api 2u.pdf

STD.API/PETRO BULL ZU-ENGL 2000 m 0732270 Ob23128 T50 m

Bulletin on Stability Design of Cylindrical Shells

API BULLETIN 2U (BULL 2U) SECOND EDITION, OCTOBER 2000

American Petroleum

1 Institute

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COPYRIGHT 2003; American Petroleum Institute

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API BULLETIN 2U (BULL ZU) SECOND EDITION, OCTOBER 2000

American Petroleum Institute



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STD-APIIPETRO BULL ZU-ENGL 2000 0732290 Ob233130 b09 M


Upstream Segment

API BULLETIN 2U (BULL 2U) SECOND EDITION, OCTOBER 2000

American Petroleum Institute



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STD*API/PETRO B U L L Z U - E N G L 2000 m 0732290 Ob23131 5q5 m

SPECIAL NOTES

API publications necessarily address problems of a general nature. With respect to paltic- ular circumstances, local, state, and federal laws and regulations should be reviewed.

API is not undertaking to meet the duties of employers, manufacturers, or suppliers to warn and properly train and equip their employees, and others exposed, concerning health and safety risks and precautions, nor undertaking their obligations under local, state, or federal laws.

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Generally, API standards are reviewed and revised, reaffirmed, or withdrawn at least every five years. Sometimes a one-time extension of up to two years will be added to this review cycle. This publication will no longer be in effect five years after its publication date as an operative API standard or, where an extension has been granted, upon republication. Status of the publication can be ascertained from the Upstream Segment [telephone (202) 682- 80001. A catalog of API publications and materials is published annually and updated quar- terly by API, 1220 L Street, N.W., Washington, D.C. 20005.

This document was produced under API standardization procedures that ensure appropriate notification and participation in the developmental process and is designated as an API standard. Questions concerning the interpretation of the content of this standard or comments and questions concerning the procedures under which this standard was dcveloped should be directed in writing to thc general manager of the Upstream Segment, American Petroleum Institute, 1220 L Street, N.W., Washington, D.C. 20005. Requests for permission to reproduce or translate all or any part of the material published herein should also bc addressed to the general manager.

API standards are published to facilitate the broad availability of proven, sound engineering and operating practices. These standards are not intended to obviate the need for applying sound engineering judgment regarding when and where these standards should be utilized. The formulation and publication of A P I standards is not intended in any way to inhibit anyone from using any other practices.

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without prior written permission from the publishel: Contact the Publisher; APl Publishing Services, 1220 L Street, N . W , washington, D.C. 20005.

Copyright O 2000 American Petroleum Institute



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STD.API/PETRO BULL ZU-ENGL 2000 6 0732290 Ob23132 481 9

This Bulletin is under jurisdiction of the API subcommittee on Offshore Structures.

This Bulletin contains semi-empirical formulations for evaluating the buckling strength of stiffened and unstiffened cylindrical shells. Used in conjunction with API Rp 2T or other applicable codes and standards, this Bulletin will be helpful to engineers involved in the design of offshore structures which include large diameter stifTened or unstiffened cylinders.

The buckling formulations and design considerations contained herein are based on classical buckling formulations, the latest available test data, and analytical studies. This second edition of the Bulletin also incorporates user experience and feedback and is intended for design and design review of large diameter cylindrical shells, typically identified as those with D/? ratios of 300 or greater.

API publications may be used by anyone desiring to do so. Every effort has been made by the Institute to assure the accuracy and reliability of the data contained in them: however, the Institute makes no representation, wamnty, or guarantee in connection with this publication and hereby expressly disclaims any liability or responsibility for loss or damage resulting from its use or for the violation of any federal, state, or municipal regulation with which this publication may conflict, or for the infringement of any patent resulting from the use of this publication.

Suggested revisions are invited and should be submitted to the general manager of the Upstream Segment, American Petroleum Institute, 1220 L Street, N.W., Washington, D.C. 20005.

iii COPYRIGHT 2003; American Petroleum Institute


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CONTENTS

P a p

I GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Limitations ....................................................... 5 1.3 Stress Components for Stability Analysis and Design ..................... 5 1.4 Structural Shape and Plate Specifications ............................... 5 1.5 Hierarchical Order and Interaction of Buckling Modes .................... 5

1.1 scope ........................................................... 5

2 GEOMETRIES. FAILURE MODES AND LOADS ........................... 7 2.1 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Failure Modes .................................................... 7 2.3 Loads and Load Combinations ....................................... 7

3 BUCKLING DESIGN METHOD ........................................ 1 1

4 PREDICTED SHELL BUCKLING STRESSES FOR AXIAL LOAD. BENDING AND EXTERNAL PRESSURE ................................ 13 4.1 Local Buckling of Unstiffened or Ring Stiffened Cylinders . . . . . . . . . . . . . . . 13 4.2 General Instability of Ring Stiffened Cylinders ......................... 14 4.3 Local Buckling of Stringer Stiffened or Ring and Stringer Stiffened Cylinders 15 4.4 Bay Instability of Stringer Stiffened or Ring and Stringer Stiffened Cylinders.

and General Instability of Ring and Stringer Stiffened Cylinders Based Upon Orthotropic Shell Theory ........................................... 15

4.5 Bay Instability of Stringer Stiffened and Ring and Stringer Stiffened Cylinders-Alternate Method ....................................... 18

5 PLASTICITY REDUCTION FACTORS .................................. 21

6 PREDICTED SHELL BUCKLING STRESSES FOR COMBINED LOADS . . . . . . 23 6.1 General Load Cases ............................................... 23 6.2 Axial Tension. Bending and Hoop Compression ........................ 23 6.3 Axial Compression. Bending and Hoop Compression .................... 23

7 STIFFENER REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 7.1 Design Shell Buckling Stresses ...................................... 25 7.2 Local Stiffener Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 7.3 Sizing of Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

8 COLUMN BUCKLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 8 . I Elastic Column Buckling Stresses .................................... 27 8.2 Inelastic Column Buckling Stresses .................................. 27

9 ALLOWABLE STRESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 9.1 Allowable Stresses for Shell Buckling Mode ........................... 29 9.2 Allowable Stresses for Column Buckling Mode ......................... 30

10 TOLERANCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 10.1 Maximum Differences in Cross-Sectional Diameters .................... 31 10.2 Local Deviation from Straight Line Along a Meridian .................... 31 10.3 Local Deviation From True Circle .................................... 31 10.4 Plate Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

V



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1 STRESS CALCULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 I 1 . 1 Axial Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 11.2 Bending Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 11.3 Hoop Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

12 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

APPENDIX A COMMENTARY ON STABILITY DESIGN OF CYLINDRICAL SHELLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Figures 2.1 Geometry of Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Geometry of Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Shell Buckling Modes for Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1 Flow Chart for Determining Allowable Stresses ...................... 12 10.1 Maximum Possible Deviation e from a True Circular Form . . . . . . . . . . . . . 32 10.2 Maximum Arc Length for Determining Plus or Minus Deviation . . . . . . . . 32 C4.1.1-1 Local Buckling Stresses for Unstiffened and Ring Stiflèned Cylinders

C4.1.I-2 Axial Compression of Fabricated Cylinders-Local Buckling in

C4.1.I-3 Axial Compression of Fabricated Cylinders-Local Buckling in

C4.1.1-4 Axial Compression of Fabricated Cylinders-Local Buckling in

C4 . I . 1-5 Bending of Fabricated Cylinders-Local Buckling in Yield and

C4 . 1 . 1-6 Comparison of Test Data with Equations 4-6 and 4-7 for Axial

C4 . 1 . 1-7 Comparison of Test Data with Equations 4-6 and 4-7 íor Axial

C4 . 1 . 1-8 Comparison of Test Data with Equations 4-6 and 4-7 for Axial

C4 . 1 . 1-9 comparison of Test Data with Equations 4-6 and 4-7 for Axial

C4 . 1 . 1 - 1 O Comparison of Test Data with Equdtions 4-6 and 4-7 for Axial

C4.1.2-1 Theoretical Local Buckling Pressure of Unstiffened or Ring Stiffened

C4.1.2-2 Theoretical Local Buckling Pressure and Number of Circumferential

C4.1.2-3 Capacity Reduction Factors for Ring Stiffened Cylinders Subjected

C4.1.2-4 Comparison of Test Stresses with Predicted Stresses for Ring Stiffened

C4.3.1-1 Axial Compression Strength of Stringer Stiffened Cylinders (Wt = 300) . . 58 C4.3.1-2 Axial Compression Strength of Stringer Stiffened Cylinders (Wt = 500) . . 59 C4.3.1-3 Comparison of Local Shell Buckling Tests with Predicted Stresses for

C4.3.2-1 Values of tz Which Minimize Equation 4-27 of Bulletin 2U . . . . . . . . . . . . . 61

[Jnder Axial Compression Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

ElasticRegion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Inelastic Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Yield and Strain Hardening Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Strain Hardening Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Compression of Ring Stiffened Cylinders ........................... 47



Comprcssion of Ring Stiffened Cylinders ........................... 50


Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Waves for Unstiffened or Ring Stiffened Cylinders . . . . . . . . . . . . . . . . . . . 53

to Hydrostatic Pressure (Nd& = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Cylinders Subjected to Hydrostatic Pressure ......................... 56

Stringer Stiffened Cylinders Under Axial Load ....................... 60

Vi



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Page

C4.5.2- 1

c5- 1 6.1-1

6.1-2

6.2- 1

6.2-2

6.2-3

6.2-4

6.2-5

6.2-6

6.2-7

c7.1-1 C8- 1 C8-2 C11.3-I

Comparison of Test Pressures with Predicted Failure Pressures

Comparison of Plasticity Equations of DNV and API Bulletin 2U . . . . . . . 66 Comparison of Test Data from Fabricated Cylinders Under Combined Axial Tension and Hoop Cornpression with Interaction Curves (Fy = 36 ksi) .................................................. 67 Comparison of Test Data from Fabricated Cylinders Under Combined Axial Tension and Hoop Compression with Interaction Curves (Fy = 50 ksi). ........................................... 68 Comparison of Test Data with Interaction Equation for Unstiffened Cylinders Under Combined Axial Compression and Hoop Compression . . 70 Comparison ofTest Data with Interaction Equation for Ring Stiffened Cylinders Under Combined Axial Compression and Hoop Compression . . 7 I Cornparison of Test Data with Interaction Equation for Ring Stiffened Cylinders Under Combined Axial Compression and Hoop Compression . . 72 Comparison of Test Data with Interaction Equation for Local Buckling of Ring and Stringer Stiffened Cylinders Under Combined Axial

Comparison of Test Data with Interaction Equation for Local Buckling of Ring and Stringer Stiffened Cylinders Under Combined Axial Compression and Hoop Compression .............................. 74 Comparison o f Test Data with Interaction Equation for Bay Instability of Ring and Stringer Stiffened Cylinders Under Combined Axial Compression and Hoop Compression .............................. 75 Comparison of Test Data with Interaction Equation for Bay Instability of Ring and Stringer Stiffened Cylinders Under Combined Axial Compression and Hoop Compression .............................. 76 Design Shell Buckling Stresses, Fic, ............................... 77

for Stringer Stiffened Cylinders. .................................. 64

Cornpression and Hoop Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Axial Compression of Fabricated CylindersXolumn Buckling. . . . . . . . . 78 Comparison of Column Buckling Equations. ........................ 79 Cornparison Between Exact and Simplified Hoop Stress Factors. . . . . . . . . 8 1

Tables 3.1 Section Numbers Relating to Buckling Modes for Different Shell Geometries . . 1 1 6.1 Stress Factors, KQ .................................................. 24



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STD*API/PETRO 8ULL ZU-ENGL 2000 II 13732270 Ob2313b 027 9

Stability Design of Cylindrical Shells

Nomenclature

Note: The terms not defined here are uniquely defined in the sections in which they are used.

i = subscript denoting direction and load. $ = longitudinal direction and any load combina-

8 = hoop direction and any load combination. x = longitudinal direction and axial compression

h = hoop direction and hydrostatic external pres-

r = hoop direction and radial external pressure

tion.

load only ( N e = O).

sure ( N d N e = 0.5).

( N 0 =O).

j = subscript denoting buckling failure mode. L = local shell buckling. B = bay instability. G= general instability. C= column buckling.

Är = A$(L,.f).

A, = cross-sectional area of one ling stiffener, in.2.

A, = cross-sectional area of one stringer stiffener, in.2.

A, = total cross-sectional area of cylinder, A, = 2nRt + N,d,y, in.2.

b = stringer spacing as an arc dimension on the shell centerline, in.

be = effective width of shell in the circumferential direction, in.

B = mean bias factor.

C,, = end moment coefficient in interaction equation.

C, = ratio of structural proportional limit to yield strength for a material.

C, = elastic buckling coefficient = o x p ~ W E r. D,,,, = maximum and minimum shell diameters used to D,n;,l determine the out-of-roundness factor, y, at a par-

ticular cross-section, in. The location giving the largest y factor should be used.

D = centerline diameter of shell, in.

D, = outside diameter of shell, in.

E = modulus of elasticity, ksi.

D,,, = nominal outside diameter of cylinder, in.

f,, = applied (computed) axial stress, ksi.

fb = applied (computed) bending stress, ksi.

fi = applied (computed) hoop stress, ksi.

= axial compressive stress permitted in the absence of bending moment, ksi.

Fb = bending stress permitted in a cylinder in the absence of axial force. ksi.

Fe = hoop compressive stress permitted in a cylinder, ksi.

FjC, = inelastic shell buckling stress for fabricated shell, ksi.

Fie, = elastic shell buckling stress for fabricated shell, ksi.

FS = factor of safety. - F;., = Fie/p.

Fic. = FiC.B. -

F." = minimum specified yield stress of material, ksi.

F,,$ = static yield stress of material (zero strain rate), ksi.

G = shear modulus, E/2 ( 1 + v), ksi.

g = M.&f&rtAA.

h, = width (or depth) of stiffening element, in.

I,,, fer = moment of inertia of stringer and ring stiffener, respectively, plus effective width of shell about centroidal axis of combined section (see Fig. 2.2), in!

Ir = moment of inertia of stringer and ring stiffener, respectively, about its centroidal axis,

Js, J , = torsional stiffness constant of stringer and ring stiffener, respectively (for general non-circular shapes use C h,vt,?/3), i n 4

K = effective length factor for column buckling.

k = ratio of axial load to circumferential load ( N d N e ) .

KG = factor used in calculating ring stiffener stresses when a cylinder is subjected to external pressure.

KL = factor used when calculating the shell stress at mid-bay, to account for the effects of a ring or end stiffeners, when a cylinder is subjected to external pressure.

K,, = effective pressure correction factor used in calculation of collapse pressure.

1 COPYRIGHT 2003; American Petroleum Institute


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STDOAPIIPETRO BULL ZU-ENGL 2000 W 0732290 Ob23137 Tb3 9

2 API BULLETIN 2U

L = unsupported length of shell between rings, in.

Lj = cylinder length for calculation of bay instability and general instability, in.

L, = effective width of shell in the longitudinal direction, in.

length of cylinder between bulkheads or lines of support with sufficient stiflness to act as bulkheads. Lines of support which act as bulkheads include end ring stiffeners, in.

ring spacing, in.

unbraced length of cylinder, in.

number of half waves into which the shell will buckle in the longitudinal direction.

applied bending moment.

the smaller of the moments at the ends of the unbraced length of a beam-column, in-kips.

the larger of the moments at the ends of the unbraced length of a beam-column, in-kips.

L, /&

bl at

number of waves into which the shell will buckle in the circumferential direction.

theoretical elastic buckling load per unit length of shell (longitudinal or circumferential) for a perfect cylinder for both bay instability and general insla- bility, kips per in.

number of stringers.

axial load per unit of circumference, kips per in.

circumferential load per uni t of length, kips per in.

applied external pressure, ksi.

theoretical elastic failure pressure for bay instability mode, ksi.

