WRC Bulletin 538,
Second Edition
ISSN 2372-1057
WRC PVRC
MPC
The Welding Research Council, Inc.
Determination of
Pressure Boundary
Joint Assembly Bolt
Loads
W. Brown
Integrity Engineering Solutions
INTENTIONALLY LEFT BLANK
ii
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
WRC - The Welding Research Council brings together science and engineering specialists in
developing the solutions to problems in welding and pressure vessel technology. They exchange
knowledge, share perspectives, and execute R and D activities. As needed, the Council organizes
and manages cooperative programs.
MPC – A Council of the WRC, the Materials Properties Council is dedicated to providing industry
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help meet today’s most advanced concepts in design and service, life assessment, fitness-forservice, 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 equipment
technologies, including evaluation of materials, design, fabrication, inspection, and testing.
For more information, see www.forengineers.org
WRC - The Welding Research Council brings together science and engineering specialists in
developing the solutions to problems in welding and pressure vessel technology. They exchange
knowledge, share perspectives, and execute R and D activities. As needed, the Council organizes
and manages cooperative programs.
WRC Bulletins contain final reports fromMPC
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by the
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Research
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– A sponsored
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societies
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reports
of
current
interest.
dedicated to providing industry with the best technology and the best data that can be obtained on
the properties of materials to help meet today’s most advanced concepts in design and service, life
Noassessment,
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implied,
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and or
reliability
and
safety. of data, analyses, graphs or any other
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Copyright © 2014 The Welding Research Council.
All rights, including translations, are reserved by WRC.
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iii
INTENTIONALLY LEFT BLANK
iv
WRC Bulletin 538
Determination of Pressure Boundary
Joint Assembly Bolt Loads
W. Brown
Integrity Engineering Solutions
v
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WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
DEDICATION
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 in WRC 538 was built. The world has lost a great
engineer and a wonderful, generous person, but he will not be forgotten.
vii
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
FOREWORD
Too often leakage and other failure of bolted joints in pressure vessels and piping have been ascribed to
improper or inadequate preloading of the bolting. ASME PCC-1-2010 Appendix O “Assembly Bolt Stress
Determination” was a major and long overdue step forward in assuring the integrity of bolted joints in
pressure equipment. It required several years of dedicated effort on the part of a group of concerned
individuals to see to it that the relevant aspects of sealing reliability were documented. To accomplish the
goal the Pressure Vessel Research Council of WRC organized an activity capably led by Warren Brown
to capture and evaluate the technology needed to support the procedures contained in PCC-1-2010. The
purpose of this Bulletin is to assure that the “paper trail”, including the state of the art finite element
analysis methods employed, leading to the ASME actions were documented and can be understood and
retrieved in the future as a basis for further progress.
Dr. Martin Prager
Executive Director
Welding Research Council
viii
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
TABLE OF CONTENTS
FOREWORD .....................................................................................................................................................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
8.2
8.3
APPENDIX A – ASME PCC-1-2010 APPENDIX O ERRATA .......................................................................24
APPENDIX B – GRAPHICAL REPRESENTATION OF F AND F2........................................................................25
APPENDIX C – EXAMPLE CALCULATIONS USING WRC 538 ......................................................................27
ix
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
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 concerned
with sealing reliability to reproduce and build on the work that went into that part of PCC-1. The intent is not to
reproduce the method or to include all details of the development of the method. Instead it is to provide
references to the documents written during the development of the method and to provide additional details to
assist in the understanding and extension of the method in the future. This WRC Bulletin provides references to
the historical development articles, an explanation of the basis for the method, a step-by-step guide as to how to
apply the ASME code equations to determine flange limits, and a commentary on the Elastic-Plastic Finite
Element Analysis (FEA) methods presented therein.
The information presented will assist in developing general limits for acceptable bolt stresses that can be applied
to flanged joints without damaging them. This is the case for both standard piping flanges and custom 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 the joint can be designed such that it is not possible to over-stress
the gasket or flanges. This approach vastly improves the practicality and reliability of the joint. By strictly
following 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 that
knowledge it is not possible to correct the root causes of joint leakage. Finally, the document provides important
insight into gasket relaxation factors.
10
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
1
INTRODUCTION
This WRC bulletin is intended to act as a reference to both chronicle the progression of and also to enable other
individuals to reproduce and/or build on the work that went into the development of the method presently detailed
in ASME PCC-1-2010 Appendix O “Assembly Bolt Stress Determination”. The intent is not to reproduce the
method or to include all details of the development of the method, but to provide reference to the appropriate
articles written during the development of the method and also to provide additional details to assist in the
reproduction 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 determine
the 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 the
assembly bolt load for pressure boundary joints commenced in early 2005 and was a direct result of field
experience at Chevron with excessive flange deformation (flange rotation) on piping joints, particularly when
assembled to high initial bolt loads. The method built on previous work by Brown on the selection of an
appropriate assembly bolt load that involved the consideration of appropriate gasket stress limits [1]. That work
considered 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 enough
