WRC PVRC MPC - falatghareh.ir · WRC Bulletin 538 is dedicated to the memory of Peter Davies. His mentorship and questioning mind helped to lay the foundations upon which the work

DeterminatDetermination ion ofofPressure BoundaryPressure BoundaryJoint Assembly BoltJoint Assembly Bolt

LoadsLoads

W. BrownW. BrownIntegrity Integrity EnEngineering Solutionsgineering Solutions

WRC Bulletin 538,WRC Bulletin 538,

Second EditionSecond Edition

ISSN 2372-1057ISSN 2372-1057

WRCWRC PVRC MPCPVRC MPC

The Welding Research Council, Inc.The Welding Research Council, Inc.

falatghareh.irfalatghareh.ir

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INTENTIONALLY LEFT BLANKINTENTIONALLY LEFT BLANK


WRC Bulletin 538Determination of Pressure Boundary Joint Assembly Bolt Loads

iii

WRC Bulletins contain final reports from projects sponsored by the Welding Research Council, importantpapers presented before engineering societies and other reports of current interest.

No warranty of any kind expressed or implied, respecting of data, analyses, graphs or any otherinformation provided in this publication is made by the Welding Research Council, and the use of anysuch information is at the user’s sole risk.

All rights are reserved and no part of this publication may be reproduced, downloaded, disseminated, orotherwise transferred in any form or by any means, including photocopying, without the express writtenconsent of WRC.

Copyright © 2014 The Welding Research Council. All rights, including translat ions, are reserved by WRC.

ISSN 2372-1057Library of Congress Catalog Number: 85-647116

Welding Research Council20600 Chagrin Blvd.

Suite 1200Shaker Heights, OH 44122

www.forengineers.org

WRC - The Welding Research Council brings together science and engineering specialists indeveloping the solutions to problems in welding and pressure vessel technology. They exchangeknowledge, share perspectives, and execute R and D activities. As needed, the Council organizesand manages cooperative programs.

MPC – A Council of the WRC, the Materials Properties Council is dedicated to providing industrywith the best technology and the best data that can be obtained on the properties of materials tohelp meet today’s most advanced concepts in design and service, life assessment, fitness-for-service, and reliability and safety.

PVRC – A Council of the WRC, the goal of the Pressure Vessel Research Council is to encourage,promote, and conduct research in the field of pressure vessels and related pressure equipmenttechnologies, including evaluation of materials, design, fabrication, inspection, and testing.

For more information, see www.forengineers.org


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WRC Bulletin 538Determination of Pressure Boundary

Joint Assembly Bolt Loads

W. Brown

Integrity Engineering Solutions


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DEDICATION

WRC Bulletin 538 is dedicated to the memory of Peter Davies. His mentorship and questioning mindhelped to lay the foundations upon which the work in WRC 538 was built. The world has lost a greatengineer and a wonderful, generous person, but he will not be forgotten.



viii

FOREWORD

Too often leakage and other failure of bolted joints in pressure vessels and piping have been ascribed toimproper or inadequate preloading of the bolting. ASME PCC-1-2010 Appendix O “Assembly Bolt StressDetermination” was a major and long overdue step forward in assuring the integrity of bolted joints inpressure equipment. It required several years of dedicated effort on the part of a group of concernedindividuals to see to it that the relevant aspects of sealing reliability were documented. To accomplish thegoal the Pressure Vessel Research Council of WRC organized an activity capably led by Warren Brownto capture and evaluate the technology needed to support the procedures contained in PCC-1-2010. Thepurpose of this Bulletin is to assure that the “paper trail”, including the state of the art finite elementanalysis methods employed, leading to the ASME actions were documented and can be understood andretrieved in the future as a basis for further progress.

Dr. Martin PragerExecutive DirectorWelding Research Council



ix

TABLE OF CONTENTSFOREWORD ..................................................................................................................................................... VIII

TABLE OF CONTENTS .................................................................................................................................... IX

ABSTRACT ....................................................................................................................................................... 10

1 INTRODUCTION ........................................................................................................................................ 11

2 HISTORY .................................................................................................................................................... 11

3 ASME PCC-1-2010 APPENDIX O METHOD EXPLANATION .............................................................. 12

4 USING ASME CODE EQUATIONS TO DETERMINE THE FLANGE LIMIT ....................................... 12

5 ELASTIC-PLASTIC FEA METHODS ...................................................................................................... 16

6 CONCLUSION ........................................................................................................................................... 18

7 REFERENCES ........................................................................................................................................... 23

8 APPENDICES ............................................................................................................................................ 24

8.1 APPENDIX A – ASME PCC-1-2010 APPENDIX O ERRATA ....................................................................... 24

8.2 APPENDIX B – GRAPHICAL REPRESENTATION OF F AND F 2........................................................................ 25

8.3 APPENDIX C – EXAMPLE C ALCULATIONS USING WRC 538 ...................................................................... 27



10

ABSTRACT

This WRC Bulletin chronicles the development of the methods detailed in ASME PCC-1-2010 Appendix O“Assembly Bolt Stress Determination”. It includes all the information necessary to enable engineers concernedwith sealing reliability to reproduce and build on the work that went into that part of PCC-1. The intent is not toreproduce the method or to include all details of the development of the method. Instead it is to providereferences to the documents written during the development of the method and to provide additional details toassist in the understanding and extension of the method in the future. This WRC Bulletin provides references tothe historical development articles, an explanation of the basis for the method, a step-by-step guide as to how toapply the ASME code equations to determine flange limits, and a commentary on the Elastic-Plastic FiniteElement Analysis (FEA) methods presented therein.

