ML20148E973
| ML20148E973 | |
| Person / Time | |
|---|---|
| Site: | Yankee Rowe |
| Issue date: | 12/11/1975 |
| From: | Duffy D, Fowler J ROCKWELL INTERNATIONAL CORP. |
| To: | |
| Shared Package | |
| ML20148E929 | List: |
| References | |
| 2573-62, NUDOCS 8010310724 | |
| Download: ML20148E973 (64) | |
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Flow Control Division Utility Products Group .< d 4 400 North Lexington Avenue 0 Pittsburgh. Pennsvivania 15208 ROCkWell Telex: 866241 Cable: ROCKWL INT PGH
. International 5
Department 744-76XXX-645 TECHNICAL STUDY Report No. 2573-62 TITLE: Energy Absorption by the size 14 Fig. 607 Valve Seat and Disk at Yankee R , I ABSTRACT ; A preliminary investigation of the deformation damage expected to occur in - valve as a result of high energy impact of the disk on the seat was made. An clostic finite-element study of the volve body and disk showed that yielding will occur first in the volve body. A mathematical model of a postulated mode of plastic failure of the seat was developed ard indicates that the valve body alo : has adequate energy-absorbing capacity to cbsorb the necessary impact energy with'a safe, functional terminal configuration. A scale model test of the valve body exhibited behavior similar the postulated failure mode, and indicated additional strength due to work hardening of the material. It is concluded that this valve can safely withstand the sudden closure which would result from an instantaneous release of pressure upstream of the valve. AUTHOR: hf,(mh[ w&, , APPROVED wkk, y K Ft. Fowler TITLE: Valve Research Monager i DATE: December 11, 1975 KEY WORDS ! Calculations; Va "es, Angle; Valves, Nuclear , l DISTRIBUTION . D. W. Duffey/B. J. Milleville J. H. Loretan R. L Lawson F L-19 Report File 2573-62 8010s1o M y
f b D.. ..irtnu nt 744-76XXX-645 Report No. 2573-62
, , Page 2 ,
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OBJECTIVE i This study was undertaken at the request of the customer to determine whethe size 14 Figure 607 main steam isolotion volves et the Yonkee Rowe nuclear power . plant are capable of safe and effective closure in the event of a cotostrophic Such a condition would cause these break in the pipe adjacent to the volve inlet. stop-check type volves to slam shut, the disks striking the sects of a velocity 65.3 f t/sec (19.9 m/s) and with on energy of 139,250 in-lb (15.7 kJ) (1)l . Due to the limited time available, this study was to be limited to on elastic finite-element analysis, hand calculations, and simple model testing. CONCI U510NS
- 1. The disk impact energy due to the sudden flow reversel ossociated with a line ;
break con be sofely obsorbed by the volve seat.
- 2. The type of deformation that will occur is a plastic flow of the seat shelf, I downward and inward, cousing a reduction in the inside diameter of the ,
volve bore below the seat. Very little radial movement of the body shell Will occur.
- 3. The volve disk is stronger than the seat by a factor of 2.23. Therefore most Any plastic deformation plastic deformation will occur in the volve seat.
that might occur in the disk will provide further energy-obsorbing capacity. f
- 4. The deformed scot in the model was coined to on excellent finish. However, no stellite was deposited on this seat as is the case in the octual volve.
Therefore, the sealing ability of the volve ofter this deforrnation has occurred However, even though the connot be predicted solely on the basis of the test. stellite might crack, intimate contact between the disk and body scoting peripheries is assured and any leakage should be negligible by compa the quantity of stoom discharged by the line break. DISCUSSION on clostic finite-element stress This investigation included three principal activities: analysis of the disk and body, a simplified plostic onolysis of the scot reg Discussion of these activities experimental study of the plastic deformation of the scot. will be presented in that order. I Numbers in parenthesis refer to references at end of paper.
C ,;artm:nt 744-76XXX-645
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Report No. 2573-62 Page 3 ELASTIC FINITE-ELEMENT ANALYSIS The lower portion of the disk and the seat region of the body were modeled using FINEL @), on exisymmetric finite-element program having rectangular and trian elements. This program has been used extensively within Rockwell and has been verified with closed-form analyses and by comparison to NASTRAN on identical models . Since the body loading includes both the seat loading due to impact and the in pressure loading above the seat, it was necessary to run two cases in or the seat deflection due to the impact loading alone. Exhibit One is the computer output for the combined pressure and impact loadin 1,000,000 the body. For a pressure load of 1000 psi (69 bor) and on impact load of lbs. (4.45 MN), the maximum stress intensity occurs just below the seat, and ha rmgnitude of 72.3 ksi (498 MPa). Comparing this wlue to the yield strength of the body material at 500F (260 from Section !!! of the ASME Code (4), is 29.1 ksi (200 MPa), shows that the oc seat loading at which yield will occur is: 1,000,000 (2 ) = 402,500 lb. (1.79 MN) 72 And the corresponding pressure loading would be: ) 29 1000 (g1) = 403 psi (28 bar) which fortunately compares well with the 424 psi @9 bar) obtained by extrapolatin the inlet pressure in the simulation study to the time of impact. Exhibit Two is the onelysis of the body under impactmm) loading only. This analysis due to impact. shows that the outward deflection of the seat is .0061" (0.16 Applying the 0.403 yield odiustment factor os above, the ediusted deflection a 402,500 lb. (1.79 MN) load would be .00245" (0.062 mm). A calculation of the elastic energy obsorbed by outward deflection of the se W = h F x = f (402,500)(.00245) = 493 in-lb. or, in SI units, f (1.79)(.062) 103 = 55.6 J which is, of course, insignificant compared to the 1,251,000 in.lb. (141.4 kJ) e ne rgy .
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DI etmant 744-76XXX-645 Report No. 2573-62
, , Pogs 4 Exhibit Three is the finite-element model of the disk. This disk model proportion to the mass at each section, in the rnanner used in the Leonard an study of nuclear swing check valves (3). The FINEL program is also used in thi - analysis .
The seat load resulting from the arbitrarily-scaled inertial loading was 45,670 lb. (.203 MN). The maximum stress intensity was 1.59 ksi (11 MPa) compared to a yield stress (Fil material) of 31.2 ksi (215 MPa)(4), indicating that the disk can withstand a seat load of: 45,670 ( 2 ) = 898,000 lb. (4.0 MN) before yielding. Since the body will begin to yield at 402,500 lb. (1.79 MN), the disk is approximately 898,000/402,500 = 2.23 times as strong as the body. By summing the products of one-half the applied forces times the deflection corresponding nodes, the elastic energy input to the disk was calculated to be 4 ; in-lb (.535 J) under the loading of the model. This must be scaled up by a factor of (402,500/45670)2 = 77.7 to correspond to the body yield load, yielding an cla: tic energy of 369 in-lb (41.6 J). The clastic energy also would include that energy obsorbed by relative motion of Inward deflection of the disk, adjusted for the yield the disk into the conical seat. load of the body, would be:
.00005 (h02 500 ) = .00044" (0.011 mm) y i <
Adding this to the outwurd deflection of the body and multiplying by half the ap j force, the energy obsorbed is: W = f (402,500)(.00044 + .00245) = 582 in.lb. l i or, in 51 units, ! 3 = 65.6 J W = f (1.79)(.011 + .062) 10 1 i
I.sortment 744-76XXX-645 .., .[ Report No. 2573-62 Page 5 v .. . The total energy that is absorbed elastically, then, up to the point of incipient yielding, would be: Energy, in-lb (J) . . l Description Body Elastic Energy 493 (55.6) 369 (41.6) Disk Elastic Energy 583 (65.6) _ . . .____..._...l Disk-Body Relative Motion Total Elastic Energy Capacity 1444 (162.8) Thus, the elastic analysis bears out the initial opinion that the amount of energ can be absorbed clastically is for less than that which would be supplied under the postulated line break conditions. Nonetheless, the clostic analysis does identify the body as th likely site of plastic deformation and further, an examination of the maximum shee , trajectories in the ; One can visualize the seat seat region (Exhibit Four) does suggest a mode of failure. deforming downward and inward due to the applied load, with material from be This concept led to the plastic analysis described the seat bulging out below the seat. below. PLASTIC SEAT ANALYSI5_ Exhibit Five shows the derivotion of a simpic equation for the amount of energy required to plastically deform the seat in a tranner suggested by the maxim trajectories of Exhibit Four. This analysis makes use of three simplifying ass 1
- 1. The effect of hoop stress is neglected since the radius of the seat Therefore the is quite large compared to the local deformations.