cases to initiate the question as to what an appropriate limit for the joint as a whole (including the flange) should
be.
This led to the publication of the initial paper on the topic by Brown in 2006 [2], which presented background on
the 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 not
appear to be valid for all cases and that a more comprehensive method would require expansion of the ASME
flange 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, as
well as a series of limits on all code flange stress locations that enabled the user to determine the assembly bolt
stress where Gross Plastic Deformation (GPD) of the flange would be expected. The developed equation and
limits 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. The
results were also verified by comparison to Elastic-Plastic FEA on ASME B16.47, SA 105, Series A, weldneck
flanges from NPS 26 to NPS 48 in pressure classes 150, 300, 600 and 900. In both cases, standard spiral wound
gasket dimensions as per ASME B16.20 were used in the analysis. For piping flanges using similar gaskets and
having similar wall thickness to those analyzed in the paper, the Elastic-Plastic FEA results could be used directly
for the flange limit in the calculation of the joint assembly bolt stress. For non-standard flanges and flanges
having significant difference in gasket or pipe wall thickness, the code equation calculation contained in the paper
offered a method of determining the flange limit. However, in developing the limits, incorrect material properties
were used in the comparison between the FEA and the code equations, which led to the code equation limits
listed 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 other
materials (SA182 F304), and the limits for the code calculation method were corrected to reflect comparison
against the correct FEA material results. These two updates to the method finalized the work with respect to
determining the flange limit for calculation of joint assembly bolt load for weldneck flanges. The information
contained in the papers written to that point was sufficient to allow determination of the approximate point of GPD
for a weldneck flange. The ASME codes, and others, use the same equations (weldneck flange) to assess a
range of configurations, from a true weldneck flange (having an integral butt welded, tapered hub) to slip-on
flanges (where the hub is fillet welded to the shell). This method may be used to approximate the behavior of slipon flanges and also integral flanges having only a radius at the hub junction. In the latter case, the approximation
will be acceptable. In the case of the slip-on flange, the assessment will be non-conservative in some cases. The
case 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 for
determination of slip-on flange strength and confirmation of the method for loose flanges or flanges without hubs
11
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
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]. It
should 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 at
a given site. The risk with using the values presented in Table O-8 of Appendix O is that they may not apply to
the actual case (for example the wall thickness of the pipe on the joint being considered may be much less than
the value used for the Appendix O calculation). Generally, the limits used to generate Table O-8 were higher than
might typically be used on piping joints, in order to provide an example that would not be taken as an absolute
limit (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 joint
leakage, 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 low
such that no damage occurs to any of the joint components during assembly or operation. Using this concept, for
most joints, results in a band of acceptable assembly bolt stress values which may be expected to work as shown
in Fig. 1, taken from Brown [1].
0% Sy Bolt
(No Load)
Gasket Stress Lost due to
Thermal Loading
Gasket Stress Lost due to
Pressure & Ext. Load ing
Z% Sy Bolt
(Max. Permissible Load)
Y% Sy Bolt
100% Sy Bo lt
(Assembly Load)
(Max. Possible Load)
X% Sy Bolt
Operational
(Min. Req’d Load)
Load
Gasket Stress Required
to Seal Gasket
Buffer against
leakage
% Sy Bo lt remain ing
during operation
Gasket Stress lost
due to Creep/Relax.
% Sy Bo lt lost during
operation
-ve +ve Buffer against
joint damage
Bolt Load
+/- Assembly Technique
and Procedure Accuracy
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 of
these values presently have an industry standard test, and therefore it is not possible to completely codify the
method at present. However, as tests are developed to establish the required information, this should be
possible. To establish the upper limits on assembly bolt stress (joint component damage), the maximum
acceptable gasket stress, and the maximum allowable assembly bolt stress that the flange will withstand must be
known. There is not presently an acceptable standard test method for establishing the maximum acceptable
gasket stress. Since the gasket values are not well defined, this bulletin will focus more on the establishment of
the 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 method
outlined in Appendix 2 of ASME [3]. The equations from that document will not be reproduced here, only the
additional 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
12
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
location and associated stress orientation:
a)
Longitudinal Hub Stress at Hub/Flange Junction ( S H
b)
Longitudinal Hub Stress at Hub/Shell Junction ( S H , existing ASME Equation [6])
c)
Radial Stress at Hub/Flange Junction ( S R , existing ASME Equation [7])
d)
Tangential Stress at Hub/Flange Junction ( ST , existing ASME Equation [8])
e)
Tangential Stress at Hub/Shell Junction ( STO , New Equation)
f , modified existing ASME Equation [6])
The stress component locations are shown in Fig. 1. The reason for the use of the modification
capture the stress at the hub/flange ring junction, versus
 SH
f  is to
S H , which is at the hub/shell junction for values of f
greater than one. The modification mentioned above to the hub longitudinal stress is to divide the calculated
value by the hub stress correction factor f . 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 f , 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 f equals one. It is not possible
to determine the stress at the hub/shell location using values of f less than one, because the equation for f
becomes inaccurate below one. However, it was found that the level of conservatism introduced by
overestimating 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
M O used in the calculations
is taken as per the equation below:
M O   B Ab hG
where
B
(1)
= the selected assembly bolt stress (MPa, psi)
Ab = the total bolt root area (mm2, in2) per Appendix 2, Notation
hG = gasket to bolt moment arm, per Appendix 2, Table 2-6
The method for calculating
STO 
STO is per the equation below:
f2
SH
f
(2)
where f = 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 f and
f 2 can have the same base equation. The two relationships (below and Appendix 2) agree across the full range
within 3%.
f 2 = a second hub stress correction factor, determined per the equation below:
13
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
2
2