P e ~ = theoretical elastic failure pressure for general instability mode, ksi.

pel, = theoretical failure pressure for local buckling mode, ksi.

p s = contribution of stringers to collapse pressure, ksi.

pee; = failure pressure For general instability mode, ksi.

P = applied axial load, ksi.

P,B = inelastic axial compression bay instability load, kips.

p ( . ~ = failure pressure for bay instability mode, ksi.

p c ~ = failure pressure for local buckling mode, ksi.

r = radius of gyration, r = (0.5R2 + O. 1 25t2)Il2 = 0.707R, in.

R =

R,. =

R0 =

R, =

t =

r,,, =

t , t, =

ts =

z, Z s =

a.. - u -

ß =

Pm PS =

Ac, Ad =

r l =

Y = h =

ho, h, =

radius to centerline of shell, in.

radius to centroidal axis of the combined ling stiffener and effective width of shell, in.

radius to outside of shell, in.

radius to centroid of ring stiffener, in.

thickness of shell, in.

thickness of web of ring stiffener, in.

effective shell thickness, t , = (A, + Let)/&, t, = (A,T + b,t)/b, in.

thickness of stiffening element, in.

distance from centerline of shell to centroid of stiffener, for ring and stringer stiffeners, respectively (positive outward), in.

capacity reduction factor to account for the diffcr- ence between classical theory and predicted instability stresses for fabricated shells.

a factor applied to the bay instability and general instability failure stresses to avoid interaction with the local buckling mode.

reduction factors used in computing collapse load for axial compression.

FiejlFy 9 FieJ/Fy

plasticity reduction factor which accounts for the nonlinearity of material properties and the effects of residual stresses.

(Dttua - Dtnin) 1OOlDwm.

XWL,

slenderness parameters as defined in text and used for computing collapse load for axial compression.

hG = nR/Lb

v = Poisson's ratio.

oiej = theoretical elastic instability stress, ksi.

y = partial safety factor.

SI Metric Conversion Factors

in. x 2.54 = mm

ksi x 6.894757 = MPa



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STD-API/PETRO BULL ZU-ENGL 2000 0 0732290 Ob23138 9 T T I

STABILITY DESIGN OF CYLINDRICAL SHELLS 3

Glossary

I - Y

amplification reduction factor (C,,,): Coefficient applied to bending term in interaction equation for members subjected to combined bending and axial compression to account for overprediction of secondary moment given by the amplification factor 1 /( 1 -f,,/F,).

asymmetric buckling: The buckling of the shell plate between the circumferential (¡.e., ring) stiffeners characterized by the formation of two or more lobes (waves) around the circumference.

axial direction: Longitudinal direction of the member.

axisymmetric collapse: The buckling of the shell plate between the circumferential stiffeners characterized by accor- dion-like pleats around the circumference.

bay: The section of cylinder between rings.

bay instability: Simultaneous lateral buckling of the shell and stringers with the rings remaining essentially round.

capacity reduction factor (a$: Coefficient which accounts for the effects of shape imperfections, nonlinear behavior and boundary conditions (other than classical simply supported) on the buckling capacity of the shell.

critical buckling stress: The stress level associated with initiation of buckling. Critical buckling stress is also referred to as the inelastic buckling stress.

distortion energy theory: Failure theory defined by the following equation where the applied stresses are positive for tension and negative for compression.

f’, - f J e + f i = f f

effective length (KLt): The equivalent length used in compression formulas and determined by a bifurcation analysis.

effective length factor (K ) : The ratio between the effective length and the unbraced length of the member.

effective section: Stiffener together with the effective width of shell acting with the stiffener.

effective width: The reduced width of shell or plate which, with an assumed uniform stress distribution, pro- duces the same effect on the behavior of a structural member as the actual width of shell or plate with its nonuniform stress distribution.

elastic buckling stress: The buckling stress of a cylinder based upon elastic behavior.

general instability: Buckling of one or more circumferential (¡.e., ring) stiffeners with the attached shell plate in ring- stiffened cylindrical shells. For a ring- and stringer-stiffened cylindrical shell general instability refers to the buckling of one or more rings and stringers with the attached shell date.

hierarchical order of instability: Refers to a design method that will ensure development of a design with the most critical instability mode (Le., general instability) having a higher critical buckling stress than the less critical instability made (i.e., local instability). hydrostatic pressure: Uniform external pressure on the sides and ends of a member. inelastic buckling stress: The buckling stress ofa cylinder which exceeds the elastic stress limit of the member material. The inelastic material properties are accounted for, including effects of residual stresses due to forming and welding. interaction of instability modes: Critical buckling stress determined for one instability mode may be affected (¡.e., reduced) by another instability mode. Elastic buckling stresses for two or more instability modes should be kept apart to preclude an interaction between instability modes. local instability: Buckling of the shell plate between the stiffeners with the stiffeners (¡.e., rings or rings 3nd stringers) remaining intact. membrane stresses: The in-plane stresses in the shell; longitudinal, circumferential or shear. maximum shear stress theory: Failure theory defined by the following equation:

(3, - 0 2 = F ,

where 01 is the maximum principal stress and (32, is the minimum principal stress, with tension positive and compression negative.

orthogonally stiffened: A member with circumferential (ring) and longitudinal (stringer) stiffeners. I radial pressure: Uniform external pressure acting only on the sides of a member. residual stresses: The stresses that remain in an unloaded member after it has been formed and installed in a structure. Some typical causes are forming, welding and cotrections for misalignment during installation in the structure. The misalignment stresses are not accounted for by the plasticity reduction factor T. ring stiffened: A member with circumferential stiffeners. shell panel: That portion of a shell which is bounded by two adjacent rings in the longitudinal direction and two adjacent stringers in the circumferential direction. slenderness ratio (&/r): The ratio of the effective length of a member to the radius of gyration of the member. stress relieved: The residual stresses are significantly reduced by post weld heat treatment. stringer stiffened: A member with longitudinal stiffeners. yield stress: The yield stress of the material determined in accordance with ASTM A307.



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STD-API/PETRO BULL ZU-ENGL 2000 D 0732290 Ob23139 83b

SECTION 1-GENERAL PROVISIONS

1.1 SCOPE

1.1.1 This Bulletin provides stability criteria for determining the structural adequacy against buckling of large diameter circular cylindrical members when subjected to axial load, bending, shear and external pressure acting independently or in combination. The cylinders may be unstiffened, longitudi- nally stiffened, ring stiffened or stiffened with both longitudinal and ring stiffeners. Research and development work leading to preparation and issue of the first and second edi- tions of this Bulletin is documented in References l through 6 and the Commentary.

1.1.2 The buckling capacities of the cylinders are based on linear bifurcation (classical) analyses reduced by capacity reduction factors which account for the effects of imperfections and nonlinearity in geometry and boundary conditions and by plasticity reduction factors which account for nonlinearity in material properties. The reduction factors were determined from tests conducted on fabricated steel cylinders. The plasticity reduction factors include the effects of residual stresses resulting from the fabrication process.

1.1.3 Fabricated cylinders are produced by butt-welding together cold or hot formed plate materials. Long fabricated cylinders are generally made by butt-welding together a series of short sections, commonly referred to as cans, with the longitudinal welds rotated between the cans.

1.2 LIMITATIONS

1.2.1 The criteria given are for stiffened cylinders with uniform thickness between ring stiffeners or for unstiffened cylinders of uniform thickness. All shell penetrations must be properly reinforced. The results of experimental studies on buckling of shells with reinforced openings and sonle design guidance are given in Ref. 2. The stability criteria of this bulletin may be used for cylinders with openings that are reinforced in accordance with the recommendations of Ref. 2 if the openings do riot exceed 10% of the cylinder diameter or 80% of the ring spacing. Special consideration must be given to the effects of larger penetrations.

1.2.2 The stability criteria are applicable to shells with diameter-to-thickness (Oh) ratios equal to or greater than 300 but less than 2000 and shell thicknesses of 5 mm (3/16 in.) or greater. The deviations from true circular shape and straightness must satisfy the requirements stated in this bulletin.

1.2.3 Special considerations should be given to the ends of members and other areas of load application where the stress distribution may be nonlinear and localized stresses may exceed those predicted by linear theory. When the localized stresses extend over a distance equal to one half wave length of the buckling mode, they should be considered as a uniform stress around the full circumference. Additional thickness or stiffening may be required.

1.2.4 Failure due to material fracture or fatigue and failure caused by dents resulting from accidental loads are not considered in the bulletin.

1.3 STRESS COMPONENTS FOR STABILITY ANALYSIS AND DESIGN

The internal stress field which controls the buckling of a cylindrical shell consists of the longitudinal membrane, circumferential membrane and in-plane shear stresses. The stresses resulting from a dynamic analysis should be treated as equivalent static stresses.

1.4 STRUCTURAL SHAPE AND PLATE SPECIFICATIONS

Unless otherwise specified by the designer, structural shapes and plates should conform to one of the specifications listed in Table 8.1.4- 1/2 of API RP 2A, 20th edition, or Table 4 of API RP 2T.

1.5 HIERARCHICAL ORDER AND INTERACTION OF BUCKLING MODES

1.5.1 This Bulletin requires avoidance of failure in any mode, and recommends sizing of the cylindrical shell plate and the arrangement and siz,ing of the stiffeners to ensure that the buckling stress for the most critical general instability is higher than the less critical local instability buckling stress.

1.5.2 A hierarchical order of buckling stresses with adequate separation of general, bay and local instability strcsses is also desirable for a cylindrical shell subjected to loading resulting in longitudinal and circumferential stresses to preclude any interaction of buckling modes. To prevent a reduction in buckling stress due to interaction of buckling modes, it is recommended that bay and general instability mode elastic buckling stresses remain at least 1.2 times the elastic buckling stress for local instability.



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SECTION 24EOMETRIES, FAILURE MODES, AND LOADS

The maximum stresses corresponding to all of the failure modes will be referred to as buckling stresses. Buckling stress equations are given for the following geometries, failure modes and load conditions.

2.1 GEOMETRIES

a. Unstiffened. b. Ring Stiffened. c. Stringer Stiffened. d. Ring and Stringer Stiffened.

The four cylinder geometries are illustrated in Figure 2.1 and the stiffener geometries in Figure 2.2.

2.2 FAILURE MODES

a. b a l Shell Buckling-buckling of the shell plate between stiffeners. The stringers remain straight and the rings remain round. b. Bay Instabdity-buckling of the stringers together with the altached shell plate between rings (or the ends of the cylinders for stringer stiffened cylinders). The rings and the ends of the cylinders remain round. c. General Instability-buckling of one or more rings together with the attached shell (shell plus stringers for ring and stringer stiffened cylinders). d. Local Stiffener Buckling-buckling of the stiffener elements. e. Column Buckling-buckling of the cylinder as a column.

The first four failure modes are illustrated in Figure 2.3.

2.3 LOADS AND LOAD COMBINATIONS

a. Determination of Applied Stresses Due to the Follow- ing Loads:

1. Longitudinal stress due to axial compressiodtension and overall bending. 2. Shear stress due to transverse shear and torsion. 3. Circumferential stress due lo external pressure. 4. Combined (von Mises) stress due to combination of loads.

h. Determination of Utilization Ratios Based on Recom- mended Interaction Relationships for Combined Loads:

I . Longitudinal (axial) tension and circumferential (hoop) compression. 2. Longitudinal (axial) compression and circumferential compression.

Note: Stresses and stress combinations considered are for in-plane loads and do not account for secondary bending stresses due to out- of-plane presslwe loading on shell plate.

Although the secondary bending stresses on orthogonally stiffened shell plate may be appreciablc, such stresses can be often conservatively neglected because of reduction i n circumferential stresses due to direct load transfer into the stiffeners. Appropriate finite element analysis may be used to determine applied stresses (see Section I l ) .



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8 API BULLETIN 2U

Unstiffened

Ring Stiffened

Stringer - Stringer Stiffened

Rind and Stringer Stiffened

L, = L,

Bulkhead - """_ L""-

_"""

_"""

I I I

if I I I I I

I I I I I

- t i - - t i

I I L r Lb

3 Lb

Figure 2.1-Geometry of Cylinder



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STD*API/PETRO BULL ZU-ENGL 2000 0732290 Ob23192 320 m

9 STABILITY DESIGN OF CYLINDRICAL SHELLS -

Shell

Section Through Stringers

Shell -,,

(Effective width) L,

t ” r

R

S R, = Radius to centroid of ring -.-

R, = Radius to centroid of effective section (shown cross hatched)

Section Through Rings

Figure 2.2-Geometry of Stiffeners



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STD*API/PETRO BULL ZU-ENGL 2000 H 0712270 UbZ3Lq3 2b7 M

10 API BULLETIN 2U

Unstiffened

Ring Stiffened

Stringer Stiffened

Rind and Stringer Stiffened

"""" """"

Local shell buckling Section 4.1

"- General instability Section 4.2

Local stiffener buckling Section 7


Bay instability Section 4.4, l a and 2a Section 4.5




Bay instability Sections 4.4.la, 4.4.2a, and 4.5

General instability Sections 4.4.1 b and 4.4.2b

Figure 2.3-Shell Buckling Modes for Cylinders



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S T D - A P I I P E T R O BULL ZU-ENGL 2000 U732270 Ob23144 %T3 m

SECTION 3-BUCKLING DESIGN METHOD

3.1 The buckling strength formulations presented in this bulletin are based upon classical linear theory which is modified by reduction factors a~ and q which account for the' effects of imperfections, boundary conditions, nonlinearity of material properties and residual stresses. The reduction factors are determined from approximate lower bound values of test data of shells with initial imperfections representative of the specified tolerance limits given in Section IO.

3.2 The general equations for the predicted shell buckling stresses for fabricated steel cylinders subjected to the individual load cases of axial compression, bending and external pressure are given by Equations 3-1 and 3-2. The equations for ao and oie, are given in Section 4 and the equations for q are given in Section 5.

a. Elastic Shell Buckling Stress

F. .-a.. 0. . 1eJ - IJ le/ (3-1 1

b. Inelastic Shell Buckling Stress

Fi,. = Fie, (3-2)

3.3 The bay instability stresses for cylinders with stringer stiffeners are given by orthotropic shell theory. This theory requires that the number of stringers must be greater than about three times the number of circumferential waves corresponding to the buckling mode. An alternate method is given for determining the bay instability stresses for cylinders which do not satisfy this requirement.

3.4 The buckling stress equations for cylindcm under the individual load cases of axial compression, bending, radial external pressure (N+ = O ) and hydrostatic external pressure (NdNe = 0.5) are given in Section 4. Interaction equations are given in Section 6 for cylinders subjected to combinations of axial load, bending and external pressure. The interaction between column buckling and shell buckling is considcred in Section 8. The method for determining the size of stiffeners is given in Section 7.

3.5 A flow chart is given i n Figure 3.1 for determining the allowable stresses. The equations for allowable stresses are given in Section 9 and equations for determining the stresses due to applied load are given in Section 1 l . A summary of the sections relating to the buckling modes for each of the different shell geometries is given on Table 3.1.

Table 3.1-Section Numbers Relating to Buckling Modes for Different Shell Geometries

Buckling Mode Unstiffened

Local Shell Buckling

Bay Instability

General Instability

Local Stiffener Buckling

Column Buckling

4. I

8.0

Geometry

Ring Stiff Stringer Stiff

4. I 4.3

4.4 4.5

4.2

7.2

8.0 8.0

7.2

Ring and Stringer Stiff

4.3

4.4 4.5

4.4 ( I b, 2b)

7.2

8.0



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STD.API/PETRO BULL ZU-ENGL 2000 m 0732270 Ob231115 03T m

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Calculate stresses for assumed shell geometry

See Section 11

Unstiffened or ring stiffened ring and stringer stiffened

' (1 Stringer stiffened or

I I I

Calculate FleL and F,,, See Section 4.1

I

Calculate FieL and Fic~ See Section 4.3

Calculate FieB and FicB See Sections 4.4 or 4.5

I I

Ring stiffened

Yes I r Yes - 7

Calculate fie^ and FicG L 1 Calculate FieG and F i c ~ See Section 4.2 r 1 See Section 4.4

Combined loads

I

Calculate Fqd and Fed For all applicable modes

See Figure 2.3 I 1

Determine stiffener sizes No See Section 7

I

Calculate FqCc See Section 8

Calculate F,, F,, Fe See Section 9

Compare allowable stresses with calculated stresses.