problem is simplified to a two-dimensional plane.
- 2. Deformation occurs along parallel slip plancs.
~
- 3. Loading occurs along the slip planes, that is, there is no effect of loading through the slip plores on the shear yield stress.
The resulting equation for the plastic energy absorbed by the seat in the defor defined is: 2 W p = 7.5844 d T yp (o2-b) For the case of the size 14 Figure 607 volve, this results in a seat ener Wp = 271,181 in-1 b (30.6 kJ)
l
. Demrtment 744-76XXX-645 RL ,rt No. 2573-62 Pag 3 6 Since the disk is subject to a steam pressure acting in the direction of travel, the t energy required to be absorbed is the sum of the kinetic energy of the disk due velocity at impact and the products of the pressure force and the distance the d travels af ter impact. This steam pressure energy is equal to the product of the pressure and the volume change, or We = PbOVb, where:
V/e = expansion work, -
= bonnet chamber pressure, and Pb Avb = bonnet chamber volume change 2
14.8 in2 (0.0954 m ) The bonnet chamber volume change is the product of the bonnet area,3), and the seat deflection, 0.190 in. (4.83 mm), or 28.2 in3 (.00046 m The bonnet chamber pressure con be obtained by extrapolation of the simulation d and is: p2 , V1P1 , 480.8896.3(264.23)- = 142 psi (9.8 bar) V2 The yields an expansion work of 4004 in.lb. (452 J). 139,250 + 4004 = 143,254 in-lb (16.2 kJ), which Therefore , the total energy input is271,181 in.lb. (30.6 kJ) seat energy abso compares favorably with the culated. Therefore, on the basis of these calculations, the seat design can safely absorb all the energy of the disk within the deformation limits described. EXPERIMENTAL SEAT STUDY in order to demonstrate the credibility of the calculation method as a means for estirrating energy absorption capabilities, a scale model of the size 24 Fig. 400 mlve sect was made up and on actual deforrration test was performed, with the relationship between loading and deflection recorded over the full travel of the The size 24 wlve seat is similar in shape to that of simulated disk into the seat. the size 14. The linear scale factor of 0.1875, Exhibit Six shows the test model dimensions. 200,000 lb. referred to the size 24 valve, was chosen in order to permit use of the (889 kN) test machine in the Rockwell materials laboratory. t t Clay impression trade of the seat in the model and viewed on on optical compara or o ver geometry was correct.
rtment 74k-76XXX-645I ---
' Report No. 2573-62 i '
Pags 7 A tensile specimen was made of the same piece of material that was used for th and was pulled to determine the yield strength of the material. Its yield strengt (0.2% offset) was 43.3 ksi (298 MPa). This is typical of the 1018 material .
- is higher than the minimum specified yield strength of the volve body material{
Knowing the actual yield strength provides a basis for comparison of the energy i absorbed in the test model to that which would be absorbed in a va ; material properties. The ratio of yield strengths is: ' i 43.3__ = ),49 29.1 l In addition, a i Exhibit Seven shows the test data plotted as a load-deflection curve. ; family of theoretical curves is shown, since the theoretical force isl coefficient of friction between the disk and seat. *l matches the data well, and since this is a reasonable coefficient of friction, the ' experimental data do seem to confirm the theory. The theoretical amount of deflection in the mode,1 that would be required to 0.088 " (2.2 mm). However, absorb the scaled equivalent of the energy of the disk is the test data indicate that, due to the large energy absorption by friction between disk and seat, only 0.058" (1.5 mm) of deflection would be required to accomplis , same amount of energy absorption. Since the frictionless assumption is more cons l o rnaximum seat deferrnation of 0.19" (4.83 mm) would be expected to occur in the 14 valve, out of a total 0.31" (7.9 mm) seat shoulder width. . The flow of ; Exhibit Eight shows the shape of the deformed model bore after the test. ' rmterial is not exactly as predicted by the mathematical model. The difference can First, the contribution of the circumferential, or hoop, be explained by two factors. strengths of the material tends to resist radial material movement more tha model. And second, strain hardening along the 22-1/2o s lip planes would terd to cause the rmterial to seek new slip directions of lesser resistance after yielding ha begun. Exhibit Nine shows the derivation of the theoretical curves of Exhibit Seven, b on the strength and dimensions of the model. 4
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, s a i REFERENCES
- 1. Disk Velocity of impact with Seat for Line Break at Upstream Side of Size 14 Fig. 607 Non-Return Valve, . _..._ . _ __
E. B. Pool, Rockwell International, Report 2573-48. i
- 2. FINEL - A Stress Analysis Program Using Axisymmetric :
Finite Elements, J. H. Fowler, Rockwell international, l. Report 2573-01-21-14. I
- 3. Verification of a Qusoi-Static Elastic-Plastic Impact Analysis for a Check Valve Used on a Nuclear Piping l System, J. W. Leonard and J. R. O' Leary, ASME Paper No. 74-WA/PVP-8.
- 4. ASME Boiler and Pressure Vessel Code, Section 111 Division 1, Subsection NA, Table 1-2.1, 1974 edition, !
