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Design Calculations forPressure-ContainingEquipment

API STANDARD 6XFIRST EDITION, XXXX 2013

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API Std 6X Ballot Draft June 25, 2013

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ContentsPage

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Special Notes

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

Neither API nor any of APIs employees, subcontractors, consultants, committees, or other assignees

make any warranty or representation, either express or implied, with respect to the accuracy,completeness, or usefulness of the information contained herein, or assume any liability or responsibilityfor any use, or the results of such use, of any information or process disclosed in this publication. NeitherAPI nor any of APIs employees, subcontractors, consultants, or other assignees, represent that use ofthis publication would not infringe upon privately owned rights.

Classified areas may vary depending on the location, conditions, equipment, and substances involved inany given situation. Users of this specification should consult with the appropriate authorities havingjurisdiction.

Users of this specification should not rely exclusively on the information contained in this specification.Sound business, scientific, engineering, and safety judgment should be used in employing the informationcontained herein. API is not undertaking to meet the duties of employers, service providers, or suppliers

to warn and properly train and equip their employees, and others exposed, concerning health and safetyrisks and precautions, nor undertaking their obligations to comply with authorities having jurisdiction.

Information concerning safety and health risks and proper precautions with respect to particular materialsand conditions should be obtained from the employer, the service provider or supplier of that material, orthe material safety datasheet.

API publications may be used by anyone desiring to do so. Every effort has been made by the Institute toassure the accuracy and reliability of the data contained in them; however, the Institute makes norepresentation, warranty, or guarantee in connection with this publication and hereby expressly disclaimsany liability or responsibility for loss or damage resulting from its use or for the violation of any authoritieshaving jurisdiction with which this publication may conflict.

API publications are published to facilitate the broad availability of proven, sound engineering andoperating practices. These publications are not intended to obviate the need for applying soundengineering judgment regarding when and where these publications should be utilized. The formulationand publication of API publications is not intended in any way to inhibit anyone from using any otherpractices.

All rights reserved. No part of this work may be reproduced, translated, stored in a retrieval system, or transmitted by any means,electronic, mechanical, photocopying, recording, or otherwise, without prior written permission from the publisher. Contact the

Publisher, API Publishing Services, 1220 L Street, NW, Washington, DC 20005.Copyright 2013 American Petroleum Institute

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Foreword

Nothing contained in any API publication is to be construed as granting any right, by implication orotherwise, for the manufacture, sale, or use of any method, apparatus, or product covered by letterspatent. Neither should anything contained in the publication be construed as insuring anyone againstliability for infringement of letters patent.

Shall: As used in a standard, shall denotes a minimum requirement in order to conform to thespecification.

Should:As used in a standard, should denotes a recommendation or that which is advised but notrequired in order to conform to the specification.

This specification was produced under API standardization procedures that ensure appropriatenotification and participation in the developmental process and is designated as an API standard.Questions concerning the interpretation of the content of this publication or comments and questionsconcerning the procedures under which this publication was developed should be directed in writing tothe Director of Standards, American Petroleum Institute, 1220 L Street, NW, Washington, D.C. 20005.Requests for permission to reproduce or translate all or any part of the material published herein shouldalso be addressed to the director.

Generally, API standards are reviewed and revised, reaffirmed, or withdrawn at least every five years. Aone-time extension of up to two years may be added to this review cycle. Status of the publication can beascertained from the API Standards Department, telephone (202) 682-8000. A catalog of API publicationsand materials is published annually by API, 1220 L Street, NW, Washington, D.C. 20005.

This standard shall become effective on the date printed on the cover but may be used voluntarily fromthe date of distribution.

Suggested revisions are invited and should be submitted to the Standards Department, API, 1220 LStreet, NW, Washington, D.C. 20005, [email protected].

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Introduction

This standard is intended to document the design methodology from the ASME Code, Section VIIIDivision 2 Appendix 4, which has been used in the oil and gas industry since the 15

th Edition of API

Specification 6A was published in 1986.

API 6A modified the rules of the ASME Code to permit higher stresses than were allowed by ASME. APIadopted a design stress intensity of 2/3 of the minimum specified yield strength.

Shortly after the 15thEdition of API 6A was published, API released the first edition of Specification 16A,

Drill-Through Equipment. Specification 16A permitted higher stresses than 6A at hydrostatic test. Where6A limited the membrane stress intensity to 83% of the minimum specified yield strength, 16A permitted90% of yield strength.

