ML20049H273

App 3F to Gessar, Dynamic Buckling Criteria for Containment Vessel.

ML20049H273
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Issue date:	02/12/1982
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... .~- _ - . - - - - . . _ . . - - - . ~ . . - - -

GESSAR II 22A7007 l 238 NUCLEAR ISLAND Rev. 0 i

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l APPENDIX 3F l

i DYNAMIC BUCKLING CRITERIA FOR I CONTAINMENT VESSEL i

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GPSSAR TT 22A7007 238 NUCLEAR ISLAND Rev. 0

s APPENDIX 3F CONTENTS Section Title Page 3F APPENDIX 3F - DYNAMIC BUCKLING CRITERIA FOR CONTAINMENT VESSEL 3F.1 INTRODUCTION 3F.1-1 3F.2 SHELLS STIFFENED WITH CIRCUMFERENTIAL STIFFENERS 3F.2-1 3F.2.1 Circular Cylindrical Shells Under Axial Compression 3F.2-1 3F.2.2 Circular cylindrical Shell in 3F*2-1 Circumferential Compression 3F.2.3 Circular Cylindrical Shells Under Torsion 3F.2-2 3F.2.4 Circular Cylindrical Shells Under Bending 3F.2-3 3F.2.5 Allowable Stresses for Circular Cylindrical Shell Under. Single Load 3F.2-4 I \ 3F.2.6 Circular Cylindrical Shell Under

Combined Loads 3F.2-4 3F.3 CYLINDRICAL SHELLS STIFFENED WITH A COMBINATION OF CIRCUMFERENTIAL AND VERTICAL STIFFENERS 3F.3-1 3F.4 DOUBLY CURVED SHELLS 3F.4-1 3F.4.1 Knuckle Region 3F.4-1 3F.4.2 Region Above the Knuckle 3F.4.2 3F.4.3 Alternate Method of Deriving Allow-able Stresses for Double Curved Shells 3F.4-3 3F.4.3.1 Biaxial Compressive and Tensile Stress Resultants 3F.4-3 3F.4.3.2 Biaxial Equal Compressive Stress Resultant 3F.4-4 3F.4.3.3 Biaxial Unequal Compressive Stress Resultant 3F.4-4 3F.5 REFERENCES 3F.5-1 O

3F-i/3F-ii

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0

() APPENDIX 3F ILLUSTRATIONS Figure Title Page 3F-1 Systems Approach to Containment Design 3F.6-1 3F-2 Increase in Axial-Compressive Buckling-

. Stress Coefficient for Cylinders Due to Internal Pressure 3F.6-2 3F-3 Buckling Coefficients for Circular Cylinders

Subjected to External Pressure 3F.6-3 3F-4 Buckling-Stress Coefficient, Cg, for Unstiffened Unpressurized Circular cylinders Subjected to Torsion 3F.6-4 3F-5 Increase in Torsional Buckling-Stress Coefficient of Cylinders Due to Internal Pressure 3F.6-5 3F-6 Buckling-Stress Coefficient, K' for Unpressurized Curved Panels Subj,ected to Shear 3F.6-6 i

/\ 3F-7 Buckling-Stress Coefficient, C3, for

\s Unstiffened Unpressurized Circular Cylinders Subjected to Bending 3F.6-7 3F-8 Increase in Eending Buckling-Stress Coefficient of Cylinders Due to Internal Pressure 3F.6-8 3F-9 Buckling-Stress Coefficient, Kc, for

Unpressurized Curved Panels Subjected to i Axial Compression 3F.6-9 3F-10 Buckling-Stress Coefficient, Ks, for Unpressurized Curved Panels Subjected to Shear 3F.6-10

, O 3F-iii/3F-iv

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0

(S/ APPENDIX 3F l

N/ DYNAMIC BUCKLING CRITERIA FOR CONTAINMENT VESSEL 3F.1 INTRODUCTION The buckling design criteria in this appendix are applicable to stiffened circular cylindrical and ellipsoidal shells. These criteria are provided for use where seismic and non-seismic dynamic loads act on the vessel and in conjunction therewith for geometries which the ASME Code provides no specific buckling criteria. It is recognized that the design of the vessel is carried out according to what is essentially a multi-level approach in which the design philosophy and criteria become progressively more accurate and less conservative than the previous one employed and this is explained by the flowchart in Figure 3F-1. Section 3F.2 sets forth the buckling design criteria for shells stiffened with circumferential stiffeners. Section 3F.3 provides the criteria for shells stiff-O)

\, ened with a combination of circumferential and vertical stiff-eners. Section 3F.4 deals with the criteria for the ellipsoidal dome. The procedures and data presented were adapted primarily from Chapter 3 of Reference 1 with the exception of buckling under axial forces, which was adapted from Reference 2 and is based on work reported in References 3 and 4. The criteria given in this appendix cover only the range of variables needed for the struc-tural steel containment vessel. Other references are also indi-cated in the text.