ASME, New York, pp. 88-93. l
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4 PAGE 4 C;KwE LL INT C'RN STIONAL low CCNT ACL DIVI 510ft . . . )RCGRAM f40.' f4CCESR26 HICHAUX e 07/24/75 illE 14 FIG. 607 BODY SEAT AREA FINITE ANALYSIS " PICTORI AL REPRESENT ATION 0 0 93 94 55 96 0 0 89 90 91 92 0 0 85 ^86 87 88 84 0 0 81 82 83 ' 0 0 77 78 79 80 O O 73 74 75 76 0 0 69 70 71 72 0 0 65 66 67 68 - 0 0 61 62 63 c4 ' 0 0 57 58 S9 60 O 52 53 54 55 56 51 0 0 0 0 0 46 0 47 48 49 50 41 0 42 43 44 45 36 0 37 38 39 40 ' 31 0 32 33 34 35 26 0 27 28 29 30 21 0 22 23 24 25 16 0 l'l 18 19 20 - 0 12 13 14 15 - 11 6 ~ 0 7 8 9 10 1 0 2 3 4 5 . O e 9 4 4 e r e e e k s t
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- 3 7.330 00 C. O. -
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13 7.330 1. 200 C. O. 14 7.780 1.200 0. O. 15 8 250 1.200 C. O. l 16- 6.440 1.,800 0. O. O. 17 6.880 1.800 0., , 18 7.330 1 800 0. O. , 19 1.80,0 0. O. 7.7_80 O. l 20 8.250 1.000 0. I 21 6.440 2.400 0. O. 22 6,.880 _2.,400 0. O_._ O. 23 7.330 2.400 0. 2.400 0. 0. 24 7.780 25 _2,.400 0. O. 8_._2 5_.0 26 o.440 3.000 0. O. 27 6.880 3.000 C. O. _3.,000 0. O. 28 7 330_ . O. 29 7.780 3.000 0. 8.250 3.000 0. O. 30 31 6.440 3.600 C. O. 32 6.680 3.600 0. O. 7.330 3.600 0. O. 33 ' 7.780 3,.600 0. O. _ 3_4 . O. 35 8.250 3.600 C. 4.200 0. O. 36 6.440 6 880 4.200 O_ . O. 3_7 . O. 38 7.330 4.200 0. 7.780 4 . 20 0 C. O. 39 40 8.250 4.200 0. O. O. 41 6.440 4.800 C. 4.800 0. O. 42 6.880 43 7.330 4.E00 0.* 0. 44 7.780 4.000 0. O. 45 8.250 4.800 C. O. 6.440 5.400 0. O. 46
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_ _ . . _ _ . . . . l p .00ES. CdCRCINATES. AND FORCES HICHAUX 07/24/75 . IZE 14 FIG. 607 BODY SEAT AREA FINITE ANALYSIS 5.1 6.4.40 5.900. __.497439.__-497439.. 52 6.560 6.020 502561. -509229. 53 6.880 6.C20 13401. -6844. 54 7. 330 6.020. .0.- O. 55 7.780 6.020 0. O. 56 8.250 6.020 0. O. 57 6.680 6.640 2.6369. .0. . 58 7.330 6.640 0. O. 59 7.780 6.640 C. O. 8 250 - 6.640 0.. O. 6..s 61 6.880 7 .240 25937. O. 62 7.330 7.240 0. O. 63 7 . 7_8,0 7. 240_
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64 8.250 7. 240 C. .O. 65 6.880 7.840 25937. 6. 6.6 7.330 7.840 O. J. 67 7.780 7.840 C. O. 68 8.250 7 840 0. O. ' 69 6.880 8.440 25937. O. 70 7.330 8.440 C. O. . 71 7.780 8.440 0. O. I 72 8.250 8.440 0. 0.. 73 6.880 9.040 25937. O. '
~ 74 7.330 9.040 0. O.
75 7.780 9.040 0. O. 76 8.250 9.040 C. O. 77 6.880 9.640 25937. O. 78 7.330 9.640 C.. O. - 79 7.780 9.640 0. O. 80 8.250' 9.640 0. O. 81 6.880 10.240 25937. O. 82 7.330 10.240 C. O. 83 '7.780 10.240 0. O. 64 8.2$0 _1C.240 _ . _ ,0 . O. 85 6.880 10.840 25937. O. 86 7.330 10.840 0. O. . 0.. O. 87 7 . 7_8 0_ . 1.0. E 4 0. _ SS 8.250 1C.840 0. O. 89 6.880 11.440 25937. O. 90 _ 7.330 _11.440 0. O. . J I 11.440 0. O. 91 7.780 ' 92 8.250 11.440 0. O. 93 6.880 _____12.040 12968. 0.. 12.040 0. O. 94 7.330 > 12.040 0. O. 95 7.780 l 9.6 8.25.0 __12 04_0 .
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' _07/24/75 IZE _14. F IG. '607_80DY , SE AT.. ARE A F INITE. ANALYSI S __MICHAUX __ _
AVERAGED STRESSES AT NCOES 8 STRESS HOOP SHEAR
- PRINCIP AL STRESSES ND. RADIAL AXIAL -0 E G__i.NT E h517.Y.. .?
-385. 34. 8348.
2796. 1474. 1804. 607. 7963. -6422. 13. 11360. 1 4937. 1468. 455. _14802._m 2 126. -6093. 3J 3_. -11815. 7. 18393. 3 19_8,. ,,11641. _2 981 1_4.50 309. -17182. 5.
-17066. 1211. 1417.. 22465.
4 194. 1371. -1369. -23739. 4.
-1453. -23654. -1274. 3.1.8 6_. __7 913 .___ ..
5 152. 1_7_9_7_. 11481. L. 6 1781. 3.34 8.231. 133. -6259. 2. " 5223. 252. 2. 14955. 7 123. -6249. 349, 208. -11663. 8 198. -11653. 3292 -169_42. 1 18476._ _248_. _ _19 9. O. 22474. 9 196.. .16938. 1534_.
- 96. -1429. -23407. 9593.
-23407. -933. -586. 8.
_ _ _ 10 -1430. 9006. 327. 1749. 12646. _, 11 1703. -540 __156 - 6 7 8.4 __._5 112. - -6740. _6.0 6 '. . __5.4 9.__
-11739. 4. 15937.
12 761 244. 19053
.13 196. -11691. 41'8.
541. 218. -16551 2. 201. -1c534. 2502. -1352. -22618. _1. 22715. _.; 14 214. 12452.
-1354. -22616. _97. 1626. -2250. 8.
15 10202. 546. 15158. 16 1548. -2172. 937, 205. -7752. 7.
- 94. -7641. 7405 -_1.1899. 6. 13 57 7.J 17 ._1.296_. 32.9 19953. ;
1,9.0.. _117.6.0.. _567.8.. -15844. 3. 921. 260. 1_8 207. -15791. 4109. -21154. 1. 22991. ' 19
-21147. 1838. 377. -1202.
-4923 8. 16589. .
20 -1210. 11666. 824. 1392. 18457. < 1282. -4813. 293. -9296. 9. 21 9161. 1453. 19881. l 22 67. -9071. . 2009. 504. -12205 9. 178. -11879. 7676. -14751.. -21087._q 350._ 5_. _ . 23 _1.432. _6336.
- 2. 23108.
213. -1461.4. _ 607. -942. -18786. 2.4
-18765. 4323. -8884. 7. 22002.
25 -963.
-8743, 13199. 1172. 1036. 22765. l 26 895. 2118. 435. -11577. 10.
- 49. -11192. 11187. -12775. 13. 22866.
27 2949. 840. 168. -12103. 10091. -13213. 9. 22357. 28 2120. 566. 231. -12879. 9144. -15178... 4 _22775.. 29
,15118. ._7597._ 937. .4 9 4 .
- 6. 28908.
.55.4._ 1558. 512. -14374.
3 0__ __ 347. -14209. 14534. 630. -14803. 11. 28064. 31 13261. 2935. 50 -14223. 1434. -13750. 17. _26520.- 32 __4142. 23708. 33 205. -12521. __1.2770. 3038. 1076. -11261. 15. 276. -10461. 12447. 361. -9818. 8.. 21573. 34 11755. 1389. 168. -9625. 132~.' -21350. 6. _36866. 35 15516. 2117. 34315. 36 -79. -21139. 3944. 807. -19269. 12.
-184cl. 15046. -15153. 20. 30650..
37 -0. 15497. 5671. 2316. 25023. 38 225. -13062. 4132. 2169. -8896. 24. 315. -7042. 16127. -2833. 27. 19519. 39 16686. 1953. 2055. 47156. 40 1060. .-1858. 2932. -2573 -32916. 6.