The information presented will assist in developing general limits for acceptable bolt stresses that can be appliedto flanged joints without damaging them. This is the case for both standard piping flanges and custom pressurevessel and heat exchanger flanges. By incorporating the equations outlined in this document, not only can thecorrect assembly bolt load be determined, but the joint can be designed such that it is not possible to over-stressthe gasket or flanges. This approach vastly improves the practicality and reliability of the joint. By strictlyfollowing these procedures it will not be possible to permanently damage the joint during assembly or operation.The method presented also, enables determining which of a joint’s components are limiting. Absent thatknowledge it is not possible to correct the root causes of joint leakage. Finally, the document provides importantinsight into gasket relaxation factors.



11

1 INTRODUCTION

This WRC bulletin is intended to act as a reference to both chronicle the progression of and also to enable otherindividuals to reproduce and/or build on the work that went into the development of the method presently detailedin ASME PCC-1-2010 Appendix O “Assembly Bolt Stress Determination”. The intent is not to reproduce themethod or to include all details of the development of the method, but to provide reference to the appropriatearticles written during the development of the method and also to provide additional details to assist in thereproduction of the method. This WRC bulletin contains an historic reference outlining the development articles,an explanation of the basis for the method, a step-by-step guide as to how to apply code equations to determinethe flange limit, and commentary on the Elastic-Plastic Finite Element Analysis (FEA) methods used.

2 HISTORY

The development of the current methods outlined in ASME PCC-1-2010 Appendix O for the determination of theassembly bolt load for pressure boundary joints commenced in early 2005 and was a direct result of fieldexperience at Chevron with excessive flange deformation (flange rotation) on piping joints, particularly whenassembled to high initial bolt loads. The method built on previous work by Brown on the selection of anappropriate assembly bolt load that involved the consideration of appropriate gasket stress limits [1]. That workconsidered only the gasket and bolt limits, and neglected the potential for the flange to be the limiting factor. Although this approach worked in most cases, it was found that excessive flange deformation occurred in enoughcases to initiate the question as to what an appropriate limit for the joint as a whole (including the flange) shouldbe.

This led to the publication of the initial paper on the topic by Brown in 2006 [2], which presented background onthe need for inclusion of a flange limit in the calculation of assembly bolt load and outlined an initial method,based on a limit on flange radial stress. However, the paper also indicated that the radial stress limit did notappear to be valid for all cases and that a more comprehensive method would require expansion of the ASMEflange design equations [3] to include the tangential (hoop) stress at the shell to hub junction.

A follow-up paper by Brown in 2007 [4] presented the method for determining the flange stress at that location, aswell as a series of limits on all code flange stress locations that enabled the user to determine the assembly boltstress where Gross Plastic Deformation (GPD) of the flange would be expected. The developed equation andlimits were verified by comparison to Elastic-Plastic Finite Element Analysis (FEA) results for ASME B16.5,SA105, weldneck flanges from NPS 2 to NPS 24 in pressure classes 150, 300, 600, 900, 1500, and 2500. Theresults were also verified by comparison to Elastic-Plastic FEA on ASME B16.47, SA 105, Series A, weldneckflanges from NPS 26 to NPS 48 in pressure classes 150, 300, 600 and 900. In both cases, standard spiral woundgasket dimensions as per ASME B16.20 were used in the analysis. For piping flanges using similar gaskets andhaving similar wall thickness to those analyzed in the paper, the Elastic-Plastic FEA results could be used directlyfor the flange limit in the calculation of the joint assembly bolt stress. For non-standard flanges and flangeshaving significant difference in gasket or pipe wall thickness, the code equation calculation contained in the paperoffered a method of determining the flange limit. However, in developing the limits, incorrect material propertieswere used in the comparison between the FEA and the code equations, which led to the code equation limitslisted in the paper being overly conservative.