The allowable stresses must be greater than the calculated stresses

for all modes of failure.

Figure 3.1-Flow Chart for Determining Allowable Stresses



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I

SECTION 4-PREDICTED SHELL BUCKLING STRESSES FOR AXIAL LOAD, BENDING AND EXTERNAL PRESSURE

This section gives equations for determining the shell buckling stresses for the load cases of axial compression, bending, radial external pressure (N$ = O) and hydrostatic external pressure (N$ = 0.5 Ne) . The general equations for predicting the elastic and inelastic buckling stresses for fabricated cylinders are given by Equations 3-1 and 3-2. The equations for determining clg and oie, are given in the following section. The equations for determining the plasticity reduction factors, q, are either given in this section or in Section 5.

The values of M, and Me appearing in the following equations are defined as:

L, b M , = - f i t

M, = - f i t

(4- 1 )

where:

L, = distance between stiffening rings,

R = shell radius, r = shell thickness,

b = arc distance between stringers.

4.1 LOCAL BUCKLING OF UNSTIFFENED OR RING STIFFENED CYLINDERS

4.1.1 Axial Compression or Bending (Ne= O)

The buckling stresses for cylinders subjected to axial compression or bending are assumed to be the same (see Com-

where

a.C.¿ =

C, = 0.605 for D/t > 300

0.207 D/r 2 I242

1 169 <0.9 D / t < I242 195 + O S ( D / r )

b. Inelastic Buckling Stresses. The buckling stresses are the smaller of the values given by Equations 4-6 and 4-7.

FXCL = FxeL

233 F , 5 F,, D / r < 600

FxcL - (4-7)

(0.5 F! D / r 2 600

4.1.2 External Pressure (N9INe = O or 0.5)

To calculate the predicted elastic local shell buckling stresses FreL and F l t e ~ for the radial and hydrostatic pressure cases, three terms ( P e ~ , KeL, and sei, must be calculated as shown below. The values of p e ~ arc determined by Equation 4-9 which was derived from the more general Equation 4-27. Equation 4-9 is a smooth lower bound curve which was obtained by letting n be a noninteger.

a. Elastic Buckling Stresses

where KeL = 1 .O if M, 2 3.42. The value of M., will be greater than 3.42 for unstiffened cylinders. When M, < 3.42 dcter- mine K ~ L from Equation 1 1.7.

“O8 E ( t / D ) ’ M , > 1.5 and A < 2.5 + 0.5

2.5 < A < O. I W( D / r ) (4-9)

where

A = M,- 1.17+ 1.068k

2A c - - - D / t

k = O for radial pressure and 0.5 for hydrostatic pressure.



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S T D - A P U P E T R O BULL ZU-ENGL zuno m O ~ Z W O I , Z ~ ~ W yo2 m

14 API BULLETIN 2U

b. Imperfection Factors. A constant value of = 0.8 is recommended for fabricated cylinders which meet the fabrication tolerances of Section l O.

c. Inelastic Buckling Stresses

See Equation 5-3 for T.

d. Failure Pressures

See a, b, and c above for determination of thc terms in Equation 4- 12.

4.1.3 Transverse Shear

Panel instability due to transverse shear and torsion can be critical at interfaces. Critical buckling stress is affected not only by the shell thickness and the panel aspect ratio, but also by the boundary conditions.

As a minimum, it is necessary to incorporate the shear stress in a von Mises stress check to assess the overall effect of combined loads.

4.2 GENERAL INSTABILITY OF RING STIFFENED CYLINDERS

4.2.1 Axial Compression or Bending (Ne = O)


F.reG = a,, = a-,, 0.605 E - ( 1 +A,)”’ (4-13) t R

-

where A,. is the ring area and L, is the ling spacing.

b. Imperfection Factors (4- 14)

0.72 if A, 2 0.2

- 5.0a.,L)A, + a,, if 0.06 < Ä r < 0.2

if Ä r 5 0.06


See Equation 5-3 for 11.

4.2.2 External Pressure (N#/Ne = O or 0.5)

a. Buckling Stresses With or Without End Pressure

(4- 15)

where KOG is given by Equation 1 1-9.

E ( t / R ) h i E l J n ’ - 1 ) Prc = 2 + (4- 17)

( n 2 + khi - I ) ( n 2 + hi) L,RfRí,

where h~ = nR/Lb, k = O for radial pressure and 0.5 Sor hydrostatic pressure, R,. is the radius to the centroid of the effective section, R , is the radius to the outside of the shell and f e , is the moment of inertia of the efíective section given by the following equation:

L,t L,? ler = I , + A, Z r - +- (4- 18)

A r + Let 12

where Zr is the distance from the centerline of the shell to the centroid of the stiffener ring (positive outward).

The value of L, can be approximated by 1.1 f i t + t,,. when My > 1 S6 and L, when M, 5 1.56. The correct value t’or n is the value which gives the minimum value ofp,G in Equa- tion 4-17. The minimum value of I I is 2 and the maximum value will be less than 10 for most shells of interest. The minimum pressure will correspond to a noninteger value of n. The pressure p e ~ is determined by trial and error.

b. Imperfection Factors. For fabricated cylinders which meet the fabrication tolerances given in Section 1 0, a constant value of = 0.8 is adequate.


FnG = rl Frec (4- 19)

FhcC = T FlwG (4-20)

See Equation 5-3 for v.


See a, b, and c above for determination of the terms in where a , ~ is given by Equation 4-4 and c = I .O. Equation 4-2 I .



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STD=API/PETRO BULL ZU-ENGL 2000 0732270 Ob2319B B97


4.3 LOCAL BUCKLING OF STRINGER STIFFENED OR RING AND STRINGER STIFFENED CYLINDERS

The following equations are based upon the assumption that the stringers satisfy the compact section requirements of Section 7. A method is presented in the Commentary for noncompact sections.


For the stringers to be effective in increasing the buckling stress, they must be spaced sufficiently close so that Me < 15 and b 2L, For values of Me > 15 or b > 2L, the buckling stresses are computed as if the stringers were omitted. How- ever, the stringers may be assumed to be effective in carrying part of the axial loading when computing the stresses due to applied loads.


F x e ~ = a.,L C, Et/R (4-22)

where a.r~ C, is determined by the following equations which depend on the value of Me. The values of a,, in Equations 4-23 and 4-24 are given by Equation 4-4. For values of M g < I .5 use Me = 1.5 in Equation 4-23. For values of Me between 3.46 and 15, aXl, C, is obtained by linear interpolation.

I .5 < M, < 3.46 (4-23)

C, = 0.605 a,, M,> 15 (4-24)

b. Inelastic Buckling Stresses

See Equation 5-3 for y.

4.3.2 External Pressure (N4/Ne = O or 0.5)

The local buckling pressure of a stringer stiffened cylinder will be greater than a corresponding unstiffened or ring stiffened cylinder if O S N , (N,7 = Number of Stringers) is greater than the number of circumferential waves at buckling for the cylinder without stringers. This is based upon the assumption that one-half wave will form between stringers at buckling. For stringers with high torsional rigidity a full wave might form between stringers with a concurrent increase in the buckling pressure. This possible increase in buckling pressure is not considered.

The buckling pressure may be found by iterating Equation 4-27 with n starting at O S N , and increasing n until a minimum pressure is attained. The pressure corresponding to n = OSN, is the minimum pressure if il is less than the pressure corresponding to n = O.5fVy+ 1. If n is greater than OSN, the stringers are ineffective.

a. Elastic Buckling Stresses With or Without End Pressure

(4-26)

where KO), = I .O if M, 2 3.42. When M, 3.42 determine K ~ L from Equation 1 1-7.

PrL = E r'R [' n2+h'-1)2 (R)' r + " ] (4-27) n ' + k h 2 - 1 12(1-v ) (n' +X*$

where h = RWL, k = O for radial pressure and 0.5 for hydrostatic pressure and v = 0.3.

h. Imperfection Factors. The test results indicate that no imperfection reduction factor is needed for stringer stiffencd cylinders. Therefore:

a& = 1 .o


FKL =II FreL (4-28)

(4-29)

See Equation 5-3 for y,


PCL = T PeL (4-30)

See a and c above for determination o f the terms in Equation 4-30.

4.4 BAY INSTABILITY OF STRINGER STIFFENED OR RING AND STRINGER STIFFENED CYLINDERS, AND GENERAL INSTABILITY OF RING AND STRINGER STIFFENED CYLINDERS BASED UPON ORTHOTROPIC SHELL THEORY

The theoretical elastic buckling loads for both bay instability and general instability are given by the following orthotropic shell equation (Equation 4-3 I ) . The elastic buckling load per unit length of shell is denoted Niej where i is the stress



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16 API BULLETIN 2U

direction andj is the buckling mode withj = E for bay instability and j = G for general instability. The bay instability stress is determined by letting the cylinder length equal the ring spacing (Lj = L,) and the general instability stress is determined by letting the cylinder length equal the distance between bulkheads or stiffener rings that are sufficiently sized to act as bulkheads (Lj = Lb).

When the rings and stringers are not sufficiently close together so that the shell plating is ful ly effective, the rigidity parameters (Ex, Eo, D,, De, DA, CA) of Equation 4-31 are modified by the ratios of effective width to stiffener spacing. Equations are given for L, and h, which are the effective widths of plate in the x and 8 directions, respectively. When L, < L,. or be < h, set v = O; otherwise V = 0.3.

The values of m and I I to use in the following equation are those which minimize N;,j where m 2 1 and n 2 2. For the following equation to be valid, the number of stringers must be greater than about 3n and the bay instability stress should be less than I .5 times the local shell buckling stress. When these conditions are not met, the equations in Section 4.5 should be used for sizing the stringers. Section 4.2 should be used for sizing the rings.

(4-3 1 )

v Et E.,, = - 1 - v 2

Et L, EA, E , = -(-)+L, I -v- L,.

Et3 (:) El,s EA.& D., =

12( 1 -v2 ) +-+-

b h

EtS EI,. EA,.Z: D, = 12( 1 -v2) L,.

+-+-

D,, = ~ V Et3 Gt3(Lc? h e ) “L‘,. +- -+ - +-+- 6(1-v’) 6 L,

where EA.SZ\ c, = - b

The term Y in Equation 4-3 1 is dependent upon the loading condition and is defined in the sections below.


The elastic buckling stresses in the longitudinal direction for the bay instability and general instability modes of failure are given by Equations 4-33 and 4-36 with Nxe, determined from Equation 4-3 1 . The following relationships for Y, r,, and L, are to be used for both bay and general instability stresses. When be < b, the values for Fxej must be determined by iteration since the effective width is a function of the buckling stress.

A.\ + bet t , = -

L, = L,.

b



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STD.API/PETRO BULL ZU-ENGL 2000 E 0732290 Ob23150 q T 7 m


a. For Bay Instability

1. Elastic Buckling Stresses. Use the following relationships together with those above for X tx, and L, to determine the bay instability buckling stresses:

3. Inelastic Buckling Stresses

F X C G = q F,,í; (4-37)

See Equation 5-3 for q.

4.4.2 External Pressure (NOIN0 = O or 0.5)

The elastic buckling stresses in the hoop direction for the bay instability and general instability modes of hilure are given by Equations 4-38 and 4-42 with Ne,, determined from Equation 4-3 l . The following relationships for Y and t , are to be used for both bay and general instability stresses.

j = B. A, = I , = J , = O, L, = L,

(4-32)

(4-33)

Y = k(z)l+[i) 2

I F , is to he substituted for F,,B when F,,B > F,y so that be = I .9t (E/F,)"2 I b.

A,. + L,? r,. = -

' r

2. Imperfection Factors

where k = O for radial pressure and k = 0.5 for hydrostatic pressure.

a. For Bay Instability

I . Elastic Buckling Stresses. Use the following relationships together with that given above for Y to determine the bay instability stresses.

A, = 5 and is given by Equation 4-4 with -

bt

- c = 1.0

3. Inelastic Buckling Stresses Le = L,, 6, = b

(4-34)

(4-38) See Equation 5-3 for q.

b. For General Instability

l. Elastic Buckling Stresses. Use the following relationships together with those above for Y, r.r, and L, to determine the general instability stresses. The value for F x c ~ in the equation for b, is given by Equation 4-25 and the value for F,,c is given by Equation 4-37.

See Equation 1 1.7 for K ~ L .


cY@B = 1 .o


(4-39)

(4-40)

j = G, L, = Lb

b, = b , . / z G S b (4-35) See Equation 5-3 for T.

(4-36) 4. Failure Pressures

2. Imperfection Factors S e e ( 1 ) and (3) above for determination of terms in Equa-

tion 4-4 l. a.,(; is given by Equation 4- 14.



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STDeAPIIPETRO BULL ZU-ENGL 2000 m 0732270 O b 2 3 2 5 1 333 m

18 API BULLETIN 2U

b. For General Instability

1. Elastic Buckling Stresses. Use the following relationships together with that above for Y to determine the -

general instability stresses.

j = G, L, = Lb

L, = 1.56 f i t I L,, be = b

NOeC FreG Or FheG = %G 7 KOG

See Equation 1 1-9 for KOG.


agC' = 0.8


FrcG = V FreiÌ

FhcC = FlleG

See Equation 5-3 for V.

4. Failure Pressures

I P& = %G T N,,G/R

(4-42)

(4-43)

(4-44)

(4-45)

See ( I ) , (2), and (3 ) above for determination of terms in Equation 4-45.

4.5 BAY INSTABILITY OF STRINGER STIFFENED AND RING AND STRINGER STIFFENED CYLINDERS-ALTERNATE METHOD

The method of determining the bay instability stresses for stringer stiffened and ring and stringer stiffened cylinders given in Section 4.4 is based upon a modified orthotropic shell equation. This equation is not valid if the minimum number of stringers is less than about three times the number of circurnfcrential waves for the bay instability mode. A further restriction requires that the bay instability stress not exceed 1.5 times the local shell buckling stress. The following equations can be used when these restrictions are not met. The rings are to be sized using the equations in Section 4.2 for ring stiffened cylinders.

4.5.1 Axial Compression or Bending (No= O)

The following method for determining the bay instability loads and stresses for axial compression and bending is quite lengthy but gives the best cosrelation between test and pre-

dicted loads of those methods considered. The method is based on the procedure proposed by Faulkner, et al. in Ref. 3 .

a. Elastic Buckling Stresses. The elastic bay instability stress F x c ~ is approximated by summing the buckling stress of a shell panel and the column buckling stress of a stringer plus effective width of shell.

where ctXLCx is determined from Equations 4-23 and 4-24 and:

b',t b' / A,, + b',t + 12 = I , , + A , Z , ~

(4-47)

b for h, 50.53

l b if h,, < 0.53

h,, = (4-50)

Me L 3.46

E 2t/D M, < 3.46 (4-52)

3.46 < M, 8.57 PIl = (4-53)

1 .O - 0.01 8 M y + 0.0O23Mi

I M, I 3.46

1.15 for h, 2 I .O

1 +0.15 h, for h,< 1.0 B = { (4-54)



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-

STD.API/PETRO BULL ZU-ENGL 2000 0732270 Ob23152 27T


h, = reL

(4-55)

I I m o if h, 10.53

R, = { I.O--( b / t - 2c I + 0 . 2 5 ~ ; h; ) I .O%,, h; - 0.28 (4-56)

I if h, >OS3

where c = 4.5 for continuous structural fillet welds.

b. Inelastic Buckling Stresses. The inelastic buckling stresses F x c ~ are computed by using the Ostenfeld-Bleich expression for tangent modulus and are given by:

where C,y is the ratio of the proportional limit to the yield strength. Reference 3 suggests a value of C, = 0.5 for nonstress relieved shells.

c. Failure Load. The failure load is the product of the failure stress and the effective area. The effective shell width for determining the fai lw load or applied stresses (see Equations 1 1-2 and 1 1-4) is given by:

O5 28 for he> 0.53 be = (4-58)

I b for h, 0.53

where

See Equation 4-50 for h(,, Equation 4-56 for R, and Equa- tion 4-57 for F x c ~ . The failure load P c ~ is computed by:

4.5.2 External Pressure (#+/#e= O or 0.5)

a. Inelastic Failure Stresses and Pressures. The failure pressure for bay instability is given by the following equation:

-

PCB = @PL i- P S ) Kp (4-60) -

The local shell buckling pressure, pel*, is determined from Equation 4-9 for a cylinder with length L, and assuming no

given by: stringer stiffeners. The pressure, p.$, and the factor K!, are

(4-61)

11.10 for g 2 500

where

g = M.r M e

The bay instability stress is given by:

See Equation 1 1-7 for KOL.