-32630. 14240. -25380. 14. 41395.
41 -2859. 5960. 547 335850 42 -904. . -23928. __ 16015. 3526. -14960. 26.
-11469. 18605. 7255. 39. 262S20 43 16. 4875. 3055. -c901.
-2928. 19351 749. 71. 20815c 44 -919.
21564. 2211. 8036. 60935c 1497. 7289. -301. -47609. 13. 45
-45210. 13326, IC379. 30. 51471 46 -2700. 13287. ~7487. -38336.
-30146. 1313S.
47 -15377. 19077. 7209. _
-835.. _.-15404. ._ 41.
63.
.__ 34481 26946c
_48 ,,_-7073. -9106. _ 2191. -6194. 435. 20751. 3412. 84. 24071:
-4438, 14398. 460.
49 24531. 1436. 50 610. 14248. _ _ _ _ _ . _ t 4
PAGE 12. _.. . . o lINEL (- 07/.24/.75 (IZEl4FJG. 607 BODY SEAT ARE A FINITE . ANALYSIS __MICHAUX 1 AVERAGE 0 STRESSES AT NODES , PRINCIPAL STRESSES O STRESS .
~ RADIAL AX1AL HOOP SHEAR NO. DE G__I NT ENS I T Y. _.'
16040. -15481. - 58248. 24. 64798. 51 -22724. -51006. 6550. 65495.
-37625 3509. 20010. -21188. -
61985. 51. . 52 -45549. 32775. 62. 44133. ! 53 - 2 9 7 9 3,.__ -22577. _11358. 5515. -19595. - 32276. 646. -8687. - 15682. 85. 54 -15621. -8747. 16595. -87. 26795. !
-6527. 166a. 20245. -442. 1689. -6550.
55 -89. _24481.. 15089. 24236. -328. 15096. -245. 56 -238. 3472. -6626., -20. 28418. 57 2314. -5466. 21792. -3218. 24592. 20889. -2796. 2721. -3704. -30. 58 1091. -2074. 4306. -2183. -61. 22401. y 59 - 613. 2737. 20218. -2779. ~ 92'i~. -82. 20535. :
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60 1103. f047'4. 2'1'456. -25. 21449. l 18883. ~864. -334. -2566. 61 -744. -2156. -365,4_. -34.. _2 089 5.,_J
-2325. 17241. -193.8. 501..
6_2 - 8. 2 8 . 2775. -1357. -51 18637. ) 63 296. 1122. 17280. -2024. 16605. 16854. -1038. 4013. 249. -73, l 64 561. 3701. -373. -67. 17395. I
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65 "721. -1W51. -53e 66 -668. -91. 15046. g -1032. 15277. I 14055. -1119. 1017. -1221 -46. 67 -129. ~75. 12682. -482. -119. -1241. -30. 13?23,] _. 68 -393 -966. -84. 14712.
- 36. 3286. 14709. -357. 3325. -3. t 69 873. -823. -73. 13380.,
70 -684. 734. 12557. -465. 11368. -457. 146_. -872 -32. _12240._q 7.1 _ -139. ,586 -3118. -3. 12706..
-3109. 9580. -140. -816. l 72 -825.
12294. -105. 39f0. 114. -88. 12180. l 73 117. 3947. -90. 10866. l
~ 64 8. 1031. 10218. -11. 1031. -648.
74
-13. -172. -840. -1. 9865.
75 -172. -840. 9025. 10983.
-857. -3651. 2.
76 -860. -3648. 7332 92.
- 89. '9813_j 3562. 9810. 63. 3563. -2.
77 -1. 270. 1031. -673. 81. 8740. 78 -630. 987. 8066.
~913. 21. 7949.
-814. 7036. 264. -112.
79 -212
-756 --3303. 5. 8927d
_ , 0 0_ - 776. -3283.. __5623. _ _2 2 8.. 2618. -216. 87. 7599. E1 -209. 2611. 739,3. 142. 6823. 398. 864. -724. 75. 82 -617. 757. 6098. 6192. 391. - 8. -875. 32. 63 -255. -626. 5317. 9, 6737. 4293. 288. -568. -2444. 64 -613. -2398. -455. 86. 5519.
-444. 1491. 5064. 142. 1501.
65 4268. 389. 595. - 7 3 6 . _,,_7 2 . . 5004._ 66 - 61 0. 469. 4488.
-390. 3759. 382 42. -728.. 41..
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-607, 1218. ~2 513'. 253.
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i ! Z E _1_4 _E I G . _60 7_ S O D Y _.S E A T. . AR E . F IN ITE . ANALYSI S__: MI CH A .LEMENT CENTER D AT A 1 O STRESS HOOP SNEAR PRINCIPAL STRESSES NO. RADIAL AXIAL DEG__1NTENSITY. 218. -3010. 1. 9328. 6319. 84. 12956. 1 215. -3007. -8751. 1. 318. ~8747. 4205. s 181. 322.
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- 58. -19657. 1061. 257. 62.
- 6. 12348. '
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- 3. -17541. 4295. 779. 37.
- 8. 19718.
16 1230. 467. -8443. 17 294. -8270. 11275. -11382_. 1.3 . 21061.._ 96.79., 2.603 93.7. 18 3.6.0_. -10805. 605. -13424. 11. 21692. 113. -12932. 6267. 2582. 22441. 19 6830. 1187. 50. -15561. 4. 20 -41. -15470. 564. -1.1999. 8. 25141._ 1734. 21 _320. -11755._ 13.142. 1439. -13198. 15. 25215. 3704. 22 433. -12192. 12017. -13136. 16. 24190.
-12077. 11054. 3745. 1169.
23 109. 17.0.. -12642.._ 8 22734._
-J 6 . - 1 ? 3 9 6 ._. 10091.. _1J 5.9.
-16815. 7. . 31656.
14 14841. 2269. 725. 25 426. -16516. 2013. .-15825. 17 . '30159. 455. .4266. 14334. 5037. 22. 2.7186.; 26 5250. 2209. -1.3084. . 122. -10997. 14102. 17. 22592. 27 13852. 2571. 615. -8740. 39103. 28 -155. -7970. -23260. 7.
- 19. -22890. 15843. 2933. 388.
-19532, 19. -35772._
29 6832. 2466. 30 87. -17153.. 16240. -13605. 29. 30457. 16851. 7073. 3077. 31 -842. -9686. 2319. -4574. 39. 22522.
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-3764. -6438. 19051. 7362. _67 .
35 -2387. 36 -1068. _ __.5154. ___.21590. . ..
- 3153.
7678. __6.472'.1.
-6212. -21625. 47. _2397 38495.
16871. 37 -14575. -13261. -914. -8393. 65 28479.!
~7024. -2283. 20085. 2893. 86. 24977.
38 _23327. 739. 9815. -1649.
-1601. 9767. . -14266. -46. 32253.
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-9602. -9375. 17987. -4777. ~4711.
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43 723. -3870. 3078. -4690. -43.
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44 18554. -2309, 4928. 45 -322. 3841. .592. -1669. -48. 18809o
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PAGE 14 siNEL' 07/.24/75..
- ZE_L42I G.__6 0 7. 8 00Y_.5E AT._. ARE A_f!N I TE_ A NA LYS I S ___M
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- 5 7 2 2 '.-~-~ ~ 2 C~. ~ -
u -; L - 32 74 144. -28. -338. 34. 5227.
-127. -239. -5256. 22. 4849.
