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  • 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 Helping You Get The Job Done Right? --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • Bulletin on Stability Design of Cylindrical Shells API BULLETIN 2U (BULL ZU) SECOND EDITION, OCTOBER 2000 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- American Petroleum InstituteCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D - A P I I P E T R O BULL ZU-ENGL 2000 0732290 Ob233130 b09 M Bulletin on Stability Design of Cylindrical Shells Upstream Segment API BULLETIN 2U (BULL2U) SECOND EDITION, OCTOBER2000 American Petroleum Institute --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD*API/PETRO BULZU-ENGL L 2000 m 0732290 Ob23131 5q5 m SPECIAL NOTES API publications necessarily address problems a general nature.With respect to paltic- of 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 theirobligations under local, state, or fed- eral laws. Information concerning safety health risks and proper precautions with respect par- and to ticular matcrials and conditions shouldbe obtained from the employer, the manufacturer or supplier of that material,or the material safety data sheet. Nothing contained in any API publication is to be construed as granting any right, by or implication or otherwise, for the manufacture, sale, use of any method, apparatus, prod- or uct covered by lettcrs patent. Neither should anything contained in the publication be con- strued as insuring anyone against liability infringement of letters patent. for Generally, API standards reviewed and revised, reaffirmed, or withdrawn at least every are 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, wherean 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 underAPI standardization procedures that ensure appropri- ate 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 com- ments 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 proven, sound engineer- of ing and operating practices. These standards are not intended to obviatethe need for apply- ingsoundengineeringjudgmentregardingwhenandwherethesestandardsshould be utilized. The formulation and publication of A P I standards isnot intended in anyway to inhibit anyone from using any other practices. Any manufacturermarkingequipment or materials in conformance withthemarking requirements of an API standard is solely responsible for complying with all the applicable requirements of that standard. APIdoes not represent, warrant, or guarantee that such prod- ucts do in fact conformto the applicable API standard. All rights reserved. No part of this work may be reproduced, storedin a retrieval system, or tmnsnzitted by any means, electronic,mechanical, photocopying, recording, otherwise, or 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 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 6 0732290 Ob23132 481 9 This Bulletin is under jurisdiction the API subcommittee on Offshore Structures. of 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 hereinare based on clas- sical 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 publicationsmay be used by anyone desiring to do so. Every effort has been made by of the the Institute to assure the accuracy and reliability data contained in them: however, the Institute makes no representation,wamnty, orguarantee in connection with this publication and hereby expressly disclaims any liability or responsibility for loss or damage resulting from its use or for violation of any federal, state, or municipal regulation with which this the 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. --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- iiiCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • CONTENTS Pap I GENERAL PROVISIONS ............................................... 5 1.1 scope ........................................................... 5 1.2Limitations ....................................................... 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 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 2 GEOMETRIES. FAILURE MODES AND LOADS ........................... 7 2.1 Geometries ....................................................... 7 2.2 Failure Modes .................................................... 7 2.3 Loads andLoadCombinations ....................................... 7 3BUCKLINGDESIGNMETHOD ........................................ 11 4 PREDICTED SHELL BUCKLING STRESSES FORAXIALLOAD. BENDING AND EXTERNALPRESSURE ................................ 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. of and General Instability 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 PLASTICITYREDUCTIONFACTORS .................................. 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 7.1Design Shell Buckling Stresses ...................................... 25 7.2Local Stiffener Buckling ........................................... 25 7.3 Sizing of Stiffeners................................................ 25 8 COLUMN BUCKLING ................................................ 27 8 . I Elastic Column Buckling Stresses.................................... 27 8.2InelasticColumnBuckling 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 Alonga Meridian .................... 31 10.3 Local Deviation From TrueCircle.................................... 31 10.4 Plate Stiffeners ................................................... 31 VCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • Page 1 1 STRESS CALCULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 I 1 . 1 Axial Stresses .................................................... 33 11.2Bending Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 11.3 Hoop Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 12 REFERENCES ....................................................... 35 APPENDIX A COMMENTARY ON STABILITY DESIGN OF CYLINDRICAL SHELLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Figures 2.1 Geometry Cylinder of ............................................ 8 2.2 Geometry Stiffeners of ........................................... 9 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 2.3 Buckling Shell Modes for Cylinders ............................... 10 3.1 Flow Chart for Determining Allowable Stresses ...................... 12 10.1 MaximumPossibleDeviation e from a True Circular Form . . . . . . . . . . . . . 32 10.2MaximumArcLengthforDeterminingPlus or MinusDeviation . . . . . . . . 32 C4.1.1-1 Local Buckling Stresses for Unstiffened and Ring Stiflèned Cylinders [Jnder Axial Compression Load ................................... 42 C4.1.I-2 Axial Compression of Fabricated Cylinders-Local Buckling in ElasticRegion ................................................. 43 C4.1.I-3 Axial Compression of Fabricated Cylinders-Local Buckling in Inelastic Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 C4.1.1-4 Axial Compression of Fabricated Cylinders-Local Buckling in Yield and Strain Hardening Regions ............................... 45 C4.I .1-5 Bending of Fabricated Cylinders-Local Buckling in Yield and Strain Hardening Regions ........................................ 46 C4.1 .1-6 Comparison of Test Data with Equations and 4-7 for Axial 4-6 Compression of Ring Stiffened Cylinders ........................... 47 C4. 1 .1-7 Comparison of Test Data with Equations4-6 and 4-7 íor Axial Compression of Ring Stiffened Cylinders........................... 48 C4.1 . 1-8 Comparison of Test Datawith Equations 4-6 and 4-7 for Axial Compression of Ring Stiffened Cylinders ........................... 49 C4.1 . 1-9 comparison of Test Data with Equations and 4-7 for Axial 4-6 Comprcssion of Ring Stiffened Cylinders........................... 50 C4. 1 . 1- 1O Comparison of Test Data with Equdtions and 4-7 for Axial 4-6 Compression of Ring Stiffened Cylinders........................... 51 C4.1.2-1 Theoretical Local Buckling Pressure of Unstiffened or Ring Stiffened Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 C4.1.2-2 Theoretical Local Buckling Pressure and Number Circumferential of Waves for Unstiffened or Ring Stiffened Cylinders. . . . . . . . . . . . . . . . . . . 53 C4.1.2-3 Capacity Reduction Factors for Ring Stiffened Cylinders Subjected to Hydrostatic Pressure(Nd& = 0.5) .............................. 55 C4.1.2-4 Comparison of Test Stresses with Predicted Stresses for Ring Stiffened Cylinders Subjected to Hydrostatic Pressure ......................... 56 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 Stringer Stiffened Cylinders Under Axial Load ....................... 60 C4.3.2-1 Values of tz Which Minimize Equation4-27 of Bulletin 2U . . . . . . . . . . . . . 61 ViCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • Page C4.5.2- 1 Comparison of Test Pressures with Predicted Failure Pressures for Stringer StiffenedCylinders. .................................. 64 c5- 1 Comparison of Plasticity Equations of DNV and API Bulletin2U . . . . . . . 66 6.1-1 Comparison of Test Data from Fabricated Cylinders Under Combined Axial Tension and Hoop Cornpression with Interaction Curves (Fy= 36 ksi) .................................................. 67 6.1-2 Comparison of Test Data from Fabricated Cylinders Under Combined Axial Tension and Hoop Compression with Interaction Curves (Fy = 50 ksi). ........................................... 68 6.2- 1 Comparison of Test Data with Interaction Equation for Unstiffened Cylinders Under Combined Axial Compression and Hoop Compression . 70 . 6.2-2 Comparison ofTest Data with Interaction Equation for Ring Stiffened Cylinders Under Combined Axial Compression and Hoop Compression . . 7 I 6.2-3 Cornparison of Test Data with Interaction Equation for Ring Stiffened Cylinders Under Combined Axial Compression and Hoop Compression 72 .. 6.2-4 Comparison of Test Datawith Interaction Equation for Local Buckling of Ring and Stringer Stiffened Cylinders Under Combined Axial Cornpression and Hoop Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.2-5 Comparison of Test Data with Interaction Equation for Local Buckling of Ring and Stringer Stiffened Cylinders Under Combined Axial Compression and Hoop Compression .............................. 74 6.2-6 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 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 .............................. 76 c7.1-1 Design Shell Buckling Stresses, Fic, ............................... 77 C8- 1 Axial Compression of Fabricated CylindersXolumn Buckling. . . . . . . . . 78 C8-2 Comparison of Column Buckling Equations. ........................ 79 C11.3-I 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 StressFactors, KQ .................................................. 24 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD*API/PETRO 8ULL ZU-ENGL 2000 I 13732270 Ob2313b 027 9 I Stability Design of Cylindrical Shells Nomenclature Note: The terms not defined here are uniquely defined the sections in fb = applied (computed)bending stress, ksi. in which they are used. fi = applied (computed) hoop stress, ksi. i = subscript denoting direction and load. $ = longitudinal direction and any load combina- = axial compressive stress permitted the absence in tion. of bending moment, ksi. 8 = hoop direction and any load combination. Fb = bending stress permitted ina cylinder in the x = longitudinal direction and axial compression absence of axial force. ksi. load only (Ne = O). Fe = hoop compressive stress permittedin a cylinder, h = hoop direction and hydrostatic external pres- ksi. sure ( N d N e = 0.5). FjC, = inelastic shell buckling stress for fabricatedshell, r = hoop direction and radial external pressure ksi. ( N 0 =O). Fie, = elastic shell buckling stress for fabricated shell, j = subscript denoting buckling failure mode. ksi. L = local shell buckling. FS = factor of safety. B = bay instability. - G= general instability. F;., = Fie/p. - C= column buckling. Fic. = FiC.B. Är = A$(L,.f). F." = minimum specified yield stress of material, ksi. A, = cross-sectional areaof one ling stiffener, in.2. F,,$ = static yield stressof material (zero strain rate), ksi. A, = cross-sectional areaof one stringer stiffener, in.2. G = shear modulus,E/2 ( 1 + v), ksi. A, = total cross-sectional area of cylinder, g = M.&f&rtAA. A, = 2nRt + N,d,y, in.2. h, = width (or depth) of stiffening element, in. b = stringer spacingas an arc dimension on the shell I, fer = moment of inertia of stringer and ring stiffener, , centerline, in. respectively, plus effective width of shell about be = effective width of shellin the circumferential centroidal axisof combined section (see Fig. 2.2), direction, in. in! B = mean bias factor. Ir = moment of inertia of stringer and ring stiffener, C,, = end moment coefficient in interaction equation. respectively, about its centroidal axis, C = ratio of structural proportional limit to yield , Js, J , = torsional stiffness constant of stringer and ring strength for a material. stiffener, respectively (for general non-circular shapes use C h,vt,?/3),i n 4 C, = elastic buckling coefficient= o x p ~ r. WE K = effective length factor for column buckling. D,, = maximum and minimum shell diameters used to ,, D,n;,l determine the out-of-roundness factor, y, at a par- k = ratio of axial load to circumferential load N d N e ) . ( ticular cross-section, in. location giving the The KG = factor used in calculating ring stiffener stresses largest y factor should be used. when a cylinder is subjected to external pressure. D = centerline diameterof shell, in. KL = factor used when calculating the shell stress at D ,= outside diameterof shell, in. mid-bay, to account for the effects a ring or end of stiffeners, when a cylinder is subjected to external E = modulus of elasticity, ksi. pressure. D,,, = nominal outside diameter of cylinder, in. K,, = effective pressure correction factor used calcula- in f,, = applied (computed) axial stress, ksi. tion of collapse pressure. --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 1COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D O A P I I P E T R O B U L L Z U - E N G L 2000 W 0732290 Ob23137 T b 3 9 2 API BULLETIN 2U L = unsupported lengthof shell between rings, in. p ( . = failure pressure forbay instability mode, ksi. ~ Lj = cylinder lengthfor calculation of bay instability p c = failure pressurefor local buckling mode,ksi. ~ in. and general instability, r = radius of gyration, r = (0.5R2 + O. 1 25t2)Il2 = L, = effective widthof shell in the longitudinaldirec- 0.707R, in. tion, in. R = radius tocenterline of shell, in. length of cylinder between bulkheads or lines of R,. = radius to centroidal axisof the combinedling stiff- support with sufficient stiflness to act as bulk- ener and effective width of shell, in. heads. Linesof support which act as bulkheads include end ring stiffeners,in. R0 = radius tooutside of shell, in. ring spacing, in. R, = radius to centroid of ring stiffener,in. unbraced length of cylinder, in. t = thickness of shell, in. number of half waves into which the shell will r,,, = thickness of web of ring stiffener,in. buckle in the longitudinal direction. + Let)/&, t, = t, t, = effective shell thickness, = (A, t, applied bending moment. + (A,T b,t)/b, in. the smallerof the moments at the endsof the ts = thickness of stiffening element, in. --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- unbraced length ofa beam-column, in-kips. z Z s = distance from centerlineof shell to centroidof , the largerof the moments at theends of the stiffener, for ring and stringer stiffeners, respec- unbraced length ofa beam-column, in-kips. tively (positive outward), in. L,/& a.. capacity reductionfactor to account forthe diffcr- - u- ence between classical theoryand predicted insta- bl a t bility stresses for fabricated shells. number of waves into which the shellwill buckle ß = a factor appliedto the bay instability and general in the circumferential direction. to instability failure stresses avoid interactionwith the local buckling mode. unit length of theoretical elastic buckling load per shell (longitudinalor circumferential)for a perfect S in Pm P = reduction factors used computing collapse load cylinder forboth bay instability and general insla- for axial compression. bility, kips perin. Ac, Ad = FiejlFy FieJ/Fy 9 number of stringers. r l = plasticity reduction factor which accounts the for in. axial load perunit of circumference, kips per nonlinearity of material properties and the effects of residual stresses. circumferential load per of length, kipsper in. unit Y= (Dttua - Dtnin) 1OOlDwm. applied external pressure, ksi. h = XWL, theoretical elastic failure pressure bay instabil- for ity mode, ksi. in ho, h, = slenderness parameters as defined text and used for computing collapse load axial compression. for P e = theoretical elastic failure pressure general ~ for instability mode, ksi. hG = nR/Lb pel, = theoretical failure pressure for local buckling v = Poissons