The buckling criteria are specified in terms of unit stresses and membrane forces in the shell and the stresses caused by multiple loads must be combined according to Section 3F.2.6. The plastic-ity correction factor has been omitted from all expressions because this factor is unity for buckling in the elasting range.

e A

kj'i 3F.1-1

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0 3F.1 INTRODUCTION (Continued)

The value of 2.0 for the factor of safety used in this appendix conforms to NRC Regulatory Guide 1.57. The method of applying the factor of safety to the criteria is covered in this appendix.

The material contained in this appendix with the exception of Sections 3F.4.1 and 3F.4.3 has been taken from Reference 2 with necessary editorial changes. This reference is a current state-of-the-art report on stability analysis directly applicable to the decign of the containment vessel and may be used to supplement the ASME Code.

The notations used in this appendix are as follows.

a, b = dimensions of curved panels C b, C = p ram ters explained in the text c' s E = Young's modulus of elasticity F, F = factor of safety K c, K p, K s, K's = parameters explained in the text L = length of cylinder, or meridional length of cylinder between circumferential stiffeners N, N = membrane stress resultants in shell P = internal pressure P = classical critical external pressure for y

spherical shells P = xternal critical pressure for spherical cap r

3F.1-2 l

.- .. . - ~ - .. . .. . . . - - - - - - - - - . . . . - . . _- .. . - . - .

GESSAR II 22A7007

, 238 NUCLEAR ISLAND Rev. 0 3F.1 INTRODUCTION (Continued)

R = radius of cylindrical or spherical shell j S = allowable compressive stress s = calculated stress N/T t = net shell thickness, after excluding corrosion allowance A = boundary function explained in Subsec-J tion 3F.4.2 p = Poisson's ratio

& = half the included angle of spherical cap O

l l

O i

i 3F.1-3/3F.1-4

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0

/] 3F.2 SIIELLS STIFFENED WITil CIRCUMFERENTIAL STIFFENERS U

3F.2.1 Circular Cylindrical Shells Under Axial Compression The critical buckling stress for a cylinder under axial compression alone is determined by the equation

=C E (F-1) cr 100

<f<4000 (F-2) where C

c

= 0.606 - 0.546 [1-exp

(- h /R/t)] for0.2<h<5 (F-3)

--O 6

] C = 0.5

-h forh<_0.2 (F-4)

[Q c -

The simply supported boundary condition will give a lower bound for the critical stress.

An increase in critical stress on account of internal pressure is permitted for R/t > 700 according to the following formula o = (C c

+ AC ) (F-5) where AC is obtained from Figure 3F-2. For R/t < 700, ACc ""Y be assumed zero.

3F.2.2 Circular Cylindrical Shell in Circumferential Compression A circular cylindrical shell under a critical external radial or hydrostatic pressure will buckle in circumferential compression.

O The critical circumferential compressive stress is given by 3F.2-1

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0 3F.2.2 Circular Cylindrical Shell in Circumferential Compression (Continued) 2 2 K n E 9 A o

er

=

2 _L_

(F-6) 12 (1 - v )

for various ranges of cylinder length defined by Z= (L2 /Rt) /1 - p2 (F-7)

Curves for determining the constant K for both radial and P

hydrostatic pressure are given in Figure 3F-3.

3F.2.3 Circular Cylindrical Shells Under Torsion The shear buckling stress of the cylinder subject to torsional loads is given by c

cr

=C s  !. (F-8)

RZ The shear buckling stress of the cylinder subject to torsion and internal pressure is determined by C Et Et s

c er

= + AC -.

s R (F-9) pg l/4 where constants C s and AC s r determined from Figures 3F-4 and 3F-5. Values of AC s r given f r internal radial pressure alone and internal pressure plus an extccrai load equal to the longi-tudinal force produced by the internal pressure.