94 142. -93. -509.
-149. ~453. -4943. 4% 0'.' ~
95 ~ ~4 5'8 2 T 1bS. "23. -55T. It .
> U- -7 z . -5l'O.
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MICHAUX 12/11/75 l 512C 14'F!b. 607 370Y SEAT AoEA FINITE ANALYSIS % 5LEMENT C5NT ER DATA AXIAL HOOP SFSAR FRINCIPAL STRESSES 9 STP.FSS NO. PADIAL DcG INT"NSI'Y < 21 3. -3520. ~5VEO . 97-~ z'le. -3 pD . 1. - 9 93 2--" ~~ ~-'l 1. 13301. 2 310. -3844. 4453. 197. 314. -8848. 194. -13969. 2616. 195. 197. -13972. 1. 16588. 3 4 59. - 17771. u El . es. >v. - tV2 /1. ' v. 40TI27 221. -3972. 6969. 291. 242. -3992. 4. 109o1. 5 313. -9022. 4999. 624. 355. -9063. 4. 14062. 6
-13378. 170f0-~ {
~ 7 1o4. -FTs5T. T2 J2'- E17. 2T1. 3.
- 48. - 19 8 E C . 1481. 28C. 52. -18884. 1. 20365. :
8 236. -4945. 794:. 537. 291. -5000. 6. 12944. I 9 15ScV;~~ l
~~ ~1 0 216. -9T0;. FO~e 3 . 1T4% . ol. -v33 7. i.
16 1. -13598. 4359. 1131, 253. -13690. 5. 18048. ! 11 12 26. -18338. 2721. 515. 41. -18053. 2. 20774.
~~~T 3 253. - c iB I . 9z6E. tie ~~ ;59. - 6687. T-- 19975T 322. ~ 100? 9. 7594. 1E17. 631. -10348. 10. 17932.
14 , 124. -l?i75. 6055. 1794. 362. -13412. 8. 19460. 15
-t. - ITc Ze . 457e.
~
641. :. -lecee. . zt?++. ic 17 277. -9073. 13854. 1272. 447. -9243. 8. 2009o. 332. -11005. 9461. 26E5. 936. -11608. 13. 21069. 18 ~~' 13 9'l . - r2T TC . 6'2:,. cT E3~ . ~679. 'r3076.
~F1. 2T3T3 P 20 -50. -14474. 7329. 1228. 54. -14578. 5. 21607.
21 29 5. -)2636. 12425. 1765. 532. -12874. 8. 25300. 29c. - 12 4T7. ITY42. 3759. IT1 ( . -139 e. 13. - 2 V9 09. - 27 23 -
- 65. -lle67. 103CO. 3799. 1205. -12788. 16. 23588.
24 -u4 -11333. 10048. 1767. 193. -11610. 9. 21659.
~~2T nh. ~rl?437. -1T762. c273. 67T. - 177 FF-- 7. ~f: r43 27 2e 410. -1449E. 13535. 5033. 1950. -16038. 17. 29573.
27 99. -10583. 13555. 5246. 2244. -12728. 22. 26263. db -16v. 35EEC. 13 54 F. c57 . ela. 37752. r9. eT2977~ 29 -l 7. -23751 14349. 2ESA. 328. -24096. 7 38445. 30 51. - 17 3 t l . 1b051. 672E. 2347. -19658. 19. 34709.
' T I-~ - e; 3. r.n. 13932. ~ "E T7 T. " 3~0 3 T . -17270. 29. z91T2.~
32 - 42 o .' ~782. 17289. 3336. 2737. -3945. 43. 21235.
-107. -32o1C. 13846. 5391. 700. -33o77. 9. 47523.
33 -t DI3; . 2, - s T9 7;- -" r2 7 E TT. f 4 3 r2 .---" TC13 e . -e0s. -258z4 4(. 35 -3755. -o1CE. 17o77 714E. 2313. -12174. 40. 29851.
-1059, 6055. 20463. 3C61. 7191. -2195. 70. 22679.
3o 47.
~~37 - 1"4 5 c a . -T:3FC. ~14 6 2 7 . - ~~12 5 E . - E6 F5~.' - 2T2 ZT- 7591a.
-o959. ?-2067. 16158. '2i41. -992. -8074. 67. 26232.
30 39 -1560. 10'91. 21c62. 571. 10419. -1607. 87. 2?269.
~~40 - v c< v . 270s. 151'67. -5340. - 414 : . -17322. -99. e75c7-~
41 -4317. -531 17:46. -4721. 26o3. -7511. -56. 25053. 3o17. 19627. -2629. 9284. -1748. -76. 21375. 42 z_., _.-. __- y g.1T,_ 0 0 2 .,73);z.-" ~ 16553. ~ 21]E7.-
. 1950. - 3 4 0 9--~ ~rT3 . 19F6TT
-1153. 15348. -4232. 3oS3. -4380. -41. 20279.
44 75. 17097.
- 21 3. 3577. 15575. ~~563. 4880. -1522. - 63.
45
~ 7,r-~ ~ 17 0.~ 189; ~ 13 517. -12CT; 13B3. - TV 2 3 . -h. l'4 5TS~~-
47 510. -4 12';41. - 2 2 e E. 2536. -2029. -42. 14570.
-5. -133. 11443. -1428. 1361. -1499. -44. 12944.
48 2209. 10724.~ ~~'-62T.'-~~~""235 5 ~ ~ ~ C 6 '. - 7 4 .--- -- 1 3 6 5 5 .
~ ' ' 4'9 T4 W 130. 150. 9289. -llle. lico. -976. -45. 10261.
50
P FXd'~is , til L SI6E 14.FlG., 607 610Y SEAT AiE A FINITE ANALYSIS FICHAUX 12/11/75 ELEF.CNT C ENT ER CATA f L 4 RA01AL AXI6L HOOP SbEAR FRINCI P AL STRESSES 9 STP"S5 ! NO. 00G INTFNSITY '
-?r23. ~10'07 4-~"
51 - 13. -133E. T95r. 23ET. ~1T1. -16. 3039. 152 -88. 7685. 1 52 157. 2003. 7837. -122.
-49. 6506.
11 5. lat. 6419. -235. 389. -87. l
$? i T 5 T.-*
^
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24 - 1~ > . 5073. 214. 2940. 103. 8 6.- -~ ~4979. 55 119. 2923.
- 48. 4097.
1' 56 95. 172. 3889. 340. 476. -208. 57 TO-~~~~- 2 Td3 . 2765. -- ~~2 C~E . ~ ~ 21. . C'259 9 . 5. ~33 E47 i 58 67. 23C7. 2476. 392. 2374. 1. 80. 2476. i
- 67. 136. 1664. 65C. 752. -549, 47, 2213. i 59 30097~
50 TB. -zJ4C. 101. 3/9. Ge. -~C210's . to. 1461. 57. 434. 1581. -104. 75. 1665. l 61 16. '
-339. 723. 761. -666. 46. 1447.