With the 19thEdition of API 6A in 2004, the design stress intensity of high-strength non-standard materials

was changed to the lower of 2/3 of the yield strength or of the tensile strength. API 16A did not makethis change.

In 2007, ASME totally rewrote Section VIII Division 2, using generally more liberal design requirements

and more stringent material requirements.

Since the earlier design and material requirements have been used successfully for over 25 years, APIelected to continue to reference the 2004 ASME Code. The methods included in this document are thoseof the 2004 Code, as modified by API product Specification 16A.

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Design Calculations for Pressure-Containing Equipment

1 Scope

This standard describes a design analysis methodology that can be applied to products and equipment in

the oil and gas industry. The methods included in this document are intended to be applicable to APIProduct Specifications including API 6A, API 16A, API 16C, and API 17D.

It is based on ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, Appendix 4 (2004 edition

with 2005 and 2006 addenda) but includes further limits established for oil and gas products as

determined by API. It includes closed-form solutions and methods for elastic analysis, elastic-plastic

analysis, and guidance on finite element analysis methods. The methodology assumes ductile metallic

material behavior and has no provision for material defects.

Fatigue analysis is outside the scope of this document.

2. Normative ReferencesThe following referenced document is indispensable for the application of this document.

ASTM A370, Test methods and definitions for mechanical testing of steel products.

3. Terms, definitions, and symbols

3.1 Terms and definitions

For the purpose of this document the following terms and definitions apply

3.1.1

operating conditionsAny combination of internal and external pressures and temperatures and applied loading to which theproduct is to be exposed in service, excluding hydrostatic shell testing

3.1.2

yield strengthThe materials minimum specified 0.2% offset yield strength obtained in accordance with ASTM A370

3.2 Symbols

For the purposes of this document, the following symbols apply.

F peak stress, included only for fatigue analysis

Pb primary bending stress

PL local primary membrane stress

Pm general primary membrane stress

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Q secondary membrane plus bending stress

Se equivalent stress based on the von Mises distortion energy theory

Si stress intensity, the equivalent stress based on the Tresca maximum shear stress theory

Sm design stress intensity

Sn principal stress, where n=1, 2, or 3

St maximum allowable general primary membrane stress intensity at test pressure

Sy material yield strength (Greek small letter tau)Shear stress

4 Elastic Analysis

4.1 General

Elastic analysis is based on the assumption that the material has a linear stress-strain relationship andtherefore does not account for yielding or plastic behavior.

4.1.1 Stress components

For elastic analysis, stress components shall be calculated, combined, and compared to limits for eachcategory of stress based on multiples of the Design Stress Intensity, Sm, for the material in use and for thecategory of stress.

The design stress intensity is 2/3 of the minimum specified yield strength Sy.

ym SS3

2

The maximum allowable general primary membrane stress intensity at hydrostatic shell test S tis 90% ofthe minimum specified yield strength.

yt SS 9.0

4.1.2 Combined stresses

Stress components shall be combined to find the stress intensity, which is defined as twice themaximum shear stress. This can be calculated as the difference between the largest and smallest of thethree principal stresses.

13 SSSi , where 123 SSS

NOTE: If permitted by the product specification, the von Mises equivalent stressmethod may be used to

combine stress components instead of stress intensity, wherever stress intensity is specified in thisstandard.

)(3 222222 zxyzxyzxzyyxzyxe SSSSSSSSSSSSS

where

Seis the equivalent stress,

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Sx,Sy, and Szare the direct stress components at the point of interest, and

Sxy, Syz, and Szxare the shear stress components.

4.2 Stress Categories

4.2.1 General

The following categories are used to classify stresses. The categories are based on the response of theloaded component if the material yield strength were exceeded.

4.2.2 Primary Stress

4.2.2.1 General

The basic characteristic of primary stress is that it is not self-limiting, and failure, or at least grossdistortion, can occur from one application of the loading. Primary stress is stress caused by theapplication of mechanical pressure, forces and moments. Primary stress includes both membrane andbending stress and is linearly distributed across the wall section. Local primary stress can redistribute, as

it does in a threaded connector. Thermal stresses are not primary stresses.