O 3F.2-2

GESSAR II - 22A7007 238 NUCLEAR ISLAND Rev. O J

, ( 3F.2.3 Circular Cylindrical Shells Under Torsion (Continued) 4 Figure 3F-4 is applicable for values of Z = hh /1 - p 2 > 100 (F-10)

For cylinders with length constant Z < 100, the shear buckling 4 stress is determined by 1

ge 3 2 E -2 s 1 a<b (F-ll) a = ,

cr 12 (1 - p2) _a_

for values of 1 2 (F-12)

Z = fp /1 - p 2 l

O where a is the effective length and b is the circumference of the 1 cylinder. The coefficient K' is given in Figure 3F-6.

3F.2.4 Circular Cylindrical Shells Under Bending i

The critical buckling stress for the cylinder under bending is

computed by the equation i

i Et (F-13) o =C l

cr b R i

where the buckling constant, Cb, s given by Figure 3F-7.

f

]

l The critical buckling stress for the cylinder under internal pressure and bending is computed by

\

c =

(Cb + ACb 3F.2-3

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0 where C b nd AC b r giv n by Figures 3F-7 and 3F-8 respectively.

Figure 3F-8 is a function of the internal pressure and the geometry.

3F.2.5 Allowable Stresses for Circular Cylindrical Shell Under Single Load For shell stability, the allowable compressive or shear stresses for a single load shall be cr S= , (F-15)

If F (factor of safety) = 2, S= (F-16) where o are specified in Subsedtions 3F.2.1 through 3F.2.4.

3F.2.6 Circular Cylindrical Shell Under Combined Loads ,

The criterion for buckling failure of the cylindrical shell under combined loading is expressed by an interaction equation of stress-ratio of the form 4

x r "< 1 (F-17)

" ~

n=1 where N ("I F

(") F N ("}

F N ("}

F 1

1+N 2 2 m m k k r = , ,,, ,,, (F-18) n g (n) g (n) g (n) g (n) t er er er er O

3F.2-4

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. O O 3F.2.6 Circular-Cylindrical Shell Under Combined Loads (Continued) x .= an index for the stress ratio.

F = factor of safety for each individual component of m _

membrane stress N compressive or shear membrane force m

and i F,= 2.is the factor of safety.

Superscripts n = 1, 2, 3, and 4 represent respectively axial compression, circumferential compression, torsion, and bending loads.

O The following interaction equations shall be used in the design of the cylindrical shell.

(1) Axial Compression and Circumferential Compression m=k N (' F m=k N ( F gy)

• + "

(2) 1

~

t m=1 cr m=1 cr l (2) Axial Compression and Bending i

( } (

m=k N F m=k N F

+ 11 ~

(1) t U (4) t I m=1 cr m=J cr l

i i

l' lO

. 3F.2-5

. , _ _ , . - . - _ _ _ , _ . ~ _ . - , , _ . . - . - _ _ - - . . _ . . . . _ _ _ _ _ -

GESSAR II 22A7007 238 NUCLEAR ISLAE4D Rev. 0 3F.2.6 Circular Cylindrical Shell Under Combined Loads (continued)

(3) Axial Compression and Torsion m=k N (l)

F ~m=k N (} F~

\^

4 (1)

"+ \'

d (3)

-< 1 (F-21) g t a m=1 cr ,m=1 cr _

(4) Axial Compression, Bending, and Torsion m=k N (n) p -

m=k N ( }

F~

g (n)

+

(3) 1I n=1,4 m=1 cr _m=1 cr .

(5) Axial Compression, Circumferential Compression Bending, and Torsion m=,k N (n) F ~m=k N (} F~

\s_, \ m m, g- m m

< 1 (F-23) 4, 4 (n) t 4 (3) t n=1,2,4 m=1 cr -1 cr The longitudinal membrane stresses produced by the non-axisymmetric pressure loads shall be considered as caused by bending loads in the interaction equations. The summation (m=1,k) is over the terms in the specified loading combination.