ratio. mode, ksi. oiej= theoretical elastic instability stress, ksi. p s = contribution of stringers to collapse pressure, ksi. y = partial safety factor. pee; = failure pressure For general instability mode, ksi. SI Metric Conversion Factors P = applied axial load, ksi. in. x 2.54 = mm P,B = inelastic axial compressionbay instability load, kips. ksi x 6.894757 = MPaCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD-API/PETRO BULL ZU-ENGL 2000 0 0732290 Ob23138 9 T T I STABILITY DESIGN CYLINDRICAL SHELLS OF 3 Glossary amplification reduction factor (C,,,): Coefficient applied hierarchicalorderofinstability: Refers to a design to bendingterm in interactionequationformemberssub- methodthatwill ensure development of a design with the jected to combined bending and axial compression to account most critical instability mode (Le., general instability) having for overprediction of secondary moment given the amplifi- by a higher critical buckling stress than the less critical instabil- cation factor 1/( 1 -f,,/F,). ity made (i.e., local instability). asymmetricbuckling: Thebucklingoftheshellplate hydrostatic pressure: Uniform external pressure on the between the circumferential (¡.e., ring) stiffeners character- sides andends of a member. --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- ized by the formation of two or more lobes (waves) around inelastic buckling stress: buckling stress cylinder The ofa the circumference. which exceeds the elastic stress limit of the member material. axial direction:Longitudinal direction of the member. The inelastic material properties are accounted for, including effects of residual stresses due to forming and welding. axisymmetric collapse: The bucklingoftheshellplate interaction of instability modes: Critical buckling between the circumferential stiffeners characterized accor- by stress determined for one instability mode may be affected dion-like pleats around the circumference. (¡.e., reduced) by another instability mode. Elastic buckling bay: The section of cylinder between rings. stresses for two or more instability modes should be kept apart to preclude an interaction between instability modes. bay instability: Simultaneous lateral buckling of the shell local instability: Buckling of the shell plate between the and stringers with the rings remaining essentially round. stiffeners with the stiffeners(¡.e., rings or rings 3nd stringers) capacityreduction factor (a$:Coefficient which remaining intact. accountsfortheeffects of shapeimperfections,nonlinear membrane stresses: The in-planestresses in the shell; behavior and boundary conditions (other than classical sim- longitudinal, circumferentialor shear. ply supported) on the buckling capacity of theshell. maximum shear stress theory: Failure theory defined critical buckling stress: The stress level associated with by the following equation: initiation of buckling. Critical buckling stress is also referred to as the inelastic bucklingstress. (3, -02 = F, where 01 is the maximum principal stress and (32, is the distortion energy theory: Failure theory defined bythe minimum principal stress, with tension positive and com- following equation where the applied stresses positive for are pression negative. tension and negative for compression. f’,- f J e +fi = ff orthogonally stiffened: A member with circumferential (ring) and longitudinal (stringer) stiffeners. I radial pressure: Uniform external pressure acting only on effective length (KLt):The equivalent lengthused in com- the sides of a member. pression formulas and determinedby a bifurcation analysis. residual stresses:The stresses that remain in an unloaded effective length factor ( K ) : The ratio between the effec- member after it has been formed and installed in a structure. tive length and the unbraced length of the member. Some typical causes are forming, welding and cotrections for effectivesection: Stiffener together the with effective misalignmentduringinstallation in the structure. The mis- width of shell actingwith the stiffener. alignmentstressesarenotaccountedfor by theplasticity reduction factor T. effectivewidth: The reduced width shell of or plate ring stiffened: member with circumferential stiffeners. A which,withanassumeduniform stress distribution, pro- duces the same effect on the behavior of a structural mem- shell panel: That portion of a shell which is bounded by ber as the actual width of shell or plate with its nonuniform two adjacent ringsin the longitudinal direction and two adja- stress distribution. cent stringersin the circumferential direction. elastic buckling stress: The buckling stress of a cylinder slenderness ratio (&/r): The ratio of the effective length based upon elastic behavior. of a member to the radius gyration of the member. of stress relieved: The residual stresses significantly are general instability:Buckling of one or more circumferen- reduced by post weld heat treatment. tial (¡.e., ring) stiffeners with the attached shell plate in ring- stiffened cylindrical shells. For a ring- and stringer-stiffened stringer stiffened:A member with longitudinal stiffeners. cylindrical shell general instability refers to the buckling of yield stress:The yield stress of the material determined in I one or more rings and stringers with the attached shell - date. Y accordance withASTM A307.COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD-API/PETRO BULL ZU-ENGL 2000 D 0732290 Ob23139 8 3 b SECTION 1-GENERAL PROVISIONS 1.1 SCOPE 1.2.3 Special considerations should be given to the ends of members and other areas of load application where the stress 1.1.1 This Bulletin provides stability criteria for determin- distribution may be nonlinearandlocalized stresses may ing the structural adequacy against buckling large diameter of exceed those predicted by linear theory. When the localized circularcylindricalmemberswhensubjected to axialload, to stresses extend over a distance equal one half wave length --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- bending, shear and external pressure acting independently or of the buckling mode, they should considered as a uniform be in combination. The cylinders may be unstiffened, longitudi- stress around the full circumference. Additional thickness or nally stiffened, ring stiffenedor stiffened with both longitudi- stiffening may be required. naland ringstiffeners. Research development and work leading to preparation and issue of the first and second edi- 1.2.4 Failure due to material fracture or fatigue and failure tions of this Bulletin is documented in References l through 6 caused by dents resulting from accidental loads are not con- and the Commentary. sidered in the bulletin. 1.1.2 The buckling capacities of the cylinders are based on 1.3 STRESS COMPONENTS FOR STABILITY linearbifurcation (classical) analysesreduced by capacity ANALYSIS AND DESIGN reduction factors which account for the effects of imperfec- tions and nonlinearity in geometry and boundary conditions The internal stress field which controls the buckling of a and by plasticity reduction factors which account for nonlin- cylindrical shell consists of the longitudinal membrane, cir- earity in material properties. The reduction factorswere cumferential membrane in-plane stresses. and shear The determinedfromtestsconductedonfabricatedsteelcylin- stresses resulting from a dynamic analysis should be treated ders. The plasticity reduction factors include the effects of as equivalent static stresses. residual stresses resulting from the fabrication process. 1.4STRUCTURALSHAPEANDPLATE 1.1.3 Fabricated cylinders produced are by butt-welding SPECIFICATIONS together cold or hot formed plate materials. Long fabricated cylinders generally are made by butt-welding together a Unless otherwisespecified by the designer, structural series of short sections, commonly referred to as cans, with shapes and plates should conform to of the specifications one the longitudinal welds rotated between the cans. listed in Table 8.1.4- 1/2 ofAPI RP 2A, 20th edition, or Table 4 of API RP 2T. 1.2 LIMITATIONS 1.5 HIERARCHICAL ORDER AND INTERACTION 1.2.1 The criteria given are for stiffened cylinders with uni- OF BUCKLING MODES form thickness between ring stiffeners or for unstiffened cyl- inders of uniform thickness. All shell penetrations must be 1.5.1 ThisBulletinrequiresavoidanceoffailurein any properly reinforced. The results of experimental studies on mode, and recommends sizing of the cylindrical shell plate buckling of shells with reinforced openings and sonle design and the arrangement and siz,ing the stiffenersto ensure that of guidance are given in Ref. 2. The stability criteriaof this bul- the buckling stress for the most critical general instability is letin may be used for cylinders with openings that are rein- higher than theless critical local instability buckling stress. forced in accordance with the recommendations of Ref. 2 if 1.5.2 A hierarchicalorder ofbucklingstresses with ade- the openings do riot exceed 10% of the cylinder diameter or quate separation of general, bay and local instability strcsses 80% of the ring spacing. Special consideration mustbe given is also desirable for a cylindrical shell subjected to loading to the effectsof larger penetrations. resulting in longitudinal and circumferential stresses to pre- 1.2.2 The stability criteria applicable shells are to with clude any interaction of buckling modes. To prevent a reduc- diameter-to-thickness (Oh)ratios equal to or greater than 300 tion in buckling stress due to interaction of buckling modes, it but less than 2000 and shell thicknesses of5 mm (3/16 in.) or is recommended that bay and general instability mode elastic greater. The deviations from true circular shape and straight- 1.2 buckling stresses remain at least times the elastic buckling ness must satisfy the requirements stated this bulletin. in stress for local instability. 5COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • SECTION 24EOMETRIES, FAILURE MODES, AND LOADS The maximum stresses corresponding to all of the failure The first four failure modes are illustrated Figure 2.3. in modes will be referred toas buckling stresses. Buckling stress equations given the are for following geometries,failure 2.3 LOADSANDLOADCOMBINATIONS modes and load conditions. a. Determination of Applied Stresses Due to the Follow- ing Loads: 2.1 GEOMETRIES a. Unstiffened. 1. Longitudinalstress due to axial compressiodtension and overall bending. b. Ring Stiffened. 2. Shear stress dueto transverse shear and torsion. c. Stringer Stiffened. 3. Circumferential stressdue lo external pressure. d. Ring and Stringer Stiffened. 4. Combined (von Mises) stress due to combination of The four cylinder geometries are illustrated in Figure 2.1 loads. and the stiffener geometriesin Figure 2.2. h. Determination of Utilization Ratios Based on Recom- for mended Interaction Relationships Combined Loads: --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 2.2 FAILURE MODES I . Longitudinal (axial) tension and circumferential(hoop) a. b a l Shell Buckling-buckling shell of plate the compression. between stiffeners.The stringers remain straight and the rings remain round. 2. Longitudinal (axial) compressionandcircumferential compression. b. Bay Instabdity-buckling of the stringers together with the altached shell plate between rings(or the ends of the cyl- Note: Stresses and stress combinations considered are for in-plane inders for stringer stiffened cylinders). rings and theends The loads and do not account for secondary bending stresses due to out- of the cylinders remain round. of-plane presslwe loading on shell plate. c.General Instability-buckling of one or more rings Although the secondary bending stresses on orthogonally together with the attached shell (shell plus stringers for ring stiffened shell platemay be appreciablc, such stresses canbe and stringer stiffened cylinders). oftenconservativelyneglectedbecauseofreduction in cir- d. Local Stiffener Buckling-buckling of the stiffener cumferential stresses due to direct load transfer into the stiff- elements. eners.Appropriatefiniteelementanalysis may be used to e. Column Buckling-buckling of the cylinder as a column. determine applied stresses (see Section l ) . I 7COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • 8 API BULLETIN 2U Unstiffened L = L, , Bulkhead """_ - L""- Ring _""" I I L r --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- Lb Stiffened _""" Stringer - I I I Stringer Stiffened if I I I I I Rind and Stringer Stiffened I I I I I 3 Lb -ti--ti Figure 2.1-Geometry of CylinderCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD*API/PETRO BULL ZU-ENGL 2000 0732290 Ob23192 320 m STABILITY DESIGN CYLINDRICAL OF SHELLS 9 - --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- Shell Section Through Stringers R Shell - ,, - . - S R, = Radius to centroid of ring R, = Radius to centroid effective section of (shown cross hatched) (Effective width) L, t ” r Section Through Rings Figure 2.2-Geometry of StiffenersCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD*API/PETRO BULL Z U - E N G L 2000 H 0712270 UbZ3Lq3 2 b 7 M 10 API BULLETIN 2U Unstiffened """" """" Local shell buckling Section 4.1 "- General instability Section 4.2 Ring Stiffened Local stiffener buckling Section 7 Local shell buckling Section 4.3 Bay instability Stringer Section 4.4, l a and 2a Stiffened Section 4.5 Local stiffener buckling Section 7 Local shell buckling Section 4.3 Local stiffener buckling Section 7 Rind and Bay instability Stringer Sections 4.4.la, 4.4.2a, and 4.5 Stiffened General instability Sections 4.4.1 and 4.4.2b b Figure 2.3-Shell Buckling Modes for Cylinders --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • 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 bucklingstrengthformulations presented in this 3.3 The bay instabilitystressesforcylinders with stringer bulletin are based upon classical linear theory which is modi- stiffeners are given by orthotropic shell theory. This theory fiedbyreductionfactors a~ and q whichaccountfor the requires that the number of stringers mustbe greater than effects of imperfections, boundary conditions, nonlinearity of about three times the number of circumferential waves corre- material properties and residual stresses. The reduction fac- sponding to the buckling mode. An alternate method is given tors are determined from approximate lower bound values of fordetermining the bay instability stresses cylinders for test data of shells with initial imperfections representative of which do not satisfy this requirement. in the specified tolerance limits given Section IO. 3.4 The bucklingstressequationsforcylindcmunderthe 3 2 The general equations for the predicted shell buckling . individual load cases of axial compression, bending, radial stresses for fabricated steel cylinders subjected the individ- to external pressure (N+ = O ) and hydrostatic external pressure ualloadcasesofaxialcompression,bendingandexternal (NdNe = 0.5) are given in Section 4. Interaction equations are pressure are given by Equations 3-1 and 3-2. The equations given in Section 6 for cylinders subjected to combinations of for a and oie,are given in Section 4 and the equations forq o axialload,bendingandexternalpressure.Theinteraction are given in Section 5. between column buckling and shell buckling is considcred in Section 8. The method for determining the size stiffeners is of a. Elastic Shell Buckling Stress given in Section 7. F. .-a.. . 0. 3.5 A flow chart is given i n Figure 3.1 for determining the 1eJ - IJ le/ (3-1 1 allowable stresses. The equations for allowable stresses are --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- given in Section 9 and equations for determining the stresses b. Inelastic Shell Buckling Stress in due to applied load are given Section 1 l . A summary of the sections relatingto the buckling modes for each of the differ- Fi,. = Fie, (3-2) ent shell geometriesis given on Table 3.1. Table 3.1-Section Numbers Relating to Buckling Modes for Different Shell Geometries Geometry Ring and Buckling Mode Unstiffened Ring Stiff Stringer Stiff Stringer Stiff Local Shell Buckling 4. I 4. I 4.3 4.3 Bay Instability 4.4 4.4 45 . 4.5 General Instability 4.2 4.4 ( I b, 2b) Local Stiffener Buckling 7.2 7.2 7.2 Column Buckling 8.0 8.0 8.0 8.0 11COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 m 0 7 3 2 2 7 0 Ob231115 03T m 12 API BULLETIN2U Calculate stresses for assumed shell geometry See Section 11 (1 Unstiffened or Stringer stiffenedor ring stiffened ring and stringer stiffened I I I I Calculate FleLand F, Calculate FieLand Fic~ See Section 4.1 See Section 4.3 Calculate FieB andFicB See Sections4.4 or 4.5 I I Ring stiffened Yes Ir Yes - 7 Calculate fie^ and FicG L 1 Calculate FieGand F i c ~ r 1 See Section4.2 See Section4.4 Combined loads I Calculate Fqd and Fed For all applicable modes See Figure 2.3 I 1 Determine stiffener sizes No Section See 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 modesof failure. Figure 3.1-Flow Chart for Determining Allowable StressesCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • SECTION 4-PREDICTED SHELL BUCKLING STRESSES FOR AXIAL LOAD, BENDING AND EXTERNAL PRESSURE Thissectiongivesequations for determining shell the b. Inelastic Buckling Stresses. The buckling stresses are the bucklingstressesfortheloadcases of axialcompression, smaller of the values given by Equations and 4-7. 