ML20070M569

Effects of Internal Pressure on Axial Compression Strength of Cylinders

ML20070M569
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Site:	Oyster Creek
Issue date:	02/28/1991
From:	Chris Miller CBI TECHNICAL SERVICES CO.
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ML20070M559	List: ML20070M554 ML20070M569 ML20070M572
References
CBI-022891, CBI-22891, NUDOCS 9103210296
Download: ML20070M569 (39)

Text

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i EFFECTS OF INTERNAL PRESSURE ON AXIAL COMPRESSION STRENGTH OF CYLINDERS Clarence D. Miller Chief Research Engineer-Structure!

CBI Technical Servicos Compar..

Plainfleid, Illinois i!

Technical Report CBI 022891 1

l!

i February 28,1991 1

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EFFECTS Of INi[RNAL PRES $URE I

ON AKIAL COMPRESSION STRENGTH OF CYLINDERS INTR 0000110N s

Experimental investigations have shown that the critical h'sckling stress of

['

a axially loaded cylinder is significantly increased by inteinal pressure. The destabilizing effect of initial imper'ections is reduced. The circumferential tensile stress induced by pressurization inhibits the diamond buckling pattern associated with elastic buckling of cylinders, and at sufficiently high e

pressurization, the cylinder buckles in the classical axisymetric mode at approximately the classical buckling stress.

Tests have been performed by several researchers on cylinders of varying geometries and materials. There was a large variation in the buckling stresses of the _ cylinders without internal pressure with minimum stresses of about 8% of the classical value and maximum stresses of over 50% of the classical value. The increases in buckling stresses due to internal pressure were found to have a much smaller variation. An analysis has been made of available test data and a design equation has been proposed for determining the increase in buckling stress of an axially compressed cylinder due to internal pressure.

i

_ ANALYSIS OF TEST DATA 3-n i

The following is a sumary of tests that have been performed on cylinders to determine the effect of internal pressure.

L Ring No. of Sets Reference Number R/t J Rt Material-Stiffened of Tests 11 682 783 7 26 Aluminum Yes 9

15 583 1750 152-263 Aluminum No 3

20 1750 103 Aluminum No 1

20 1006,2734 56-146 Stainless Steel No 3

22 514 90 136 Aluminum No 1

23

-602-52 Aluminum No 1

24 1250 141 Aluminum No 1

43 400-2000 40-89 Mylar No 38 I

_ ~.

i

l t

The data taken from these references is plotted in Figures la Im in nondimentional form of d versus ).

5 fand p.[ f buckling stress determined from tests, psi ocr internal pressure, psi p

Young's modulus, psi E

R

= radius, in.

thickness, in.

t

=

The tests by Dow and Peterson (11) and those by Weingarten, et. al. (43) 4 show that the maximum buckling stresses obtained approach the classical buckling stress of:

I for v 0.3 (1) o)-

Eh=0.605Eh c

3 3 (1 9 )

f This corresponds to & = 0.605.

3 The buckling stresses of the samt cylinders without internal pressure (0 a

)^

0) varied widely from 6 0.14 to 0.29. There is also a great variation in the minimum and maximum values of 5 for the other sets of test data.

A study was also made to determine the increase in the buckling stress due to internal pressure for each set of tests. The results are presented in Figures 2a 2e in nondimensional form of Cp vs. p.

s

1. cr-(C,+C)Eh (2) p 2

a

c C = 3 C,

p where Co is the value of 6 for an un,nressurized cylinder (p = 0).

The tests performed by Weingarten, et. al. (43) on mylar cylinders shew 7

increases in the values of Cp with increases in the R/t ratio. No similar correlation was found for the aluminum and stainless steel cylinders. The shapes of the curves are seen to be quite similar for all materials and R/t ratios.

A lower bound curve of all test data has been developed and is recommended for a design equation for elastic buckling cylinders with R/t ratios of 800 to 2000.

The formula for this curve is given by Eq. 3.

1.06

~

(y )

C

=-

E 3.24 + 1/p DESIGN PROCEtXIRE The allowable buckling stress for a cylinder subjected to combined axial compression and internal pressure can be determined by the following equation.

r ni" (4) f

=

xc 7 s F,-(C,+C)Ek (5) x p

fxc design buckling stress, psi elastic design buckling stress, psi fxe

=

FS factor of safety

=

plasticity reduction factor n

C p given by Eq. 3

=

3

I' j

The following equations taken from API Bulletin tu (45) are recommended for determining the buckling stresses of unpressurized fabricated cylinders with or without ring stiffeners.