1 I

I I

3F.2-6

GESSAR II 22A7007-238 NUCLEAR ISLAND Rev. 0 O 3F.3 CYLINDRICAL SIIELLS STIFFENED WITH A COMBINATION OF CIRCUMFERENTIAL AND VERTICAL STIFFENERS Based on preliminary design, the Mark III containment has circumferential stiffeners only. Vertical stiffeners may be utilized after final analyses, if necessary, to limit the shell axial membrane compressive stress to the applicable allowable stresses. If the shell is to be provided with permanent cir-cumferential and vertical stiffeners, the circumferential stiffeners shall be designed to have a spring stiffness at least great enough to-enforce nodes in the vertical stiffeners so as to preclude a general instability mode of buckling failure thus ensuring that if buckling occurs,'it will occur in stiffened panels between the circumferential stiffeners. An acceptable procedure for determining the critical buckling stresses in the vertical stiffeners and stiffened panels is outlined in Section 3.4, Reference 1.

In addition, for shells stiffened with a combination of circumferential and vertical stif feners under combined load, the criterion for buckling' failure of the shell plate is expressed by an interaction equation of stress ratios in the form 4 ,

r U

-<1 (F-24) n=1 similar to the interaction equations of Subsection 3F.2.6.

The critical buckling stresses for the shell plates between the circumferential and vertical stiffeners shall be determined by the following equations.

O 3F. 3- 1

GESSAR II 22A7007 238 NUCLEAR ISLAND Revo 0 3F.3 CYLINDRICAL SHELLS STIFFENED WITH A COMBINATION OF CIRCUMFERENTIAL AND VERTICAL STIFFENERS (Continued) l (1) Curved Panel Under Axial Compression The critical buckling stress for a curved cylindrical panel under axial compression alone is determined by the equation

-2 n E t (F-25) a =K er c 12 (1 - p 2) _b_

for various ranges of cylinder length given by Z= [1 - p 2 (F-26)

The constant K is determined from Figure 3F-9.

c (2) Curved Panel in Circumferential Compression O

The critical buckling stress of a curved cylindrical panel under circumferential compression shall be determined by Subsection 3F.2.2 equations.

l (3) Curved Panel Under Torsion The shear buckling stress of a curved cylindrical panel l

l subjected to torsional loads is given by 1

i

~~2 2

o = g 7 E t

, a>b (F-27) cr s 12 (1 - p 2) _g_

l 9

3F.3-2 l

t

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0 ,

! 3F.3 CYLINDRICAL SHELLS STIFFENED WITH A COMBINATION OF

CIRCUMFERENTIAL AND VERTICAL STIFFENERS (Continued) for values of Z= /1 - p 2 (F-28)

The coefficient K s is given in Figure-3F-10. For cylindrical panels with length a less than the arc length b the shear buckling stress is determined by K' n 2 E -2 i s 1 o# = ,

-b (F-29) 12 (1 - p2) _a_

for values of 2

Z = "Rt- /1 - p2 (F-30)

U Curves for determining K' are given in Figure 3F-6.

(4) Curved Panels Under Bending I

I The critical buckling stress for a curved panel in bending shall be computed using the equation for axial I

compression given in (1).

I 3F.3-3/3F.3-4

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. O O 3F.4 DOUBLY CURVED SilELLS V

The dome of the Mark III steel containment is a 2:1 ellipsoidal shell. The juncture region of the shell where the cylindrical part of the vessel meets with the het.d is called the knuckle region.

The following paragraphs present design criteria for both the knuckle region and rest of the vessel head.

3F.4.1 Knuckle Region In order to analyze the knuckle region of pressure vessel heads, it was shown in Reference 5 that it is reasonable to assume that the allowable compressive stress level might in many cases approximate the level of compressive stresses permitted in axially loaded cylinders, m -

fl 1

/ j

/ bV $[

, /

q / l b

+.

Y (a)

! tff s

% H1 m &

/ \e.% +

D +

H2

,rl } /

,. i. .

(b) 3F.4-1

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0 3F.4.1 Knuckle Region (Continued)

Sketches a and b show the analogy between compressive stresses in the knuckle region of pressure vessel heads and compressive stresses in axially loaded cylinders.

Sketch a illustrates the case where the compressive stresses are latitudinal in direction and result from an internal pressure. The latitudinal compressive stress in the knuckle area is equivalent to the axial compressive stress in a cylindrical shell with radius R y. Sketch b illustrates the converse of this case, where the external pressure sets up meridional compressive stresses which, in the knuckle region, is equivalent to the axial compressive stress in a cylinder with radius R 2 The t/R ratios for the Mark III steel containment dome are all less than 0.0067 (i.e.,

elastic buckling behavior would be assumed rather than a plastic yielding type of failure when it is subjected to compressive loads).