(4-62)

(4-63)

b. Elastic Buckling Stresses. The elastic buckling stresses for radial pressure (i = r) and hydrostatic pressure (i = h ) are determined from the collapse stresses by dividing by the plasticity factors determined from Equation 5-3.

(4-64)

The values for A are determined from Equation 5-3 by tirst multiplying both sides of the equation by A. The left side of the equation becomes T A which is equal to Fic.dFy The values of F i c ~ are given by Equations 4-57 and 4-63.

The following example will illustrate the procedure. Assume a nonstress relieved cylinder with FiCs = 30.0 ksi and Fy = 50.0 ksi.

Rewriting Equation 5-3

q = - +0.18 as qA=Oo.45+0.I8A 0.45

A

in material elasto-plastic region and equating it to Equation 4-64

TA = F i c ~ 1 Fy

0.45 + O. 18A = 30.0 I 50.0

yielding A = 0.8333

Thus, Fies = AFy = (0.8333) (50.0) = 41.67 ksi, or

Since q = F i c . ~ / AFy = (30.0) / (0.8333) (50.0) = 0.720



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SECTION !+PLASTICITY REDUCTION FACTORS

The predicted elastic buckling stresses given in Section 4 plasticity Reduction Factors for Nonstress Relieved Shells for local shell buckling, bay instability and general instability must be reduced by a plasticity factor when the elastic buck-

buckling stresses are given by Equation 3-2 which is repeated ling stresses exceed 0.55 F,. The predicted inelastic shell

r 1 il' A I0.55

"*tO.18 i f O . S S < A 5 1 . 6 A

below. rl=. (5-3) 1.31

F. ,. - F. . (5- 1 ) I + 1.15A if I .6 < A < 6.25

. 1 /A if A 2 6.25 KJ - re)

The ratio of the buckling stress to the yield stress can be determined from Equation S-2. The product YA is determined where from Equation 5-3. This ratio is a measure of how efficiently the shell material is utilized. Fic i

A = A , . = - A = A d = - Fici Fi,, 1 F,, = q A (5-2) F?. F?.

See Section 4 for Fie, and Section 7 for Tiej.



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SECTION &PREDICTED SHELL BUCKLING STRESSES FOR COMBINED LOADS

Interaction equations arc given for determining the failure stresses for cylinders subjected to combined loads. The stresses due to bending moment are treated as equivalent axial stresses. The interaction equations are applicable to all modes of failure and to both elastic and inelastic buckling stresses. Each mode must be checked independently.

6.1 GENERAL LOAD CASES

In the following equations for NQ and Ne, P is the total axial load including any pressure load on the end of the cylinder, M is the bending moment and p is the external radial pressure.

a. Axial Compression and Hoop Compression

NQ = P I (21tR)

Ne = P R ,

b. Bending and Hoop Compression

N$ = M I (M*)

N e = P R ,

c. Axial Compression, Bending and Hoop Compression

N$ = P I ( h R ) + M 1 (xR2)

Ne = P R ,

6.2 AXIALTENSION, BENDING AND HOOP COMPRESSION

The failure stresses are the lower of the values determined from Equations 6-1 and 6-2. The longitudinal stress F$,. is the sum of the axial and bending stresses.

F,,,. = Fr(> ( 1 -0.25 ““i) F?.

where Faj is the failure stress in the hoop direction corresponding to Fwj which is the coexistent failure stress in the axial direction, and Frc, is the predicted failure stress for radial pressure. Fw. is given by Equations 4-10,4-19,4-28, 4-39,4-43, and 4-63.

The values of F@; and Fe,, are determined from Equations 6-1 and 6-2 by letting F*. = Fe(j k K,+iKe, where k = N d N e and then solving for Fe, . See Table 6.1 for Ki.

6.3 AXIAL COMPRESSION, BENDING AND HOOP COMPRESSION

The following equation is applicable to any combination of axial compression, bending and external pressure. The axial buckling stress, Fej. is the sum of the longitudinal stresses due to axial compression and bending. I f the bending stress is greater than the axial stress, the failure stresses are determined from Section 6.2. Fe,; is the failure stress in the hoop direction.

R i - c R, R , , + R i = 1.0 (6-3)

where

R,, = F+, I Fxc,

Rh = Fec, I F,,

The equations for c are dependent upon the cylinder geometry.

a. Unstiffened and Ring Stiffened Cylinders (all buckling modes)

c = F,,., + F,.(,j

F,. - 1.0

b. Stringer Stiffened and Ring and Stringer Stiffened Cylinders

1 . Local Buckling ( j = L )

0.4( + F,.‘,;) c =

F,. - 0.8

2. Bay Instability and General Instability (i = B, j = G)

The buckling stresses for any combination of longitudinal compression and hoop compression, NdNe, are determined by the following procedure for each of the buckling modes.

Step 1. Calculate F.rc, and Frc. from the equations in Sec- tion 4.

Step 2. Solve for F&, in Equation 6-3 by letting F*, = Fec, k K~jlKej.

where

k = NdNe

KQ, = axial stress modifier (see Table 6. I),

KO; = hoop stress modifier (see Table 6.1).



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Table 6.1-Stress Factors, Ku

Kìj Ring

Unstiffened Stiffened

I .o 1 .o

I .O

I .O Equation 11-7

I Equation 1 1-9

Stringer Stiffèned

1 .o

t/t., Section 4

Equation

1. I

1-7

Same as Kor.

Ring and Stringer Stiffened

1 .o

t/t r Section 4.4.1

t 4 r Section 4.4. I

Equation I 1-7

Same as KOL

Equation 1 1-9



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SECTION 7-STIFFENER REQUIREMENTS

The flow chal1 in Figure 3.1 shows the procedure for determining the allowable stresses for all buckling modes. The sizes of the stringers are determined from the bay instability mode equations and the sizes of the rings are determined from the general instability mode equations.

The shell buckling stress equations were developed on the basis of no interaction between the buckling modes. The buckling stresses for local buckling, however, may be reduced if the predicted buckling stress for either bay instability or general instability is approximately equal to thc predicted local buckling stress. Similarly, if the predicted general instability stress is approximately equal to the bay instability stress, the actual stress for either of these modes may be less than predicted.

Mode interaction can be avoided by applying a factor ß to the strains corresponding to the buckling stresses. It is desirable to provide a hierarchy for failure with general instability preceded by bay instability and bay instability preceded by local shell buckling. A minimum factor o f ß = 1.2 is recommended for both the bay and general instability modes. The designer may elect to select a higher ß value for the general instability mode.

7.1 DESIGN SHELL BUCKLING STRESSES

The buckling stresses which include the factor ß will be called the design shell buckling stresses and are given by the following equations:

- F . reJ . = F . te/ ./P (7- 1 ) - F. . -

1cJ - Fie; -

(7-2)

where ß = 1.0 for local buckling and 1.2 for bay instability and general instability. The values of q are determined from Equation 5-3 for h = Ad.

7.2 LOCAL STIFFENER BUCKLING

To preclude stiffener buckling prior to shell buckling, the local stiffener buckling stress must be greater than the shell buckling stress given by the foregoing equations. The local stiffener buckling stress can be assumed to be equal to the yield stress for stiffeners which satisfy the following compact section requirements. For stiffeners not meeting these requirements, the local stiffener buckling stress can be determined from Equation C7-1 in the Commentary.

a. Flat Bar Stiffener, Flange of a Tee Stiffener and Outstand- ing Leg of an Angle Stiffener

where h, is the full width of a flat bar stiffener or outstanding leg of an angle stiffener and one-half of the full width of the flange of a tee stiffener and is the thickness ofthe bar, leg of angle or flange of tee.

b. Web of Tee Stiffener or Leg of Angle Stiffener Attached to Shell

(7-4)

where h,y is the full depth of a lee section or full width of an angle leg and r, is the thickness of the web or angle leg.

7.3 SIZING OF STIFFENERS

The stringer properties are determined by equating the elastic design stresses for local buckling and bay instability and the ring properties are determined by equating the elastic design stresses for local buckling and general instability. This is equivalent to equating the buckling strains corresponding to Fic, and F i c ~ .

The equations for F*; and F&; are given in Section 6 for cylinders subjected to combined loads. For cylinders subjected to single loads F e , = Fxe; and Fee; = Frej. When the axial stress is tension, only the hoop stress equatlon must be checked. For this case let Fee, = Fm;.

a. Stringers

-

- F$e5 = F e ß I 1.2 L F ~ L (7-5)

Foe5 = Feeß I I .2 2 fee^ (7-6) -

b. Rings - F ~ C = F ~ G I 1.2 t F , ~ L (7-5) - FeeG = Feet I 1.2 2 fee^ (7-6)

The following general procedure may be used Tor determining the stiffener sizes:

1. Calculate the local shell buckling stresses F ~ L and fee^.

2. Assume a stringer size and calculate the bay instability stresses F ~ B and Fee0. Equations 7-5 and 7-6 must be satisfied. Repeat this step until the desired correlation is obtained. It may not be practical to have the same margins between local buckling and bay instability for both equations.

3. Repeat step 2 for ring stiffened cylindcrs by satisfying Equations 7-7 and 7-8.



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SECTION &COLUMN BUCKLING

The shell buckling stresses given by Equations 4-6, 4-7, and 4-25 for cylinders subjected to axial compression only, and by Equation 6-3 for cylinders subjected to axial compression combined with hoop compression do not include the effect of column buckling. The buckling stress of a tubular column is determined by substituting the shell buckling stresses, F*L, for the yield stress in the column buckling equation. Without external pressure F+. = Fxc,. The buckling stress of a tubular column is equal to the shell buckling stress for cylinders with &/r i 0.5 J-;. For longer columns the buckling stresses are given by the following equations. These equations are based on the premise that the stiffeners for stiffened cylinders are sized in accordance with the bulletin and only the local shell buckling mode is considered to interact with column buckling.

8.1 ELASTIC COLUMN BUCKLING STRESSES

where

CL,^ = 0.87

8.2 INELASTIC COLUMN BUCKLING STRESSES

FQK=

where

c,. =

For axial load only F+.L = where F\.(.L is given by Equations 4-6, 4-7, and 4-25. For axial load combined with external pressure, F ~ L is determined from Equation 6-3.



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SECTION SALLOWABLE STRESSES

The allowable stresses for short cylinders, &/r I 0.5 ,./mi, are determined by applying an appropriate factor of safety to the predicted buckling stresses given in Sections 4 and 6. Without external pressure F+. = F,,. The effects of imperfections due to out-of-roundness and out-of-straightness on the shell buckling stresses are very significant in the elastic range but have little effect in the yield and strain hardening ranges. Therefore a partial factor of safety, y, that is dependent upon the buckling stress is recommended. The value of y is 1.2 when the buckling stress is elastic and 1 .O when the buckling stress equals the yield stress. A linear variation is recommended between these limits. The equation for y is given below. A value of y = 1.0 may be used for axial tension stresses and for column buckling mode stresses.

FiCi I0 .55 F ,

y = 1.444 - 0 . 4 4 4 F i c j / F , . 0.55 F , < Fic, < F,. 1: F i , = F , (9- I )

- For longer cylinders, KL,/r > 0.5 A-., is subjected to axial compression, the cylinders will fail in the column buckling mode and the column buckling stresses are given by Fquation 8-2. An interaction equation is given in this section for long cylinders Subjected to bending in combination with axial compression. This same interaction equation can be used when the cylinder is also subjected to external pressure.

The allowable stresses F,,, Fb, and Fe are to be taken as the lowest values given for all modes of failure. If the stiffeners are sized in accordance with the method given in Section 7, only the local shell buckling mode need be considered in the equations which follow. The allowable stresses must be greater than the applied stresses which can be calculated using the equations given in Section 11 or by more exact methods using computer codes. The factor of safety, FS, is provided by the design specifications. In general, FS = 1.67 y is suggested for normal design conditions and FS = 1 . 2 5 ~ for extreme load conditions where a one-third increase in allowable stresses is appropriate.

9.1 ALLOWABLE STRESSES FOR SHELL

-

BUCKLING MODE

The following equations provide the allowable stresses for the local shell buckling mode. The same equations are applicable to other modes of failure by substituting the design

~ inelastic buckling stresses given in Equation 7-2 for those modes in the equations. The following equations should be

- satisfied for all loads. See Section 1 I fori,, fb, andfq.

LI + f b < fe < Fe

9.1.1 Axial Tension

F,. F , = - F , = O F S

9.1.2 Axial Compression or Bending

See Equations 4-6,4-7, and 4-25 for F X ( . ~ .

9.1.3 External Pressure

a. Radial Pressure Only (N,$Ne = O )

See Equation 4- 1 O for F r C ~ .

b. Hydrostatic Pressure (N,#Ne = 0.5)

(9-2

(9-3)

(9-4)

(9-5)

See Equation 4- 1 I for F l 1 ( . ~ .

9.1.4 Axial Tension and Hoop Compression and Axial Tension, Bending, and Hoop Compression

See Equations 6- 1 and 6-2 for [email protected] and Fec!,.

9.1.5 Axial Compression and Hoop Compression and Axial Compression, Bending, and Hoop Compression

See Equation 6-3 for F+.j and Fecj,

9.1.6 Bending and Hoop Compression

See Equation 6-3 for FQ(.L and FeCL. 29

(9-7)



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9.2 ALLOWABLE STRESSES FOR COLUMN a. Forf,,lF,, 5 O. I5 BUCKLING MODE

f, f h -+-<1.0 (9- 1 O) F , FI, When KLJr > 0.5 the following equations as

well as those in Section 9.1 must be satisfied:

9.2.1 Axial Compression b. ForJjF,, O. 15

See Equation 8-2 for F$,c.

(9- I I )

9.2.2 Axial Compression and Bending 9.2.3 Axial Compression, Bending, and Hoop

Members subjected to both axial compression and bending Compression

I stresses should satisfy Equations 9-10 and 9- 1 I . See Qua- Members subjected to combinations of axial compression, tions 9-9 for F,, and 9-3 for Fb and Paragraph 3.3. Id Member bending and hoop compression should satisfy Equations 9-10 Slenderness of API RP 2A (Ref. IO) for C,, and K . C, must and 9-1 1 with F,, determined from Equation 9-9 and Fb from be greater than or equal to 1 - f,/F',. Equation 9-7.



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SECTION 10”TOLERANCES

The foregoing rules are based upon the assumption that the cylinders will be fabricated within the following tolerances. The Commentary provides additional information on the buckling strength of cylinders which do not meet these tolerances. The requirements for out of roundness are from the ASME fressure Vessel Code ( 1 2) and the requirement for straightness is from the ECCS rules ( 1 3).