4-6 bending,radialexternalpressure (N$ = O) andhydrostatic external pressure (N$ = 0.5 Ne). The general equations for FXCL = FxeL predicting the elastic and inelastic buckling stresses for fabri- cated cylindersare given by Equations 3-1 and 3-2.The equa- 233 F , tions for determining clg and oie, are given in the following 5 F,, D / r < 600 section. The equations for determining the plasticity reduc- FxcL - (4-7) tion factors, q, are either given this section or in Section 5. in D / r 2 600 (0.5 F! The values of M, and Me appearing in the following equa- tions are definedas: 4.1.2 External Pressure (N9INe= O or 0.5) L, b M, = - To calculate predicted the elastic local shell buckling M ,= - (4- 1 ) fit f i t stresses FreL and F l t e ~ the radial and hydrostatic pressure for cases, three terms ( P e ~ KeL, and sei, must be calculated as , where: shown below. The values of p e arc determined by Equation ~ L, = distance between stiffening rings, 4-9 which was derived from the more general Equation 4-27. Equation 4-9 is a smoothlowerboundcurvewhichwas R = shellradius, obtained by letting n be a noninteger. r = shellthickness, a. Elastic Buckling Stresses b = arc distance between stringers. 4.1 LOCAL BUCKLING OF UNSTIFFENED OR RING STIFFENED CYLINDERS 4.1.1 Axial Compression or Bending (Ne= O) where KeL = 1.O if M, 2 3.42. The value of M.,will be greater The buckling stresses for cylinders subjected to axial com- than 3.42 for unstiffened cylinders. When M, < 3.42 dcter- pression or bending are assumed to be the same (see Com- mine K ~ from Equation 1 1.7. L “O8 E (t/D)’ M , > 1.5and A < 2.5 + 0.5 I 2.5 < A < O. I W( D / r ) where (4-9) C = 0.605 for , D/t > 300 0.207 D/r 2 I242 a.C.¿ = 1 169 195 + O S ( D / r ) <0.9 D / t < I242 where A = M,- 1.17+ 1.068k 2A c - -D / t - k = O for radial pressure and 0.5 for hydrostatic pressure. --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 13COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD-APUPETRO BULL ZU-ENGL zuno m O ~ Z W I , Z ~ ~ Wy o 2 O m 14 API BULLETIN 2U b. Imperfection Factors. A constant value of = 0.8 is c. Inelastic Buckling Stresses recommended for fabricated cylinders which meet the fabri- (4- 15) cation tolerancesof Section l O. c. Inelastic Buckling Stresses See Equation5-3 for 11. 4.2.2 External Pressure (N#/Ne= O or 0.5) a. Buckling Stresses Withor Without End Pressure See Equation 5-3 for T. d. Failure Pressures where KOG is given by Equation 1 1-9. E ( t / R )E liJ n ’ h - 1) Prc = 2 + (4- 17) (n2 + khi - I )(n2 + hi) L,RfRí, See a,b,and c above for determination of thc terms in Equation 4- 12. where h~ = nR/Lb, k = O for radial pressure and Sor hydro- 0.5 static pressure, R,. is the radius to the centroid the effective of 4.1.3TransverseShear section, R , is the radius to the outside of the shell and f e , is the momentof inertia of the efíective section given the fol- by Panel instabilitydue to transverse shear and torsion can be lowing equation: critical at interfaces. Critical buckling stress is affected not only by the shell thickness and the panel aspect ratio, but also L,t L,? by the boundary conditions. l e r= I , + A, Zr- A r + Let +- 12 (4- 18) As a minimum, it isnecessarytoincorporatethe shear stress in a von Mises stress check to assess the overall effect of combined loads. where Zr is the distance from the centerline of the shell to the centroid of the stiffener ring (positive outward). 4.2 GENERAL INSTABILITY OF RING STIFFENED The value of L, canbeapproximated by 1.1 f i t + t,,. CYLINDERS --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- when My > 1S6 and L, when M, 5 1.56.The correct value t’or 4.2.1 Axial Compression or Bending (Ne = O) n is the value which gives the minimum value ofp,G Equa- in tion 4-17. The minimum value of I I is 2 and the maximum a. Elastic Buckling Stresses shells of interest. The min- value will be less than 10 for most imum pressure will correspond to a noninteger value of n. t - The pressure p e is determinedby trial and error. ~ F.reG = a,, = a-,, 0.605 E - ( 1 +A,)”’ (4-13) R b. ImperfectionFactors. For fabricatedcylinders which meet the fabrication tolerances givenSection 1 0, a constant in value of = 0.8 is adequate. c. Inelastic Buckling Stresses FnG = rl Frec (4- 19) where A,. is the ring area L, is theling spacing. and FhcC = T FlwG (4-20) b. Imperfection Factors See Equation 5-3 for v. (4- 14) 0.72 if A,2 0.2 d. Failure Pressures - 5.0a.,L)A, + a,, if 0.06 < Ä r < 0.2 if Ä r 5 0.06 See a, b, and c above for determination of the terms in where a , is given by Equation 4-4 and = I .O. ~ c 4-2 I . EquationCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D = A P I / P E T R O BULL ZU-ENGL 2000 0732270 Ob2319B B 9 7 STABILITY DESIGNOF CYLINDRICAL SHELLS 15 4.3 LOCAL BUCKLING OF STRINGER STIFFENED The buckling pressure may be found by iterating Equation OR RING AND STRINGER STIFFENED 4-27 with n starting at O S N , and increasing n until a mini- CYLINDERS mum pressure is attained.The pressure corresponding to n = OSN, is the minimum pressure if il is less than the pressure The following equations are based upon theassumption corresponding to n = O.5fVy+1. If n is greater than OSN, the that the stringers satisfy the compact section requirements of stringers are ineffective. Section 7. A method is presented in the Commentary for non- compact sections. a. Elastic Buckling Stresses With Without End Pressure or 4.3.1 Axial Compression or Bending (Ne = O) (4-26) 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 where KO),= I .O if M, 2 3.42. When M, 3.42 determineK ~ L stresses are computed as if the stringers were omitted. How- from Equation 1 1-7. ever, the stringers may be assumed to be effective in carrying part of the axial loading when computing the stresses due to applied loads. PrL = E rR n+kh2-1 [ n2+h-1)2 r 12(1-v ) () " ] R+ +X*$ (n (4-27) a. Elastic Buckling Stresses F x e ~ a.,LC Et/R = , (4-22) where h = RWL, k = O for radial pressure and 0.5 for hydro- static pressure andv = 0.3. where a . rCis determined by the following equations which ~, h. Imperfection Factors. Thetestresultsindicatethat no depend on the value of Me.The values of a,, Equations in imperfection reduction factor is needed for stringer stiffencd 4-23 and 4-24 are given Equation 4-4. For valuesof M g < by cylinders. Therefore: I .5 use Me = 1.5 in Equation 4-23. For valuesof Me between 3.46 and 15, aXl, is obtained by linear interpolation. C, a = 1 .o & c. Inelastic Buckling Stresses F K L =II FreL (4-28) I .5 < M, < 3.46 (4-23) (4-29) C, = 0.605 a,, M , > 15 (4-24) See Equation 5-3 for y, b. Inelastic Buckling Stresses d. Failure Pressures PCL= T PeL (4-30) See Equation 5-3 fory. See a and c above for determination o f theterms in Equation 4-30. 4.3.2 External Pressure (N4/Ne= O or 0.5) 4.4 BAY INSTABILITY OF STRINGER STIFFENED The local buckling pressure of a stringer stiffened cylinder OR RING AND STRINGER STIFFENED will be greater than a corresponding unstiffened or ring stiff- CYLINDERS, AND GENERAL INSTABILITY OF ened cylinder if O S N , (N,7 = Number of Stringers) is greater RING AND STRINGER STIFFENED than the number of circumferential wavesat buckling for the CYLINDERS BASED UPON ORTHOTROPIC cylinder without stringers. This is based upon the assumption SHELL THEORY that one-half wave will form between stringers at buckling. For stringers with high torsional rigidity a full wave might The theoretical elastic buckling loads for both bay instabil- formbetweenstringers with aconcurrentincrease in the ity and general instability are given the following orthotro- by buckling pressure.This possible increasein buckling pressure pic shell equation (Equation 4-3 I). The elastic buckling load is not considered. per unit length of shell is denoted Niej where i is the stress --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • 16 API BULLETIN 2U direction andj is the buckling mode withj = E for bay insta- bility and j = G for general instability. The bay instability stress is determined by letting the cylinder length equal the ringspacing (Lj = L,) andthegeneralinstability stress is determined by letting the cylinder length equal the distance v Et E.,, = - 2 between bulkheadsor stiffener rings that are sufficiently sized 1-v to act as bulkheads(Lj = Lb). Whentheringsandstringersarenotsufficiently close together so that the shell platingis fully effective, the rigidity L,Et -(-)+L, E , = I - v - L,. EA, parameters (Ex, Eo, D,,De, DA, CA) of Equation 4-31 are modified by the ratios of effective width to stiffener spacing. Equations are givenfor L, and h, which are theeffective 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 equationare Et3 ):( El,s EA.& --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- D., = +-+- b h those which minimize N;,j where m 2 1 and n 2 2. For the fol- 12( 1 - v 2 ) lowing equation to be valid, the number of stringers must be greater than about 3n and the bay instability stress should be EtS EI,. EA,.Z: less than I .5 times the local shell buckling stress. When these D, = +-+- conditions are not met, the equations in Section 4.5 should be 12( 1 -v2) L,. used for sizing the stringers. Section 4.2 should be used for sizing the rings. D,, = ~ V Et3 +-Gt3(Lc?- h e ) +-+- -+ “L‘,. (4-3 1) 6(1-v’) 6 L, where c, = EA.SZ - b The term Y in Equation 4-3 1 is dependentupon the loading condition andis defined in the sectionsbelow. 4.4.1 Axial Compression or Bending (Ne = O) The elastic buckling stresses in the longitudinal direction for the bay instability and general instability modes of fail- ure are given by Equations 4-33 and 4-36 with Nxe, deter- mined from Equation 4-3 1. The following relationships for Y, r,, and L, are to be used for both bay and general instabil- ity stresses. When be < b, the values for Fxej must be deter- mined by iteration since the effective width is a function of the buckling stress. A. + bet t, = - b L, = L,.COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 E 0732290 Ob23150 q T 7 m --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- DESIGNSTABILITY OF CYLINDRICALSHELLS 17 a. For Bay Instability 3. Inelastic Buckling Stresses 1. Elastic Buckling Stresses.Use the following relation- FXCG = q F,,í; (4-37) together with those ships abovefor X tx, and L, to determine the bay instability buckling stresses: See Equation 5-3 for q. j = B. A, = I , = J , = O, L, = L, 4.4.2 External Pressure (NOIN0= O or 0.5) The elastic buckling stresses in the hoop direction for the (4-32) bay instabilityandgeneralinstabilitymodesof hilure are given by Equations 4-38 and 4-42 with Ne,, determined from Equation 4-3 l . The following relationships for and t, are to Y (4-33) be used for both bay and general instability stresses. F , is to he substituted for F,,B when F,,B > F,y so that Y = k(z)l+[i) 2 I be = I .9t (E/F,)"2 Ib. 2. Imperfection Factors A,. + L,? r,. = - r where k = O for radial pressure and k = 0.5 for hydrostatic pressure. a. For Bay Instability - A, = 5t andisgiven b by Equation 4-4with I . Elastic Buckling Stresses. Use the following relation- ships together with that given above Y to determine the for - bay instability stresses. c = 1.0 3. Inelastic Buckling Stresses Le = L,, 6, = b (4-34) See Equation 5-3 for q. (4-38) b. For General Instability See Equation 1 1.7 for K ~ L . l.Elastic Buckling Stresses. Use the following relation- 2. Imperfection Factors ships together with those above for Y, r.r, and L, to determine the general instability stresses. The valuefor cY@B = 1 .o F x c ~ the equation for b, is given by Equation 4-25 and in the value forF,,c is given by Equation 4-37. 3. Inelastic Buckling Stresses j = G, L, = Lb (4-39) (4-40) 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- a.,(;is given by Equation 4- 14. tion 4-4 l.COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D e A P I I P E T R O BULL ZU-ENGL 2000 m 0732270 O b 2 3 2 5 1 3 3 3 m 18 API BULLETIN 2U b. For General Instability dictedloads of thosemethodsconsidered. The methodis based on the procedure proposed Faulkner, etal. in Ref. 3. by 1. Elastic Buckling Stresses. Use the following relation- shipstogether with thatabove for Y todeterminethe - a. Elastic Buckling Stresses. The elastic bay instability general instability stresses. stress F x c ~ approximated by summing the buckling stress is of a shell panel and the column buckling stress of a stringer j = G, L, = Lb plus effective widthof shell. L, = 1.56 fit L,, I be = b NOeC FreG Or FheG = %G 7 KOG (4-42) where ctXLCx determined from Equations and 4-24 and: is 4-23 See Equation 1 1-9 forKOG. b,t b/ 2. Imperfection Factors = I,, + A , Z , (4-47) A,, + b,t 12 ~ + agC = 0.8 3. Inelastic Buckling Stresses FrcG = V FreiÌ (4-43) b for h, 50.53 FhcC = FlleG (4-44) See Equation 5-3 for V. 4. Failure Pressures lb if h,,< 0.53 I P& = %G T N,,G/R (4-45) h,, = (4-50) 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 MeL 3.46 CYLINDERS-ALTERNATE METHOD (4-52) E 2t/D M , < 3.46 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- The method of determining the bay instability stresses for stringerstiffenedandringandstringerstiffenedcylinders given in Section 4.4 isbasedupon a modifiedorthotropic shellequation. This equationisnotvalid if theminimum number of stringers is less than about three times the number of circurnfcrential waves for the bay instability mode. A fur- therrestrictionrequiresthatthe bay instabilitystressnot 3.46 < M, 8.57 exceed 1.5 times the local shell buckling stress. following The PIl = (4-53) equations can be used when these restrictions are notmet. 1 .O - 0.01 8 M y + 0.0O23Mi The rings are to be sized using the equations in Section 4.2 for ring stiffened cylinders. I M, I3.46 4.5.1 Axial Compression or Bending (No= O) The following method for determining the bay instability 1.15 for h, 2 I .O B = { (4-54) loads and stresses for axial compression and bending is quite 1 +0.15 h, for h,< 1.0 lengthy but gives the best cosrelation between test and pre-COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • - STD.API/PETRO BULL ZU-ENGL 2000 0732270 Ob23152 27T STABILITY DESIGN CYLINDRICAL SHELLS OF 19 stringerstiffeners. The pressure, p.$, andthefactor K!, are h, = (4-55) reL given by: if h, 10.53 (4-61) I Imo R, = { ) I.O--( b / t - 2c I + 0 . 2 5 ~ ; I .O%,, h;- 0.28 (4-56) h; (4-62) I if h, >OS3 11.10 for g 2 500 where c = 4.5 for continuous structural fillet welds. where b. Inelastic BucklingStresses. The inelastic buckling g = M.r M e stresses F x c ~ computed by usingtheOstenfeld-Bleich are expression for tangent modulus and given by: are The bay instability stress is given by: (4-63) See Equation 1 1-7 for KOL. where C,yistheratiooftheproportional limit to the yield b. ElasticBuckling Stresses. The elastic buckling stresses strength. Reference 3 suggests a value of C, = 0.5 for non- for radial pressure (i = r) and hydrostatic pressure (i = h ) are stress relieved shells. determined from the collapse stresses dividing by the plas- by c. Failure Load. The failure load is the product of the failure ticity factors determined from Equation 5-3. stressandtheeffectivearea. The effectiveshellwidthfor determining the failw load or applied stresses(see Equations (4-64) 1 1-2 and 1 1-4) is given by: The values for A are determined from Equation by tirst 5-3 O5 28 for he> 0.53 multiplying both sides of the equation by A. The left side of be = (4-58) the equation becomesT A which is equal to Fic.dFy The val- ues of F i c ~ givenby Equations 4-57 and 4-63. are Ib for h, 0.53 The following example will illustrate procedure. the Assume a nonstress relieved cylinder with FiCs = 30.0 ksi and where Fy = 50.0 ksi. Rewriting Equation 5-3 0.45 q = - +0.18 as qA=Oo.45+0.I8A See Equation 4-50 for h(,,Equation 4-56 for R, and Equa- A tion 4-57 for F x c ~The failure load P c is computed by: . ~ in material elasto-plastic region and equating it to Equation 4-64 TA = F i c 1Fy ~ 4.5.2 External Pressure(#+/#e= O or 0.5) 0.45 + O. 18A = 30.0 I 50.0 a. Inelastic Failure Stresses and Pressures. Thefailure pressure forbay instability is given the following equation: by yielding A = 0.8333 - Thus, Fies = AFy = (0.8333) (50.0) = 41.67 ksi, or PCB = @PL iPS) Kp - (4-60) - Since q = F i c ./~AFy = (30.0) / (0.8333) (50.0) = 0.720 The local shell buckling pressure, pel*, is determined from Equation 4-9 for a cylinder with length L, and assuming no --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D - A P I / P E T R O BULL ZU-ENGL 2000 W 0732290 Ob23153 LOb m SECTION !