3P.4.2 Region Above the Knuckle The following theoretically derived expressions for spherical caps subject to uniform external pressure may be used for calculating the allowable compressive stress in the portion of the head above the knuckle. The critical buckling pressure for the cap (P ) is expressed as the product of the classical buckling pressure for a complete spherical shell and a boundary function f(A).

P er

=P f (A) (F-31) el where 2

2 t p_

P = E (g) cl

[3 (1 -p 2))l/2 O

3F.4-2

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0

[xv') 3F.4.2 Region Above the Knuckle (Continued)

A= [12 (1 - p2))l/4 ( ) 2 sinh (F-33)

& = half the included angle of the cap F (A) = function of boundary conditions.

The cap may be assumed clamped at its edges. The lower bound for f(A) is then given by f(A) [0.14 +

= ], A > 2. (F-34)

A 3F.4.3 Alternate Method of Deriving Allowable Stresses for Double Curved Shells

(/

(, The orthogonal stress components of a biaxial stress state are obtained on the basis of cylindrical buckling formula and then combined (Subsection 3F.4.3.1) to yield an allowable buckling stress for a shell with double curvature. There are three com-pressive and tensile stress resultsnta.

3F.4.3.1 Biaxial Compressive and Tensile Stress Resultants The allowable stress is the same as for a uniaxial compressive stress state and is given by S = 0.0625 Et/R, for > 160. (F-35)

If compressive stress is latitudinal, use R = Ry; if meridional, use R = R 2'

f-s For R/t < 160, use subparagraph NE-3133.6 of Section III of the kj ASME Code.

3F.4-3

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0 3F.4.3.2 Biaxial Equal Compressive Stress Resultant The biaxial compression in this case is the same as the compression in a sphere per ASME Code. The allowable for this stress state shall be taken as one-half of the uniaxial compression allowable calculated under Subsection 3F.4.3.1.

3F.4.3.3 Biaxial Unequal Compressive Stress Resultant In the case of biaxial compression in which the latitudinal and meridional unit forces are of unequal magnitude, the forces acting on an element of the head may be shown diagrammatically in the following manner.

SMALLER FORCE SMALLER GREATER MINUS

,, q

, SMALLER FORCE GREATER  %

GREATER .. ..

FORCE FORCE

< L d k SMALLER SMALLER GREATER MINUS FORCE SMALLER FORCE It will be noted that the smaller force in this case is assumed to be correlated to that portion of the greater force which is equal in magnitude to the smaller force but acts perpendicular to the latter as in a sphere. It seems reasonable to assume further that the difference between the two unit forces could be treated as analogous to a uniaxial longitudinal force on a cylindrical shell. IIence , it is recommended that, where unequal biaxial compressive forces exist, both of the following two expressions should be satisfied.

O 3F.4-4

GESSAR II 22A7007 238 NUCLEAR-ISLAND Rev. O d

, 3F.4. 3.3 Biaxial Unequal Compressive Stress Resultant (Continued) i Smaller Stress Difference in stresses I

Max allowable stress per ASME Max allowable stress 1 .0

. Code for sphere based on R for cylinder based on R associated with the greater associated with the-l stress greater stress e

and i

) Smaller stress Max allowable stress for sphere < l.0 i based on R associated with the smaller stress i In these expressions, the phrase, based on R associated with the greater (or smaller) stress," means that if the greater (or smaller) stress is circumferential, R shall be taken as equal to j R y and if the greater (or smaller) staress is meridional, R shall be taken as equal to R t

{~'}

s/

2' i

-The first expression may be rewritten as follows:

1 S S -S s, cg cs

~< l.0 (F-36) a O

.I b a I

l Prom paragraph 3F.4.3.2, the allowable compressive stress under i equal biaxial stress state is one-half the uniaxial allowable, f Substituting Sg = 0.5 S we btain a

L

! S +S eg cs (F-37)

, S ~< l.0. ,

a where S a is the allowable stress for a cylinder having a radius of curvature R g associated with direction of the greater stress.

f 3F.4-5

. , , , _ _ . . _ - . - - . _ - _ _ . . _ _ , _ , , , . , . , - , , , , , , . , . , _ _ _ . , , _ , , _ , _ _ . . ,._,_,,._._7__._,.,__,,,,y.,,____., _

, .._.. ,,__,,-,,,,.m_,.,._._,_.,_m_ __

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0 3F.4.3.3 Riaxial Unequal Compressive Stress Resultant (Continued)

The second expression can be written as S

cs < l.0. (F-38)

S -

b In this expression S i the allowable stress for a sphere based b

on R g associated with the smaller stress. In the above the subscript i= 1 or 2.