10.1 MAXIMUM DIFFERENCES IN CROSS- SECTIONAL DIAMETERS

The diRerence hetween the maximum and minimum diameters at any cross section should not exceed 1 % of the norni- na1 diameter at the cross section under consideration.

102 LOCAL DEVIATION FROM STRAIGHT LINE ALONG A MERIDIAN

Cylinders designed for axial compression should meet the following tolerances. The local deviation from a straight line measured along a meridian over a gauge length Lx should not exceed the maximum permissible deviation e.r.

10.3 LOCAL DEVIATION FROM TRUE CIRCLE

Cylinders designed for external pressure should meet the following tolerances. The local deviation from a true circle should not exceed the maximum permissible deviation obtained from Figure 10-1. Measurements are to be made with a gauge or template with the arc length obtained from Figure 10-2.

Additionally the difference between the actual radius to the shell at any point and the theoretical radius should not exceed 0.005R.

10.4 PLATE STIFFENERS

The lateral deviation of the free edge of a plate stiffener should not exceed 0.002 times the length of the stiffener. The length of a stringer stiffener is the distance between rings. The length of a ring stiffener is the distance between stringers when present, or nfUn where n is determined from Equation 4- 17. A conservative value for n is given by Equation 10-3.

II’ = 1.875 - f i t 2 4 R

( 10-3) L,,

L.r = 4 f i t but not greater than L,.



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32 API BULLETIN 2U

)(R 100 m 1op

IOD

Qo

* 100

110

100

m 10 m

a

m rg

50

26 om o 10 2 I 4 I 6 7 m n m

Boy Length+Outside Diameter, Lr/Oo

Figure 10.1-Maximum Possible Deviation efrom aTrue Circular Form

Bay Length; Outside Diameter Lr/Oo Figure 10.2-Maximum Arc Length for Determining Plus or Minus Deviation



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STD-APIIPETRO BULL ZU-ENGL 2000 m 0732290 Ob231b2 219 W

SECTION 11-STRESS CALCULATIONS

The computed stresses in stiffened cylindrical shells may differ from the membrane stress o f unstitrened shells. Equa- tions are given below for correction factors which account for the load sharing effects of the various stiffening elements.

11.3 HOOP STRESSES

The effects of the longitudinal stiffeners on the hoop stresses are neglected. The imperfection and plasticity factors given in Sections 4 and 5 are also based upon this assump tion. The external pressure, p . is assumed to be uniform over the cylinder.

a. Unstiffened and Stringer Stiffened Cylinder

11.1 AXIAL STRESSES

In Equations 1 1 - 1 and I 1-2, P is the total axial load including any pressure load on the end of the cylinder.

a. Unstiffened and Ring Stiffened Cylinders PR,, f e = f ( 1 1-5)

D

f' = 2KRr r

( 1 1 - 1 ) b. Ring Stiffened and Ring and Stringer Stiffened Cylinders h. Cylinders With Longitudinal Stiffeners. When the

stringers are not spaced sufficiently close to make the shell fully effective, the effective area is used to determine the axial and bending stresses. The factor Q,, is a ratio of the effective area to the actual area. Q,, = 1.0 for the local shell buckling mode. See Equations 4-32,4-35, and 4-58 for be.

I . Stress in Shell Midway Between Rings. This swess must be less than the allowable hoop stresses, Fe, for local shell buckling and bay instability.

( 1 1-6)

P f' = G, ( 1 1-3) where

for M, 2 3.42 K0L = { :*yey for M,<3.42

where ( 1 1-7)

Q - , ' E A + b t

u A,s+ bt E =

I - 0.3k 1 + L , r / A A , = 2ttRt + N,A,v

A =A, (R/R,J2

M,=L,I f i t

11.2 BENDING STRESSES

In Equations 1 1-3 and 1 1-4, M is the bending moment at the cross section under consideration.

a. Unstiffened and Ring Stiffened Cylinders M, I 1.26

M, < 3.42

M,, 2 3.42

for - 0.46M, for 1.26 <

for ( 1 1-3)

k = N d N e (see Section 6.1 for N+ and Ne)

R, = Radius to centroid of stiffening ring

Le = 1 S6 f i t + t,. I L,

2. Stress in a Ring Stiffener. This stress must be less than the allowable hoop stress, Fe, for general instability.

where

K , = 1 + 0 S t / R 1 + 0.25( r / R)?

The value of Kb is approximately I .O.

b. Cylinders with Longitudinal Stiffeners

See Equation 11-2 for definition of Q,,. ( 1 1-8)

M QJ R't,

f h = - ( 1 1-4) where

( 1 1-9) I L J K e , = ( 1 - 0 . 3 k ) - 2 0 A r + Let

- where

te = t + A,y /b and k and L, are the same as in Equation 1 1-7. 33



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SECTION 12-REFERENCES

1. Miller, C. D. Grove, R. B., and Vojta, J. F., “Design of Stiffened Cylinders for Offshore Structures,” American Weld- ing Society Welded Offshore Structures Conference, New Orleans, Louisiana, December 198’3.

2. Miller, C. D., “Experimental Study of the Buckling of Cylindrical Shells with Reinforced Openings,” ASMWANS Nuclear Engineering Conference, Portland, Oregon, July 1982.

3. Faulkner, D., Chen, Y. N. and deOliveira, J. G., “Limit State Design Criteria for Stiffened Cylinders of Offshore Structures,” ASME 4th National Congress of Pressure Vessels and Piping Technology, Portland, Oregon, June 1983.

4. Stephens, M., Kulak, G . and Montgomery, C., “Local Buckling of Thin-Walled Tubular Steel Members,” Third International Colloquium on Stability of Metal Structures, Toronto, Canada, May 1983.

5 . Sherman, D. R., “Flexural Tests of Fabricated Pipe Beams,” Third International Colloquium on Stability of Metal Structures, Toronto, Canada, May 1983.

6. Miller, C. D., Kinra, R. K. and Marlow, R. S., “Tension and Collapse Tests of Fabricated Steel Cylinders,” Paper W C 42 I 8, Offshore Technology Conference, May 1982.

7. American Institute of Steel Construction, “Manual of Steel Construction,” 8th Edition, 1981.

8. Wilson, W. M., “Tests of Steel Columns,” University of Illinois Engineering Experiment Station Bulletin, No. 292, 1937.

9. Chen, W. F. and Ross, D. A., “The Strength of Axially Loaded Tubular Columns,” Fritz Engineering Lab Report No. 393.8, Lehigh University, September 1978.

10. American Petroleum Institute, Recommended Practice for Planning, Designing, and Constructing Fixed Wshore Platforms, API RF’ 2A, Nineteenth Edition. August 1, 1 9 9 I .

1 1. American Petroleum Institute, Recotnrrlended Practice for Planning, Designing, and Constructing Fixed Wshorr Platfonns, API RP 2A, Twentieth Edition, July 1, 1993.

12. American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section VIII, Division I and 2 and Sec- tion III, Subsection NE, 1983.

13. European Convention for Constructional Steelwork, “European Recommendations for Steel Construction,” Sec- tion 4.6, Buckling of Shetls, Publication 29, Second Edition, 1983.



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STD*API/PETRO BULL ZU-ENGL

APPENDIX A-COMMENTARY

Table of Contents

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

C 1 . GENERAL PROVISIONS .............................................. 39 CI . 1 scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 C1.2 Limi~ations ...................................................... 39 (21.4 Material ........................................................ 39

C2 . GEOMETRIES. FAILURE MODES AND LOADS .......................... 39

C3 . BUCKLING DESIGN METHOD ........................................ 40

C4 . PREDICTED SHELL BUCKLING STRESSES FOR AXIAL LOAD. BENDING AND EXTERNAL PRESSURE .......................................... 41 C4.1 Local Buckling of Unstiffened or Ring Stiffened Cylinders . . . . . . . . . . . . . . . 41 C4.2 General Instability of Ring Stiffened Cylinders ......................... 54 C4.3 Local Buckling of Stringer Stiffened or Ring and Stringer Stiffened Cylinders 57 C4.4 Bay Instability of Stringer Stiffened or Ring and Stringer Stiffened Cylinders

and General Instability of Ring and Stringer Stiffened Cylinders Based Upon Orthotropic Shell Theory ........................................... 57

Cylinders-Alternate Method ....................................... 63 C4.5 Bay Instability of Stringer Stifiened and Ring and Stringer Stiffened

C5 . PLASTICITY REDUCTION FACTORS .................................. 65

C6 . PREDICTED SHELL BUCKLING STRESSES FOR COMBINED LOADS . . . . . . 65 C6.1 Axial Tension. Bending and Hoop Compression ........................ 65 C6.2 Axial Compression. Bending and Hoop Compression .................... 65

C7 . STIFFENER REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 C7.1 Design Shell Buckling Stresses ...................................... 69 C7.2 Local Stiffener Buckling ........................................... 69

C8 . COLUMN BUCKLING ................................................ 69

C9 . ALLOWABLE STRESSES ............................................. 80

C10.TOLERANCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 CIO . 1 Maximum Differences in Cross-section Diameters ..................... 80 C10.2 Local Deviation from Straight Line Along a Meridian . . . . . . . . . . . . . . . . . . . 80 C10.3 Local Deviation from True Circle ................................... 80 C10.4 Plate Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

C 1 1 . STRESS CALCULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 C1 1.2 Bending Stresses ................................................ 80 Cl 1.3 Hoop Stresses ................................................... 80

Cl 2 . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82



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APPENDIX A-COMMENTARY ON STABILITY DESIGN OF CYLINDRICAL SHELLS

Introduction

This commentary provides the designer with the basis for the design methods presented in Bulletin 2U. The design criteria are applicable to shells that are fabricated from steel plates where the plates are cold or hot formed and joined by welding. The stability criteria are based upon classical linear theory which has been reduced by capacity reduction factors and plasticity reduction factors which are determined from approximate lower-bound buckling values of test data of shells with initial imperfections which are representative of the tolerance limits given in Section 10 of the Bulletin.

The most commonly used rules for the design of cylinders for offshore structures in the United States are those given by the American Petroleum Institute, API RP 2A ( 1 ). These rules are limited, however, to unstiffened or ring stiffened cylinders and cones with diametedthickness ( D r ) ratios that are less than or equal to 300. The members of many of the new plat- form concepts for deep water exceed this limit. Also the effects of stiffening rings on the buckling strength is considered only for external pressure loading.

Det Norske Veritas (2) updated its criteria for buckling strength analysis in 1982. These criteria can be applied to unstifiened, ring stiffened, or ring and stringer stiffened cylinders having larger D/r values. Close stiffener spacing is emphasized and, in fact, for stringer spacing in excess of a moderate value (Me = 3.0) the stiffening effect of the stringers is neglected. These criteria formulate a characteristic stress for both local shell and bay instability (termed “panel buckling” by DNV). The characteristic stress is in terms of a buckling coefficient that DNV recommends be determined by a more refined analysis or model tests. In lieu of this, DNV provides empirical equations based upon approximate methods for calculating the buckling ccdlìcients. The calculated buckling strengths for stringer stiffened cylinders of Ref. 2 were found to be generally conservative, but also quite inconsistent with the various test results. The criteria given in Bulletin 2U provide more accurate predictions and a more complete description of the possible buckling modes.

The Bulletin follows closely the recommendations given in Ref. 4 I with some modifications based upon further analysis of available test data. The proposed criteria are also similar to those given by ASME Code Case N-284 (3) for design of containment vessels. Reference 41 includes modifications which were based upon several test programs conducted on fabricated cylinders after Ref. 3 was written. Reference 4 includes a comparison of the test data that was available before 1979 with the equations of Ref. 3. Much of the test data was from models that do not meet the definition of fabricated cylinders given in Section l . l of the bulletin. This com-

menlary contains comparisons of the predicted buckling stresses given by the Bulletin 2U equations with test data for fabricated cylinders only. Additional modifications are to be expected after the completion of two ongoing test programs. A test program is in progress to determine the effecls of external pressure on beam columns. The first phase which has been completed (Ref. 5) , was a series of 64 tests on short columns. The second phase will be tests on long columns with different lengths and is to be completed in 1987. Almost a l l of the tests on fabricated ring and stringer stiffened cylinders reported in Ref. 6 were made on stress relieved test models and the stringers did not meet the compact section requirements of Section 7. Additional tests are now in progress using test models with compact stiffeners that have not been stress relieved.

Cl General Provisions C1.l SCOPE

The present rules are limited to cylindrical shells.

Cl -2 LIMITATIONS

The minimum thickness of in. is quite arbitrary. Many tests have been performed on fabricated steel models with f = 0.075 in. These models requiltd very closely controlled fabrication and welding procedures to obtain the desired tolerances, however. Also, the thinner models are much more sensitive to nonuniform distribution of loads. The limit of R / r S l o 0 0 corresponds to the largest R/r ratio for a fabricated model test.

Cl .4 MATERIAL

The stability criteria are applicable to steels which have a well defined yield plateau such as those specified in Table 2.9.1 of API RP 2A or Table I l . 1. I of API RP 2T. Most of the materials used for model tests had minimum specified yield strengths of 36 or 50 ksi. A few additional models have been made from steels with 80 to 1 0 0 ksi yield strengths.

C2 Geometries, Failure Modes and Loads The geometric proportions of a tubular member will vary

widely depending on the application. The load carlying capacity is determined by the shell buckling strength for short members with KL, /r less than about 12. For longer members the strength of the member is also dependent upon the column buckling strength.

The shell buckling strength is a function of both the geometry and the type of load or load combination. Unstiffened



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shells fail by local shell buckling. The failure stress will be less than the yield stress for Wt values greater than about 30 for members subjected to axial compression and for Rh values greater than about IO for members subjected to external pressure. The post buckling strength is very low for unstiffened shells and may be as low as 20% or less of the prebuck- ling strength.

The axial compression buckling stress can be increased by the addition of stringers (longitudinal stiffeners). The stringers carry part of the load as well as increase the local shell buckling stress. They must be placed less than about I O f i apart to be effective for axial compression. The stringer spacing must be less than one half the wave length determined for a shell without stringers to bc effective in increasing the failure stress for external pressure. The use of stringers introduces two more possible modes of failure. The stringer elements must be compact sections (see Section 7) or local buckling of the stringers may occur. Another possible mode of failure is the buckling of the stringers and shell plating together. This mode of failure is termed bay instability and the failure stress is mainly a function of the moment of inertia of the stringers and attached shell. Waves form in both the longitudinal and circumferential directions for axial compression loads. A single half wave forms in the longitudinal direction and several waves form in the circumferential direction for external pressure. If the bay instability stress is greater than the local shell buckling stress, the cylinder will continue to cmy load after local shell buckling occurs. If there is only a small difference, local shell buckling will probably initiate the bay instability mode. Bulletin 2U recommends that the shell be designed so that the bay instability stress is 1.2 times the local shell buckling stress.

Ring stiffeners are much more effective than stringers in increasing the buckling stress of a cylinder subjected to external pressure. The buckling stress is increased for values of U R < 2.85 f i r . For greater distances between rings the buckling pressure is the same as that of an unstiffened cylinder. The use of rings introduces two more possible modes of failure. One mode is local buckling of the ring elements which can be avoided by the use of compact sections. The other mode of failure is the buckling of one or more rings together with the shell (and stringers when used). This mode of failure is called general instability and the failure stress is a function of the moment of inertia of the ring together with an effective width of shell. This mode of failure should be avoided because it results in gross distortions of the shell. Local shell buckling may precipitate a general instability failure if there is only a small difference in the buckling stresses for the two modes. The bulletin recommends that the shell be designed so that the general instability stress is 1.2 times greater than the local buckling stress for both ring stiffened cylinders and ring and stringer stiffened cylinders. These provisions do not provide a margin between the bay

and general instability modes. This is left to the discretion of the designer. The factor 1.2 provides sufficient margin so that local buckling should always be the initial mode of failure.