+PLASTICITY REDUCTION FACTORS Thepredictedelasticbucklingstressesgiven 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- r1 il A I0.55 lingstressesexceed 0.55 F,. The predictedinelasticshell buckling stresses are given by Equation 3-2 which is repeated "*tO.18 ifO.SS<A51.6 A below. rl=. 1.31 (5-3) F. ,. - F. . if I .6 < A < 6.25 KJ - re) (5- 1 ) I + 1.15A The ratio of the buckling stress to the yield stress can be .1/A if A 2 6.25 determinedfromEquation S-2. The product YA is determined where from Equation 5-3. This ratio is a measure of how efficiently the is utilized. Fici A=A,.=- A = A d = -Fici Fi,, 1 F,, = q A (5-2) F?. F?. See Section4 for Fie, and Section 7 for Tiej. --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 21COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • SECTION &PREDICTED SHELL BUCKLING STRESSES FOR COMBINED LOADS Interaction equations arc given for determining the failure 6.3 AXIAL COMPRESSION, BENDING AND HOOP stresses cylinders for subjected to combined loads. The COMPRESSION stresses duetobendingmomentaretreated as equivalent The following equation is applicable to any combination of axial stresses. The interaction equations are applicable to all axial compression, bending and external pressure. The axial modes of failure and to both elastic and inelastic buckling buckling stress, Fej. is the sum of the longitudinal stresses stresses. Each mode mustbe checked independently. If due to axial compression and bending. the bending stress is greater than theaxialstress,thefailurestressesaredeter- 6.1 GENERALLOADCASES mined from Section 6.2. Fe,; is the failure stress in the hoop In the following equations for NQ and Ne, P is the total direction. axial load including any pressure load on the endthe cylin- of R i - c R, R , , + R i = 1.0 (6-3) der, M is the bending moment and p is the external radial pressure. where a. Axial Compression and Hoop Compression R,, = F+, I Fxc, NQ = P I (21tR) Rh = Fec, I F,, The equations for are dependent upon the cylinder geom- c Ne = P R , etry. b. Bending and Hoop Compression a. Unstiffened and Ring Stiffened Cylinders (all buckling N$ = M I (M*) modes) N e =P R , F,,., + F,.(,j c = - 1.0 c. Axial Compression, Bending and o p Compression Ho F,. N$ = P I ( h R ) + M 1 (xR2) b. StringerStiffenedandRingandStringerStiffened Ne = P R , Cylinders 1. Local Buckling ( j = L ) 6.2 AXIALTENSION, BENDING AND HOOP COMPRESSION 0.4( + F,.‘,;) c= - 0.8 F,. The failure stresses are the lowerof the values determined from Equations 6-1 and 6-2. The longitudinal stress F$,. is 2. Bay Instability and General Instability i= B , j = G) ( the sum of the axial and bending stresses. F,,,. = Fr(>( 1 -0.25 ““i) F?. The buckling stresses for any combination of longitudinal compression and hoop compression, N d N e , are determined by the following procedure for each the buckling modes. of Step 1. Calculate F.rc, and Frc.from the equations in Sec- tion 4. where Faj is the failure stress in the hoop direction corre- Step 2. Solve for F&, in Equation 6-3 by letting F*, = Fec, sponding to Fwj which is the coexistent failure stress in the k K~jlKej. axialdirection,and Frc, is thepredictedfailurestressfor radial pressure. Fw. is given by Equations 4-10,4-19,4-28, where 4-39,4-43, and 4-63. k = NdNe The values of F@; and Fe,, are determined from Equations KQ, = axial stress modifier (see Table 6. I), 6-1 and 6-2 by letting F*. = Fe(j k K,+iKe, where k = N d N e and then solving forFe,. See Table6.1 for Ki. KO; = hoop stress modifier (see Table 6.1). --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 23COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO B U L L ZU-ENGL 2000 0732290 Ob23155 T87 m 24 API BULLETIN 2U Table 6.1-Stress Factors, Ku Ring Stringer Ring and Stringer Kìj Unstiffened Stiffened Stiffèned Stiffened I .o 1.o 1.o 1.o t/t., t/t r Section 4 1. I Section 4.4.1 I .O t4r Section 4.4. I I .O Equation 11-7 Equation 1-7 Equation I 1-7 Same as Kor. Same as KOL I Equation 1 1-9 Equation 1 1-9 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • SECTION 7-STIFFENER REQUIREMENTS The flow chal1 in Figure 3.1 shows the procedure for deter- where h, is the full width of a flat bar stiffener or outstanding miningtheallowablestresses for allbucklingmodes.The leg of an angle stiffener and one-halfof the full width of the sizes of the stringers are determined from thebay instability flange of a tee stiffener and is the thickness ofthe bar, leg of modeequationsandthesizesoftheringsaredetermined angle or flange of tee. from the general instability mode equations. b. Web of Tee Stiffener orLeg of Angle Stiffener Attached to The shell buckling stress equations were developed on the Shell basis of no interactionbetweenthebucklingmodes. The buckling stresses for local buckling, however, be reduced may if the predicted buckling stress for either bay instability or (7-4) generalinstabilityisapproximatelyequal to thcpredicted --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- local buckling stress. Similarly,if the predicted general insta- bilitystressisapproximatelyequaltothe bay instability where h,yis the full depth of a lee section or full width of an stress, the actual stress for either of these modes may be less angle leg andr, is the thicknessof the web or angle leg. than predicted. Mode interaction can be avoided by applying a factor ß to 7.3 SIZING OF STIFFENERS the strains corresponding to the buckling stresses. It is desir- Thestringerproperties are determined by equatingthe able to provide a hierarchy for failure with general instability elastic design stresses for local buckling and bay instability preceded bybay instability and bay instability preceded by and the ring properties are determinedby equating the elastic local shell buckling. A minimum factor o f ß = 1.2 is recom- design stresses for local buckling and general instability. This mended for both the bay and general instability modes. The is equivalent to equating the buckling strains corresponding to designer may elect to select a higher ß value for the general - Fic, and F i c ~ . instability mode. The equations for F*; and F&; are given in Section 6 for cylinderssubjectedtocombinedloads.Forcylinderssub- 7.1 DESIGN SHELL BUCKLING STRESSES jected to single loads F e , = Fxe; and Fee; = Frej.When the The buckling stresses which include the factor ß willbe axial stress is tension, only the hoop stress equatlon must be called the design shell buckling stresses and are given the by checked. For this case let = Fm;. Fee, following equations: a. Stringers - . ./P FreJ. = F te/ . (7- 1) - F$e5 = F e ß I 1.2 L F ~ L (7-5) - F1cJ. - - . - Fie; (7-2) - Foe5 = Feeß I I .2 2 fee^ (7-6) where ß = 1.0 for local buckling and 1.2 for bay instability and general instability. The values of q are determined from b. Rings - Equation 5-3 for h = Ad. F ~ = F ~ IG t F , ~ L C 1.2 (7-5) - 7.2 LOCAL STIFFENERBUCKLING FeeG = Feet I 1.2 2 fee^ (7-6) To preclude stiffener buckling prior to shell buckling, the The following general procedure may be used Tor deter- local stiffener buckling stress must be greater than the shell mining the stiffener sizes: buckling stress given by the foregoing equations. The local stiffener buckling stress can be assumed to be equal to the 1. Calculatethelocalshellbucklingstresses F ~ and L yield stress for stiffeners which satisfy the following compact fee^. section requirements. stiffenersmeeting For not these 2. Assume a stringer size and calculate the bay instability requirements, the local stiffener buckling stress can be deter- stresses F ~ and Fee0. Equations 7-5 and 7-6 must be sat- B mined from Equation C7-1 in the Commentary. isfied.Repeatthisstep until thedesiredcorrelation is a. Flat Bar Stiffener, Flange of a Tee Stiffener and Outstand- obtained. It may not be practical to have the same margins ing Leg of an Angle Stiffener between buckling local and bay instability both for equations. 3. Repeat step 2 for ring stiffened cylindcrs by satisfying Equations 7-7 and 7-8. 25COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD-APIIPETRO BULL ZU-ENGL 2000 0732270 Ob23157 B 5 1 M SECTION &COLUMN BUCKLING The shell buckling stresses given by Equations 4-6, 4-7, where and 4-25 for cylinders subjected to axial compression only, CL,^ = 0.87 and by Equation 6-3 for cylinders subjectedto axial compres- sioncombinedwithhoopcompression do notinclude the effect of column buckling. The buckling stress of a tubular 8.2 INELASTIC COLUMN BUCKLING STRESSES column determined is by substituting shell the buckling stresses, F*L, fortheyieldstress in thecolumnbuckling equation. Without external pressureF+. = Fxc,. The buckling stress of a tubular column is equal the shell buckling stress to for cylinders with& / r i J-; 0.5 . For longer columns FQK= the buckling stresses are given by the following equations. These equations are based on the premise that the stiffeners for stiffened cylinders are sizedin accordance with the bulle- tin and only the local shell buckling mode is considered to interact with column buckling. where 8.1 ELASTICCOLUMNBUCKLING STRESSES c,.= For load axial 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 ~ isLdetermined from Equation 6-3. --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 27COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • SECTION SALLOWABLE STRESSES Theallowablestressesforshortcylinders, &/r I 0.5 9.1.1 Axial Tension ,./mi, by applying an appropriate factor are determined to in of safety the predicted buckling stresses given Sections 4 F,. F, = - F, = O (9-2 and 6 . Without external pressure F+. = F,,. The effects of FS imperfections due toout-of-roundnessandout-of-straight- ness on the shell buckling stresses are very significant in the 9.1.2 Axial Compression or Bending in elastic range but have little effect the yield and strain hard- ening ranges. Therefore a partial factor of safety, y, that is dependent upon thebucklingstressisrecommended. The (9-3) value of y is 1.2 when the buckling stress is elastic and 1 .O when the buckling stress equals the yield stress. linear vari- A See Equations4-6,4-7, and 4-25 for F X ( . ~ . ation is recommended between these limits.The equation for y is given below. A value of y = 1.0 may be used for axial 9.1.3 External Pressure tension stresses and for column buckling mode stresses. a. Radial Pressure Only(N,$Ne = O ) :1 FiCi I 0 . 5 5 F , (9-4) y = 1.444 - 0 . 4 4 4 F i c j / F , . 0.55 F , < Fic, < F,. Fi, = F , (9- I ) See Equation 4-1O for F r C ~ .- Forlonger cylinders, KL,/r > 0.5 is A-., subjected to b. Hydrostatic Pressure (N,#Ne = 0.5) axial compression,the cylinders will fail in the column buck-- lingmodeandthecolumnbucklingstressesaregiven by (9-5) Fquation 8-2. An interaction equation is givenin this section for long cylinders Subjected to bending in combination with axialcompression.Thissameinteractionequationcanbe See Equation 4-1 I for F l 1 ( . ~ . used when the cylinder is also subjected external pressure. to The allowable stresses F,,, Fb, and Fe are to be taken as the 9.1.4 Axial Tension and Hoop Compression and lowest values given for all modes of failure. If the stiffeners Axial Tension, Bending, and Hoop are sized in accordance with the method given in Section 7, Compression only the local shell buckling mode need be considered in the equations whichfollow. The allowable stresses must be greaterthantheappliedstresseswhichcan be calculated usingtheequationsgiven in Section 11 or bymoreexact methods using computer codes. The factor of safety, FS, is See Equations 6-1 and 6-2 for F@.Land Fec!,. provided by the design specifications. In general, = 1.67y FS FS is suggested for normal design conditions and = 1 . 2 5 for ~ 9.1.5 Axial Compression and Hoop Compression extreme load conditions where a one-third increase in allow- and Axial Compression, Bending, and Hoop able stresses is appropriate. Compression 9.1 ALLOWABLE STRESSESFOR SHELL (9-7) BUCKLING MODE The following equations provide the allowable stresses for See Equation 6-3 for F+.j and Fecj, the local shell buckling mode. The same equations are appli- cabletoothermodes of failure by substitutingthedesign 9.1.6 Bending and Hoop Compression ~ inelastic buckling stresses given in Equation for 7-2those modes in the equations. The following equations should be - satisfiedfor all loads.SeeSection 1 I fori,, fb, andfq. LI +f b < fe < Fe See Equation 6-3 for FQ(.Land FeCL. --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 29COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 0 7 3 2 2 7 0 Ob23157 b2q 13 30 API BULLETIN 2U 9.2 ALLOWABLE STRESSES FOR COLUMN a. Forf,,lF,, 5 O. I5 BUCKLING MODE f, - <f1h. 0 -+ (9- 1O) When KLJr > 0.5 the following equations as F, FI, well as those in Section 9.1 must be satisfied: b. ForJjF,, O. 15 9.2.1 Axial Compression (9- I I ) See Equation8-2 for F$,c. 9.2.2 Axial Compression and Bending 9 2 3 Axial .. Compression, and Bending, Hoop Compression Members subjectedto both axial compression and bending stresses should satisfy Equations 9-10 and 9- 1 I . See Qua- Members subjected tocombinations of axial compression, tions 9-9 for F,, and 9-3 for Fb and Paragraph 3.3. Id Member I Slenderness of API RP 2A (Ref. IO) for C,, and K . C must be greater than or equal to 1 -f,/F,. , bending and hoop compression should satisfy Equations Equation 9-7. 9-10 and 9-1 1 with F,, determined from Equation 9-9 and Fb from --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D * A P I / P E T R O BULL 2U-ENGL 2000 W 0732290 Ob23Lb0 3Yb D SECTION 10”TOLERANCES The foregoing rules are based upon the assumption that the 10.3 LOCAL DEVIATION FROM TRUE CIRCLE cylinders will be fabricated within the following tolerances. Cylinders designed for external pressure should meet the The Commentary providesadditional information the on following tolerances. The local deviation from a true circle buckling strength of cylinders whichdo not meet these toler- should not exceed maximum the permissible deviation ances. The requirements for out of roundness are from the obtained from Figure 10-1. Measurements are to bemade ASME fressure Vessel Code ( 1 2) and the requirement for with a gauge or template with the arc length obtained from straightness isfrom the ECCS rules(1 3). Figure 10-2. to Additionally the difference between the actual radius the 10.1 MAXIMUMDIFFERENCES IN CROSS- shell at any point and the theoretical radius should not exceed SECTIONAL DIAMETERS 0.005R. The diRerence hetween the maximum and minimum diam- eters at any cross section should not exceed 1 % of the norni- 10.4 PLATE STIFFENERS na1 diameter at the cross section under consideration. 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 102 LOCAL DEVIATION FROM STRAIGHT LINE from Equation 4- 17. A conservative value for n is given by ALONG A MERIDIAN Equation 10-3. Cylinders designed for axial compression should meet the R following tolerances. The local deviation from a straight line II’ = 1.875 - f i t 2 4 ( 10-3) measured along a meridian over a gauge length Lxshould not L,, exceed the maximum permissible deviation e.r. L.r = 4 fit but not greater thanL,. 31 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • 32 API BULLETIN 2U )R ( 100 m 1op IOD Qo * 100 110 100 a m 10 m m rg 50 26 om o 10 2 I 4 I 6 7mnm 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 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D - A P I I P E T R O BULL ZU-ENGL 2 0 0 0 m 0732290 Ob231b2 219 W SECTION 11-STRESS CALCULATIONS The computed stresses in stiffened cylindrical shells may 11.3 HOOP STRESSES differ from the membrane stress o f unstitrened shells. Equa- tions are given below for correction factors which account for Theeffects of longitudinal the stiffeners on hoop the the load sharing effects of the various stiffening elements. stresses are neglected. The imperfection and plasticity factors given in Sections 4 and 5 are also based upon this assump 11.1 AXIAL STRESSES tion. The external pressure, p . is assumed to be uniform over the cylinder. In Equations 1 1 - 1 and I 1-2, P is the total axial load includ- of ing any pressure load on the end the cylinder. a. Unstiffened and Stringer Stiffened Cylinder a. Unstiffened and Ring Stiffened Cylinders PR,, fe = f ( 1 1-5) D r ( 1 1-1) f = 2KRr b. Ring Stiffened Ring Stringer and and Stiffened h. Cylinders Longitudinal With Stiffeners. Whenthe Cylinders stringers are not spaced sufficiently close to make the shell I . Stress inShellMidwayBetweenRings. This swess used fully effective, the effective area is to determine the axial Fe, must be less than the allowable hoop stresses, for local and bending stresses. The factor Q,, is a ratio of the effective shell buckling and bay instability. area to the actual area. Q,, = 1.0 for the local shell buckling mode. See Equations4-32,4-35, and 4-58 for be. ( 1 1-6) P where (1 1-3) f = G, where Q - , A + b E t K0L { for M, 2 3.42 = :*yey for M,<3.42 ( 1 1-7) u A,s+ bt I - 0.3k E = A , = 2ttRt + N,A,v 1 +L,r/A A =A, (R/R,J2 11.2 BENDINGSTRESSES In Equations 1 1-3 and 1 1-4, M is the bending moment at M,=L,I fit the cross section under consideration. for M , I 1.26 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- a. Unstiffened and Ring Stiffened Cylinders - 0.46M, for 1.26 < M, < 3.42 ( 1 1-3) for M,, 2 3.42 k = N d N e (see Section 6.1 for N+ and Ne) where R, = Radius to centroid of stiffening ring 1 +0St/R K, = 1 + 0.25( r / R)? Le = 1S6 f i t + t,. I L, The value of Kb is approximately I .O. 2. Stress in a Ring Stiffener. This stress must be less Fe, than the allowable hoop stress, for general instability. b. Cylinders with Longitudinal Stiffeners See Equation 11-2 for definition of Q,,. ( 1 1-8) M where fh = - ( 1 1-4) QJ Rt,- where te = t + A , y / b K e , = ( 1 -0.3k)- L J 2 0 A r + Let and k and L, are the sameas in Equation 1 1-7. ( 1 1-9) I 33COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD*API/PETRO BULL 2U-ENGL 2000 D 0 7 3 2 2 7 0 Ob23Lb3 0 5 5 SECTION 12-REFERENCES --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 1. Miller, C. D. Grove, R. B., andVojta, J. F., “Design of 7. American Institute of Steel Construction, “Manual of Stiffened Cylinders for Offshore Structures,” American Weld- Steel Construction,” 8th Edition, 1981. ing SocietyWeldedOffshoreStructuresConference, New Orleans, Louisiana, December 198’3. 