In a paper presented by Brown the following year [5], the method was further developed to include FEA of othermaterials (SA182 F304), and the limits for the code calculation method were corrected to reflect comparisonagainst the correct FEA material results. These two updates to the method finalized the work with respect todetermining the flange limit for calculation of joint assembly bolt load for weldneck flanges. The informationcontained in the papers written to that point was sufficient to allow determination of the approximate point of GPDfor a weldneck flange. The ASME codes, and others, use the same equations (weldneck flange) to assess arange of configurations, from a true weldneck flange (having an integral butt welded, tapered hub) to slip-onflanges (where the hub is fillet welded to the shell). This method may be used to approximate the behavior of slip-on flanges and also integral flanges having only a radius at the hub junction. In the latter case, the approximationwill be acceptable. In the case of the slip-on flange, the assessment will be non-conservative in some cases. Thecase of a loose ring flange can be addressed in the same way as the ASME code, with only the tangential stress(ST) being calculated and by using the same limits as outlined in this document. A more accurate method fordetermination of slip-on flange strength and confirmation of the method for loose flanges or flanges without hubs



12

can be found in Brown [6]. The information and tables contained in the final paper were incorporated directly into ASME PCC-1-2010 Appendix O. Further background and commentary on the method is outlined in Brown [7]. Itshould be noted that the guidance provided in ASME PCC-1 Appendix O is intended to serve as an example only.By using this WRC bulletin, it is possible to calculate actual specific cases or a general case for all piping joints ata given site. The risk with using the values presented in Table O-8 of Appendix O is that they may not apply tothe actual case (for example the wall thickness of the pipe on the joint being considered may be much less thanthe value used for the Appendix O calculation). Generally, the limits used to generate Table O-8 were higher thanmight typically be used on piping joints, in order to provide an example that would not be taken as an absolutelimit (or rather, would not limit the actual case, if interpreted as an absolute limit).

An appendix has been added to this document (Appendix A), which outlines four errata to the current (2010)version of Appendix O that will be corrected in the next revision.

3 ASME PCC-1-2010 APPENDIX O METHOD EXPLANATION

The basic premise of the method outlined in ASME PCC-1-2010 Appendix O is that in order to avoid jointleakage, the joint must be assembled to a bolt stress level which provides adequate stress to seat the gasket,adequate stress to provide sufficient residual stress on the gasket during operation and also be sufficiently lowsuch that no damage occurs to any of the joint components during assembly or operation. Using this concept, formost joints, results in a band of acceptable assembly bolt stress values which may be expected to work as shownin Fig. 1, taken from Brown [1].

Figure 1 – Bolt Assembly Load Selection Criteria

In order to determine the lower limits of assembly bolt stress levels, several gasket properties must be known,such as minimum seating stress, percentage gasket relaxation, and minimum stress during operation. None ofthese values presently have an industry standard test, and therefore it is not possible to completely codify themethod at present. However, as tests are developed to establish the required information, this should bepossible. To establish the upper limits on assembly bolt stress (joint component damage), the maximumacceptable gasket stress, and the maximum allowable assembly bolt stress that the flange will withstand must beknown. There is not presently an acceptable standard test method for establishing the maximum acceptablegasket stress. Since the gasket values are not well defined, this bulletin will focus more on the establishment ofthe maximum acceptable bolt stress, based on the flange limit.

4 USING ASME CODE EQUATIONS TO DETERMINE THE FLANGE LIMIT

The details outlined in this document assume that the user is familiar with the ASME flange design methodoutlined in Appendix 2 of ASME [3]. The equations from that document will not be reproduced here, only theadditional required equations and the basic structure of the calculation and limits will be presented.

The method consists of calculating the flange stress levels at the following combinations of flange geometry

Buffer against

leakageGasket Stress Required

to Seal Gasket

Gasket Stress lost

due to Creep/Relax.

Gasket Stress Lost due to

Pressure & Ext. Loading

Gasket Stress Lost due to

Thermal Loading0% Sy Bolt

(No Load)

Z% Sy Bolt

(Max. Permissible Load)

% Sy Bolt remaining

during operation

Y% Sy Bolt

(Assembly Load)

Buffer against

joint damage

100% Sy Bolt

(Max. Possible Load)

% Sy Bolt lost during

operation

Operational

Load

X% Sy Bolt

(Min. Req’d Load)

Bolt Load

-ve +ve

+/- Assembly Technique

and Procedure Accuracy



13

location and associated stress orientation:

a) Longitudinal Hub Stress at Hub/Flange Junction ( H S f , modified existing ASME Equation [6])

b) Longitudinal Hub Stress at Hub/Shell Junction ( S , existing ASME Equation [6])

c) Radial Stress at Hub/Flange Junction ( RS , existing ASME Equation [7])

d) Tangential Stress at Hub/Flange Junction ( T S , existing ASME Equation [8])

e) Tangential Stress at Hub/Shell Junction ( TOS , New Equation)

The stress component locations are shown in Fig. 1. The reason for the use of the modification H S f is to

capture the stress at the hub/flange ring junction, versus H S , which is at the hub/shell junction for values of

greater than one. The modification mentioned above to the hub longitudinal stress is to divide the calculated

value by the hub stress correction factor . This factor is either equal to or greater than one. When equal to

one, the calculated stress is at the hub/flange junction. When greater than one, the calculated stress is at the

hub/shell junction. By dividing by , the value of longitudinal hub stress at the hub/flange junction is always

found. The stress at the hub/shell junction will be over-predicted in cases where equals one. It is not possible

to determine the stress at the hub/shell location using values of less than one, because the equation for

becomes inaccurate below one. However, it was found that the level of conservatism introduced byoverestimating the tangential stress at the hub/shell junction, which occurs in some cases, was minimal.