A stringer stiffened cylinder may continuc to carry load after the shell has buckled locally between stringers until failure occurs by bay instability. This mode of failure when due to external pressure or external pressure combined with axial compression results in the postbuckling formation of a series of longitudinal plastic hinges between stringers at locations around the circumference where the circumferential waves are radially outward. The formation of hinges may also occur in the rings due to local buckling of the ring elements. Under axial compression load the mode of failure is a joint collapse of stringers and shell. The post buckling load may be as much as 80% of the collapse load for either axial compression or external pressure if the plastic hinges do not develop in the rings.

Column buckling is buckling of the cylinder as a column. A tubular column can be treated similar to other types of columns by substituting the shell buckling stress for the yield stress in the column buckling equation. If the recommendations of the Bulletin are followed, the local shell buckling stress will always be the lowest shell buckling stress value and will be used in place of the yield stress in the column buckling equations.

C3 Buckling Design Method The design of cylinders for compressive loads is an itera-

tive procedure. The steps to follow are given in a flow chart in Figure 3.1. The first step in the design process is to assume a shell geometry and calculate the applied stresses with the aid of the equations in Section 1 1. The next step is to calculate the local shell buckling stresses from Section 4 for individual load cases and Section 6 for combined load cases. Equations for column buckling stresses are given in Section 8. The allowable stresses can then be determined from Section 9. The shell geometry can be adjusted to give the desired agreement between applied and allowable stresses.

The next step is to determine the stiffener sizes if rings and/ or stringers are used. The stiffener elements should satisfy the requirements of Section 7.3. The flow chart in Figure 3.1 shows that when stiffeners are used the bay instability and general instability stresses are determined from Sections 4 and 6. As discussed in Section C2 it is desirable to have the failure stresses for bay instability greater than the local buckling stresses and the general instability stresses higher than the bay instability stresses. This procedure will prevent one mode of failure from initiating another mode of failure. The separation of the local buckling mode from the bay or general instability modes is accomplished with the factor ß given in Section 7. The separation of' the bay and general instability modes is left to the discretion of the designer.



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C4 Predicted Shell Buckling Stresses for Axial Load, Bending and External Pressure

The theoretical elastic buckling stress equations given in the Bulletin are based upon classical theory with simple sup- porl boundary conditions and Poisson's ratio of 0.3. The differences between tests on fabricated cylindrical shells and the theoretical stresses are accounted for by the factor au. This factor is equivalent to the ratio of the strain in a fabricated cylinder under load to the strain in the tensile coupon from which the material properties are determined. The values of ao apply to cylinders with initial shapes which meet the fabrication tolerances of Section 10. Design guidance is also given in the commentary for cylinders which do not meet the tolerances of the Bulletin.

C4.1 LOCAL BUCKLING OF UNSTIFFENED OR RING STIFFENED CYLINDERS

The buckling strength of a section of shell between ring stiffeners is assumed to be the same as an unstiffened shell.

C4.1.1 Axial Compression or Bending

- Equation 4-2 was determined from Equation 1 1-8, p. 465 of Ref. 7. The minimum stress is found by letting n = O and m = 1. This equation is given below using the nomenclature of Bulletin 2U.

where

h =

rn =

Il =

rnnR - L '

number of half waves in the longitudinal direction at buckling,

number of circumferential waves at buckling.

An analysis of axial compression and bending tests of unstiffened cylinders is given in Ref. 8. Equation 4-4 is taken from this reference. Similarly, an analysis of axial compression tests on ring stiffened cylinders is given in Ref. 9. Equa- tions 4-5 and 4-7 are taken from this reference.

Equations 4-6 and 4-7 are plotted for yield stresses of 36, 50, and 60 ksi in Figure C4. I . 1-1. This figure shows that rings are ineffective for R/t < 200 when Fy = 60 ksi and for R/t < 320 of Fy = 36 ksi. Test data is compared with Equa- tion 4-2 in Figure C4. l . 1-2 for unstiffened cylinders which failed elastically and with Equation 4-7 in Figures C4.1.I-3

to C4.1.1-5 for unstiffened cylinders which failed inelasti- cally. There is only one bending test shown on Figure C4. l . 1-2 and two bending tests shown on Figure C4. I . 1-3. Since these tests fall within the scatter band of the axial compression tests, Equations 4-2 and 4-7 are used for cylinders subjected to either axial compression or bending. The failure stresses for axially compressed cylinders reach a plateau equal to the yield stress at a ?/R ratio of 0.015 whereas the failure stresses for bending reach a plateau of about 1.08 Fy and as the ratio Et/F,R increases the failure stresses increase to values corresponding to the plastic moments.

Comparisons are made between the test and predicted stresses for ring stiffened cylinders in Figures C4.1.1-6 to C4.1 .I-IO. The transition between stiffened and unstiffened cylinders is difficult to detine because of lack of test data. The ring stiffened cylinder tests are limited to L/&r I 6 except for one set of tests. All of these tests indicate that the failure stress for LI f i t = 4 is approximately the same as that for L l G r = 6. Therefore, the test stresses at L/&t = 6 should be the same as an unstiffened cylinder. This is not the case, however. The unstiffened cylinder test stresses are approximately */3 of the test stresses for a ring spacing of LIfif = 6. The unstiffened cylinder tests were conducted at the University of Illinois i n 1933 (IO). The failure stresses may bc low because the ends of the cylinders were neither machined nor welded to a bearing plate. Shims were used to f i l l gaps between the specimens and the testing machine. All of the cylinders with large R / r values were made from thin sheet material, '/32 in. thickness. The thin material made the models quite sensitive to nonuniform bearing. New tests are needed to resolve the questions raised.

C4.1.2 External Pressure

Equation 4-9 is determined from Equation 4-27 (See 4.3.2). This equation is very accurate for all values of k I I .O where k = NJNo. A nondimensionalized plot of Equation 4-9 is given on Figures C4.1.2- 1 and C4.1.2-2.

An evaluation of tests on unstiffened and ring stiffened cylinders subjected to external pressure is given in Ref. I l . A constant value of = 0.8 is recommended for cylinders which meet the fabrication tolerances of Section IO. For cylinders with Rh ratios less than about 60 the following equation was found to give a lower bound on test data for cylinders which exceeded the specified tolerance for y.

a,, = 1 - 0 . 2 h



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42 API BULLETIN 2U



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49 STABILITY DESIGN OF CYLINDRICAL SHELLS



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A

Figure C4.1.2-1-Theoretical Local Buckling Pressure of Unstiffened or Ring Stiffened Cylinders



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Y

Figure C4.1.2-2-Theoretical Local Buckling Pressure and Number of Circumferential Waves for Unstiffened or Ring Stiffened Cylinders



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54 API BULLETIN 2U

where D,,,,,,, Dlnirr, and D,,,,,, are the maximum, minimum and nominal outside diameters at the cross-section which gives the largest value for y. See Figure C4.1.2-3. Compari- sons are made between the test and predicted stresses in Fig- ure C4.1.2-4.

Theoretical methods have been developed by several authors to account for the effects of imperfections. All of these methods are based upon the assumption that the initial out-of-roundness is similar in form to the assumed buckling mode shape. The bending stresses resulting from the initial out-of-roundness are combined with the membrane stresses. The buckling pressure is determined by equating the combined hoop stress to the yield stress or by the von Mises failure theory. Reference I 1 gives a comparison of test pressures to those predicted by the methods of Timoshenko & Gere (7), Galletly and Bart ( 1 2), and Sturm (13). The correlation between these theories and test results is very poor and the methods are much too conservative to be practical for use. The ratios ofpTe~&Theory varied from I .93 to 3.25 for the theory of Timoshenko and Gere and from 1.40 to 2.82 for the other two theories.

Millcr and Grove (14) have found an alternate method which provides excellent correlation for cylinders of all geometries. The theoly behind the method is that a flat spot on the shell having a larger than nominal radius of curvature will buckle at a lower pressure. Also, it was noted from experimental results that an imperfect shell will buckle in the same or nearly the same number of waves as a shell without imperfections. To determine the local buckling pressure, the local radius measured over half of a theoretical wave length is substituted for the nominal radius in the theoretical shell equation. The buckling pressure is taken as the minimum pressure given by either n or n + 1 where n is the theoretical wave number for the shell without imperfections.

Since the local shell imperfections are measured over a half wave length, the gage angle, 20, is equal to R h radians (0 = 7d2n). The local radius, RL, can be computed by know- ing the versine, m , and the half chord, c, col-responding to the versine.

A comparison of test results with the proposed method was made for 30 cylinders in Ref. 14 and the average of PThenry was I .O07 with a convergence of 13.2%). Tests include elastic and elastic-plastic values with Rh ratios from 14 to 500 and yield stresses of 3 1 .O to 6 I .7 ksi.

C4.2 GENERAL INSTABILITY OF RING STIFFENED CYLINDERS


Equation 4-13 was determined from Equation 29 of Ref. 15 for U = O. An analysis of available test data is given in Ref. 16 and Equation 4-14 is based upon this study. The imperfection factor a , ~ is a constant when the area of the stiffener exceeds 20% of the shell area. It is equal to an unstiffened cylinder when the stiffener area is zero. A straight line variation is assumed between these two limits. Additionally, it is recommended that the minimum area of the stiffener must equal 6% of the shell area for it to be effective. Test data is compared with Equation 4-14 in Figure C4.2. I - I .


The equation for external pressure is based upon the split rigidity principle where the first term is the contribution of the shell of length bctwccn bulkheads and the second term is the contribution of the effective ring section. The shell contribution is taken from Equation 4-27. Only the second term of this equation is used since the first term has little contribution if included. The second term of Equation 4-1 1 is the buckling pressure for a ring under uniform load which is given by Equation d, p. 289, of Ref. 7.

A comparison of test data with Equation 4-17 was made in Ref. I 1 . A constant value of CXOG = 0.8 is recommended for cylinders which meet the fabrication tolerances of Sec- tion IO. For cylinders with R/? ratios less than about 60, the following equation was found to give a lower bound on test data for cylinders which exceed the specified tolerance for y.

sec = 0.96 - 0 . 2 ~ for y 5 3

The above equation is compared with test data in Figure C4. I .2-3 and Equation 4- 16 is compared with test data in Fig- ure C4. I .2-4. There is no test data in the inelastic region for general instability failures.

Theoretical methods have been developed for predicting the effect of out-of-roundness on the general instability pressure. The test results are compared with the methods of Sturm ( I 3), Kendrick ( I 7), Hom ( 1 8) and Griernann (19) in Ref. 11. The closest correlation for instability is given by Griemann with the ratios ~ f p ~ ~ , ~ j p ~ j , ~ ~ ) ~ ~ ranging from 0.58 to 0.77 compared with 1.16 to 2.55 for Sturm. The theories of Kendrick and Hom gave ratios as high as 2.73 and 3.30. A later comparison was made with Kendrick's elasto-plastic theory (see Ref. 20, p. 637). This method gave ratios of 2.43 to 6.23.



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STD.API/PETRO BULL ZU-ENGL 2000 0732270 Ob23183 743 m

STA6lLlTY DESIGN OF CYLINDRICAL SHELLS 57

C4.3 LOCAL BUCKLING OF STRINGER STIFFENED OR RING AND STRINGER STIFFENED CYLINDERS


Equation 4-23 is a modification of Equation 1 1-14, p. 487 of Ref. 7. This equation is given below using the nomenclature of Bulletin 2U.

(C4.3.1-1)

where M0 = b l f i t . The first term has been reduced by a factor of 0.9 and was introduced in the second term to account for impelfections. When the panel width is realer than two times the panel length (b > 2L) orb > 3.46 Je Rt , the buckling stress is the same as a complete cylinder. For smaller values of b the panel will subdivide during buckling into squares with one half wave in the hoop direction (n = 1) and L/& half waves in the axial direction (m = L b ) .

The local shell buckling stress is based upon the assumption that the stringers meet the requirements of Section 7.2. If these requirements are not met, the local buckling stress of the stringers given by Equation C7-I should be used in place of the yield stress for determining 11.

The test data for local buckling is very limited. There is insufficient data to accurately define the transition between a stiffened panel and an unstiffened panel. The maximum value of M0 is 6 for test models which failed elastically. The buckling stresses at this stringer spacing are still significantly higher than those of an unstiffened cylinder. The same obser- vation was made for ring stiffened cylinders under axial load (See C4. l . 1 ). This further suggests that the buckling stresses for unstiffened cylinders should be higher than those given by the equations in the Bulletin. The stringers are assumed to be ineffective for Me > I5 and a linear transition is used for Me values between 3.46 and 15. For smaller values of Me the shell buckling stresses are about the same as for a flat plate. The test data is compared with Equations 4-22 and 4-25 using the yield stress of the plate material in Figures C4.3.1-1 and 2. The stringers for many of the cylinders did not meet the compact section requirements of Section 7.2. The test data is replotted in Figure C4.3.1-3 using the stress from Equation C7- 1 as the yield stress.


The local buckling pressure of a stringer stiffened cylinder can be determined from the same equation as a ring stiffened

cylinder when the minimum value for I I is based upon one- half the buckle wave length between stringers (!I = N,&! where N,T equals the number of stringers). The value of I I for an unstiffened cylinder can be readily determined from Fig- ure C4.3.2- 1. The stringers are inepective when N,J2 is less than n for a cylinder without stringers.

Equation 4-27 is a simplified equation which gives nearly identical results for radial pressure ( k = O ) and hydrostatic pressure ( k = 0.5) as the more exact equations of Sturm ( 1 3) and von Mises (Equations 1 and 6 of Ref. 2 1 ). This equation has also been compared with the theoretical equation for buckling of a cylinder under combined axial compression and hoop compression (Equation d, p. 496 of Ref. 7). The agreement is excellent for values of k I 1 .

An analysis of available test data is given in Ref. 14. A comparison of test results with the theoretical predictions indicates that impelfections permitted by the Bulletin do not significantly affect the huckling capacities of stringer stiffened cylinders subjected to external pressure. The reason may be that the stringers essentially tix the nominal radius and the membrane stress is a function of the nominal radius, not the local radius. ln comparison, the buckling pressures and stresses of ring stiffened cylinders are best predicted using the measured local radius.

For a shell without stringers, the shell is free to deflect and rotate at points of inflection of the buckle waves. This pro- duces a buckle pattern with a uniform in-out pattern. Stringer stiffened cylinders provide restraint in the radial direction and some restraint against rotation, depending on the torsional stiffness of the stringers. The buckle wave may vary between a half and a full wave between stringers. The shell panels which buckle inward are much more pronounced than those that buckle outward.

C4.4 BAY INSTABILITY OF STRINGER STIFFENED OR RING AND STRINGER STIFFENED CYLINDERS AND GENERAL INSTABILITY OF RING AND STRINGER STIFFENED CYLINDERS BASED UPON ORTHOTROPIC SHELLTHEORY

Equation 4-31 is a modification of the equation given in Ref. 22 for simply supported ollhotropic shells i n which the effective membrane thickness i n the longitudinal direction is equal to the area per unit length of shell and the bending rigidity is based upon the effective moment of inellia per unit length of shell. This equation has been modified so that it also applies to stiffened shells with stringers that arc not spaced close enough to make the shell plate fully effcctivc. This effect is accounted for in the rigidity parameters (E.r, EO, DX, De and D a ) of Equation 4-3 1 by introducing the ratios of bdb and L,/L,. When both ratios equal 1 .O the rigidity factors are the same as those givcn in Ref. 23, p. 306, for a stiffened shell with the plate fully effective. When both ratios equal z.ero, the



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STABILIW DESIGN OF CYLINDRICAL SHELLS 59



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62 API BULLETIN 2U

rigidity factors are the same as those given in Ref. 23, p. 303, for a gridwork shell. The equations for the rigidity parameters are given below. The first term in each equation is the Bulletin nomenclature, and the second term is Ref. 23 nomenclature.

a. Stii'fened Shell-Plate Fully Effective

E t E A , E , = D - , + - G,, = D,,+ = -- Et Cr $-G- L, 2 ( 1 + v ) -

~~3 E I , EA,.Z: D , = K -

- 12(1 -v2) L , +-+-

L,

b. Gridwork Shell

(Itr and I',, are moment of inertia about the weak axis of the stiffeners.)