8. Wilson, W. M., “Tests of Steel Columns,” University of IllinoisEngineeringExperimentStationBulletin, No. 292, 2. Miller, C. D., “ExperimentalStudy of the Buckling of 1937. Cylindrical Shells with Reinforced Openings,” ASMWANS Nuclear Engineering Conference, Portland, Oregon, July 9. Chen, W. F. andRoss, D. A., “TheStrength ofAxially 1982. No. Loaded Tubular Columns,” Fritz Engineering Lab Report 393.8, Lehigh University, September 1978. 3.Faulkner,D., Chen, Y. N. anddeOliveira,J. G., “Limit StateDesignCriteriaforStiffened Cylinders of Offshore 10. AmericanPetroleumInstitute, RecommendedPractice Structures,” ASME 4th National Congress Pressure Vessels of for Planning,Designing, andConstructing Fixed Wshore and Piping Technology, Portland, Oregon, June 1983. Platforms, API RF’2A, Nineteenth Edition. August 1, 1 9 9 I . 4. Stephens, M.,Kulak, G . andMontgomery,C.,“Local 1 1. AmericanPetroleumInstitute, Recotnrrlended Practice Buckling of Thin-WalledTubularSteelMembers,”Third for Planning,Designing,andConstructing Fixed Wshorr InternationalColloquiumonStability of MetalStructures, Platfonns, API RP 2A, Twentieth Edition,July 1, 1993. Toronto, Canada, May 1983. 12. American Society of Mechanical Engineers, Boiler and 5 . Sherman, D. R., “Flexural Tests of FabricatedPipe Pressure Vessel Code, Section VIII, DivisionI and 2 and Sec- of Beams,” Third International Colloquium on StabilityMetal tion III, Subsection NE, 1983. Structures, Toronto, Canada, May 1983. 13.EuropeanConvention Constructional for Steelwork, 6. Miller, C. D., Kinra, R. K. and Marlow, R. S., “Tension “European Recommendations for Steel Construction,” Sec- and Collapse Tests of Fabricated Steel Cylinders,” Paper C W tion 4.6, Buckling o Shetls, Publication 29, Second Edition, f 42 I 8, Offshore Technology Conference, May 1982. 1983. 35COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • 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 Stiffenedor Ring and Stringer StiffenedCylinders 57 C4.4 Bay Instability of Stringer Stiffenedor Ring and Stringer Stiffened Cylinders and General Instabilityof Ring and Stringer Stiffened Cylinders Based Upon Orthotropic Shell Theory........................................... 57 C4.5 Bay Instability of Stringer Stifiened and Ring and Stringer Stiffened Cylinders-Alternate Method ....................................... 63 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 Differencesin 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 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 37COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D = A P I / P E T R O BULL ZU-ENGL 2000 W 0732270 Ob23Lb5 928 W APPENDIX A-COMMENTARY ON STABILITY DESIGNOF CYLINDRICAL SHELLS Introduction menlary contains comparisons of the predicted buckling stresses given by the Bulletin 2U equations with test data for This commentary provides the designer with the basis for fabricated cylinders only. Additional modifications are to be the design methods presented in Bulletin 2U. The design cri- expected after the completion of two ongoing test programs. teria are applicable to shells that are fabricated from steel A test program isin progress to determine the effecls of exter- plates where the plates are cold or hot formed and joined by nal pressureonbeamcolumns.Thefirstphasewhichhas welding. The stability criteria are based upon classical linear been completed (Ref. ) , was a series of 64 tests on short col- 5 theory which has been reduced by capacity reduction factors umns. The second phase will be tests on long columns with and plasticity reduction factors which are determined from different lengths and is be completed in 1987. Almosta l l of to approximatelower-boundbucklingvaluesoftestdataof the tests on fabricated ring and stringer stiffened cylinders shells with initial imperfections which are representative of reported in Ref. 6 were made on stress relieved test models the tolerance limits givenin Section 10 of the Bulletin. and the stringers did not meet the compact section require- The most commonly used rules for the designof cylinders ments of Section 7. Additional tests are now in progress using for offshore structures in the United States are those given by test models with compact stiffeners that have not been stress RP the American Petroleum Institute, API 2A ( 1 ). These rules relieved. are limited, however, to unstiffened ring stiffened cylinders or and cones with diametedthickness ( D r ) ratios that are less Cl General Provisions than or equal to 300. The members of many of the new plat- C1.l SCOPE formconceptsfordeepwaterexceedthis limit. Alsothe effects of stiffening rings on the buckling strength is consid- The present rulesare limited to cylindrical shells. ered only for external pressure loading. DetNorskeVeritas (2) updateditscriteriaforbuckling Cl -2 LIMITATIONS strengthanalysis in 1982.Thesecriteriacan be appliedto unstifiened, ring stiffened, ring and stringer stiffened cylin- or Theminimumthicknessof in. isquitearbitrary. Many ders having larger D/r values. Close stiffenerspacingis tests have been performed on fabricated steel models with emphasized and, in fact, for stringer spacing in excess of a f = 0.075 in. These models requiltd very closely controlled moderate value(Me= 3.0) the stiffening effect of the stringers fabrication and welding procedures to obtain the desired tol- is neglected. These criteria formulate a characteristic stress erances, however. Also, the thinner models are much more for both local shell and bay instability (termed “panel buck- sensitive to nonuniform distribution of loads. The limit of R/r ling” by DNV). The characteristic stress in terms of a buck- is S l o 0 0 corresponds to the largest R/r ratio for a fabricated ling coefficient that DNV recommends be determined by a model test. more refined analysis model tests. In lieu of this, DNV pro- or vides empirical equations based upon approximate methods Cl .4 MATERIAL for calculating the buckling ccdlìcients. The calculated buck- The stability criteria are applicable to steels which have a ling strengths for stringer stiffened cylinders of Ref. 2 were well defined yield plateau such as those specified in Table found to be generally conservative, also quite inconsistent but 2.9.1 of API RP 2A or Table I l . 1. I of API RP 2T. Most of the with the various test results. The criteria givenin Bulletin 2U materials used for model tests had minimum specified yield provide accurate more predictions a complete andmore strengths of 36 or 50 ksi. A few additional models have been description of the possible buckling modes. made from steels with 80 to 1 0 0 ksi yield strengths. The Bulletin follows closely the recommendations given in Ref. 4 I with some modifications based upon further analysis of available test data. proposed criteria arealso similar to The C2 Geometries, Failure Modes and Loads those given by ASME Code Case N-284 (3) for design of The geometric proportions of a tubular member will vary containment vessels.Reference 41 includes modifications widely depending the on application. The load carlying which were based upon several test programs conducted on capacity is determinedby the shell buckling strength for short fabricatedcylindersafterRef. 3 waswritten.Reference 4 members with KL, /r less than about 12. For longer members includes a comparison ofthetestdatathatwasavailable the strength of the member is also dependent upon the col- before 1979 with the equations of Ref. 3. Much of the test umn buckling strength. data was from models that do not meet the definition of fabri- The shell buckling strengthis a function of both the geom- in cated cylinders given Section l . l of the bulletin.This com- etry and the type of load or load combination. Unstiffened --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 39COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • shells fail by local shell buckling. The failure stress will be and general instability modes. This is left to thediscretion of less than the yield stress for Wt values greater than about30 so the designer. The factor 1.2 provides sufficient margin that for members subjected to axial compression and for Rh val- local buckling should always be the initial mode failure. of ues greater than about IO for members subjected to external A stringer stiffened cylinder may continuc to carry load pressure. The post buckling strength is very low for unstiff- after theshell has buckledlocallybetween stringers until ened shells andmay be as low as 20% or less of the prebuck- failure occurs by bay instability. This mode of failure when ling strength. due to external pressure or external pressure combined with The axial compression buckling stress can increased by be axial compression results in the postbuckling formation of a the addition of stringers (longitudinal stiffeners). The string- series of longitudinalplastichingesbetween stringers at ers carry part of the load as well as increase the local shell locations around the circumference where the circumferen- buckling stress. They must be placed less than about IO f i tial waves are radially outward.The formation of hinges may apart tobe effective for axial compression.The stringer spac- also occur in the rings due to local buckling of the ring ele- ing must be less than one half the wave length determined for ments. Under axialcompression load the modeof failure is a a shell without stringers to bc effective in increasing the fail- joint collapse of stringers and shell. The post buckling load ure stress for external pressure. The useof stringers intro- may be as much as 80% of the collapse load for either axial duces two more possible modes of failure. The stringer compression or external pressure if the plastic hinges do not elements must be compact sections (see Section 7) or local develop in the rings. buckling of the stringers may occur. Another possible mode Column buckling is buckling of the cylinder as a column. of failure is the buckling of the stringers and shell plating A tubular column can be treated similar to other types of col- together. This mode of failure is termed bay instability and umns by substituting the shell buckling stress for the yield the failure stress is mainly a function of the moment of inertia stress in the column buckling equation. If the recommenda- of the stringers and attached shell. Waves form in both the tions of the Bulletin are followed, the local shell buckling longitudinal and circumferential directions for axial compres- stress will always be the lowest shell buckling stress value sion loads.A single halfwave forms in the longitudinaldirec- and will be used in place of the yield stress in the column tion and several waves form in the circumferential direction buckling equations. for external pressure. Ifthebay instability stress is greater than the local shell bucklingstress, the cylinder will continue C3 BucklingDesignMethod to c m y load after local shell buckling occurs. there is only If a small difference, local shell buckling will probably initiate The design of cylinders for compressive loads is an itera- --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- thebay instability mode. Bulletin 2U recommends that the tive procedure.The steps to follow are given a flow chart in in shell be designed so that the bay instability stress is 1.2 times Figure 3.1. The first step in the design process is toassume a the local shell buckling stress. shell geometry and calculate the applied stresses with the aid Ring stiffeners are much more effective than stringers in of the equations in Section 1 1. The next step is to calculate increasingthebuckling stress of a cylinder subjected to the local shell buckling stresses from Section4 for individual external pressure. The buckling stress is increased for values load cases and Section 6 for combined loadcases. Equations of U R < 2.85 f i r . For greater distances between rings the forcolumnbucklingstresses are given in Section 8. The buckling pressure is the same as that of an unstiffened cylin- allowable stresses can then be determined from Section 9. der. The use of rings introduces two more possible modes of The shell geometry can be adjusted to give the desired agree- failure. Onemodeislocalbucklingof the ring elements ment between applied and allowable stresses. which can be avoided by the use of compact sections. The The next step is to determine stiffener sizesif rings and/ the other mode of failure is the buckling of one or more rings or stringers are used. stiffener elements should satisfy the The together with the shell (and stringers when used). This mode requirements of Section 7.3. The flow chart in Figure 3.1 of failure is called general instability and the failure stress is shows that when stiffeners are used the bay instability and a function of the moment of inertiaof the ring together with general instability stresses are determined from Sections 4 an effective width of shell. This mode of failure should be and 6. As discussed in Section C2 it is desirable to have the avoided because it results in gross distortions of the shell. failure stressesfor bay instability greater than thelocal buck- Localshellbuckling may precipitate a generalinstability ling stresses and the general instability stresses higher than failure if there is only a small difference in thebuckling the bay instability stresses. This procedure will prevent one stresses for the two modes.The bulletin recommends that the mode of failure from initiating another mode of failure. The shell be designed so that the general instability stress is 1.2 separation of the local buckling mode from bay or general the times greater than the local buckling stress both ring stiff- for instability modes is accomplished with the factor ß given in enedcylindersandringand stringer stiffened cylinders. Section 7. The separation of the bay and general instability These provisions do not provide a margin between the bay modes is left to the discretion of the designer.COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STABILITY DESIGNOF CYLINDRICAL SHELLS 41 C4 Predicted Shell Buckling Stresses for to C4.1.1-5 for unstiffened cylinders which failed inelasti- Axial Load, Bending and External cally. There isonly one bendingtestshownon Figure Pressure C4. l . 1-2 and two bending tests shown on Figure C4.I . 1-3. The theoretical elastic buckling stress equations given in Since these tests fall within the scatter band of the axial the Bulletin are based upon classical theory with simple sup- compression tests, Equations 4-2 and 4-7 are used for cyl- porl boundary conditions and Poissons ratioof 0.3. The dif- inders subjected to either axial compression or bending. ferences between testson fabricated cylindrical shells and the The failure stresses for axially compressed cylinders reach theoretical stresses are accounted for by the factor au. This a plateau equal to the yield stress at a ?