The only other modification to the standard Appendix 2 equations is that the moment O used in the calculations

is taken as per the equation below:

O B b G A (1)

where B = the selected assembly bolt stress (MPa, psi)

b = the total bolt root area (mm2, in

2) per Appendix 2, Notation

Gh = gasket to bolt moment arm, per Appendix 2, Table 2-6

The method for calculating TOS is per the equation below:

2TO H S S

f (2)

where = the hub stress correction factor, per Appendix 2, Fig. 2-7.6 or the below equation. The below

equation for f is provided as an alternative to the Appendix 2 equation, in order that the expressions for and

2 can have the same base equation. The two relationships (below and Appendix 2) agree across the full range

within 3%.

2 = a second hub stress correction factor, determined per the equation below:



14

2 2

1 1 1

0 0 0 0 0 0

2 2

1 1 1

0 0 0 0 0 0

g g gh h h+ + + + +

g h g h g h

g g gh h h1+ + + + +

g h g h g h

n

a c e g i k

b d f h j

(3)

And

1max 1.0, f

2 2

0

max 0.25, 0.35h

f for h

2 3

0

max 0.25, 0.35 f for h

where the definition of 1 , 0 , and 0 are as per ASME Appendix 2 and the constants a through , for each

of the variables, are defined per the table below:

Graphical representations of and 2 are shown in Appendix B of this document. These plots are similar to the

existing plots of in ASME VIII, Div. 1, Appendix 2.

f f 2 f 3

a -0.71375912 -0.01447638 -0.06456312

b -0.12846279 -0.27814745 -0.08232239

c 1.08037907 0.01035395 0.13691677

d 0.99766848 1.37984158 -0.77879888

e 1.21823466 -0.34346764 0.14909019

f 0.01024612 0.02536192 0.00660062

g 0.4262313 -0.00145080 0.06162520

h 1.42049760 2.25543162 0.74639834

i -0.70278181 -0.60889597 -0.07959500

j -0.02483937 -0.15735462 0.09851673

k -1.59460436 1.22516062 -0.11214360

By using the equations below and those contained in ASME Appendix 2, the stress levels at the followinglocations can be compared with the limits listed following them. Note that the limits are based on material yield at

assembly (ambient) temperature yaS . In addition, it should be noted that these limits are selected with the

expectation that some localized yielding of the flange is acceptable and does occur in most flange cases whenassembled to sufficient bolt stress to ensure joint integrity. The limits are applied using the elastic equations and,



15

therefore, indicate stress levels that are well above yield. However, they have been verified against Elastic-Plastic FEA to be below the point of GPD for the flange, which is the true limit of flange strength (as opposed tolocalized yielding, which has no effect on flange strength).

a) Longitudinal Hub Stress: 2.0 H yaS S

b) Tangential Stress at Hub/Flange Junction: 1.5T yaS S

c) Tangential Stress at Hub/Shell Junction: 1.0TO yaS S

d) Combined Stress at Hub/Flange Junction: 3.0 H T yaS f S S

e) Combined Stress at Hub/Flange Junction: 3.0 R T yaS S S

f) Combined Stress at Hub/Shell Junction: 3.0 H TO yaS S S

g) Radial Stress at Hub/Flange Junction: 2.0 R yaS S

In order to determine the flange limit on assembly bolt stress max f S , the assembly bolt stress is increased until

one of the above limits is exceeded. The above limits were determined by comparison to Elastic-Plastic FEAresults and give, in most cases, a result that is within 10% of the value calculated using Elastic-Plastic FEA. Thisis considered sufficiently accurate for the intended purpose. When considering these limits by comparison topressure vessel and piping design practices it is necessary to remember that the flange stresses arepredominantly controlled by the bolt load. The bolt load is set at assembly and creates secondary stresses in the joint, since once assembled the joint deformation is displacement controlled. Therefore, the presence of localizedportions of the flange at yield should not be a concern. Under repeated assembly and operational cycles theflange will shake-down to a final stress state where no further yielding occurs. The above stress limits are chosenwith this in mind and will seem excessive by comparison to present flange design stress limits, due to the differentintent of the flange design method (to adequately size the flange) versus this method (to determine the strength ofthe flange). A more practical measure to use for flange design would be the method contained in this document,with the flange stresses calculated at bolt yield. This would ensure that the flange was never the limiting strengthcomponent of the joint.