G J , GJ b L,

D, , = K.,$ + K = - + -r

The bay instability modc is determined by letting the length of the cylinder equal the ring spacing. The general instability mode is determined by letting the length of cylin-

der equal the overall length. Local buckling of the stiffener elements is not accounted for in Equation 4-3 l . Although several methods for predicting the effects of local stiffener buckling have been investigated, further study is deemed necessary. The present recommendation is to substitute the buckling stress given by Equation C7-I for the yield stress.

An analysis of approximately 300 tests from data published prior to 1977 is contained in Ref. 24. Local buckling of stiffeners occurred on only a few models. The applied loads were either axial compression or bending moment. A large lest program (6) was conducted by CBI Industries in I983 on ring and stringer stiffened cylinders subjected to combinations of axial compression and external pressure. The fabrication methods and materials used for the test models were representative of offshore structures. The R/t values were 190, 300 and 500 and the material was hot rolled steel sheets with ield stresses of 50 to 80 ksi. The stringer spacings were b l / Rt o f 2 . 2 , 3 , and (i. The test results are analyzed and compared with Equation 4-31 in Ref. 14.

Many of the models had stiffeners which did not satisfy the compact section requirements of Section 7.2. For the analysis of these models an effective yield stress was substituted for the actual yield stress. The effective yield stress is used for all failure modes. The effective yield stress was taken as the buckling stress of a bar stiffener determined from the AlSI Cold Formed Steel Design Manual (25). The buckling stress was assumed to be 1.67 times the allowable stress given in Equation 3.2-2 of Ref. 25 (see Equation C7- I) .


When the study of Ref. 24 was made, a factor of 1.7 rather than 1.9 was used in Equation 4-32 for 6, and 0.9 rather than 1.0 in Equation 4-35. The plasticity factors were determined from Equation 5-3. The correct mode of failure was predicted for almost all models. The higher factor of 0.9 is based upon the tests reported in Ref. 14.

a. Bay Instability A majority of the test models in Ref. 24 were one bay long

(stringers only) while all the models of Ref. I4 were 3 bays long with the end bays 0.7 times the length of the center bay. The one bay models failed at values of 0.8 to 2.5 times the predicted values. This wide range is attributed to the effects of end fixity. Reference 24 included a group of tests on models with multiple bays subjected to bending moments. The shells were not fully effective (6, < 6). The test stresses were 0.9 to 2 . I times the stresses given by Equation 4-34 (with changes noted in Par. 1 ) . Most of the tests in Ref. 14 were made on stress relieved models. Additional tests are now in progress on nonstress relieved models.

b. General Instability None of the tests in Ref. 14 failed in the general instability

mode. There were two groups of tests in Ref. 24 which failed



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STD.API/PETRO BULL ZU-ENGL 2000 m 0732290 Ob23189 3bL

sTAElLlTY DESIGN OF CYLINDRICAL SHELLS 63

by general instability. The cylinders subjected to axial load failed at stresses 1 .O to 1.3 times the values given by Equation 4-37 (with changes noted in Par. I ) and the cylinders sub- jecled to bending moment failed at 0.8 to 1.3 times the predicted values.


External pressure tests have been conducted on ring and stringer stiffened cylinders with pressure loadings corresponding to k = O. 0.5 and 1.8 where k = NJNe. The results of these tests were analyzed i n Ref. 14.

a. Bay Instability The bay instability stresses given by the equations in Sec-

tion 4.4 require that the minimum number of stringers must be about 3 times the number of circumferential waves for this mode. Several of the test models did not satisfy this requirement. For these models the buckling stresses are predicted by the bay instability formulations of Section 4.5.

If the local shell buckling stress is significantly less than the bay instability stress the accuracy of Equation 4-31 decreases. This equation has been found to provide good correlation for stringer stiffened shells when the bay instability stresses do not exceed 1.5 times the local shell buckling stresses. A ratio of I .2 is recommended. This corresponds to the value of ß recommended for Equation 7- I .

h. General Instability One test (Ref. 40) has been conducted where the cylinder

failed by general instability when subjected to external pressure. The rules suggest that the general instability stresses should be I .2 times the local shell buckling stresses (ß = 1.2). This can be accomplished with little additional material in the rings because the general instability stress is a function of the moment of inertia of the effective ring section. The irnperfec- tion factor for ring stiffened cylinders is also recommended for ring and stringer stiffened cylinders.

C4.5 BAY INSTABILITY OF STRINGER STIFFENED AND RING AND STRINGER STIFFENED CYLINDERS-ALTERNATE METHOD

The buckling stresses given by the equations in Section 4.4 are based on small deformation theory. The strains at which buckling occurs are typically less than the yield strain.

When stringer stiffeners are used on a cylinder, local buckling of the shell plate between stiffeners may occur without

precipitating a collapse of the cylinder. If the local shell buckling stress is significantly less than the bay instability stress the modified orthotropic shell equation (Equation 4-31) becomes increasingly less accurate as the difference becomes greater. A ratio of bay instability stress to local shell buckling stress of I .2 is recommended. Also, Equation 4-31 is not applicable to stiffened shells with less than about three stringers for each wave length in the bay instability mode.

An alternate method is given in Ref. 28 for those cases where the orthotropic shell equation should not be used. Equations were derived hased upon the formation of a collapse mechanism. The equations of Section 4.5 for axial compression are taken from Ref. 28. An error in the formulations has been corrected.


The failure load given by Equation 4-59 was developed by Faulkner, Chen and de Oliveira (28) . A discrete stiffener-shell approach was used for determining the elastic collapse load and the inelastic collapse load was then determined by using the Ostenfeld-Bleich equation. Specific values were assumed for factors such as the shell shape reduction and bias factors. The values for coefficient c in Equation 4-53 are subject to further review. The authors of Ref. 28 also suggest c = 3.0 for light fillets and c = O for stress relieved shells. The method of Section 4.5.1, although highly empirical, provides the best correspondence between test and predicted loads of any of the methods that have been studied.

A much simpler alternate method has been developed by the ECCS Committee on Buckling of Shells for Ref. 37. This method is being studied as an alternative to the equations in Section 4.5. I .


The formulations for bay instability under external pressure are taken from Ref. 41. The external pressure load for bay failure is assumed to be made up of two components similar to Equation 4-17 for ring stiffened cylinders. The first term in Equation 4-60 is the buckling capacity of a cylinder with the stringers removed and the length equal to the ring spacing. The second term is the pressure that will develop through the formation of plastic hinges in the composite stiffener and shell. This total is then modified by an effective pressure correction factor, K,,, determined from tests. Equa- tion 4-60 is compared with test data in Fig. C4.5.2- l .



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STAElLlW DESIGN OF CYLINDRICAL SHELLS 65

C5 Plasticity Reduction Factors The elastic buckling stress of a fabricated cylinder, FjCj is

the product of the elastic buckling stress for a perfect shell and the capacity reduction factor ao, which accounts for the differences in geometry and boundary conditions between the fabricated shell and a perfect shell. The factor a~ can also be considered to be the ratio of the strain in a tensile coupon used to determine the material properties and the strain in the fabricated cylinder under applied load. When Fi,j exceeds the elastic limit of the shell material after fabrication, the buckling stress is given by FjC, which is the product of the elastic shell buckling stress and the plasticity reduction factor, q.

Many formulations for q have been determined theorcti- cally for various load conditions (Ref. 26). For fabricated cylinders the differences in for different load conditions are found to be less significant than the effects of residual stresses on r(. The following simple expression is found to give good agreement with test results (Ref. 27).

(C5- 1 )

To apply this equation requires that E, be determined from a stress strain curve which includes the effects of the residual stresses due to fabrication. Also the strain at which E, is determined must correspond to the strain of the fabricated shell. The factor A in Equation 5-3 is the ratio of the strain in a fabricated cylinder to the yield strain. The application of Equa- tion C5- l is described in Ref. 27.

A more direct approach is given in the Bullctin. Equation 5-3 was obtained directly from test data for nonstress relieved cylinders. Most of the ring and stringer stiffened models have received post weld heat treatment prior to testing. Equation C5-2 was obtained from test data for stress relieved cylinders.

II if A 20.67

if 0.67 < A < 4.17 ((3-2) 1 + 2.29A

i f A24.17

Equations 5-3 and C5-2 are only applicable to steel materials with well defned yield stress plateaus. Equation C5-2 applies to cylinders that have received post-weld heat treatment. Some residual stress remains in a shell after post weld heat treatment because the shell is plastically deformed in the fabrication process.

One test program was recently completed and another is in progress which will provide additional data for better defining the plasticity factors for cylinders without post weld heat treatment. Figure C5-I shows a comparison of Equations 5-3 and CS-2 with equations used by DNV and ECCS and an equation suggested by J. P. Kenny (43).

C6 Predicted Shell Buckling Stresses for Combined Loads

The tests in Ref. 29 indicate that the buckling stresses for cylinders subjected to bending are approximately the same as for cylinders under axial compression for Rh values greater than 150. Other tests (30) showed that for cylinders wilh Wf values less than 48 the buckling stresses for bending are higher. Since there are no bending test results on fabricated cylinders for the R/t range between 48 and 150 it is rccom- mended that the axial cornpression allowable he used for bending stresses for all R/r values greater than 48.

C6.1 AXIALTENSION, BENDING AND HOOP COMPRESSION

The theoretical elastic buckling equation for a cylinder subjected to combinations of axial tension and hoop compression indicates that it is safe to assume no interaction for elastic buckling ( S e e Figure 1 1-22 of Ref. 7). However. Ref. 31 shows that interaction must be considered for buckling stresses in the elastic as well as the inelastic range. Equation 6-1 was shown to he a lower bound on test data for buckling stresses not limited by the stress intensity.

The stress intensity was found to be limited by the Hencky- von Mises distortion energy theory for all but a few tests. However, the more conservative maximum shear S~IXSS the- 01y given by Equation 6-2 is recommended for design.

The failure stresses are thc lower of the values determined from Equations 6-1 and 6-2. Test data is compared with the interaction curves in Figures C6. I - I and C6.I-2. Also shown are the Hencky-von Mises C U I V ~ laheled p = 0.5 and a modification labeled p = 0.75 which has merit as an alternate to Equation 6-2. The curve labeled API is the interaction curve given in API RP 2A ( 1 ) and is the same as Equation 6-3 with C = 1.5, FxCj = F, and FKj = F/,(? This equation is less conservative than Hencky-von Mises for cylinders with values of F,,c. approaching Fy and values offr exceeding 0.5 F,, as shown in Fig. C6.1- 1 (a).

C6.2 AXIAL COMPRESSION, BENDING AND HOOP COMPRESSION

Probably the greatest differences in the various recommended rules for shell buckling are the interaction equations for cylinders subjected to combinations of axial compression and external pressure. Seven different recommendations are discussed in Ref. 27. Equation 6-3 is based upon a method proposed by Miller and Grove (42).

The interaction equation for combinations of axial compression and hoop compression is a modification of the Hencky-von Mises failure theory. Equation 6-3 is identical to this theory when c = 1.0. Test data was found to conform quite closely to the interaction curves obtained by varying the value for c. The value of c was found to vary with FrC,/Fy and



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Figure 6.1-l-Cornparison of Test Data from Fabricated Cylinders Under Combined Axial Tension and Hoop Compression with Interaction Curves (Fy = 36 ksi)



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fe 'Fye (b) Group 7

3 0 o 1980 TESTS o 1981 TESTS

Figure 6.1-2-Comparison of Test Data from Fabricated Cylinders Under Combined Axial Tension and Hoop Compression with Interaction Curves (F, = 50 ksi)



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Fn/FY where Fx,:, is the failure stress for axial compression only and Fm, is the failure stress for hoop compression only. When both Fm; and Fm; equal F, c = 1.0. The values for c decrease with decreasing values of Frc, and Fm; and Equation 6-3 becomes a straight line for c = -2.0. The values for c were found to be less for stringer stiffened cylinders than for unstiffened and ring stiffened cylinders.

The equation for c for ring stiffened and unstiffened cylinders is given by Equation 6 - 4 . This equation is similar to the equation in Ref. 42. Equations 6-5 and 6-6 were determined from test data for stringer stiffened cylinders. Comparisons of Equation 6-3 with test data are shown in Figures C6.2-I to C6.2-7.

C7 Stiffener Requirements C7.1 DESIGN SHELL BUCKLING STRESSES

A factor ß has been added to the shell buckling stress equations to provide a convenient method for separating the local buckling mode from the bay and general instability modes of failure. The factor is applied to the failure strain rather than the failure stress. For elastic buckling the design shell buckling stresses are inversely proportional to ß whereas for inelastic buckling the ratio of F;c.Fi(j is less than ß. A plot of Fic.Fy vs. (Fie#ß)IF,. is given in Figure C7.1-l. The upper curve with ß = 1 .O corresponds to the shell buckling stress equations and the lower curve defines the design shell buckling stresses for the bay and general instability modes of failure.

C7.2 LOCAL STIFFENER BUCKLING

The recommended buckling criteria require that the stiffeners be adequately proportioned so that local instability of the stiffeners is prevented. The requirements of Equations 7-3 and 7-4 will preclude this mode of failure for the most generally used stiffener configurations. These requirements are the same as those specified by AISI (25) for fully effective sections. For other configurations, the AISI or other guidelines must be consulted. Equation 7-3 was determined from AISI Equation 3.2- 1 and Equation 7-4 from AISI Equation 2.3. I - 1.

The buckling stresses of bar stiffeners which do not meet the compact section requirements are assumed to be 1.67 times the allowable stresses given by AISI Equation 3.2-2 which follows:

Fxc. = ( 1.28 - 0.75h,J Fy for 0.375 < h,? < 0.846 (C7- 1 )

h+& h F,. t ,

When stringer stiffeners are noncompact sections the failure stress from Equation C7-I should be substituted for the yield stress when determining the local shell buckling stresses for axial compression or bending and the bay instability stresses for all load conditions. When ring stiffeners are non-

compact sections the failure stress fmm Equation C7-1 should be substituted for the yield stress when determining the general instability stress for all load conditions.

C8 Column Buckling The buckling stress in the axial direction may be less than

the shell buckling stress due to column buckling. The column buckling stress is determined by substituting the shell buckling stress for the yield stress in the column buckling equation. The AISC (33) and AlSI (25) specifications use the CRC Column-Strength Curve. This cquation can be moditied to account for column and shell buckling interaction by substituting the shell buckling stress F@. for the yield stress. The buckling stress for a tubular column, F*.(:, is given by:

(C8-

The shell buckling stress F+, should be taken as the lowest stress for all possible modes of failure. This will always be the local shell buckling stress if the Bulletin rules are followed. The elastic column buckling stress, F*c, is given by the following equation:

(C8-3)

where KL, is the effective column length and r is the radius of gyration.

The test results on fabricated tubular columns from Refs. 34 and 35 were compared with Equation C8-1 in Ref. 8 and several test points were found to be less than the predicted value. Equation 8-2 of the Bulletin which was taken from Ref. 8 is based upon a lower bound of test data. The comparison of test data with Equation 8-2 is shown in Figure CS-l. There is no data from fabricated cylinders in the elastic region. A reduction factor of 0.87 is assumed. The AISC Specification (33) gives an allowable stress of 0.522 times the Euler buckling stress. The factor 0.87 is equal to 1.67 x 0.522.

The differences between test results and the predicted values when Fkc is determined from Equation C8-I arc par- tially compensated for in the AlSC specification by using a variable factor of safety whereas a constant factor of safety can be used with Equation 8-2. Also Equation 8-2 reflects that no reduction in buckling stress occurs due to overall length for short columns (KL,/r < 0.5 Comparisons of the column buckling curves given by the Bulletin, CRC Column- Strength Curve, and AlSC are shown in Figure C8-2. The buckling stress curve for AISC is equal to 1.6676, where F,, is Lhe allowable stress.