4.2.2.2 Primary Membrane Stress Intensity

Primary membrane stress intensity is calculated from the average values of the stress componentsthrough the wall of the vessel. Depending on the extent of the stress, it can be classified as either generalor local.

a) General Primary Membrane Stress Intensity, Pm: Membrane stress distributed in a way such that loadredistribution cannot occur, and loading beyond the yield strength can proceed to failure. GeneralPrimary Membrane Stress Intensity is caused only by mechanical loads and excludes effects due todiscontinuities and areas of stress concentration. Pmshall not exceed Sm at operating conditions. Athydrostatic shell test, the general primary membrane stress intensity shall not exceed S t.

b) Local primary Membrane Stress Intensity, PL: Local Primary Membrane stress is caused only bymechanical loads. Discontinuities are considered while areas of stress concentration are not. Thefollowing is a direct quote from ASME Section VIII Division 2 Appendix 4 2004:

Cases arise in which a membrane stress produced by pressure or other mechanical loading andassociated with a primary and/or a discontinuity effect would, if not limited, produce excessivedistortion in the transfer of load to other portions of the structure. Conservatism requires that such astress be classified as a local primary membrane stress even though it has some characteristics of asecondary stress. A stressed region may be considered as local if the distance over which the stressintensity exceeds 1.1 Smdoes not extend in the meridional direction more than 1.0(Rt)

1/2, where R is

the midsurface radius of curvature measured normal to the surface from the axis of rotation and t isthe minimum thickness in the region considered. Regions of local primary membrane stress whichexceed 1.1 Smshall not be closer in the meridional direction than 2.5(Rt)

1/2where R is defined as (R1

+ R2)/2, and t is defined as (t1+ t2)/2, where t1 and t2 are the minimum thicknesses at each of theregions considered, and R1 and R2 are the midsurface radii of curvature measured normal to thesurface from the axis of rotation at these regions where the membrane stress exceeds 1.1 S m.Discrete regions of local primary membrane stress, such as those resulting from concentrated loadsacting on brackets, where the membrane stress exceeds 1.1 Smshall be spaced so that there is nooverlapping of the areas in which the membrane stress exceeds 1.1 Sm. An example of a localprimary membrane stress is the membrane stress in a shell produced by external load and moment ata permanent support or at a nozzle connection.

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c) Local primary membrane stress intensity PLshall not exceed 1.5 Sm.

4.2.2.3 Primary Bending Stress Intensity

The components of primary bending stress intensity Pb are calculated from the linear primary stresscomponent distributions that have the same net bending moment as the actual stress component

distribution. Primary bending stress components are defined as being proportional to the distance fromthe centroid of a solid section and exclude discontinuities and stress concentrations.

When the bending stress components are combined with the membrane stress components at eachsurface, the resulting stress intensities PL+Pbshall not exceed 1.5 Sm.

4.2.2.4 Extreme Conditions

Higher allowable primary stresses are permitted when wind, earthquake, or wave action loads are addedto the operating condition loading:

mbL

mL

mm

SPP

SP

SP

8.1

8.1

2.1

The wave loading shall be the largest load with one probable occurrence in 20 years. Secondary stresslimits are not increased for these conditions.

4.2.3 Secondary Stress

Secondary stress Q is caused by the constraint of adjacent parts or by self-constraint of the structure, andyielding can cause the magnitude of the stress to be reduced. One load cycle can cause local yieldingand stress redistribution but cannot result in failure or gross distortion.

Secondary stresses are membrane plus bending stresses that can occur at gross structural

discontinuities, from general thermal stress, from mechanical preload conditions, or from combinations ofthese sources.

The secondary stress variation, for any sequence of test or operating conditions, shall not exceed 3 S m.

4.2.4 Peak Stress

Peak stress F is the increment of stress added by a stress concentration or other source that does notcause noticeable distortion. Such sources include thermal stress in a cladding material with a differentcoefficient of expansion from the base material; transient thermal stress, or the non-linear portion of athermal stress distribution. The only concern with peak stress is that it can cause the initiation of a fatiguecrack or brittle fracture.

The total stress, including peak stress, may be used in fatigue analysis, which is beyond the scope of thisstandard. One acceptable method for fatigue analysis is in the 2004 ASME Boiler and Pressure VesselCode, Section VIII Division 2, Appendix 5.

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5 Special stress considerations

5.1 Temperature effects

The effect of temperature on the mechanical properties of the material shall be considered if the ratedinternal temperature exceeds 250 F.

5.2 Bearing Stress

Bearing stress is allowed to exceed the yield strength of the material provided that the other stresses inthe vicinity of the bearing load are within acceptable limits. When bearing loads are applied to partshaving free edges, the possibility of a shear failure shall be considered.