/R ratio of 0.015 factor is equivalent the ratioof the strainin a fabricated cyl- to whereas the failure stresses for bending reach a plateau of inderunderloadtothestrain in thetensilecouponfrom about 1.08 Fy and as the ratio Et/F,R increases the failure which the material properties are determined. The values of stresses increase to values correspondingto theplastic aoapply to cylinders with initial shapes which meet the fabri- moments. cation tolerancesof Section 10. Design guidance is also given Comparisons are made between the test and predicted in the commentary for cylinders which do not meet the toler- stresses for ring stiffened cylinders in Figures C4.1.1-6 to ances of the Bulletin. C4.1 .I-IO. The transition between stiffened andunstiff- ened cylinders is difficult to detine because of lack of test C4.1 LOCAL BUCKLING OF UNSTIFFENED OR data. The ring stiffened cylinder tests are limited to L/&r RING STIFFENED CYLINDERS I6 except for one set of tests. All of these tests indicate that the failure stress for L I f i t = 4 is approximately the The buckling strength of a section of shell between ring same as that for L l G r = 6 . Therefore, the test stresses at stiffeners is assumed to the same as an unstiffened shell. be L/&t = 6 should be the same as an unstiffened cylinder. This is not the case, however. The unstiffened cylinder test C4.1.1AxialCompressionorBending stresses are approximately */3 of the test stresses for a ring- Equation 4-2 was determined Equation from 1 1-8, p. 465 spacing of LIfif = 6. The unstiffened cylinder tests were of Ref. 7. The minimum stress is found by letting n = O and conducted at the University of Illinois in 1933 (IO). The m = 1. This equation is given below using the nomenclature failure stresses may bc low because the ends of the cylin- of Bulletin 2U. ders were neither machined nor welded to a bearing plate. Shims were used to fill gaps between the specimens and the testing machine. All of the cylinders with large R/r val- ues were made from thin sheet material, /32 in. thickness. The thin material made the models quite sensitive to non- uniform bearing. New tests are needed to resolve the ques- --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- tions raised. where rnnR C4.1.2 External Pressure h = - L Equation is 4-9 determined fromEquation (See 4-27 4.3.2). This equation is very accurate for all values of k I I .O rn = number of half wavesin the longitudinal direction where k = NJNo. A nondimensionalized plot of Equation 4-9 at buckling, is given on Figures C4.1.2-1 and C4.1.2-2. Il = number of circumferential waves at buckling. An evaluation of tests on unstiffened and ring stiffened cyl- inders subjected to external pressure is given in Ref. I l . A An analysis ofaxialcompressionandbendingtests of constant of value = 0.8 isrecommended cylinders for unstiffened cylinders is given in Ref. 8. Equation 4-4 is taken which meet the fabrication tolerances of Section IO. For cyl- from this reference. Similarly, an analysis of axial compres- inders with Rh ratios less than about 60 the following equa- sion tests on ring stiffened cylinders is givenin Ref. 9. Equa- tion found give was to a lower bound test for on data tions 4-5 and 4-7 are taken from this reference. cylinders which exceeded the specified tolerance y. for Equations 4-6and 4-7 are plotted for yield stresses of 36, 50, and 60 ksi in Figure C4. I . 1-1. This figure shows that a,, = 1 - 0 . 2 h 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-3COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • 42 2U API BULLETIN --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STABILITY DESIGN CYLINDRICAL SHELLS OF 43 ... ,.. ... .. .-* I . - . I .. .* _. .. *, .. _ I .. ., .- .. I , .. ?. +. .. c. .. -4 3 . I ) “ I .# .. , . 1 c ? .. t . --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- A * . I. .. ., . I ” .COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D * A P I / P E T R O BULL ZU-ENGL 2000 W 0732270 Ob23170 295 m 44 API BULLETIN 2U --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D = A P I / P E T R O B U L L ZU-ENGL 2000 0732290 Ob23171 1 2 1 m STABILITY DESIGN CYLINDRICAL SHELLS OF 45 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • 46 API BULLETIN 2U --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 m 0 7 3 2 2 7 0 Ob23173 T T V m STABILITY DESIGN CYLINDRICAL OF SHELLS 47 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 m 0732270 Ob2317V 730 m 48 API BULLETIN2u --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STABILITY DESIGN CYLINDRICAL SHELLS OF 49 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 m 0732290 Ob2317b 703 m 50 API BULLETIN 2U --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D - A P I / P E T R O BULL ZU-ENGL ZOCIO . 0732270 P Ob23177 bllT m --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D = A P I / P E T R O BULL ZU-ENGL 2000 I 0732270 Ob23178 5 8 b I 52 API BULLETIN 2U --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- A Figure C4.1.2-1-Theoretical Local Buckling Pressureof Unstiffened or Ring Stiffened CylindersCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STABILITY DESIGNOF CYLINDRICAL SHELLS 53 Y --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- Figure C4.1.2-2-Theoretical Local Buckling Pressure and Number Circumferential Waves of for Unstiffened or Ring Stiffened CylindersCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D * A P I / P E T R O BULL ZU-ENGL 2000 0 7 3 2 2 7 0 O b 2 3 L B O L3q 54 2U API BULLETIN where D,,,,,,, Dlnirr, D,,,,,, maximum,minimum and arethe C4.2 GENERAL INSTABILITY OF RING andnominal outside diameters atthecross-sectionwhich STIFFENED CYLINDERS gives the largest value for y. See Figure C4.1.2-3. Compari- sons are made between the testand predicted stresses in Fig- C4.2.1AxialCompressionorBending ure C4.1.2-4. Equation 4-13 was determined from Equation 29 of Ref. Theoretical methods have developed been by several 15 for U = O. An analysis of available test data is given in authors to account for theeffects of imperfections.All of Ref. 16 and Equation 4-14 is based upon this study. The these methods are based upon the assumption that the initial imperfection factor a , is a constant when the area of the ~ out-of-roundness is similar in form to the assumed buckling stiffener exceeds 20% of the shell area. It is equal to an mode shape. The bending stresses resulting from the initial unstiffened cylinder when the stiffener area is zero. A out-of-roundness are combined with the membrane stresses. straight line variation is assumed between these two limits. The buckling pressure is determined by equating the com- Additionally, it is recommended that the minimum area of bined hoop stress to the yield stress or by the von Mises fail- the stiffener must equal 6% of the shell area for it to be ure theory. Reference I 1 gives a comparison of test pressures effective. Test data is compared with Equation 4-14 in to those predictedby the methodsof Timoshenko & Gere (7), Figure C4.2.I - I . GalletlyandBart (1 2), andSturm (13). The correlation between these theories and test results is very poor and the methods are much too conservative to be practical for use. C4.2.2 External Pressure The ratios ofpTe~&Theory varied from I .93 to 3.25 for the the- The equation for external pressure is based upon the split ory of Timoshenko and Gere and from 1.40 to 2.82 for the rigidity principle where the first term is the contribution of the other two theories. shell of length bctwccn bulkheads and the second term is the MillcrandGrove (14) have found an alternatemethod contribution of the effective ring section. The shell contribu- which provides excellent correlation cylinders for of all tion is taken from Equation 4-27. Only the second term of this geometries. The theoly behind the method is that a flat spot equation is used since the first term has little contribution if on the shell havinga larger than nominal radiusof curvature included. The second term of Equation 4-1 1 is the buckling will buckle at a lower pressure. Also, was noted from exper- it pressurefor a ringunderuniformloadwhichisgiven by imental results that an imperfect shell will buckle in the same or nearly the same number of waves as a shell without imper- Equation d, p. 289, Ref. 7. of fections. To determine the local buckling pressure, the local A comparison of test data with Equation 4-17 was made radius measured over half a theoretical wave length is sub- of in Ref. I 1. A constant value of CXOG 0.8 is recommended = stituted for the nominal radius in the theoretical shell equa- for cylinders which meet the fabrication tolerances of Sec- tion. The buckling pressure is taken as the minimum pressure tion IO. For cylinders with R/? ratios less than about 60, the given by either n or n + 1 where n is the theoretical wave following equation was found togive a lower bound on number for the shell without imperfections. test data for cylinders which exceed the specified tolerance Since thelocalshellimperfections are measured over a for y. half wave length, the gage angle, 20, is equal to R h radians (0 = 7d2n). The local radius, RL, can be computed by know- sec = 0.96 - 0 . 2 ~ for y 5 3 ing the versine,m , and the half chord, c, col-responding to the versine. The above equation is compared with test data in Figure C4. I .2-3 and Equation 4- 16 is compared test datain Fig- with 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 ~ ~ , ~ranging from 0.58 ~ ~ j p ~ j , ~ ~ ) A comparison of test resultswith the proposed method was to 0.77 compared with 1.16 to 2.55 for Sturm. The theories madefor 30 cylinders in Ref. 14 and the average of of Kendrick and Hom gave ratios as high as 2.73 and 3.30. PThenry was I .O07 with a convergence of 13.2%). Tests include A later comparison was made with Kendricks elasto-plastic elastic and elastic-plastic values with Rh ratios from 14 to theory (see Ref. 20, p. 637). This method gave ratios of 2.43 500 and yield stresses 3 1 .O to 6 I .7 ksi. of to 6.23. --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STABILITY DESIGN CYLINDRICAL OF SHELLS 55 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
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  • STD.API/PETRO B U L L ZU-ENGL 2000 0732270 Ob23183 743 m STA6lLlTY DESIGN CYLINDRICAL SHELLS OF 57 C4.3 LOCAL BUCKLING OF STRINGER cylinder when the minimum value for I I is based upon one- STIFFENED OR RING AND STRINGER halfthebucklewavelengthbetweenstringers (!I = N,&! STIFFENED CYLINDERS where N,Tequals the number of stringers). The value of I I for an unstiffened cylinder can be readily determined from Fig- C4.3.1 AxialCompression or Bending ure C4.3.2- 1. The stringers are inepective when N,J2 is less Equation 4-23 is a modification of Equation 1 1-14, p. 487 than n for a cylinder without stringers. of Ref. 7. This equation is given below using the nomencla- Equation 4-27 is a simplified equation which gives nearly ture of Bulletin 2U. 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 (C4.3.1-1) hasalsobeencompared with thetheoreticalequationfor buckling ofa cylinder under combined axial compression and hoop compression (Equation d, p. 496 of Ref. 7). The agree- of ment is excellent for values k I1. An analysis of available test data is given in Ref. 14. A comparison of testresults with thetheoreticalpredictions indicates that impelfections permitted by the Bulletin do not where M0 = b l f i t . The first term has been reduced by a fac- significantly affect the huckling capacities of stringer stiff- tor of 0.9 and introduced was in thesecond term to to ened cylinders subjected external pressure. The reason may accountforimpelfections.Whenthepanelwidthisrealer be that the stringers essentially tix the nominal radius and the than two times the panel lengthb > 2L) orb > 3.46 Rt , the ( buckling stress isthe same as a complete cylinder. For smaller Je membrane stress is a function of the nominal radius, not the local radius. ln comparison, the bucklingpressuresand values of b thepanelwillsubdivideduringbucklinginto stresses of ring stiffened cylinders are best predicted using the squares with one half wave in the hoop direction ( n = 1) and measured local radius. L/& half waves in the axial direction(m= L b ) . For a shell without stringers, the shell is free deflect and to The local shell buckling stress is based upon the assump- rotate at points of inflection of the buckle waves. This pro- tion that the stringers meet the requirements of Section 7.2. If duces a buckle pattern with a uniform in-out pattern. Stringer these requirements are not met, the local buckling stress of stiffened cylinders provide restraintin the radial direction and the stringers givenby Equation C7-I should be used in place somerestraintagainstrotation,dependingonthetorsional of the yield stress for determining 11. stiffness of the stringers. The buckle wave may vary between The test data for local buckling is very limited. There is a halfand a full wavebetweenstringers.Theshellpanels insufficient data to accurately define the transition between a which buckle inward are much more pronounced than those stiffened panel and an unstiffened panel. maximum value The that buckle outward. of M0 is 6 for test models which failed elastically.The buck- lingstressesatthisstringerspacingarestillsignificantly C4.4 BAY INSTABILITY OF STRINGER higher than those of an unstiffened cylinder. The same obser- STIFFENED OR RING AND STRINGER vation was made for ring stiffened cylinders under axial load STIFFENED CYLINDERS AND GENERAL (See C4. 1 ). This further suggests that the buckling stresses l. INSTABILITY OF RING AND STRINGER --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- for unstiffened cylinders should higher than those given by be STIFFENED CYLINDERS BASED UPON the equations in the Bulletin. The stringers are assumedto be ORTHOTROPIC SHELLTHEORY ineffective for Me > I5 and a linear transition is used for Me values between 3.46 and 15. For smaller values of Me the Equation 4-31 is a modification of the equation given in shell buckling stresses are about the same as for a flat plate. Ref. 22 for simply supported ollhotropic shells i n which the The test data is compared with Equations 4-22 and 4-25 using effective membrane thickness i n the longitudinal direction is the yield stress of the plate material in Figures C4.3.1-1 and equal to the area per length of shell and the bending rigid- unit 2. The stringers for many of the cylinders did not meet the ity isbasedupontheeffectivemomentofinelliaper unit compact section requirements of Section 7.2. The test data is length of shell. This equation has been modified that it also so replotted in Figure C4.3.1-3 using the stress from Equation applies to stiffened shells with stringers that arc not spaced C7- 1 as the yield stress. closeenoughtomaketheshellplate fully effcctivc.This effect is accounted for in the rigidity parameters (E.r, EO, DX, C4.3.2 External Pressure 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 local buckling pressure of a stringer stiffened cylinder the sameas those givcn in Ref. 23, p. 306, for a stiffened shell can be determined from the same equation a ring stiffened as with the plate fully effective. When both ratios equal z.ero, theCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D - A P I I P E T R O BULL ZU-ENGL 2000 Sl 0732290 Ob231811 B A T 58 BULLETIN API 2U --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD-API/PETRO B U L L ZU-ENGL 2000 D 0732290 Ob23185 ?Lb W STABILIW DESIGN CYLINDRICAL OF SHELLS 59 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