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Figure 6.2-1-Comparison of Test Data with Interaction Equation for Unstiffened Cylinders Under Combined Axial Compression and Hoop Compression



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STDDAPIIPETRO BULL ZU-ENGL 2000 m 0732270 Ob23L77 Y38 m


Figure 6.2-2"Comparison of Test Data with Interaction Equation for Ring Stiffened Cylinders Under Combined Axial Compression and Hoop Compression



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Figure 6.2-3-Comparison of Test Data with Interaction Equation for Ring Stiffened Cylinders Under Combined Axial Compression and Hoop Compression



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Figure 6.2-4-Comparison of Test Data with Interaction Equation for Local Buckling of Ring and Stringer Stiffened Cylinders Under Combined Axial Compression and Hoop Compression



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Figure 6.2-!j-Comparison of Test Data with Interaction Equation for Local Buckling of Ring and Stringer Stiffened Cylinders Under Combined Axial Compression and Hoop Compression



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STABILITY DESIGN OF CYLINDRICAL SHELLS

Figure 6.2-&Comparison of Test Data with Interaction Equation for Bay Instability of Ring and Stringer Stiffened Cylinders Under Combined Axial Compression and Hoop Compression



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Figure 6.2-7"Comparison of Test Data with Interaction Equation for Bay Instability of Ring and Stringer Stiffened Cylinders Under Combined Axial Compression and Hoop Compression



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STABlLllY DESIGN OF CYLINDRICAL SHELLS 77



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79 STABILITY DESIGN OF CYLINDRICAL SHELLS



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C9 Allowable Stresses The allowable stresses for axial compression and bending

are assumed to be equal for the shell buckling modes of failure. Equations 9-2 through 9-8 are obtained by applying factors of safety to the failure stresses given by the equations in Sections 4 and 6 .

The allowable stress equations for the column buckling mode for members subjected to axial compression and bending stresses are the same as given in AISC (33). Equations 9- 1 0 and 9-1 I are simpler in form than the AISC equations because the properties of tubular members are identical in the X and Y directions. When external pressure is combined with axial compression and bending the stresses for F,, and Fb are determined from the shell buckling interaction equations.

Cl O Tolerances The tolerances for out-of-roundness are from the ASME

Pressure Vessel Code (36) and the requirement for straightness is from the ECCS rules (37).

C10.1 MAXIMUM DIFFERENCES IN CROSS- SECTION DIAMETERS

The equation for maximum differences provides a shell that appears reasonably round to the eye. One exception is for a shape conforming to n = 3. Provision is made for this case by the second paragraph of Section 10.3.

C10.2 LOCATION DEVIATION FROM STRAIGHT LINE ALONG A MERIDIAN

The reference length L, = 4 f i is related to the size of the potential buckles. There we no published papers which show a correlation between measured values of e, and the reduction in axial strength. In Ref. 37 when e, = 0.02Lx the values of a , ~ are halved. When the ratio is between O.OILx and 0.02Lx, linear interpolation between a , ~ and 0 . 5 ~ ~ ~ 1 , is recommended for the reduction factor.

C1 0.3 LOCAL DEVIATION FROM TRUE CIRCLE

Figures I O. I and 10.2 are based upon the following equation developed by Windenburg (38).

(CIO-1)

This equation is based upon the analogy between a pressure vessel and a column by considering the shell of the pressure vessel to be made up of a series of columns with length of one-half wave length. The eccentricity of a column corresponds to the out-of-roundness of a cylinder. The constants in Equation C 1 O. 1 were derived from available test data to provide tolerance limits which would reduce the collapsing strength by a maximum of 20% = 0.8).

The value of I I is the number of waves in the cylinder at collapse and e is the allowable deviation measured over one half wave length. The values of n were determined from the equation for hydrostatic pressure developed by Sturm (1 3). Identical values for II can be determined from Equation 4-27. Noninteger values are selected for tz and I I couesponds to the lowest buckling pressure for the assumed geometry. The arc length in Figure 10.2 is given by Arc = 7tD/2tz.

C1 0.4 PLATE STIFFENERS

The permissible lateral deviation of the free edge of a plate stiffener corresponds to the fabrication tolerances specifed for the models reported in Ref. 6 .

The value of n given by Equation 10-3 is based upon the assumption that the stiffening ring will buckle into one-half the number of waves of an unstiftened shell of length Lb This equation can be safely used in lieu of Equation 4- 17 because it will always predict a smaller value of n.

Cl 1 Stress Calculations C1 1.2 BENDING STRESSES

The bending stress in a cylinder is given by the equation

M f = - I’ S

where

S = 7tR2t 1 + 0.25( t /R’ )

1 + (0 .5 r ) /R = 7t (D: - D4) /320 , ,

C1 1.3 HOOP STRESSES

a. Stresses in Shell Midway Between Rings Equation I 1-6 is a simplification of the equation for 6 5

given by Kendrick (p. 407 of Ref. 39) for the mean circumferential stress between stiffeners. The simplitications are made in the terms L, and y. The expressions from Ref. 39 are as follows:

L, = ( 2 N ) / a + t,r 5 L,

sinh-cos- + cosh-sin- aL aL aL aL 2 2 2 2

sinhaL + s i n a l y = 2

N = . coshaL - COSCXL slnhaL + sinaL

A comparison of the exact with the simplified hoop stress factors is shown in Figure C1 1.3- I .



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0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

O

Figure Cl 1.3-1”Comparison Between Exact and Simplified Hoop Stress Factors



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b. Stress in a Ring Stiffener 10. Wilson, W. M. and Newmark, N. M., “The Strength of Equation 11-9 is a simplification of Kendrkk’s equation of Thin Cylindrical Shells as Columns,” University of Illi-

(p. 407 of Ref. 39) for the circumferential stress in the flange nois Engineering Experiment Station Bulletin, No. 255, of a ring stiffener. The expression from Ref. 39 follows: 1933.

I 1. Miller, C. D. and Kinra, R. K., “External Pressure Tests of Ring Stiffened Fabricated Steel Cylinders,” Paper OTC 4 107, Offshore Technology Conference, May 198 I .

12. Galletly, G. D. and Bart, R., “Effects of Boundary Condi- where L, is defined in C 1 1.3 and tions and Initial Out-of-Roundncss on the Strength of

R, = radius to point of stress determination, Thin-Walled Cylinders Subjected to External Hydrostatic Pressure,” DTMB Report 1505, May 1962.

R2 A = - A , . 13. Sturm, R. G., “A Study of the Collapsing Pressure of R;. Thin-Walled Cylinders,” University of Illinois, Engineer-

ing Experiment Station Bulletin No. 329, 1941. To obtain Equation 1 1-8, the factor k , which is equal to

N$/No, is substituted for the quantity 0.5 in the above equation.

14. Miller, C. D. and Grove, R. B., “Interpretive Report on the Conoco/ABS Test Program,” Contract No. R-0578, CBI Industries, November 1983.

Cl 2 References 15. Becker, H. and Gerard, G., Elastic Stability of Orthotro-

1.

2.

3.

4.

5.

6.

7.

8.

9.

American Petroleum Institute, Reconznaetaded Practice for Planning, Designing and Constructing Fixed Offshore Platfonns, API RP 2A, Fifteenth Edition, October 22, 1985.

Det Norske Veritas, Rules for the Design Construction and lnspection of Ojshore Structures, Appendix C, 1977 (Rev. 1982).

American Society of Mechanical Engineers, Boiler and Pressure Vessel Code Case N-284, “Metal Containment Shell Buckling Design Methods,” Nuclear Code Case Book, 1986.

Miller, C.D., “Commentary on ASME Code Case N-284, Preliminary Report,” Chicago Bridge and Iron Company, Dec. 1979.

Kiziltug, A.Y., Grove, R. B., Peters, S. W. and Miller, C . D., “Collapse Tests of Short Tubular Columns Subjected to Combined Loads,” Final Report, Contract No. UI- 85 1604, CBI Industries, Dec. 1985.

Vojta, J. F. and Miller, C. D., “Buckling Tests on Ring and Stringer Stiffened Cylindrical Models Subject to Combined Loads,” Final Report, Contract No. 1 1896, Vol. I-Main Report and 3 Volume Appendix, CBI Industries, Inc., April 1983.

Timoshenko, S. P. and Gere, J. M., Theory of Elastic Sta- bd&, 2nd Edition, McGraw Hill, New York, 1961.

Miller, C. D., “Axial Compression and Bending Strength of Unstiffened Steel Cylinders,” Research Report, CBI Industries, October 1984.

Miller, C. D., “Axial Compression Strength of Ring Stiff- ened Cylinders,” Research Report, CBI Industries, May 1984.

pic Shells, Journal of the Aerospace Sciences, Vol. 29, No. 5, May 1962, pp. 505-5 12.

16. Miller, C. D., “Buckling Stresses forAxially Compressed Cylinders,” Jourmil of the Structural Division, ASCE, Vol. 103, NO. ST3, March 1977, PP. 695-72 I .

17. Kendrick, S. B., “Collapse of Stiffened Cylinders Under External Pressure,” Paper No. C190/72, Proceedings oj institution of Mechanical Engineers Conference on Ves- sels Under Buckling Conditions, London, Dec. 1972, pp. 33-42.

18. Hom, K., “Elastic Stress in Ring-Frames of Imperfectly Circular Cylindrical Shells Under External Pressure Loading,” DTMB Report 1066, Nov. 1957.

19. Greimann, L. F., DeHart, R. C., and Ranz, D. R., “Effect of Out-of-Roundness and Residual Stresses on Ring Reinforced Steel Shells,” Southwest Research Institute Report, Project No. 03-2435, AIS1 Project 155, Oct. 1969.

20. Faulkner, D., Cowling, M. J., and Frieze, P. A., Editors, Integrity of Wshore Structures, Applied Science Publish- ers, London and New Jersey, 198 1.

21. Windenburg, D. F. and Trilling, C., “Collapse by Instabil- ity of Thin Cylindrical Shells Under External Pressure,” Trums. ASME, Vol. 56, No. 1 1, November 1934, pp. 819- 825 or Pressure Vessel arad Pipirag Design, Collected Papers 1927- 1959, ASME, New York, 1960, pp. 6 12-624.

22. Block, D. L., Card, M. F., and Mikulas, M. M., “Buckling of Eccentrically Stiffened Orthotropic Cylinders,” NASA TN-2960, August 1965.

23. Flugge, W., Stresses in Shells, Springer-Verlag, Belin/ GottingerhIeidelberg, 1960.



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STAElLlTY DESIGN OF CYLINDRICAL SHELLS 83

24. Miller, C. D., “Buckling Stresses of Ring and Stringer Stiffened Cylindrical Shells under Axial Compressive Load,” Research Report. Chicago Bridge & Iron Co., April 1977.

25. American Iron and Steel Institute, Cold-F¿wmed Steel Design Manual, 1983 Mition.

26. Gerard, G., “Plastic Stability Theory of Geometrically Orthotropic Plates and Cylindrical Shells,” Journal of Aerospace Sciences, August 1962, pp. 956-962.

27. Miller, C. D. and Grove, R. B., “Current Research Related to Buckling of Shells for Offshore Structures,” Paper OTC 4474, Offshore Technology Conference, May 1983.

28. Faulkner, D., Chen, Y. N., and de Oliveira, J. G., “Limit State Design Criteria for Stiffened Cylinders of Offshore Structures,” 4th ASME PV&P Conference, Portland, Oregon, June 1983.

29. Stephens, M. J., Kulak, G., and Montgomery, C. J., “Local Buckling of Thin-Walled Tubular Steel Mem- bers,” Pmceedings of Third Internationcrl Colloquiutn on Stability of Metal Structures, Toronto, Canada, SSRC, May 1983, pp. 489-508.

30. Shemlan, D. R., ‘Flexural Tests of Fabricated Pipe Beams,” Third International Colloquium on Stability of Metal Structures, Toronto, Canada, SSRC, May 1983.

31. Miller, C. D., Kinra, R. K., and Marlow, R. S. , ‘Tension and Collapse Tests of Fabricated Steel Cylinders,” Paper OTC 42 18, Offshore Technology Conference, May 1982.

32. Johnston, B. G., editor, Guide to Stubiliry Design Criteria for Metal Srrucrures, 3rd Edition, Wiley, New York, 1976.

33. American Institute o í Steel Construction, Manual ofsteel Construction, 8th Edition, I98 I .

34. Chen, W. F. and Ross, D. A., “The Strength of Axially

35.

36.

37.

38.

Loaded Tubular Columns,” Fritz Engineering Lab Report No. 393.8, Lehigh University, September 1978.

Wilson, W. M., ‘‘Tests of Steel Columns,” University of Illinois Engineering Experiment Station Bulletin, No. 292, 1937.

American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section VIII, Division 1 and 2 and Section III, Subsection NE, 1983.

European Convention for Constructional Steelwork, “European Recommendations for Steel Construction,” Section 4.6 Buckling of Shells, Publication 29, Second Edition, 1983.

Windenburg, D. F., “Vessels Under External Pressure,” Pressure Vessel and Piping Design, collected papers 1927-1959, ASME, 1960, PP. 625-632.

39.

40.

41.

42,

43.

44.

45.

46.

47,

48.

49.

50.

l

Sill, S. S., Editor, The Stress Analysis of Pressure Vessels 2nd Pressure Components, Pergamon Press, 1970.

Kinra, R. K., “Hydrostatic and Axial Collapse Tests of Stiffened Cylinders,” Paper OTC 2685, Offshore Tech- nology Conference, May 1976.

Miller, C. D., Grove, R. B., and Vojta, J. F., “Design of Stiffened Cylinders for Offshore Structures,” American Welding Society Welded Otfshore Structures Conference, New Orleans, Louisiana, December 1983.

Miller, C. D. and Grove, R. B., “Collapse Tests of Ring Stiffened Cylinders Under Combinations of Axial Com- pression and External Pressure,” ASME, PVP Confer- ence, Chicago, Illinois, July 20-24, 1986.

Review and Verification of API Bulletin 2U, J. P. Kenny &L Partners Ltd. Report, Project No. 15191, Report No. 35301001, Rev. 2, February 1986.

Marzullo, M. A. and Ostapenko, A., ‘‘Tests on Two High- Strength Short Tubular Columns,” Frik Engineering Lab. Report No. 406. I 0, May 1977.

Odland, J. O., “An Experimental Investigation of the Buckling Strength of Ring Stiffened Cylindrical Shells Under Axial Compression,” Norwegian Maritime Research, No. 4, 1981, pp. 22-39.

Dowling, P. J. and Harding, J. E., “Experimental Behav- ior of Ring and Stringer Stiffened Shells,” Buckling of Shells in Offshow Structures, Edited by Harding, Dowl- ing and Agelidis, Granada, London, Toronto, Sydney, New York, Sept. I98 1.

Ostapenko, A. and Grimm, D. F., “Local Buckling of Cylindrical Tubular Columns Made of A-36 Steel,” Lehigh University, Fritz Engineering Lab. Report No. 450.7, February 1980.

Eder, M. F., Grove R. B., Peters, S. W., and Miller, C . D., “Collapse Tests of Fabricated Cylinders Under Combined Axial Compression and External Pressure,” Final Report for API PRAC Project 82/83-46 and CBI Contract 2 1738, CBI Industries, lnc., Research Laboratory, Plaintìeld, Illi- nois, February 1984.

Sherman, D. R., “Bending Capacity of Fabricated Pipes,” The University of Wisconsin-Milwaukee, College of Engineering and Applied Science, February 1983.

Miller, C. D., “Summary of Buckling Tests on Fabricate Steel Cylindrical Shells In USA,” Buckling of Shells in Offshore Structures, Edited by Harding, Dowling and Agelidis, Granada, London, Sydney, New York, 1982, pp. 429-472.



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