62 29. 86. f5YlT-'I
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- 15. -a6I. c223. 375. T67. -7T6.
z4. zevT. i 67 -52. 144. -4347. 126. 205. -114. 64. 4552. 68 -11. 9. -4042. 266. 265. -267. 46. 4307. i c9 a1. -r34. -T7E57-" 17 f .~"-~ ~ ~ ~7T 9'.~ - -2Gr. 2 7--' 3'E E T.~ 70 -55292. -34666. -1630. 22722. -20026. -69932. 57. 68302. 71 -36336. -40902. 3546. 14512. -21950. -55288. 41. 53835. 4'336. T503 4" ->rST. -6pI9). 13. ( 0U 3D-- ; (e - v u v. - e i l a c. . i
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7 l MGRAM fiO.' NCCESR26' 08/14/75 ' S. MICHAUX : 6 TNC H FIG. 6b7 0!SC FINITE ELEMENT ANALYSIS 5 d NTRI NCOUP ' hPZ NF NSUPP IBP1'MAXITS NPLOT 23 0. _ .i 62' NPR 32 0 NT- NOREGT NR 2 10._0_0 0 11 2 -
-68 14 16 s :
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7- 7 A R.g ,- . (9 18 11 19 26 25 18 4 11 10 12 11 4 12 19 9 17 24 23 16 20 27 26 19 5 9 2 10 17 16 11 18 17 10 16 25 24 17 3 1C 22 15-~2T~3~d 2~9 2'7 26 '3T 3'8~~2 5 ' 8~ l 6 2'3 50 49: 38
~
2'~ T ~'8 1-~~T'~1 o TS 23 36 35 22 40 51 50 39 39 45 44 33 37 34 23 34 34 25- 38 37 24 24 36 36 47 46 35 35 46 45 57~7 4 38 49 48 37 37 46 47 Sy 49 49 59 58 48 48 58 68 59 60 6C
^" 3 3~ M -~41 12~~5'i~~~El 6T ~~60 44 44 54 53 43 60 69 46 46 56 55 45 45 55 54 77 76 67 77 86 85 76 57 56 66 67 58 68 86 77 59 6~~ 6 6 75'~ 7 4'~6'S :
'7 i
69 76 77 68 78 E7 T6~~~7 6 65~-~67.73-~67 66 6'5~~5 64 63 54; 5tF 57~~E6 57~~67~-~T6~- 75 74 73 64 74 83 82 73 55 71; 56 c5 64 55 65 71 62 72 81 80 75 84 83 74 63 62 53 63. 72 91i 72 54 ~ ~ 88 8L-~9'2" ~10 0~~ 9 9 63 _73_ 82_.81 8 2'~ "b 2~~ 8 9 64 73 g0~ 8'3~~83 9 C'~~~8'9 q1
- _.g . . .. )._.97 2 gg g4 89 37 96 68 91 99 98 90 90 98 97 89 - . -
0 29 41 40 @ J ~ 39 0 29 30 41
~ l 4it14Got. Ao'~FTEFC RT 5 26 0 29 40 0 70 69 60 0 26 7/ 0 29 39 0 61 70 60 29 93 86 0 _52 ..61_.51 86 0 94 8
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_ g7 78 0~~87 94 95 88 0 88 of 00 E 93 10C 92 0 96 93 92 85 0 < 93 85 86 0 3; 2 31 0 - .... 43 42. 32 0 1 86 do 81 0 - 2.3100 2 5500 ~ ~ ~ ~ ~ ~ ~ ~ ~ R L AT7 tCE .97000 1.5700
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FROGRAM t40, = NCCESR 26 : 08/14/75 , : NALYSIS S. MICHAUX .
.14 IWCH F IG. _607 O!SC ' FIN ITE ELEMENT A .
fig 3AL L ATTICE PCSITICNS ' 1 1- 12 - 2 1 11 . '
.3 1 10 -
4 .1 8' a 5 1 7 , 6 1 4 . i; 7 1 1 6 2- 12 . i 1 9- 2 11 ' . 10 2 10 - f fl 2 8 .. 12 2 7 13 2 4
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- 40 6 4 41 6 2 42 7 16 ' '
43 '8 15
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CCKw S LL . ,1 NT ES N t T I C'IS L * - . . - . L Cd ' C CNT R C1 O l v i S ! *;N ~ ~ ~ ~ ~ . RCG R AM NO. NCCESR26 0 8/_1.4 / 7_5. , S, MICHAUX 14 If*CH F I G. 607 DISC FINITE EL_EfENT ANALYSIS . .;. NCDAL. L ATTICE PCSITIONS , ' i 51 8 4 . 4 T2 8 3 ~ 53 9 15 . 54 9 14 55 9 13 - - - - - -- -
-.-2.L"~**.
56 9* 12 - 57' 9 11 10 58 9 . 59 9 8 60 9 7 61 9 4 . 62 10 15
- _j 63
- 10 14 - a 64 10 13 * - -
{ 65 10 12 t 66 10 11 ~~ 6'7 l'd. 10 - 68 10 8 . 69 10~ 7 .
~
70 10 5 ' 71 11' 15 72 11 14, _ 73 11 1.2 3. . 74 . 11 12 , 11 -1 75 11 '
~
76 fi 10 - 77 11 8 ~ 78 11 7 Y9 fl 6 . E0 12 15 __ 61 12 14 ~ 82 f2 13 ' '- - 63 12 12 ~ 84 12 11
. e'5 f2 10 86 12 8 '
12 7 - _ __.8 7 _,g ' 53 13 13 , ., _ 90 13 12 . fl T3 l'1 - 92 13 10 - e 93 13 9 . 94 13 8
. 95 14 15 ~
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0 8L14 L7.5_ ', MGRAM NO. NCCESR26 S. MICHAUX E ANALYSIS _i INCH FIG. 607 OISC FINITE Et, FENT .
.l f '.CT ORI A1. P.F P R ESD4T AT ICN l
0 0 0 0 0 C C 0 0 31 42 71 80 0 95 l 0 0 0 0 43 53 62 96 0 0 0 32 63 72 81 88 : 0 0 C'~4' 4~~~5 4 97 ! 0 o T3 64 73 82 89
~~~D O' ~d 34 0 45 55 23 90 98 i 0 0 0 0 O 46 56 65 74 22 0 39 0 75 84 91 99 j 6 15 47 57 66 1
23 0 36 0 67 76 85 92 100 ' 2 9 lb 48 58 0 10 17 24 C .37 0 0 C 0 0 93 , 3 0 0 0 94 0 1 0 0 0 0 66 77 86 0 - 0 38 0 49 59 0 0
- 4 1'l 16-~~2 5 60 65 78 87 0 39 0 50 0 0 0 ~
12 19 26 0 C 79 5 0 0 0 0 0 0 0 0 0 7C 0 0 V O , 0 0 0 0 0 i
~~ 0 0 0~0 0 40 0 51 61 C 0 0 4 0 0 13 20 27 29 C C 0 6 0 0 C 52 0' O O 0 0 0 0 0 .
0 41 0 0 C O 0 0 0 0 0 C 0 0 0 0' O O
.-- l 28 30 C )
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- 5. MI C il Ayf. 08/14/,75 o 4 INCH' FIG. 607 0150 FIh1TE ELEMENT ANALYSIS Ax1 AL' PRESSURE, TYPE, NODES .
1 1 8
-2J9.00 ~~
15 B 7 5'O'.00 2 1 15 22
-250.00 1 22
-250.0C 1 .
3_5 42
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- 302 00 1 ,
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.COE S, ' COCRD IN AT ES . ANC FORCES .
08/14/75 ' . . S. MICHAUX 1H L4 INCH F IG. 607 OISC FINITE ELEMENT ANALYSIS il O.
-40. If 0.0 2.500 O.
1 2.160 C. '
~
2 00 0. O. 3- .0.0 1.790 _0. _e. 1 .,4 2 0 _ C. - 4 _O . 0 0. O.