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  • S T D - A P I I P E T R O BULL ZU-ENGL zooo m O ~ ~ Z Z L Z ~ U s w U ~ O STABILITY DESIGN CYLINDRICAL SHELLS OF 61 -U c O .- c D W --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD=API/PETRO ULL U-ENGL B Z 2000 m 0732270 O b 2 3 L B B q 2 5 m 62 2U API BULLETIN rigidity factors are the same as those given in Ref. 23, p. 303, der equal the overall length. Local buckling of the stiffener for a gridwork shell. The equations for the rigidity parameters elements is not accountedfor in Equation 4-3 . Although sev- l are given below.The first termin each equationis the Bulletin eral methods for predicting the effects local stiffener buck- of nomenclature, and the second term is Ref. nomenclature. 23 ling been have investigated, study further deemed is necessary. The present recommendation is to substitute the a. Stiifened Shell-PlateFully Effective buckling stress given by Equation C7-I for the yield stress. An analysis of approximately 300 testsfromdatapub- in lished prior to 1977 is contained Ref. 24. Local bucklingof 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 E,=D - A ,E t ,+ - G , , = D,,+ - Et E = - Cr $-G- L, 2( 1 +v)- ring and stringer stiffened cylinders subjected to combina- tions of axial compression and external pressure. fabrica- The tionmethodsandmaterialsusedforthetestmodelswere representative of offshore structures. The R/t valueswere 190, 300 and 500 and the material was hot rolled steel sheets with ield stresses of 50 to 80 ksi. The stringer spacings were ~~3 E I , EA,.Z: / b l Rt o f 2 . 2 , 3 ,and (i. The test results analyzed and com- are D,=K - +-+- pared with Equation 4-31 in Ref. 14. - 12(1 -v2) L , L, Many of the modelshad stiffeners which did not satisfy the of compact section requirements Section 7.2. For the analysis of these models an effective yield stress was substituted for the actual yield stress. The effective yieldstress is used for all failuremodes. The effectiveyield stress wastaken as the buckling stress of a bar stiffener determined from the AlSI Cold Formed Steel Design Manual (25). The buckling stress was assumed to be 1.67 times the allowable stress given in Equation 3.2-2 of Ref.25 (see EquationC7- I). --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- b. Gridwork Shell C4.4.1 Axial Compression or Bending When the study of Ref. 24 was made, a factor of 1.7 rather than 1.9 was used in Equation 4-32 for 6, and 0.9 rather than 1.0 in Equation 4-35. The plasticity factors were determined from Equation 5-3. correct modeof failure was predicted The for almost all models.The higher factor of 0.9 is based upon the tests reportedin Ref. 14. (Itr and I,, are moment of inertia about the weak axis of the stiffeners.) a. Bay Instability A majority of the test models in Ref.24 were one bay long (stringers only) while all the models of Ref. I4 were 3 bays long with the end bays 0.7 times the length of the center bay. The one bay models failed at values of 0.8 to 2.5 times the predicted values. to This wide range is attributed the effectsof end fixity. Reference 24 included a group of tests on models G J , GJ D,, = K.,$ + K = -+ r - with multiple bays subjected to bending moments. shells The b L, were not fully effective (6, < 6). The test stresses were0.9 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. The bay instability modc determined is by letting the b. General Instability lengthofthecylinderequaltheringspacing. The general None of the tests in Ref. 14 failed in the general instability instability mode is determined by letting the length of cylin- mode. There were two groupsof tests in Ref. 24 which failedCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • ~ - ~~ 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 precipitating a collapse of the cylinder. If the local shell buck- failed at stresses 1 .O to 1.3 times the values given by Equation ling stress is significantly less than the bay instability stress 4-37 (with changes noted in Par. I ) and the cylinders sub- the modified orthotropic equation shell (Equation 4-31) jecled to bending moment failed at 0.8 to 1.3 times the pre- becomes increasingly less accurateas the difference becomes dicted values. greater. A ratio of bay instability stress to local shell buckling stress of I .2isrecommended.Also,Equation4-31is not C4.4.2 External Pressure applicable to stiffened shells less than about three string- with ers for each wave length in the bay instability mode. External pressure tests have been conducted on ring and stringer stiffened cylinders pressure with loadings corre- An alternatemethod isgiven in Ref.28forthosecases sponding to k = O. 0.5 and 1.8 wherek = NJNe. The results of wheretheorthotropicshellequationshould notbe used. these tests were analyzedin Ref. 14. Equations were derived hased upon the formation of a col- lapse mechanism. The equations Section 4.5 for axialcom- of a. BayInstability pression are taken from Ref. 28. An error in the formulations The bay instability stresses given by the equations in Sec- has been corrected. tion 4.4 require that the minimum number of stringers must be about 3 times the number of circumferential waves for this C4.5.1AxialCompressionorBending mode. Several of the test models did not satisfy this require- ment. For these models the bucklingstresses are predicted by The failure load given by Equation 4-59 was developed by the bay instability formulationsof Section 4.5. (28). Faulkner, Chen and de Oliveira A discrete stiffener-shell If the local shell buckling stress is significantly less than approach was used for determining the elastic collapse load the instability bay stress accuracy the of Equation 4-31 and the inelastic collapse load was then determined by using decreases. This equation has been found to provide good cor- the Ostenfeld-Bleich equation. Specific values were assumed relation for stringer stiffened shells when the bay instability for factors suchas the shell shape reduction and bias factors. stressesdo not exceed 1.5 timesthelocalshellbuckling The values for coefficient c in Equation 4-53 are subject to stresses. A ratio of I .2 is recommended. This corresponds to further review.The authors of Ref. 28 also suggestc = 3.0 for the value of ß recommended for Equation 7-. I light fillets and c = O for stress relieved shells. The methodof Section4.5.1,althoughhighlyempirical,provides the best h. General Instability correspondence between test and predicted loads ofanyof One test (Ref. 40)has been conducted where the cylinder the methods that havebeen studied. failed by general instability when subjected to external pres- sure.Therulessuggestthatthegeneralinstabilitystresses A much simpler alternate method has been developed by should be I .2 times the local shell buckling stresses (ß = 1.2). the ECCS Committee on Buckling of Shells for Ref. 37. This This canbe accomplished with little additional material thein method is being studied as an alternative to the equations in rings because the general instability stress a function of the is Section 4.5. I . moment of inertia of the effective ring section. irnperfec- The tion factor for ring stiffened cylinders is also recommended C4.5.2 External Pressure for ring and stringer stiffened cylinders. The formulations for bay instability under external pres- sure are taken from Ref. 41. The external pressure load for C4.5BAYINSTABILITYOF STRINGER be bay failure is assumed to made up of twocomponents sim- STIFFENED AND RING AND STRINGER ilartoEquation 4-17 for ring stiffened cylinders. The first STIFFENED CYLINDERS-ALTERNATE term in Equation 4-60 is the buckling capacity of a cylinder METHOD with the stringers removed and the length equal to the ring The buckling stresses givenby the equations in Section 4.4 spacing. The second term is the pressure that will develop are based on small deformation theory. The strains at which through the formation of plastic hinges the composite stiff- in buckling occurs are typically less than the yield strain. enerandshell.Thistotal isthenmodifiedbyaneffective a When stringer stiffeners are used on cylinder, local buck- pressure correction factor, K,,, determined from tests. Equa- ling of the shell plate between stiffeners may occur without tion 4-60 is compared with test data Fig. C4.5.2-l . in --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 m 0732290 0b23190 O83 m 64 API BULLETIN2U u m (D (D 8 (Y RI B B --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL Zoon m n732290 ob23171 TIT m STAElLlW DESIGNOF CYLINDRICAL SHELLS 65 C5 PlasticityReductionFactors C6 Predicted Shell Buckling Stresses for The elastic buckling stress of a fabricated cylinder, FjCj is Combined Loads the product of the elastic buckling stress for a perfect shell The tests in Ref. 29 indicate that the buckling stresses for and the capacity reduction factor ao,which accounts for the the cylinders subjected to bending are approximately same as differences in geometry and boundary conditions between the for cylinders under axial compression for R h values greater fabricated shell and a perfect shell. The factora~can also be than 150. Other tests (30) showed that for cylinders wilh W f considered to be the ratio of the strain in a tensile coupon valueslessthan 48 thebucklingstressesforbendingare used to determine the material properties and the strainin the higher. Since there are no bending test results on fabricated fabricated cylinder under applied load. When exceeds the Fi,j cylinders for the R/t range between 48 and 150 it is rccom- elastic limit of the shell material after fabrication, the buck- mendedthattheaxialcornpressionallowableheusedfor ling stress is givenby FjC, which is the product of the elastic bending stresses forall R/r values greater than48. shell buckling stress and the plasticity reduction factor, q. Many formulations for q havebeen determined theorcti- C6.1AXIALTENSION,BENDINGAND HOOP cally for various load conditions (Ref. For fabricated cyl- 26). COMPRESSION indersthedifferences in fordifferentloadconditionsare found tobe less significant than the effects of residual stresses The theoreticalelasticbucklingequationfor a cylinder on r(. The following simple expression is found to give good subjected to combinations axial tension and hoop compres- of agreement with test results (Ref. 27). sion indicates that it is safe to assume no interaction for elas- tic buckling ( S e e Figure 1 1-22 of Ref. 7). However. Ref. 31 shows interaction that must be considered buckling for (C5- 1 ) 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 To apply this equation requires thatE, be determined from stresses not limited by the stress intensity. a stress strain curve which includes the effects the residual of The stress intensity was found tobe limited by the Hencky- stresses due to fabrication. Also the strain at which E, is deter- von Misesdistortionenergytheoryfor all but a few tests. mined must correspond to the strain of the fabricated shell. However, the more conservative maximum shear the- --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- S~IXSS The factor A in Equation 5-3 is the ratioof the strain in a fab- 0 y given by Equation 6-2 is recommended for design. 1 ricated cylinder to the yield strain. The application of Equa- The failure stresses are thc lower the values determined of tion C5- l is described in Ref. 27. from Equations 6-1 and 6-2. Test data is compared with the A more direct approach is given in the Bullctin. Equation interaction curves in Figures C6. I - I and C6.I-2. Also shown 5-3 was obtained directly from test data for nonstress relieved are the Hencky-von Mises U I V ~ C laheled p = 0.5 and a modifi- cylinders. Mostof the ring and stringer stiffened models have cation labeled p = 0.75 whichhasmerit as an alternate to received post weld heat treatment prior to testing. Equation Equation 6-2. The curve labeled API is the interaction curve C5-2 was obtained from testdata for stress relieved cylinders. 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 con- = if A 20.67 II servative than Hencky-von Mises for cylinderswith values of F,,c. approaching Fy andvalues offr exceeding 0.5 F,, as if 0.67 < A < 4.17 ((3-2) shown in Fig. C6.1- 1 (a). 1 + 2.29A if A24.17 C6.2 AXIAL COMPRESSION, BENDING AND HOOP COMPRESSION Equations 5-3and C5-2 are only applicable to steel materi- Probablythegreatestdifferences in thevariousrecom- als withwell defned yieldstressplateaus.Equation C5-2 mended rules for shell buckling are the interaction equations applies to cylinders that have received post-weld heat treat- for cylinders subjectedto combinations of axial compression ment. Some residual stress remains in a shell after post weld and external pressure. Seven different recommendations are heat treatment because the shell is plastically deformed the in discussed in Ref. 27. Equation 6-3 is based upon a method fabrication process. proposed by Miller and Grove(42). One test program was recently completed and another in is The interaction equation for combinations of axial com- progress which will provide additional data for better defining pression hoop and compression is a modification the of theplasticityfactorsforcylinderswithout post weldheat Hencky-von Mises failure theory. Equation6-3 is identical to treatment. Figure C5-I shows a comparison of Equations 5-3 thistheorywhen c = 1.0. Testdatawasfound to conform and CS-2 with equations used by DNV and ECCS and an quite closely to the interaction curves obtained by varying the equation suggested by J. P. Kenny (43). value for c. The value of c was found to vary with FrC,/Fy andCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • 66 API BULLETIN 2U --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 0 7 3 2 2 9 0 Ob23173 872 STABILITY DESIGN CYLINDRICAL SHELLS OF 67 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- " 1-1.2 fsFy0 ( e ) Group 5 Figure 6.1-l-Cornparison o Test Data from Fabricated Cylinders Under Combined f Axial Tension and Hoop Compression with Interaction Curves = 36 ksi) (FyCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 m 0732270 Ob23174 727 m 68 2U API BULLETIN fe Fye ( b ) Group 7 30 o 1980 TESTS o 1981 TESTS Figure 6.1-2-Comparison of Test Data from Fabricated Cylinders Under Combined (F, Axial Tension and Hoop Compression with Interaction Curves = 50 ksi) --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D = A P I / P E T R O BULL ZU-ENGL 2000 m 0732270 Ob21195 b b 5 D STABILITY DESIGN CYLINDRICAL SHELLS OF 69 Fn/FY where Fx,:, is the failure stress for axial compression compactsections failure fmm the stress Equation C7-1 only and Fm, is the failure stress for hoop compression only. should be substituted for the yield stress when determining When both Fm; and Fm; equal F, c = 1.0. The values for c all the general instability stress for load conditions. decrease with decreasing valuesof Frc, and Fm; and Equation 6-3 becomes a straight line for = -2.0. The values forc were c C8 Column Buckling foundto be lessforstringerstiffenedcylindersthanfor unstiffened and ring stiffened cylinders. The buckling stress in the axial direction may be less than The equation for c for ring stiffened and unstiffened cylin- the shell buckling stress to column buckling. The column due ders is given by Equation 6 - 4 . This equation is similar to the buckling stress is determined by substituting the shell buck- equation in Ref. 42. Equations 6-5 and 6-6 were determined ling stress for the yield stress in the column buckling equa- from test data for stringer stiffened cylinders. Comparisons of tion. The AISC (33) and AlSI (25) specifications use the CRC Equation 6-3 with test data are shown in Figures C6.2-I to Column-StrengthCurve.Thiscquationcan be moditiedto --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- C6.2-7. account for column and shell buckling interaction by substi- tuting the shell buckling stress F@. for the yield stress. The C7 Stiffener Requirements buckling stress fora tubular column, F*.(:, is given by: C7.1DESIGNSHELLBUCKLINGSTRESSES A factor ß hasbeenadded to the shellbuckling stress equations to provide a convenient method for separating the localbucklingmodefromthebayandgeneralinstability modes of failure. The factor is applied to the failure strain (C8- rather than the failure stress. For elastic buckling the design shell buckling stresses areinverselyproportional to ß whereas for inelastic buckling the ratio of F;c.Fi(j is less The shell buckling stressF+, should be taken as the lowest than ß. A plot of Fic.Fyvs. (Fie#ß)IF,. is given in Figure stress for all possible modes of failure. This will always be C7.1-l. The upper curve with ß = 1 .O corresponds to the the local shellbucklingstress if theBulletinrulesarefol- shell buckling stress equations and the lower curve defines lowed. The elastic column buckling stress, F*c, is given by the design shell buckling stresses for the bayand general the following equation: instability modes of failure. (C8-3) C7.2LOCALSTIFFENERBUCKLING The recommended buckling criteria require that the stiffen- where KL, is the effective column length and is the radius of r ers be adequately proportioned so that local instability of the gyration. stiffeners is prevented. The requirements of Equations 7-3 The test results on fabricated tubular columns from Refs. and 7-4 will preclude this mode of failure for the most gener- 34 and 35 were compared with Equation C8-1 in Ref. 8 and ally used stiffener configurations. These requirementsare the several test points were found to be less than the predicted same as those specified by AISI (25) for fully effective sec- value.Equation 8-2 oftheBulletinwhichwastakenfrom tions. For other configurations, the AISI or other guidelines Ref. 8 is based upon a lower boundof test data.The compari- must be consulted. Equation 7-3 was determined from AISI son of test data with Equation 8-2 is shown in Figure CS-l. Equation 3.2-1 and Equation 7-4 from AISI Equation 2.3.I - 1. Thereisno data fromfabricatedcylinders in theelastic The buckling stresses of bar stiffeners which do not meet region. A reductionfactor of 0.87 isassumed. The AISC thecompactsectionrequirementsareassumedto be 1.67 Specification (33) gives an allowable stress of 0.522 times the times the allowable stresses given byAISIEquation3.2-2 Euler buckling stress. The factor 0.87is equal to 1.67x 0.522. which follows: The differences between test results and the predicted val- Fxc.= ( 1.28 - 0.75h,J Fy for 0.375 < h,? 