX =0.222456 SHN 9 - 8 7 6 7 SHX - 6 9 4 . 6 5 3 HV =1 YV =-0.8 DIST-718.786 XF -303.031 ZF ~639.498 AMGZ=-911 CENTROID H I D O E N
-a767
-7716
-6664
-5613
-4562
-3511
-2459 L
WSTER CREEK DW BMALYSIS - OCWFOGS (IMO SAND, REFUELING)
6SbZ-TIS&-
Z9SP-ETSS-9999-91Lf-6918-
ANSYS 4.4A1 DEC 10 1392 10 :37 :5 6 POST1 STRESS STEP=l ITER=1 FACT-5.91 ux 0 NODAL OMX - 0 . 0 0 5 1 7 5 SHN -0.oasi74 SMX - 0 . 0 0 3 2 6 xv =I zv =.I-1
- DIST=100.004
- XF -29.455
- YF = O . 46O¶54
- ZF ~365.922
-
AMGZ- 9 0 CEMTROID HIDDEN
-0.00Sl.74
-0.004237
-0.01133
-0.002362
- -0.001425
-0.4aa~-03 0 - 449E-03 0.001386 0.002323 0.00326
..OYTER CREEK D R W E L L AQjalYSIS - OCRFOGBSS (NO SAND, REFUELING)
i ANSYS 4.4Al DEC 7 1992 12 :44: 31 POST1 STRESS STEP=l ITERa.1 SX (AW)
MIDDLE ELEM CS D#X =0.211959 SPON --3547 SMX -6041
-+9
xv =1 P YV -0 .a C DIST1718.786 XF -3113.031.
F ZF t639.498 AMCZ-- 9 0 3 CENTROID H I D O E M
-3547
-2482
-1416
-350.884 714.437 1980 2845 O W V E R CREEK DRYWELL ANALYSIS - OYCRlS (NO SAND, REFUELIWG)
AMSYS 4 . 4 A 1 DEC 7 1992 1 2 :33: 33 POST1 STRESS STEPml ITER= 1 SX (AVG)
MIDDLE E L E M cs DMX -0.211959 SMN a - 3 5 4 7 SM% =6041 xv =I LV =-I
- DIST-121-539 c.
- XF 046.39 V F a-1.382
- ZF -3132.as7
-
ANCZm 9 0 4
0 CENTROID H I D D E N
-3547
-2482
-1416
-350.884
-
714.437 1780 284s 3910 4976 6041 I OYSTER CREEK O R Y W L L A W L V S I S = OYCRlS (NO WPQD, REFUELING) I
TbT2- U O'EIE-6f OP- m 6PQS-8109-L869-BStiL-
AMSYS 4.4A1 DEC 7 1992 12 : 3 4 : 18 POST1 STRESS STEP-1 ITER=l SY (AVG)
MIDDLE ELEM CS RWX -0.211959 SMM -.-7956 SMX 5 7 6 6 . 9 5 3 xv -1 zv =-I
- D I S T = 1 2 1 - 539 "
- XF ~46.39 0
\
- YF 0-1.382
@ZF ~ 3 8 2 . 8 5 7 ANCZ--90 CENTROID H I D D E N
-7956
-6987
-6018
-5049
-4079
-3110 n -2141
-1172
- -202.3U1 766.953 OYSTER CREEK DRYWELL A M L Y S I S - OYCRlS I N 0 SAND. REFUELING1
APPLIED MERIDIONAL AH0 CIRCUHFEREHllAL STRESSES - REFUELING CCNOlTION ONE FOOT IMCREASE !N FIXITY CASE; STRESS RUN: 0CRFRLSB.CUT AVERAGE APPLIED MERIDIONAL STRESS:
The average meridional s t r e s s is defined as the average stress across the e l e v a t i o n inctuding nodes 1419 through 1467. Stresses a t nodes 1419 and 1467 are weighted only one h a l f as nuch as the ather nodes because they Lie on the edge o f the mcdeLed l/lOth section o f the drywelt and thus represent only 1/2 o f the area represented by t h e other nodes.
- of Nodes X
- of Meridional Meridional Nodes Nodes Stress ( k s i ) Stress (ksi)
..--. .................... ...............
1419-1667 1 -7.726 -7.726
-
1 423 1 663 2 -7.?38 -15.476 1427-1659 2 -7.760 -15.520 1431
- 1455 2 -7.682 -15.364 3435.145 1 2 s7.394 -14.788 7439- 1447 2 -7.011 -16.028 1443 1 -6.831 -6.834
_____ ---I. ...............
Total: 12 -89.736 12
...............