- h2 2

< 0.9 P/t < 610 (6) 3 0.125 R/t > 610 (7)

For ring stiffened cylinders subj' acted to internal pressure, use the greater of Coc or Co + Cp in Eq. 5.

The term c is defined below.

' 2.64 M s 1.5 3.13/M.42 3,$ < g 4 gg O

c=

, 1. 0 M > 15 where:

M = L/,k L=

length of cylinders between rings or total length of an unstiffened cylinder, in To determine tne buckling stress in the inelastic range, the effective stress, Fe, rather than the elastic buckling stress, Fxe, will be used to determine the plarticity reduction factor n.

F, = (F,pj,lp j p,)ln (7) 2 p

F, - p,R/t (8) 1 4

1 A < 0.55

.45/A + 0.18 0.55 < A < 1.6 (9) 11 * '

3,31 1.6 < a < 6.25 1 + 1.156 l

1/A A 2 6.25 L

w A=

y COMPARISON WIT 11 OTHER DESI,GN RECOP94ENDAT10NS Design rules are given in Space Vehicle Design Criteria, NASA SP 8007 (46) 6 and Shell Analysis Manual, NASA CR 912 (47). Both references present a graph for determination of Cp which was based upon Tig. 13 of Ref. 20. The following equation is a very close approximation to the curve given in these t'eferences.

1.25 (10)

C P

5 + 1/p The following is another approximation developed by CBI Oak Brook Engineering of the design curve given in the above references.

C = 0.01983 + 0.7886p 1.5272p2 + 1.520Ep3 (11) p

-0.73323[+0.1339Bp-5 These two equations are compared with Eq. 3 in Fig. 3. The equations fall slightly above E4 3 for values of p < 0.2 and below Eq. 3 for p > 0.2. The increased values of Cp dven by Eq. 3 are supported by all of the available test data which is significantly greater than the data base considered in Ref. 20, 5

Design rules are also given in Buckling of Steel Shells.

European given e a furciion of thi R/t titio as well as p.

Recommendations (48) with Cp These rules follow closely the curves derived / rom Ref. 43, and shown on Fig. 2e, for values of ) < 0.2 but are much flatter for larger values of p. These rules are compared with Eq. 3 in Fig. 4. 7.ie Cp values derived from these rules may be unconservative for values of p < 0.4.

APl>LICATION TO CONES S

The design procedure for cylinders can be applied to pressurised cones be substituting Re for R and Le for L in the design equi.tions.

I s

B

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(-'

WFxe APPL 1 CAT 10NTOSPH1RE The theoretical buckling stress of a cylinder under uniform external pressure is the same as a cylinder under Axial compression. API specifications (49,50) are based gon the arsumption that unstiffened spheres under nial compression only will fail at the same stress as an unstiffeaed cylinder under axial compression. It therefore appears reasonable to assume that the rules determined for cylinders subjected to in' ernal pressure can tie applied to spheres.

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REFERENCES References 1 to 44 are the output from a search of the CBI computerized bibliography on shell stability for references which contain appluable test data or discuss test dr,ta given in other references.

I i

R EFE1 CNCED u

SHELL TYPE ALL T' ired INCLUDED U11FFENING:

SiliTENEP AND/OR UNB11FF ENED L DAD TYFE t COMil'NED LOADD A X 1 (u COMPREUH10N INTERNAL P R E SUUR(:

DA1A TYPE:

CONSTRUC1]ON ALL TYPEU MATERIAL t

ALL MA1(*IALU p

DURND, A.D.

' DESIGN CRITERIA 0.0.bADED CYLINDii$CALAND (Ct'UER, E.U.bCECRAF1, 1.

ALMROTH, L

!W. I L ',, '

J.

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7, NO.

6, JUNE 1970, PP. 7 1.'- > h.

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3.

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PROC. AIAA/ASME/SAE 171H STRUCT., DYNAMICS, AND MATERIAL CONFERENCE, MAY 1976 0 1 1 1 00 0 1 1 1 3 1 0000 4

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1TY OF THIN 5.

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INDE COMPRE

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Ufn,.

1960.

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6, PERhAGON PRESS, 1976, l

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~

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GEIER.

B.

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' DESIGN C06E CONCERNING ISOTROPIC dYL1hDERS, REPORT, PP.

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AND SECHLER E.E.

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PRESSURE -JOURNAL OF AERONAUTICAL SCIENCE,~ VOL. ;24, NO. 5, MAY-1957,0 0-1 1 PP. 351-356.

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L O'1 1 - 1.1. 1 1 1 0031 1000 0

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!J R17. GERARD G.

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3783, AUG. 1957.