The preceding limits are for the flange assembly case. Typically this is the controlling case, since gasketrelaxation will result in a much lower residual bolt stress during subsequent joint operation. However, in caseswhere the flange yield strength will be reduced by a greater amount than the expected joint relaxation, it isnecessary to also consider the flange operating case. In order to do that, (in ASME PCC-1-2010) in all casesanalyzed during the development of this method, including piping, pressure vessel, and heat exchanger flanges,the Radial Stress (SR) was never found to control on its own. It is included here as a limit in order to reflect thestress checks currently performed in ASME VIII, Div. 1, Appendix 2.

In some cases (e.g., high temperature stainless steel flanges) the yield strength of the flange may reducesignificantly during operation. In those cases, the flange limit should be reduced by the ratio of the yield

max f yo yaS S S . A useful ratio for determining if this adjustment must be performed is to compare the reduction

in yield to the amount of relaxation occurring, and if the reduction ratio exceeds the relaxation, the effect should

be included. This check is expressed as follows: the reduction factor should be included if 1.25 yo yaS S g .

The additional reduction in gasket relaxation (1.25 term) is included to capture possible variances in actualrelaxation versus test or assumed values.

The change made between this version and ASME PCC-1-2010 is the use of a “<” rather than a “>” sign, and thechange to the remaining relaxation factor (rather than the relaxation loss factor). Practically, the aboveconsideration can be implemented by the following modification to the preceding limits:



16

yS = the lesser of yaS or yoS

and yoS = the greater of 1.25 yoS g or yoS

Where g is the gasket relaxation factor from PCC-1 Appendix O (typically taken as 0.7 unless gasket test data

is available), yaS is the assembly (ambient) temperature yield of the flange material and yoS is the operating

temperature yield of the flange material.

a) Longitudinal Hub Stress: 2.0 H yS S

b) Tangential Stress at Hub/Flange Junction: 1.5T yS S

c) Tangential Stress at Hub/Shell Junction: 1.0TO yS S

d) Combined Stress at Hub/Flange Junction: 3.0 H T yS f S S

e) Combined Stress at Hub/Flange Junction: 3.0 R T yS S S

f) Combined Stress at Hub/Shell Junction: 3.0 H TO yS S S

g) Radial Stress at Hub/Flange Junction : 2.0 R yS S

5 ELASTIC-PLASTIC FEA METHODS

The FEA that was performed to establish GPD limits for different flange configurations was based onaxisymmetric approximation of the flange geometry. The reduction in accuracy by assuming axisymmetricbehavior was more than offset by the reduction in assessment time, which was significant given the large numberof FEA assessments required. It should be noted at this point that a sensitivity study into such factors as theelement order, contact assumptions, and mesh density was performed subsequent to the finalization of theresults. It was found that, depending on the assumptions made, the answer for the point of GPD could be madeto vary by 2 to 3% between different identical geometry models. However, this variation, while significant from anacademic sense, was well within the accuracy of other factors that commonly occur in bolted joint practice.

Three such factors are:

a) The effect of assembly method inaccuracy on achieved bolt load. This factor is well documented andcommonly the achieved accuracy for controlled joint assembly is within the ±10% to ±30% range.

b) The as-delivered material yield strength versus the minimum specified strength is often around 70 MPa(10ksi) higher. For common flange materials, this means that the actual GPD is likely to be around 30%higher than the GPD calculated using the minimum specified yield strength.

c) For standard piping flanges, the exact shape of the hub is not well defined in the B16.5 and B16.47standards. The hub height, h, can be varied from the full height of the flange to a minimum 45° angle hub.The difference in strength between a full height hub and a 45° hub can be significant. For an NPS 20, cl.150flange, Elastic-Plastic FEA demonstrated that the 45° hub had a maximum allowable assembly bolt load ofless than 30% of the full height hub geometry flange. Most suppliers tend to deliver flanges with hubs closerto the full height condition. For this reason, it was assumed in the analysis conducted that the hub heightcorresponded to the full possible height. It should be noted that this may not be conservative in all cases,depending on the flange supplier.

As can be seen from the above factors, it would be very easy to over think this problem and end up with so manyvariations of flange limits, for every different possible combination, that the end result would not be practical orusable. The intent of the FEA work was, therefore, to provide a basis upon which an approximate code equationmethod could be verified such that, if desired, other variables could be incorporated into the assessment on anas-needs basis using the code equation method. The goal was to achieve agreement between the methods of



17

around ±10% in order to be satisfied that both methods resulted in an answer that would be sufficiently accuratefor the purposes of selecting an assembly bolt load.

The following FEA modeling simplifications/assumptions were made in order to facilitate the assessment and/or toachieve as accurate as possible a result:

1) The flange geometry was taken from the appropriate ASME standard, with the assumption that the hubheight was a full height hub. One half of the flange pair was modeled, with symmetry being assumedthrough the central plane of the gasket.

2) The gasket sealing element geometry was taken as a spiral wound gasket in accordance with ASMEB16.20. The inner and outer rings were not modeled, so any possible contact between the flange andthose components was neglected.

3) The FEA models were constructed using first-order axisymmetric elements for the flange, first-orderplane stress elements for the bolts/nuts, and Abaqus gasket elements with normal direction behavioronly (GKAX4N) (See Fig. 3).