Average H e r i d i o n e l Stress: -7.478 tksi)
AVE3AGE APPLIED CIRCUMFERENTIAL STRESS:
The c i r c m f e r e n t i a l s t r e s s i s averaged along the v e r t i c a l l i n e frem node 1223 t o ncde 2058.
- of Nodes X
- of C i rcumferentiel Modes Nodes Stress ( k s i )
_ _ _ .--.-- _
1223 0 0.000 1419 1 0.505 1615 1 4.165 1811 1 5.866 2058 1 5.024
..... ...............
Total: 4 15-54 4
...............
Average C i r c u n f e r e n t i a l Stress: 3.W (ksi)
OCRFSTOL.UK1
ANSYS 4.4A1 DEC 8 1992 6:15:38 POST1 STRESS STEP= 1 I TER= 1 FACT=6.739 ux D NQDGL DMX =0.003681 SMN =-0,00368 SMX =0.001848 xv =t zu =-I
~DZST=l10,004 wXF =29.455
- YF =O .46O954 wZF =365,922 ANGZ=-F)O CENTROID HIDOEN
-0 00368
-0.003065
-0 ,a02451
-
-0.00 1837
-0.00 1223
-0,609E-03 0.567E-05 0,620E-03 0.001 234 0.001848 OYSTER CREEK ORYWELL ANALYSIS - ocrfs-s (NO SAND, REFUELING)
ANSYS 4.4A1 DEC 9 1992 I1 :35 :17 P O S T l STRESS STEP-I.
ITER=1 FACT-6.887 ux D NODAL DMX = O I O O ! i 1 3 6 SMN = - 0 . 0 0 5 1 3 4 St4X = O . 0 0 3 2 4 4 xv -1 zv --1 3DIST=110.004 W F -29.455 ,
4 V F = O . 46O954 .
i 92F -365.922
-
M G Z = 90 CENTROID H I O D E W "
-0.005134
- a . 004203
-0.003273
-0.002342
-a. o a m i i
-1.480E-03 0.451E-03 0.001382 O.OO2313
- a. 003244
CALCUUTION OF ALLOWABLE BUCKLING STRESSES - REFUELING CASE, NO SAND ONE FOOT INCREASE IN FIXITY CASE; STRESS RUN OCRFRLSB.OUT, BUCKLING RUN 0YCRSBBK.OUT LOAD ITEM PAHAMETER UNITS VALUE FACTOR I----- ................................................ ------- ------- ------
- DRYWELL GEOMETRY AND MATERIALS 1 Sphere Radius, R (in.) 420 2 Sphere Thickness, t (in.) 0.736 3 Material Yield Strength, Sy (ksi) 38 4 Material Modulus of Elasticity, E (ksi) 29600 5 Factor of Safety, FS - 2
- BUCKLING ANALYSIS RESULTS 6 Theoretical Elastic Instability Stress, Ste (ksi) 50.394 6.739
+** STRESS ANALYSIS RESULTS 7 Applied Meridional Compressive Stress, sm (ksi) 7.478 8 Applied Circumferential Tensile Stress, Sc (ksi) 3.885
- CAPACITY REDUCTION FACTOR CALCULATION 4
9 Capacity Reduction Factor, ALPHAi - 0.207 10 Circumferential S t r e s s Equivalent Pressure, Peq (psi) 13.616 11 X I Parameter, X= (Peq/4E) ( d / t ) 2 ... 0.075 12 Delta C (From Figure - ) - 0.064 13 Modified Capacity Reduction Factor, ALPHA,i,mod - 0.313 14 Reduced Elastic Instability S t r e s s , Se (ksi) 15.753 2.107
- PLASTICITY REDUCTION FACTOR CALCULATION 15 Y i e l d Stress Ratio, DELTA=Se/Sy - 0.415 16 Plasticity Reduction Factor, N U i - 1.000 17 Inelastic Instability Stress, Si. = N U i x S e (ksi) 15.753 2.107
- ALLOWABLE COMPRESSIVE STRESS CALCULATION 18 Allowable Compressive Stress, Sal1 = S i / F S (ksi) 7.877 1.053 19 Compressive Stress Margin, M=(Sall/Sm -1) x 100% (%I 5.3 k
REFNSND2 .WK1