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0 1 0 L

4 9

l s

l

~

t t

i c

I

18. GDRMAN D.

' STABILITY OF CYLINDRICAL SHELLS SUDJECTED TO i

AXIAL LOADING ADN INTERNAL PRESSURE,1965.

REPORT SURI NO.

1100-33, SYRACUSE UNIV. RES. INST.,

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FED.

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ET. AL.

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J.

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21. HAYASHI I.

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22. HOLHES M.

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' DUCKLING OF THIN-AND SCHWARTZ E.P. ION AND INTERNAL PRESSURE

23. LO H.

CRA1E H.

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4

20. RAFEL N.

AND SANDLIN C.W.

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01 01 0001 0031 0000 2

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'A SURVEY OF DUCKLING THEORY AND EXPERIMENT FOR THICKNESS'169, REPORT NO.

TDR-469(3560-30)TN-1, CONTRACT NO.

AF04 (J95)

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31. SEIDE P.

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NASA TN D-1510, DEC. 1962, PP. 401-426.

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000

32. SEIDE P.

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NATIONAL CONGRESS OF APPL. MECH.,

PP. 761-773.

0101 00 1 1 0031 0000 0

000 33.-SINGER,UNDdR EXTERNAL PRESSURE, TOREION,AND AXIAL COMPRESSION,'

J.

ECKSTEIN A.

AND BARUCH M.

'3UCKLING OF CONICAL SHELLS TECHN ICON-ISRAEL INSTITUTE OF TCCHNOLOGY, TAE REPORT 19, SEPT. 1962.

01 11 011 1 00300100 2

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34. SINGER J.

ET AL

' BUCKLING OF ISOTROPIC ORTH 0 TROPIC AND RING-SfIFFENED CObICAL SHELLS

• TAE REPORI NO. 30, TECHNION ISRAEL INST. OF TECH., SEPT. $963.

01 1 101 1 1 1 0300 100 124 125 0 0

35. SINGER J.

ET AL

' EXPERIMENTAL AND THEORETICAL STUDIES ON DUCKLIbG Of CONIChL AND CYLINDRICAL SHELLS UNDER COMHINED LOADING,' TAE REPORT 48, TECHNION-ISRAEL INGT. OF TECH.,

JUNE 1966.

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36. STOCKER J.

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AND GRAFTON P.

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LITERATURE bN THE EUCKLING CHARACTERISYICS OF CONICAL SHELLS',

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LOADED bETAL SHELLS,OF REVOLUTION IN THE ELASTIC-PLASTIC FOR THE VERIFICATION OF NONLINEAR COMPUTER PROGRAMS,' UNIV. OF ESSEN REP 0R' 30,1 SEPTEMBER 1986. (GERMAN) l 0

1 1 00 1 1 003 1 1 1 1 1 4

3 00 10

s.

r-i i

30. TENNYSON

'THE EFFECT OF SHAPE IMPERFECTIONS AND R.C.YHE DUCKLINO OF CIRCULARCYLINDERS STIFFENING ON 251-27$. DUCKLING OF STRUCTURES, SPRINGER-VERLAG, 1976, PP.

I 01 1 1 001 1 1 1 31 0000 5

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39. THIELEMANN W.

F.

'NEW DEVELOPMENTS IN THE N0ff-LINEAR THEORIES Ok THE DOCKLING OF 1HIN CYLINDRICAL SHELLS AERONAUTICS AND ASTRONAUTICS PROC., DURANT CENTENNIAL CONF.

PP.76-119.

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25 0 0

40. VERONDA D.R.

AND WEINGARTEN V.I.bSCE JOURNAL

'STADILITY OF PRESSURIZED HYPERBOLDIDAL SHEl.LS OF THE ENGINEERING MECHANICS DIVISION, 50. EMS, OCT. 1975, PP. 663-670.

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41. WE3NER P.D.

AND SMITH S.A.JR.I ' MAXIMUM MOMENT CAPADIL3TY OF PIPE WITH,VARIOUS D/l RATIOS TRANS. OF ASME, J.

OF ENGR.

FOR INDUSTRY, AUG. 1976, PP. 1167-1111.

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E.J.

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MORGAN, E.J.,

AND SEIDE, P.,

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, STABILITY OF THIN SHELL STRUCTURES REPORT NO. STL/1R

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NO.

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~

6 9

y

- w e

1 4

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45.

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46.

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14-23.