4) The gasket element elastic behavior was taken from flat-platen room temperature testing of a spiralwound gasket (see Fig. 4).

5) The gasket element surfaces were tied to the flange raised face. Since the gasket elements used donot allow tension or shear to be generated this has no effect in terms of overly restraining the joint, aswould be the case with other methods of modeling the gasket.

6) The nut width was taken as the across flats dimension of the appropriate size standard heavy hex nut.

7) In general, the contact between the flange and the nut was modeled as rough friction with no lateralmovement and the ability to separate after contact. This means that the reaction point between the nutand the flange will move inward as the flange is loaded and rotates. In a very few cases, however, itwas necessary to tie the nut to the flange in order to achieve convergence. Those cases will slightlyunder-estimate the point of GPD due to the additional restraint in movement.

8) The width of the bolt, as modeled with Plane Stress elements, was taken as ¾ of the actual boltdiameter in order that the bending moment of inertia for the plane stress representation was identical tothe actual multiple cylindrical bolt cross-section. This bending is due to flange rotation and is significantin that it controls the amount of movement of the nut reaction point inward as the flange rotates.

9) The depth of the plane stress elements was calculated in order that the overall total area of theelements matched the total tensile area of the flange bolts. Note that root area was not used (as isrequired in code calculations) as the tensile area is considered to be more appropriate in terms of actual joint elastic interact ion behavior. However, particularly in the larger size flanges, the two areas could beinterchanged without significant effect on the end result.

10) The bolt load was applied using the “*Pretension” command in Abaqus. This command reduces thelength of the elements across a plane on the bolt until the desired preload is established. The load wasapplied in 35 MPa (5ksi) increments until GPD was found.

11) The point of GPD was determined from the FEA results as the FEA step where the slope of the changein flange rotation versus applied bolt load was greater than two times the initial elastic portion of theslope (See Fig. 5).

12) The bolt-hole region of the flange was modeled using anisotropic elastic material properties. Since thestress levels in that region did not typically approach yield, the use of elastic properties should not haveaffected the obtained GPD value. The material properties (subscripts indicate direction, as per the codeequations) used were:

Tangential Young’s Modulus = Very Small Value (Negligible)

Radial and Longitudinal Young’s Modulus = f E 1 0.25 b bhn d C

Radial/Longitudinal Shear Modulus = Radial and Longitudinal Young’s Modulus / 2.6

Other Shear Moduli = Very Small Value (Negligible)

where f E = Young’s Modulus, bn = number of bolts, bhd = diameter of bolt hole, C = bolt pitch

circle diameter

This results in the following values for each of the materials used in this study:



18

SA-105 SA-182 F304

Material Young’s Modulus 202,500 MPa 193,500 MPa

Young’s Modulus (Tangential) T E 1 MPa 1 MPa

R E and H E 151,875 MPa 145,125 MPa

Shear Modulus RG 58,413 MPa 55,817 MPa

RT G and TH G 0.5 MPa 0.5 MPa

13) The Elastic-Plastic stress-strain behavior was taken from ASME II-D material properties for SA-105 andSA-182 F304 materials using the MPC method outlined in ASME Section VIII Div. 2 (see Fig. 6).

Further examples of FEA plots are shown in Fig. 7 to Fig. 9. The plots are chosen to highlight different categoriesof stress component limits and are provided for information only, since the actual GPD point was determinedpurely from flange rotation results. The first plot is of a standard NPS 20, cl.150 flange, which has GPD occurring

at the hub to shell junction TOS . The second plot is of a 24 inch heat exchanger joint, which has two different

flanges. One of them has GPD occurring at the hub to shell junction TOS and the other at the hub in the axial

direction H S . The final example is a B16.47 Series A, NPS 46, cl. 300 flange, which shows failure due to the

combination of H S and T S . Examples of the calculations outlined in this WRC bulletin for some standard

flanges are shown in Appendix C, for information.

6 CONCLUSION

The information presented in this WRC bulletin will assist in developing general limits to the acceptable bolt stressthat can be applied to flanged joints without damaging them. This is the case for both standard piping flanges andcustom pressure vessel and heat exchanger flanges. By incorporating the equations outlined in this document,not only can the correct assembly bolt load be determined, but in fact at the design stage, the joint can bedesigned such that it is not possible to over-stress the gasket or flanges. This vastly improves the practicality ofthe joint, in that it will therefore not be possible to overstress and permanently damage the joint during assemblyor operation. In addition, the method outlined is essential for determining the root cause of joint leakage, sincewithout knowledge as to which of the joint components, if any, are limiting, it is not possible to categoricallyidentify the root cause of joint leakage.