- 5 0.0 1.C50 O.
0.530 C. 6 C.0 0. O. 0.0 .- . . . . . . - 7 0.0 -325. 27500 C. -
- -~
8 0.41d 0. O. 9 0.410 2.160 O. e c. i; 10 0.410 1.790 O. I 1.420 0. 11 0.41C , C. O. 0.410 1.050 12 13 C.410 C.530
~~
0.C 0. C. O. O. }g
. 14 C.410 0. -887.
15 0.970 2.500 O. 16 C.970 2.,160 _0 _. O. ' C. . 17 0.970 1 790 O. 1 420 0. 18 C.970 C. O. 19 C.970 1.C50 O. 0.530 C. ; C.WO 20 - C. O. '
- C.970 0.C 21 2.500 0. -2077.
22 1.570 C. O. . 23
~
1 570 2.f60 O. 1.790 0. - l 24 1.570 0. O. l 25 1.570 1.420 O. 1 050 C. - l 26 1.570 C. O. 27 1.570 C.530 O.' 0.0 0. 28 1.570 0. O. 29 2.310 0.530 O. C.C 0.
- 30 2.310 C. -2964.
31 2.550 4.500 O.
]
- 3. E30 C. ,
32 2.550 C. O. 33 2.550 3.390 O. 2.950 0. 34 2.550 C. - l '7'5T. IS 2T'Ef 27500 2.160 'O. O. 36 2.'550 C. O. 37 2.550 1.790 O. 1.420 0. f5 2.550 C. O. . 39 2.55C 1.C50 O. C.530 0. 40 2.550 _ C. O. 2.550 0.C80 _ 41 4.500 '0; -5602. - 42 2.850 C. -5696.. - 4.3 3.500 __.3 .. E30 . --
- 0. O.
44 3.300 3.290 O. 2.950 - C. , 45 3.500 O. ~~ 46 3.5CO 2.500 ~C. O'. 2.160 C. 47 3 300 C. O. 40 3.b00 1.790 O. 1.420 0. 49 3.500 ~~ C. O.
~~~50 3.500 1.C50 "e _ _
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{iCDE SCOPRDIN , AT ES . AND FCFCES S. HICHAUX 08/14/75 .,
- 2. 4 INCH FIG. 607 DISC FINITE ELEMENT ANALYSIS 0.530 C. 'O.
51 3.500 O. 3.500 C.330 C. ' 52 -6638. 53 4.250 ~3.830 0. l C. O. 54 4.250 3.390 O. . 4.250 2 950 0 55 O. 4.250 2.500 C. ' 56 0. O. 57 4.250 2.160 ~~ O. 4.25C 1.790 0. 58 0. O. . _ _ _ __ 59 4.250 1.420 O. 4.250 1.C50 C. 60 ~ O. J 61
~
4 250 f.33U 0. 3.E30 C. -7546. 62 5.000 O. J 63 5.000 3.390 0. ;) 279'60 C. O. *) 64 57J00 O. 65 5.000 2.500 0. - f' 2.160 0. O. 66 5.00'0 O. I 67 5.000 1.790 0. 1.420 0. D. ' 68 5.000 0. O.
- 69 5.000 1.C50
~ -
CT73D
- 0. O.
TD ~5TO0b , 3.E30 0. -6312. . 71 5.790 O. 5.790 3.390 C. 72 O. ~~ 73 5.790 2.950 0. ' 2.500 C. O. 74 5.790 O. 75 5.790 2.160 0. ~ C. 0. 1.T90 76 5~790 O. 1.420 C. 77 5.790 C. O. . 78 5.790 1.050 C.940 0. O. 79 5.790 . 3.630 C. -5371. C0 6.190 O. 81 . 6.190 3.390 0. 279sa C. O. U.YG0
~
82 83 6.190 2.500 C.' O. O. 84 6.190 2.160 0. l 1.790 0. O. l 85 6.190 O. 86 6.190 1.420 0. 1.C50 -22635. O. 87 6.190 O.
~8 8 6.5s0 f~390 0.
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'ROGRAM NO. f4CCESR 26 S . MI C_H__A.U_X 08/14/75 , ,i 4 INCH FIG. 607 DISC'FItJITE ELEMENT ANALYSIS ;!
;TIFFNESS MATRIX WIOTH FROM 1 TO 32 t:
. e iAUSS-SEIDEL ITERATICN C ON V E R G'cN C E AT ITERATICtf NO. AND BETA l' ki
~
100 1.79699 .
.15141E 1.79699 j
.38823E-06 200
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.1'20 2 5 E - O o 400 1.79699 l
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, , PAGE 9
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'08/14/75 S. MIC H AUX 4 '
"eT ' AN ALYSIS 4 INCH FIG. 607 015C'FI' .
1 '0DAL DISPL ACEf4ENT S' . ZDE UR . M ;
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,21 .6 22 -0.0000341 ~
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'24 -0.0000127 J4 25 -0.0000031 '6 -
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! Eh'ET ' . 08/14/.75 5._M. I C.H AU X _ LINCH FIG. cu.7..D IS C__E lh !.T_E_E L E M EN T A N A l.) 315 . AV ER A GE D, ST REL L ES AT,60 DES a O STRESS HOOP SHEAR PRINCIPAL STRESSES NO. RADIAL AXIAL D E.G___I N_T.EN S I T 816.
-395. -1212. 90.
-1212. O. 545.
1 -1212. 995. O. -226. -771 90.
-771. -226. -771. -470. 90. 258.
2 3 -470. -212. -470 O. O.
-212.
- 1"7 2. -132.
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- 97. O. 0 581., l 5 97. -138. '
-80.
O. 5_0.1. . O. 949. l 6 _501. - 8,0 . 50_1. O. 1141. 192. 7 1141. 192. 1141. -344. -1138. 87. 830.
-1135. -346. -1174. 43.
-762. 84. 566. '
8 61. -195. 9 -755. -202. -759.
-166. -475. 75. 308.
-456. 77. 48. 161. I 10 - 4 5'~4 . -187. -76. -237.
-166. -147. -170. 80.
128.. -141. 17. 269. l 11 105. 77. 574. ' 12 104. -116. ST3. --51, 6. Sfo . 55 934.
~
13 568. J56. 1102. 197. 2.
- 198. 1131. 28. 89. 735. '
14 1101. -1100. 10. -365 -1064. 522.' 15 -1064. -365.
- 26. - 2'3 9. -7W$. 87.
-7T4. -240. -7T1. -189. -441. 78. 260.1 16
-201. -449. 52. 42. _149. j 17 -430. 74. -86. -235.
-167. -166. -161. 17. 202. I 10 -153
- 96. 80. 121. 569.,
19 97. -136. 498. -70. 6.
-63. 499. 62. .
2, 892.! 20 491. 975. 137. 974. 136. 1030. 31.
-995. 67. 724.
21 35. -323. 497.
-993. -325. -1047. -649. 82.
' .! 2
-7C9. 57. -212.
3 -642.' -220. '
-174. -422. 65. ^ 248.1
-219. -421. 96. ~
-289'. 40. 267.!
24 -377.
- 152. 1 31 . -22'. 350.l 25 -132. - l'f9 . 188. -162. 21,
-117. 148. 117. -110. 9. 559.l 26 14 3. 82. 436.
-98. 449. l'2'0. 5. ~ 8 20. '
423.
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27 431 53 . 835. 501 liS6 l~21!'-' 391. -83. 13. 28
-58. 418. 106. 5, 701 29 366. 778. 56. 680. 77.