O O

3F.4-6

GESSAR II 22A7007 238 NUCLEAR ISLAND R v. 0

() 3F.5 REFERENCES

1. Baker, E. II . , Capelli, A. P., Kovalevsky, L., Rish, F. L.,

and Verette, R. M., "Shell Analysis Manual," NASA Contractor Report CR-912, Washington, DC, April 1968.

2. Citerly, R. L., " Stability Criteria for Primary Metal Containment Vessels under Static and Dynamic Loads,"

Report Number NEDE-21564, prepared by Anamet Laboratories for the General Electric Company, January 1977.

3. Weingarten, V. I., Morgan, E. J., and Seide, Paul, " Elastic Stability of Thin-Walled Cylindrical and Conical Shells under Axial Compression," AIAA Journal, Vol 3, Number 3, March 1965.

4. Miller, C. B., " Buckling Stresses for Axially Stressed Cylinders," Journal of ASCE Structural Division, Vol 103, No. ST3, March 1977.

5. Dvorak, J. J., dnd McGrath, R. V., "Diaxial Stress Criteria for Large Low Pressure Tanks," Welding Research Council Bulletin No. 69, June 1961.

O

(_,/ -

J 5

v 3F.5-1/37,5_3

O a w)

REDESIGN I NO INITIAL DESIGN j g AND EXAMINATION OF PRACTICALITY

• YES NEED FOR MEET YES - STOP RE-ANALYSIS CRITERIA -

I

? jg PERFORM STATIC AND A NO DYN AMIC ANALYSIS TO SPECIF IC ATION NO REQUIREMENTS PERFORM NON-LINEAR YES NON LINEAR DYNAMIC ANALYSIS FOR VERIFICATION ,

CRITICAL LOADING AN A LYSIS SATISFY O I M NO ASME PRIMARY '

W STRESS INTE NSITY REDESIGN YES j g FOR ECONOMY  :

7 DESIR AB LE gg on w YES I MM M Cn NO NO YES SATISFY h GROSS CHECK.. YES ws STABILITY YES NON-LINEAR YES ANALYSIS

?

VERIFICATION REQUIRE RE-DESIGN MATERI AL USED h ANALYSIS E F FICIENTLY DESIRED I NO y IS GROSS 1 r NO INSTABILITY R GION S STOP 'F ABRICABILITY. CONSTRUCT 4-7 BILITY. ECONOMY

• • ASME CRITERIA AND CRITERIA

'm IN APPENDIX INCLUDING YES 4 OVER ALL STAPILITY i

ALLOWAB LES *"THIS STEP CAN BE SKIPPED BY C EXCEEDED GOING DIRECTLY TO IDENTIFY CRITICAL -

• ** PERFORM SEMI-EMPIRICAL  ? FOR NON-LINEAR VERI ICA- N LOADING AND REGION PANEL STABILITY ANALYSIS TlON ANALYSIS TN o>

<4

= 0 o

Figure 3F-l. Systems Approach to Containment Design o4

l 1.0 I

l N

w CD l

' z

.1 Ce CO w o~ g -

OM '

M U3

.": _ M t/3 l m >> .

M i

WW '

sH U3 H g

z

.i e

R h > nn 0.01 0 01 0.1 1.0 to P/E (R/t)

N xw o>

<4 Figure 3F-2. Increase in Axial-Corpressive Buckling-Stress $

Coefficient for Cylinders Due to Internal Pressure C" O O O

O O O P

nmm P R ,

dl A P

e L --*-

o,c

= K 2 -

12(1-u 2) (t/L) 8 - Z = L /R2 t (1 - u2) 6 -

M P er

• R C3 4 -

g I

y CO O tn KP

? 2 -

h o pp i

1 LJ NN gg 10 -

8 -

LATERAL PRESSURE g ON LY P = 0 6 - 0 4 ~~

LATERAL AND AXI AL PRESSURE P = pwR2 2 -

i I I Il! l l l l l l l l l l l l 2 4 6 8 2 4 6 8 2 4 6 8 g 2 4 6 8 j w

Z mw o>

< -a

. o Figure 3F-3. Buckling Coefficients for Circular Cylinders o e

Subjected to External Pressure

0 62 I

N L 0.60 -

t R

0.58 -

t 1 ocr - CE 3 gj4 0.56 -

t2 2 = - J1-p2 Rt VALIDFOR y Z > 100 FOR SIMPLY SUPPORTED EDGES w 0.54 - Z > 100 FOR CLAMPED EDGES W z

Cs CO w n en m e tn 0.52 -

]y

, ww

.c.