19

Radial Stress Axial Stress Hoop Stress

Figure 2 – Flange Stress Component Locations

Figure 3 – FEA Model Plot (NPS 12, cl.300 flange)

First-order Axisymmetric

GasketElements

PlaneStressElements

First-order Axisymmetric AnisotropicProperties



20

Figure 4 – Gasket Mechanical Behavior

Figure 5 – Example Flange Rotation vs. Bolt Load Plot (NPS 16, cl.300)

LOADING

mm MPa

0.000 0.0

0.024 9.6

0.102 21.8

0.479 34.1

0.774 46.8

1.000 64.6

1.250 99.9

UNLOADING 1

0.708 0.0

0.749 10.0

0.762 22.5

0.770 35.3

0.774 46.8

UNLOADING 2

1.202 0.0

1.233 19.8

1.239 39.9

1.244 59.8

1.247 80.2

1.250 99.9

-3

-2.5

-2

-1.5

-1

-0.5

0

0 0.2 0.4 0.6 0.8 1 1.2

Bolt Stress / Yield

F l a n g e R o t a t i o n ( d e g r e e s )

Rotation (deg)

Normalised on Load

s

t

t r s s (



21

Figure 6 – Flange Material Elastic-Plastic Properties

Figure 7 – 20in., cl.150, SA182-F304 FEA Results (MPa)

0

50

100

150

200

250

300

350

400

450

500

0.00E+00 2.00E-02 4.00E-02 6.00E-02 8.00E-02 1.00E-01

Strain

S t r e s s ( M P a )

SA182 F304

SA105

Sh ST SR

StrengthLimited by ST0



22

Figure 8 – 24in. Heat Exchanger FEA GPD Results (psi)

Figure 9 – 46in., Cll.300, SA182-F304 FEA Results (MPa)

ShST

Strength Limitedby ST0 Sh

ST

StrengthLimited By SH

Sh

StrengthLimited By(SH + ST)

ST

von Mises



23

7 REFERENCES

1. Brown, W., 2004, “Efficient Assembly of Pressure Vessel Bolted Joints” Proceedings of the ASME PVP2004, ASME, San Diego, USA

2. Brown, W., Reeves, D., 2006, “Considerations for Selecting the Optimum Bolt Assembly Stress For PipingFlanges”, Proceedings of the ASME PVP 2006, ASME, Vancouver, Canada, PVP2006-ICPVT11-93094

3. ASME. 2007, ASME Section VIII, Division 1, Boiler and Pressure Vessel Code, American Society ofMechanical Engineers, NY, USA

4. Brown, W., Reeves, D.., 2007, “ An Update on Selecting the Optimum Bolt Assembly Stress For PipingFlanges”, Proceedings of the ASME PVP 2007, ASME, San Antonio, Texas, PVP2007-26649

5. Brown, W., 2008, “Selecting the Optimum Bolt Assembly Stress: Influence of Flange Material on FlangeLoad Limit ”, ASME PVP Conference, Chicago, IL, PVP2008-61709

6. Brown, W., 2008, “Selecting the Optimum Bolt Assembly Stress: Influence of Flange Type on Flange LoadLimit ”, ASME PVP Conference, Chicago, IL, PVP2008-61708

7. Brown, W., 2010, “Background on the New ASME PCC-1-2010 Appendices D & O Guidelines for AllowableGasket Contact Surface Flatness and Defect Depth &Assembly Bolt Load Selection”, ASME PVPConference, Bellevue, WA, PVP2010-25766

8. ASME PCC-1-2010 “Guidelines for Assembly of Pressure Boundary Bolted Joints”, ASME, NY, 2010



24

8 APPENDICES

8.1 Appendix A – ASME PCC-1-2010 Appendix O Errata

Errata #1 – Usage of the flange rotation limit ( g max) is not consistent throughout the appendix. The definitionimplies that the limit is associated with the sum of the mating flange rotations, but the limits listed in O-4.1(a) arefor single flanges and the flange rotation levels listed in the Tables (O-3, O-5, and O-7) are for single flanges. Thelimit definition and references throughout the Appendix should be changed to ensure it is clear that the limitapplies to single flange rotation. Therefore, for a flange pair, the gasket will see the combined rotation of bothflanges, but each flange will be checked independently against the flange rotation limit.

Errata #2 – The incorrect WRC bulletin (WRC 528) was referenced in Appendix O, it should be this bulletin (WRC538).

Errata #3 – The incorrect method was used to determine if the reduction in flange material yield should beaccounted for in an assessment. The correct method is as per outlined in this WRC bulletin.