205d. 675. 82. 37. -836. 12. 30
-800. -2013. 173. 14. 1640..
31 1. 130. -268. -804.
-771. -1907. -651. 15 121%l 32 -301. 71. -367. ~ 900d 33 -386. ~632. -1582.
-3T3. -480. "3.
-12'1'3. 8. 515q W -31Y. -4 ifC . -80.
-40. -420. -662.
-426. -934. -529. 77. 360q 35 .655 -633 55. -273 318d
-516. -285. -107. -425, 56.
36
-207. -368 148. 44. 345l
-325. 37. -309.
37
-144. -127. . 173. -186. 31. 413!
38 -128. 151 182. 227. '
~515; 11 8. -77. 4'63'. ~ ~C 4'6 . 20.
39 D. (69. ~~164. ~34. 14. 611l 40 404'. 131. 518.
-1. 577 15. 1749 41 485. 176. -130. -819.
1141
-771. -1879. -714.' 36.
42 -178.~~ ^2 560. -1413. 211. -270.
- 36. 921
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4
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220.~~~ ~~ ~ ~ 5 5 . 532
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' MEF AGED ST RESSES AT NODES , O STRESS , HOOP SHEAR PRINCIPAL STRESSES INTENSITY NO. RADIAL AXIAL CEG
- 66. 23. 410.
145. 473. 41 3. 127. 477 -20. 19. 515 51 151. 470. , 418. 32. 495 ~528. 58.. 828. 52 -1140, 97. -312.
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62 -151.- -78. -443. 35.
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63 -- 2 0 0 . 66. -566.
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-38. -343. 434. 822.
67 -400. 317. 127. ~695. 65.
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6S 95. 104.
-347. 84. -40. -183. 70. 258.
69 78, 60.
-155. 33 75. -336. o. 727.
70 -681. 60. 46. 71 37. -326. -37. -412. 19. 576.
-613. 117. 573.
72 -78. -371. 232. 11. -562. 27.
-107. -443 -547. "749. 31. 828.
73 366. 79.
-141. -529. -504. -926. 35. 1066.
74 503. 140. '
-21 6. -570. -494. 1253.
75 624. 196. -1057. 43. 76 -351. -48C. -478.
- 95. -1075. 58. 1171.
-226. -468. 523. ~
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- 4 0'8 . 3'29. 17. -123'5. ~7 27.
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-1086. -642. 492. 37. 1461.
ES -394. 703. -741.'. -2202.
-1274. -1668. -1076. -2594. 54. 14190 S6 671. -1175.-
67 -2114. -1654. -1261.
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- 45. 616 9 ~.5 -404. -355.
- 92. -9. -624. 9.
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577. -1155. -2382. 35.
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- 92. . - 1. 0 2 . 159. 43. -1. 274 9 0. . . .
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a PAGE 13 j F i tM L' 08/14/75 S. MICHAUX .1.4_.,J NC H F I'G . 60 7 D I,5 C F IN I T E_E. ley E N_T_, A.N A L,Y.S I.S_ _ '
+
ELEMENT CENT ER CAT A . SYP.ESS l PRINCIPAL STP. ESSES ' 8 AXIAL HOOP SHEAR DEG INTENSITY, No. RADI.tL * - ~
-5. -1. 800 7V5. -9. 795. 780.
~
1 7 f5. ' 5.- 741. -17. 2. 763. 28. 739. 2 740. -16. 683. -19. 5. 720. 55. 3877 3 679. -15 3f'6. -71. "2 .
-71. STS. 14. 398.
4~ ST5. 314, 62. 321. -77. 9. 311. -67. -124. 13. 435., 5 95. 311. 289 -102. 294. -141.
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- 65. -13Y. -36. 72. - 3' O .
- 25. 167.
7 64. -1. -168.
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38. G
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-151. -330~
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9 -18. f7. - l '8~3 . . ~~f Ci -I25. -Y88'. - 3~2 5 .
-170. -331. 70. 161.
-186. -318. 51. 174.-
11 -312. -154. -328. 58.
-302. 79. 403.:
12 -279. -203. fi. -22'2
-625. "86.
- 6f3. - 2'2"4 . - 62'3 .
-215 -610. 85. 398..
1~3
-21E. -614. 33. 93. 3631 14 -608. 40. -234. -576.
- 572. -239. -598. 89. 724".1 15
~ 2TI . -9Y0. f8. -276. -f60.
693. f6- - 9 6 0-~ ' -2. -227. -889. ~90.
-889. -227. -920. -863. 89. 651a 17 16. -240.
-862. -240. -891 -40. "8. ~6'7 7 0 10 86. ST2.
1V (4'0. -17. 6f8. 114. -234. 34. 348d
-125. -7. 161 49. 289d 20 6.
143 -57. -347.
- 260.
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76.
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21 ~222. -181.
- 94. -2"O 6. -494. 328d
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2 70. 174. 409 24 221. -17.
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- 88. -371. 52. - 459:
-85. -210. 223. 57. 462' 26 -197. 210. -9. -471.
27 -336. -144. -426.
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-~2UU; ~629. 1T1. 39. 605)
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26~ -349. 57. -270. -385.
-316. -339. -
-875. -479. 23. 951l 29 105 -190.
33 -236. ~433. -1142. ~
-263.
- 5 7 2'. 21. [217!
-T24. -is20. 123. 33, 307 2 - 2T1. *141. 259. ~49.
166. 44. 251. 54. 457 S2 -9. 217. 199. -258. 33 -101. /.e 1.
~ 2 6 T-~ ~ 175. - 413~.~ ~ 57. ,
588l
~4. - 19 9~. 57. 649 as -2'42 ~~ 295. 136. -513.
-324. -53. -371.. -568. 55. 63e 35
-143. -531. 301. 70.
682 36 -355.
-'706' 283. 221. ~ 5 9 6' .~~ ' 5 0 .
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37 -358. - 2 5 8 '.
-139. -611. 45. 774
-377. -913. 236. 52. 864 36 -373. 183. -306. -684.
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-76. 217. 17 3~.
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-657.
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( PAGE 14
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- 4 'i i . 47. ,
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bl ~74. -624. 386. -664. 37. 759.
-320. -278. 364. 95. 22. 610.
52 -393 -548. 55. ~556. 53 - 177. ~
.-T73. 211. 44. 731.
54 -3'O . - ~s71." 285. -29. -599.
- 32. 632. ~
-325 -760. 15. -484.
55 -302. -617. 224. -3'9'2. l'6 . 531.
-125. -344. 106. Sf. 721.
56 -523. -407. 40. 57 -22.. -361 111. -181.
- 16. 673.,
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59 -61. -313. -710.
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-476. -578. 11. 641.
-89. -837. 117. 63. 441.
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62 41.
-404. 73. -310 5. 476.
- 63. 15. -402. 28. 20.
-308. -456. 72. -323. -10. ~395.
64 18.
-250. - 67 .
-269. -T . 302.
. 65 60. -312. -
-20. 14. 346.
- 12. - 2's 7 . -2li7 11. -256. 1.
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66 -336. 4.
-228. O. 412.
- 11. -256. 1. 7. 556.:
67 s -405. 19, 68 7. - 228. 172. 418. -141. 328.
- 81. 361 223. -100. 2.4 .
69 358. 228. 120. -65. 19. 466.. 169. -47. 146. 402. 661'.~ 70 -13. 356. 394.
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