0.846 < (C7- 1 ) ueswhen F k c is determinedfromEquation C8-I arcpar- tially compensated for in the AlSC specification by using a variable factor of safety whereas a constant factor of safety h+& h F,. can be used with Equation 8-2.Also Equation 8-2 reflects that t, no reduction in buckling stress occurs due to overall length When stringer stiffeners are noncompact sections the fail- for columns short (KL,/r < 0.5 Comparisons of the ure stress from Equation C7-I should be substituted for the column buckling curves givenby the Bulletin,CRC Column- yield stresswhen determining thelocal shell buckling stresses StrengthCurve,and AlSC areshown in FigureC8-2.The foraxialcompression or bendingandthe bay instability buckling stress curve for AISC is equal to 1.6676, where F,, stresses for all load conditions. When ring stiffeners are non- is Lhe allowable stress.COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO B U L L ZU-ENGL 2000 m 0732270 O b 2 3 L 7 b 5TL m 70 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- API BULLETIN 2U Figure 6.2-1-Comparison of Test Data with Interaction Equation for Unstiffened Cylinders Under CombinedAxial Compression and Hoop CompressionCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STDDAPIIPETRO BULL ZU-ENGL 2000 m 0732270 Ob23L77 Y38 m STABILITY DESIGN CYLINDRICAL OF SHELLS 71 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- Figure 6.2-2"Comparison of Test Data with Interaction Equation for Ring Stiffened Cylinders Under Combined Axial Compression and Hoop CompressionCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 m 0732290 0623178 374 m 72 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 2U API BULLETIN Figure 6.2-3-Comparison of Test Data with Interaction Equation Ring Stiffened Cylinders for Under Combined Axial Compression and Hoop CompressionCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- STABILITY DESIGN CYLINDRICAL SHELLS OF 73 of Figure 6.2-4-Comparison of Test Data with Interaction Equation for Local Buckling Ring and Stringer Stiffened Cylinders Under Combined Compression and Hoop Compression AxialCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D - A P I / P E T R O BULL ZU-ENGL 2000 m 0732270 Ob23200 852 m 74 API BULLETIN 2U --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- Figure 6.2-!j-Comparison of Test Data with Interaction Equation Local Bucklingof Ring and for Stringer Stiffened Cylinders Under Combined Axial Compression and Hoop CompressionCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD-APIIPETRO BULL ZU-ENGL 2000 0732290 Ob23201 799 D STABILITY DESIGN CYLINDRICAL SHELLS OF --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- for Figure 6.2-&Comparison of Test Data with Interaction Equation Bay Instabilityof Ring and Stringer Stiffened Cylinders Under Combined Axial Compression and Hoop CompressionCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD-API/PETRO BULL ZU-ENGL 2000 D 0732290 Ob23202 h 2 5 m 76 API BULLETIN 2U --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- Figure 6.2-7"Comparison of Test Data with Interaction Equation Bay Instabilityof Ring and for Stringer Stiffened Cylinders Under Combined Axial Compression Hoop Compression andCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD*API/PETRO BULL ZU-ENGL 2000 9 0732290 Ob23203 5bL STABlLllY DESIGN CYLINDRICAL SHELLS OF 77 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 m 0732290 Ob23204 4 T 8 m 78 API BULLETIN 2U --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D - A P I I P E T R O BULL ZU-ENGL 2000 m 0732290 Ob23205 33‘4 m STABILITY DESIGN CYLINDRICAL SHELLS OF 79 --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D * A P I / P E T R O BULL ZU-ENGL 80 API BULLETIN 2U ~~ C9 AllowableStresses The value of I I is the number of waves in the cylinder at collapse and e is the allowable deviation measured over one The allowable stresses for axial compression and bending half wave length. The values of n were determined from the are assumed to be equal for the shell buckling modesof fail- equation for hydrostatic pressure developed by Sturm (1 3). ure. Equations 9-2 through 9-8 are obtained by applying fac- Identical values forII can be determined from Equation4-27. tors of safety to the failure stresses given by the equations in Noninteger values are selected for and II couesponds to the tz Sections 4 and 6 . lowest buckling pressure for the assumed geometry. The arc The allowable stress equations for thecolumnbuckling length in Figure 10.2 is given by Arc = 7tD/2tz. mode for members subjected to axial compression and bend- ing stresses are the sameas given in AISC (33).Equations 9- C10.4 PLATESTIFFENERS 1 0 and 9-1 I are simpler in form than the AISC equations because the propertiesof tubular members are identicalin the The permissible lateral deviation of the free of a plate edge X and Y directions. When external pressure is combined with stiffener corresponds to the fabrication tolerances specifed F,, axial compression and bending the stresses for and Fb are for the models reportedin Ref. 6 . determined from the shell buckling interaction equations. The value of n given by Equation 10-3 is based upon the assumption that the stiffening ring will buckle into one-half C O Tolerances l the number of waves of an unstiftened shelllength Lb This of equation can be safely used in lieu of Equation 4- 17 because The tolerances for out-of-roundness are from the ASME it will always predicta smaller value of n. Pressure Vessel Code (36) and the requirement for straight- ness is from theECCS rules (37). C 1 StressCalculations l C10.1MAXIMUMDIFFERENCES IN CROSS- C11.2 BENDING STRESSES SECTION DIAMETERS The bending stressin a cylinder is given the equation by The equationformaximumdifferencesprovides a shell that appears reasonably round the eye. One exception is to for f = - M a shape conforming to n = 3. Provision is made for this case I’ S by the second paragraph Section 10.3. of where C10.2 LOCATION DEVIATION FROM STRAIGHT 1 + 0.25(t/R’) LINE ALONG A MERIDIAN S = 7tR2t = 7t ( D : - D 4 ) / 3 2 0 , , 1 +(0.5r)/R The reference length L, = 4 f i is related to the size of the potential buckles. There we no published papers which C11.3 HOOP STRESSES show a correlation between measured values of e, and the a. Stresses in Shell Midway Between Rings reduction in axial strength. In Ref. 37 when e, = 0.02Lx the Equation I 1-6 is a simplification of the equation for 6 5 values of a , are halved. When the ratio is between O.OILx ~ given by Kendrick (p. 407 of Ref. 39) for the mean circumfer- and 0.02Lx, linear interpolation between a , ~ 0 . 5 ~ ~is 1 , and ~ ential stress between stiffeners.The simplitications are made recommended for the reduction factor. in the terms L, and y. The expressions from Ref. 39 are as follows: C10.3 LOCAL DEVIATIONFROM TRUE CIRCLE Figures I O. I and 10.2 are based upon the following equa- L, = ( 2 N ) / a + t,r 5 L, tion developed by Windenburg(38). aL sinh-cos- aL + cosh-sin- aL aL 2 2 2 2 (CIO-1) y = 2 sinhaL + s i n a l This equation is based upon the analogy between a pres- coshaL - COSCXL N = . sure vessel anda column by considering the shell the pres- of slnhaL + sinaL sure vessel to be made up of a series of columns with length of one-half wave length. The eccentricity of a column corre- sponds to the out-of-roundness a cylinder. The constants in of Equation C 1O. 1 were derived from available test data to pro- videtolerancelimits whichwouldreduce collapsing the A comparison of the exact with the simplified hoop stress strength by a maximumof 20% = 0.8). factors is shown Figure C11.3-I . in --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`---COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • ~ S T D - A P I I P E T R O BULL ZU-ENGL 2 0 0 0 m 0732290 Ob23207 107 m STABILITY DESIGN CYLINDRICAL SHELLS OF 81 1.o 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 FactorsCOPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • S T D * A P I / P E T R O BULL 82 API BULLETIN 2U - b. Stress in a Ring Stiffener 10. Wilson, W. M. and Newmark, N. M., “The Strength of Equation 11-9 isa simplification of Kendrkk’s equation of Thin Cylindrical Shells as Columns,” University of Illi- (p. 407 of Ref.39) for the circumferentialstress in the flange nois Engineering Experiment Station Bulletin, No. 255, of a ring stiffener. The expression Ref. from 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, 198I . May 12. Galletly, G. D. and Bart, R., “Effects of Boundary Condi- where L, is defined in C 1 1.3tions Initial and and Out-of-Roundncss on Strength the of R, = radius point to of stress determination, Thin-Walled Cylinders Subjected to External Hydrostatic Pressure,” DTMB Report 1505, 1962. May R2 A = -A,. Sturm, 13. R. G., “A Study Collapsing Pressure the of of R;. University Cylinders,” Thin-Walled of Illinois, Engineer- ing Experiment Station Bulletin 329, 1941. No. 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 equa- 14. Miller, C. D. and Grove, R. B., “Interpretive Report on tion. the Conoco/ABS Test Program,” Contract No. R-0578, CBI Industries, November 1983. Cl 2 References 15. Becker, H. and Gerard, G., Elastic Stability o Orthotro- f pic Shells, Journal of the Aerospace Sciences, Vol. 29, --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 1. AmericanPetroleum Institute, Reconznaetaded Practice No. 5, May 1962, pp. 505-5 12. for Planning, Designing and Constructing Fixed Offshore Platfonns, API RP 2A,FifteenthEdition,October22, 16. Miller, C. D., “Buckling Stresses forAxially Compressed 1985. Cylinders,” Jourmil o the Structural Division, ASCE, f 2. Det Norske Veritas, Rules for the Design Construction Vol. 103, NO.ST3, March 1977, PP. 695-72 I . and lnspection o Ojshore Structures, Appendix C, 1977 f 17. Kendrick, S. B., “Collapse of Stiffened Cylinders Under (Rev. 1982). External Pressure,” Paper No. C190/72, Proceedings oj 3. American Society of Mechanical Engineers, Boiler and institution o Mechanical Engineers Conference on Ves- f Pressure Vessel Code Case N-284, “Metal Containment sels Under Buckling Conditions, London, Dec. 1972, pp. ShellBucklingDesignMethods,”Nuclear Code Case 33-42. Book, 1986. 18. Hom, K., “Elastic Stress in Ring-Frames of Imperfectly 4. Miller, C.D., “Commentary on ASME Code Case N-284, Circular CylindricalShells Under External Pressure Preliminary Report,” Chicago Bridge and Iron Company, Loading,” DTMB Report 1066, Nov. 1957. Dec. 1979. 19. Greimann, L. F., DeHart, R. C., and Ranz, D. R., “Effect 5. Kiziltug, A.Y., Grove, R. B., Peters, S. W. and Miller, C . of Out-of-Roundness Residual and Stresses onRing D., “Collapse Testsof Short TubularColumns Subjected ReinforcedSteelShells,”SouthwestResearchInstitute to CombinedLoads,”FinalReport,Contract No. UI- Report, Project No. 03-2435, AIS1 Project 155, Oct. 85 1604, CBI Industries, Dec. 1985. 1969. 6. Vojta, J. F. and Miller, C. D., “Buckling Tests on Ring 20. Faulkner, D., Cowling, M. J., and Frieze, P. A., Editors, andStringerStiffenedCylindricalModelsSubjectto Integrity of Wshore Structures, Applied Science Publish- CombinedLoads,”FinalReport, Contract No. 1 1896, ers, London andNew Jersey, 1981. Vol. I-Main Report and 3 Volume Appendix, CBI 21. Windenburg, D. F. and Trilling,C., “Collapse by Instabil- Industries, Inc., April 1983. ity of Thin Cylindrical Shells Under External Pressure,” 7. Timoshenko, S. P. and Gere, J. M., Theory of Elastic Sta- Trums. ASME, Vol. 56, No. 1 1, November 1934, pp. 819- bd&, 2nd Edition, McGraw Hill,New York, 1961. 825 or Pressure Vessel aradPipirag Design, Collected 8. Miller, C. D., “Axial Compression and Bending Strength Papers 1927- 1959, ASME, York, 1960, pp. 6 12-624. New of Unstiffened Steel Cylinders,” Research Report, CBI 22. Block, D. L., Card, M. F., and Mikulas,M. M., “Buckling Industries, October 1984. of Eccentrically Stiffened Orthotropic Cylinders,” NASA 9. Miller, C. D., “Axial Compression Strengthof Ring Stiff- TN-2960, August 1965. ened Cylinders,” Research Report, CBI Industries, May 23.Flugge, W., Stresses in Shells, Springer-Verlag,Belin/ 1984. GottingerhIeidelberg, 1960.COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • STD.API/PETRO BULL ZU-ENGL 2000 0732290 Ob23207 T B T m STAElLlTY DESIGN CYLINDRICAL SHELLS OF 83 24.Miller, C. D., “Buckling Stresses of Ring and Stringer 39. Sill, S. S., Editor, The StressAnalysis o Pressure Vessels f StiffenedCylindricalShellsunderAxialCompressive 2nd Pressure Components,Pergamon Press, 1970. L a , ResearchReport. Chicago Bridge & Iron Co., od ” 40. Kinra, R. K., “Hydrostatic and Axial Collapse Tests of April 1977. Stiffened Cylinders,” Paper OTC 2685, Offshore Tech- 25. AmericanIronandSteelInstitute, Cold-F¿wmedSteel nology Conference, May 1976. Design Manual, 1983 Mition. --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- 41. Miller, C. D., Grove, R. B., and Vojta, J. F., “Design of 26.Gerard, G., “PlasticStabilityTheory of Geometrically Stiffened Cylinders for Offshore Structures,” American OrthotropicPlatesandCylindricalShells,” Journal of Welding Society Welded Otfshore Structures Conference, Aerospace Sciences, August 1962, pp.956-962. lNew Orleans, Louisiana, December 1983. 27. Miller, C. D. Grove, B., and R. “Current Research Related to Buckling of Shells for Offshore Structures,” 42, Miller, C. D. and Grove, R. B., “Collapse Tests of Ring Paper OTC 4474, Offshore Technology Conference, May Stiffened Cylinders Under Combinations of Axial Com- 1983. pressionandExternalPressure,”ASME,PVPConfer- July 20-24, 1986. ence, Chicago, Illinois, 28. Faulkner, D.,Chen, Y. N., and de Oliveira, J. G., “Limit State Design Criteria for Stiffened Cylinders of Offshore 43. Review and Verification of API Bulletin 2U, J. P. Kenny Structures,” ASME 4th PV&P Conference,Portland, & Partners Ltd. Report, Project No. 15191, Report No. L Oregon, June 1983. 35301001, Rev. 2, February 1986. 29.Stephens, M. J.,Kulak, G., and Montgomery, C. J., 44. Marzullo, M. A. and Ostapenko, A.,‘‘Tests on Two High- “Local Buckling of Thin-WalledTubularSteelMem- Strength Short Tubular Columns,” Engineering Lab. Frik bers,” Pmceedings of Third Internationcrl Colloquiutn on Report No. 406. I 0, May 1977. Stability o Metal Structures, Toronto, Canada, SSRC, f May 1983, pp. 489-508. 45. Odland, J. O., “An ExperimentalInvestigation of the Buckling Strength of Ring Stiffened Cylindrical Shells 30. Shemlan, D. R., ‘Flexural Tests of Fabricated Pipe UnderCompression,” Axial NorwegianMaritime Beams,” Third International Colloquium on Stability of Research, No. 4, 1981, pp. 22-39. Metal Structures, Toronto, Canada, SSRC, 1983. May 31. Miller, C. D., Kinra, R. K., and Marlow, R. S., ‘Tension 46. Dowling, P. J. and Harding, J. E., “Experimental Behav- and Collapse Tests of Fabricated Steel Cylinders,” Paper ior of Ring and Stringer Stiffened Shells,” Buckling of OTC 42 18, Offshore Technology Conference, May 1982. Shells in Offshow Structures, Edited by Harding, Dowl- ingandAgelidis,Granada,London,Toronto,Sydney, 32. Johnston, B. G., editor, Guide to Stubiliry DesignCriteria New York, Sept. I98 1. for Metal Srrucrures, 3rd Edition, Wiley, New York, 1976. 33. American Instituteo í Steel Construction,Manual ofsteel 47, Ostapenko, A.and Grimm, D. F., “LocalBuckling of Construction, 8th Edition, I98 I . Cylindrical Tubular Columns Made of A-36 Steel,” LehighUniversity,FritzEngineering Lab. ReportNo. 34. Chen, W. F. and Ross, D. A., “The Strength of Axially 450.7, February 1980. Loaded Tubular Columns,” Fritz Engineering Lab Report No. 393.8, Lehigh University, September 1978. 48. Eder, M. F., Grove R. B., Peters, S. W., and Miller, C . D., 35. Wilson, W. M., ‘‘Tests of Steel Columns,” University of “Collapse Tests Fabricated Cylinders Under Combined of IllinoisEngineeringExperimentStationBulletin, No. Axial Compression and External Pressure,” Final Report 292, 1937. for API PRAC Project 82/83-46 and CBI Contract 2 1738, CBI Industries, lnc., Research Laboratory, Plaintìeld, Illi- 36. American Society of Mechanical Engineers, Boiler and nois, February 1984. Pressure Vessel Code, Section VIII, Division 1 and 2 and Section III, Subsection NE, 1983. 49. Sherman, D. R., “Bending Capacityof Fabricated Pipes,” 37. European ConventionConstructional for Steelwork, The University ofWisconsin-Milwaukee, College of “European Recommendations for Steel Construction,” Engineering and Applied Science, February 1983. Section 4.6 Buckling of Shells, Publication 29, Second 50. Miller, C. D., “Summary of Buckling Tests on Fabricate Edition, 1983. Steel Cylindrical Shells InUSA,” Buckling of Shells in 38. Windenburg, D. F., “Vessels Under External Pressure,” Offshore Structures, Edited by Harding,Dowlingand Pressure Vessel and Piping Design, collected papers Agelidis, Granada, London, Sydney,New York, 1982, pp. 1927-1959, ASME, 1960, 625-632. PP. 429-472.COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.
  • --`,,,`,`,,`,`,`,`,,,`,```,,``,-`-`,,`,,`,`,,`--- Additional copies available from API Publications Distribution: and (202) 682-8375 InformationaboutAPIPublications,Programs and Servicesis available on the World Wide Web at: http://www.api.org American 1220 L Street, Northwest Petroleum Washington, D.C. 20005-4070 Institute 202-682-8000 Order No. G02U02COPYRIGHT 2003; American Petroleum Institute Document provided by IHS Licensee=Shell Services International B.V./5924979112, User=, 05/27/2003 23:55:18 MDT Questions or comments about this message: please call the Document Policy Management Group at 1-800-451-1584.