Errata #4 – The incorrect limits were used to create Tables O-4M and O-4. The corrected tables, using the flangestress limits defined in this document, are as follows:

Table O-4M Replacement Table O-4 Replacement

150 300 600 900 1500 2500 150 300 600 900 1500 2500

2 450 310 515 332 413 447 2 65 45 75 48 60 65

2.5 576 284 388 377 441 496 2.5 83 41 56 55 64 72

3 724 394 545 517 432 531 3 105 57 79 75 63 77

4 445 561 633 417 492 454 4 65 81 92 61 71 66

5 402 724 663 468 528 501 5 58 105 96 68 77 73

6 541 593 630 543 605 535 6 78 86 91 79 88 78

8 724 614 657 463 576 557 8 105 89 95 67 83 81

10 5 03 639 566 444 627 543 10 73 93 82 64 91 79

12 7 12 607 563 494 554 594 12 103 88 82 72 80 86

14 583 454 513 526 485 14 84 66 74 76 70

16 563 398 508 532 487 16 82 58 74 77 71

18 614 472 594 534 521 18 89 69 86 77 76

20 568 451 482 545 501 20 82 65 70 79 73

24 479 365 450 546 481 24 69 53 65 79 70

26 218 242 359 448 26 32 35 52 65

28 193 264 354 399 28 28 38 51 58

30 228 290 447 465 30 33 42 65 67

32 173 272 396 460 32 25 40 58 67

34 160 296 463 418 34 23 43 67 61

36 207 261 404 436 36 30 38 59 63

38 211 557 623 551 38 31 81 90 80

40 199 536 634 532 40 29 78 92 77

42 218 581 626 585 42 32 84 91 85

44 221 676 638 570 44 32 98 93 83

46 238 724 687 563 46 35 105 100 82

48 222 524 605 625 48 32 76 88 91



25

8.2 Appendix B – Graphical Representation of f and f 2

1

10

1

f ( l o n g i t u d i n a l s t r e s s f a c t o r )

g1 /g0

0.05

0.1

0.2

0.3

0.35

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

h/(sqrt(B.g0)

32 4 5

h/(B*g0).

h/(B*g0)0.5



26

0.25

2.5

1

f 2

( h o o p f a c t o r )

g1 /g0

0.05

0.1

0.2

0.3

0.35

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

h/(sqrt(B.g0)

32 4 5

h/(B*g0).

h/(B*g0)0.5



27

8.3 Appendix C – Example Calculations Using WRC 538

The below examples are presented for comparison purposes, dimensions are in mm and results in MPa. Theyare calculated using a flange yield stress of 345 MPa.

Flange Size NPS 44 16 24 12

Flange Class Class 150 300 300 900

Flange Spec ASME B16.47A B16.5 B16.5 B16.5

Pipe Outside Diameter (mm) Pipe OD 1117.6 406.4 609.6 323.9

Pipe Wall Thickness (mm) g0 9.5 7.9 14.3 17.5

Flange Bore (mm) B 1098.5 390.6 581.1 288.9

Flange Outside Diameter (mm) A 1405.0 647.7 914.4 609.6

Hub Outside Diameter (mm) X 1145.0 483.0 701.0 419.0

Hub Thickness at Flange Ring (mm) g1 23.2 46.2 60.0 65.0

Flange Thickness (mm) t 100.4 55.6 68.3 79.2

Hub Height (mm) h 76.0 88.8 98.1 120.8

Bolt Circle Diameter (mm) C 1314.0 571.5 812.8 533.4

Bolt Diameter (mm) b 38.1 31.8 38.1 34.9

Bolt Area (mm²) Ab 906.5 599.3 906.5 745.2

Number of Bolts nb 40 20 24 20

Gasket Inner Diameter (mm) Gask ID 1124.0 422.4 628.7 323.9

Gasket Outer Diameter (mm) Gask OD 1165.2 463.6 685.8 368.3

Flange Young's Modulus (MPa) E 202500 202500 202500 202500

Poisson’s Ratio Poisson’s 0.3 0.3 0.3 0.3

Hub Thickness Ratio g1/g0 2.4 5.8 4.2 3.7

Hub Length Ratio h/ho 0.7 1.6 1.1 1.7

Axial Stress Hub Factor f 1.00 1.00 1.42 1.00

Hoop Stress Hub Factor f 2 0.59 0.79 0.93 0.27

Basic Gasket Width (mm) b0 10.3 10.3 14.3 11.1

Effective Gasket Width (mm) b 8.1 8.1 9.5 8.4

Gasket Reaction Diameter (mm) G 1149.0 447.4 666.8 351.5

Gasket Moment Arm (mm) hG 82.5 62.0 73.0 90.9

Bolt Stress (MPa) Sb 221 399 365 494

Bolt Load (N) W 8025408 4785057 7950404 7368113

Axial Stress (MPa) SH 418 312 374 393

Radial Stress (MPa) SR 45 370 335 490

Tangential Stress at hub/flange (MPa) ST 295 194 165 246

Tangential Stress at hub/shell (MPa) STO 245 245 245 107

Flange Rotation @ W f 0.9 0.4 0.4 0.2


28



WRC PVRC MPC

The Welding Research Council, Inc.

The Welding Research Council brings together science and

engineering specialists in developing the solutions to problemsin welding and pressure vessel technology. They exchangeknowledge, share perspectives, and execute R & D activities. Asneeded, the Council organizes and manages cooperative programs.


WRC PVRC MPC - falatghareh.ir · WRC Bulletin 538 is dedicated to the memory of Peter Davies. His mentorship and questioning mind helped to lay the foundations upon which the work

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