HH tO H 0.50 -

h Z

C 0.48 -

0.46 -

O.44 0 1000 2000 3000 4000 g R/t %N o>

<: -a

.o C

Figure 3F-4. Buckling-Stress Coefficient, C3, for Unstiffened Unpressurized ay Circular Cylinders Subjected to Torsion O O O

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. O O

10 8 -

6 -

P 3 p NO EXTERNAL P AXtAL LOAD 4 - T d] c- l[]l J l

d- P=0 2 -

• l

• 1.0 -

8 -

6 -

EXTERNAL AXtAL LOAD 4 -

DALANCES LONGITUDINAL PRESSUHE LOAD P

• p w H2

.1 Cs 2 -

01 -

O -

6 4 -

2 0 01 2 4 6 8 2 4 6 8 2 4 6 8 g 2 4 6 8 2 P/E (H/t) i l

l Figure 3F-5. Increase in Torsional Buckling-Stress Coefficient of Cylinders Due to Internal Pressure i

l 3F.6-5 l

l

GESSAR II 22A7007 238 flUCLEAR ISLAND Rev. O O

8 -

n2E b

7 \, ace

=

K, 1211 - u2]

I'I*I 4 - l i NN Z 2

= ~ 41 - y2 a 20 FOR SIMPLY SUPPORTED EDGES Z > 80 FOR CLAMPED EDGES M 0.25 -

co Cd g CO

• O in

. 0.20 -

{ CD NN d ss 0.15 - CD s b

z O

0.10 -

0.05 -

0  !

0 1000 2000 3000 4000 R)t M MN o>

<w Figure 3F-7. Buckling-Stress Coefficient, Cb, f r Unstiffened Unpressurized

• Circular Cylinders Subjected to Bending o4

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. O O

10 8 -

M M 6 -

4 - P w NO EXTERNAL

, AXI AL LOAD P=0

~

eL ->

1.0 -

8 -

6 -

4 -

EXTERNAL AXIAL LOAD ACb BALANCES LONGITUDINAL PRESSURE LOAD P = p w R2 0.1 -

8 -

6 -

4 -

2 -

0.01  !  !  !  ! !  !  !  ! I O 01 2 4 6 8 10 0.10 1.0 102 P/F (R/t)2 l Pigure 3P-8. Increase in Bending Buckling-Stress Coefficient l of Cylinders Due to Internal Pressure 1

0 3P.6-3 i

GESSAR II A 007 238 NUCLEAR ISLAND Rev. O O

l 104 a 0.5 6 b 4 -

h 2 -

R R/t t

103 -

M 8 - ,2g

" Kc t/b] g 300 6 - 8cr 12[1-p2]

500 2 = [-p2 3W Kg 2 .

102 8 -

O 6 -

4 -

2 -

SIMPLY SUPPORTED EDGES to - = = = CLAMPED EDGES 8 -

6 -

4 r

2 -

I l

1.0 i i , i l i i e i l , , , , l , , , , 1 , , , ,

1.0 2 4 6 8 10 2 4 6 8102 2 4 6 8103 2 4 6 8104 2 4 6 8 105 Z

l l

Figure 3F-9. Buckling-Stress Coefficient, K c, for Unpressurized Curved Panels Subjected to Axial Compression.

O 3F.6-9

GESSAR II 22A7007 238 NUCLEAR ISLAND Rev. 0 0

104 8 -

6 -

4 -

h

(

\

2 -

H 8 - aeb 6 bib

,27

" 12 [1 - p2] 10 4 -

1.5 2.0 KS 2

• d1-92 2 - 3.0 102 _

8 -

6 -

4 -

2 -

10 8

0 ==r - SIMPLY SUPPORTED EDGES 4 -

2 l  ! . . I , ,

i i . .l . , i i , i i i 2 4 6 8 2 4 6 8 2 4 6 8 2 4 G 8 2 103 104 Figure 30-10. Buckling Stress Coefficient, K s, for Unpressurized Curved Panels Subjected to Shear l

l 3P.6-10 l

l --