12

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+ 7. Pace 2-4. Section 2 3 This section states that Reference 2-6 was used to calculat.o the plasticLty reduction factor for tra meridional direction elastic buckling stross. Since this approach apparently has not boon incorporated into code caso N-284, the sensitivity of the resulte should be etudied by using other methods which address this effect. Rgsponset Using the approach outlin d in Codo Case N-284, (Ref. 2-1 of the CE Report) the calculated value of the plasticity reduction factor lu 1.0, i.e., no reduction need be made in the calculatad value of elautic buckling stress. The approach outl.ined in Refer 0nce 2-6 takos a more conservative approach resulting 124 lower piasticity reduction factors. This more caneervative approach in the one used in the analysis (Ro!, 2-6). RZ:032120 8

= i I 8. Paco 3-3 J ee_ond varacraoh For the etability analyslo the stiffnese fer the sandbod was assumed to be 366 pel/ inch and no sensitivity studies are reported. As described in Question 5, the results of the stability analysis with the sand removed should be provided.

Response

CE Report index 9-4 e.utitled "Im ASME Section VIII Evaluation of Oyster Creek Drywell for Uithout Sahd Case Part 2 s cability Analyele" submitted March 4, 1991 defronetrates code complianco vitnout sand. Therefore, sensitivity of buckling capacity to variations of ttv) sa.nd spring etif f ness is not a concerr. \\ / 5 h RZ:C3212073 o

K 9. P_fLie 3-6. Section 3. 5 6 2 h The first sento we sta.tes that "the ,>si external pressure load for the refueling case t, applied tr. t he ext.. nal faces of all of the drywell ind vent shell ele. ens. Uni.cou it can be demonstrated that this 9ssure actually is preocat at.all times during normal operation and re mling, the eff'act on the buakling analysis results of assuming no t x s,

• nal pressure fo'l L;hese two load cases should be reported.

A rt)trmore, is it possible to have an external pressure greater than 2 p s 3. et; t.hs drywell shell? I t so, an enveloping pressure case should be e.cact kerud in the analysis. b Resnonue: The ; pei external pressure results in a compressive stress in the shell in the sondbed region of Pl</2T = (2

• 420)/(2* 0.736) = 570 poi e'en 4 i

small compared to the ts;al applied f rom other sourc2 s. The 2 ;si to ] t.ho plant clesign basis and it is the onveloping pressure. Rocardtr<ms e 7 the cause nf dif ferential pressure between the reacto'c building and the ') dryvell, the maximum differential preenure is.1.0 paid. There ti.t s %c k 20-in::t, vacuum breakere between the reactor building and the tares. E These are set to to open at 0.5 paid. FLrther, t'wr0 're 34 13-inch vacuum breakers betweta the torus and the drywell. No are also se'; a to open at 0.5 paid. The maxira idf feregrial pressuta ?.. arrived at by aa(t.r,; these two setpoints. = s Em 1-

haB,

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O i d i Part til Genaral ] l } l I RZ:C3212073 ~ - - ~.

10. Justification for the use of ASME Section III, Subsection NE has been provided to evaluate the Oyster Creek Steel drywell; taking into consideration design, materiale, fabrication, inspection and testing with exception of the commente indicated above, the justification appears to be reasonable.

Since the present-day quality assurance and quality control requirements for the design and construction of nuclear power were in the formative stage at the time when the Oyster Creek Plant was designed and constructed, indicate what quality assurance and quality control programs were implemented for the Oyster Creek drywell. Indicate if documentation of the program is available. PM D2J1f28 The quality assurance and quality control programs implemented for the Oyster Creak drywell ate available and documented in the original (docketed) Oyrter Casek FDSA" %mendments 15, 27, and 39. Amendment 15, Section IV, provides the containment ehell fabrication, erection and testing history. Section VI provideo detaile on the fabrication and installation of the containment penetrations and nozzles. Amendment 27 provides the plant Quality Assurance Report with Amendment 39 providing expanded information on organizational structures and remporaibility for quality ef forte by organizational componente and subcentractors. Amendment 39 describes Burne & Roe's subcontractor resoonsibilities a part of which resulted in the issuance of D&R Specification S-2299-4 to Chicago Dridge & Iron fer the containment construction. Section II of ' nis specification (copy attached) provides additional specific containment quality requiremente consistent with the above mentioned FDSAR Amentimente. 4 It2tC3212073

s SUPPLEMEtiTIOJESPONSE_11QJ.Q Oyster Creek Durns and Roe Specification S-2299-4, Section II ( Addendurn No. 5), dated June 10, 1964. iC b $.f ,h RZ:C32020S$ . - _ _ - _ _ _ _ _ _ _ - _ _ _ _ - _ _ - _ _ _ - _ _ _ _ _ _ _. _.}}