5.3 Pure Shear

The average primary shear stress across a section loaded under design conditions in pure shear (forexample, keys, shear rings, or screw threads) shall be limited to 0.6 Sm.

mS6.0max

The maximum primary shear at the periphery of a solid circular section in torsion shall be limited to 0.8Sm..

mS8.0max

For hydrostatic test conditions primary shear stress shall not exceed 0.6 St.

tS6.0max

5.4 Progressive distortion of non-integral connections

Screwed-on caps, screwed-in plugs, shear ring closures, breech lock closures, clamps and unions areexamples of non-integral connections which are subject to failure by bell-mouthing or other types ofprogressive deformation.

If any combination of loading produces yielding, such joints are subject to ratcheting because the matingmembers can slip at the end of each complete cycle, and start the next cycle in a new relationship withone another. Additional distortion may occur at each subsequent cycle so that interlocking parts likethreads can lose engagement. Therefore, primary plus secondary stresses which could produce slippageshall be limited to Sy.

5.5 Triaxial Stresses

The algebraic sum of the three primary principal stresses (1+2+3) shall not exceed four times thedesign stress intensity Sm. The sum of the local primary membrane plus bending principal stresses shallbe used for checking this criterion.

5.6 Stress Linearization

When it is necessary to extract the membrane and bending stresses from finite-element analyses, anumerical technique called linearization shall be used. This procedure involves numerical integration ofthe stress components to separate the membrane and bending portion of the stress from the total stress.The total stress includes the non-linear peak stress.

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NOTE Guidance on linearization can be found in the ASME Boiler and Pressure Vessel Code, SectionVIII, Division 2, Annex 5A.

6 Non-linear analysis

6.1 General

The limits on primary and secondary stresses need not be satisfied if thorough non-linear finite elementanalyses are performed. The effect of temperature on material properties shall be considered.

Limit Analysis can be used to verify the actual rated load capacity but shall not be used for assessinglocal strain, ratcheting or shakedown. Plastic Analysis can be used for assessing local strain, ratchetingand shakedown but shall not be used to verify the actual rated load capacity.

The von Mises yield criterion and associated flow rule shall be used in limit analysis and plastic analysis.

6.2 Limit analysis

Limit analysis assumes elastic-perfectly plastic material properties, and may be based on small-

displacement analysis. The stress-strain curve that is used has a bi-linear representation. This curve, forstress less than the yield strength has a slope equal to the elastic modulus of the material. Above yield,the slope is as near zero as practical. A zero slope can cause numerical problems in most finite-elementprograms when yield is exceeded.

Loading is incrementally increased until the model diverges due to reaching the collapse load. Actualrated load capacity can be no more than 2/3 of the limit analysis collapse loading.

Limit analysis may be used to justify high primary stresses but not secondary stresses.

6.3 Plastic Analysis

Plastic analysis is a method of structural analysis by which the structural behaviour under given loads is

computed by considering the actual material stress-strain curve and may assume small or largedeformation theory as required. This method is more accurate than limit analysis because strainhardening effects are included.

The material stress-strain curve may be obtained by either actual material test data or approximated viaanalytical methods using minimum specified yield and ultimate tensile strength values (for example,ASME, Sect. VIII Div.2, Annex 3D).

If a stress-strain curve from actual testing is used, appropriate corrections may be needed to ensure thatthe data used in the analysis is representative of the minimum specified yield strength of the material.Shakedown Analysis

Shakedown analysis can be used to justify high local primary and secondary stresses. Actual true-stress

and true-strain curves are to be used as they are used for plastic analysis in section 6.3.

The design is acceptable if shakedown occurs. That is, after successive applications of the designloading, there is no progressive distortion or stress ratcheting. In addition the deformations which occurprior to shakedown shall not exceed specified functional limits of the design. It is acceptable to include theeffect of hydrostatic testing as well as operational loading.

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Bibliography

[1] API Specification 6A, Wellhead and Christmas Tree Equipment

[2] API Specification 16A, Drill-Through Equipment

[3] API Specification 16C, Choke and Kill Equipment

[4] API Specification 17D, Subsea Wellhead and Christmas Tree Equipment

[5] 2004 ASME Boiler and Pressure Vessel Code, Section VIII Pressure Vessels, Division 2Alternative Rules, with 2005 and 2006 Addenda, American Society of MechanicalEngineers, New York, NY, Part AD-132.2 and Appendix 4

[6] ASME Boiler and Pressure Vessel Code, Section VIII Pressure Vessels, Division 2 Alternative Rules, American Society of Mechanical Engineers, New York, NY, Annex 5A

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