 g1   h   g1   h 
 g  h  
 a +c   +e   +g   +i   +k  1   

 g0   h 0   g0   h 0 
 g 0  h 0  
fn  
2
2

 g1   h   g1 
 h 
 g  h  
1+b   +d   +f   +h   +j  1   

 g0   h 0   g0 
 h0 
 g 0  h 0  
(3)
And
f  max 1.0, f1 
f 2  max  0.25, f 2 
for
h
 0.35
h0
f 2  max  0.25, f3 
for
h
 0.35
h0
where the definition of
g1 , g 0 , h and h0 are as per ASME Appendix 2 and the constants a through k , for each
of the f variables, are defined per the table below:
Graphical representations of f and
f 2 are shown in Appendix B of this document. These plots are similar to the
existing plots of f in ASME VIII, Div. 1, Appendix 2.
f
f2
f3
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 following
locations can be compared with the limits listed following them. Note that the limits are based on material yield at
assembly (ambient) temperature
S  .
ya
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 when
assembled to sufficient bolt stress to ensure joint integrity. The limits are applied using the elastic equations and,
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WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
therefore, indicate stress levels that are well above yield. However, they have been verified against ElasticPlastic FEA to be below the point of GPD for the flange, which is the true limit of flange strength (as opposed to
localized yielding, which has no effect on flange strength).
a)
Longitudinal Hub Stress:
SH  2.0S ya
b)
Tangential Stress at Hub/Flange Junction:
ST  1.5S ya
c)
Tangential Stress at Hub/Shell Junction:
STO  1.0S ya
d)
Combined Stress at Hub/Flange Junction:
e)
Combined Stress at Hub/Flange Junction:
f)
Combined Stress at Hub/Shell Junction:
 SH f  ST   3.0S ya
 SR  ST   3.0S ya
 SH  STO   3.0S ya
g)
Radial Stress at Hub/Flange Junction:
SR  2.0S ya


In order to determine the flange limit on assembly bolt stress S f max , the assembly bolt stress is increased until
one of the above limits is exceeded. The above limits were determined by comparison to Elastic-Plastic FEA
results and give, in most cases, a result that is within 10% of the value calculated using Elastic-Plastic FEA. This
is considered sufficiently accurate for the intended purpose. When considering these limits by comparison to
pressure vessel and piping design practices it is necessary to remember that the flange stresses are
predominantly 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 localized
portions of the flange at yield should not be a concern. Under repeated assembly and operational cycles the
flange will shake-down to a final stress state where no further yielding occurs. The above stress limits are chosen
with this in mind and will seem excessive by comparison to present flange design stress limits, due to the different
intent of the flange design method (to adequately size the flange) versus this method (to determine the strength of
the 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 strength
component of the joint.
The preceding limits are for the flange assembly case. Typically this is the controlling case, since gasket
relaxation will result in a much lower residual bolt stress during subsequent joint operation. However, in cases
where the flange yield strength will be reduced by a greater amount than the expected joint relaxation, it is
necessary to also consider the flange operating case. In order to do that, (in ASME PCC-1-2010) in all cases
analyzed 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 the
stress 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 reduce
significantly during operation. In those cases, the flange limit should be reduced by the ratio of the yield
S
f max
S yo S ya  . 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
S
yo
S ya   1.25 g .
The additional reduction in gasket relaxation (1.25 term) is included to capture possible variances in actual
relaxation 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 the
change to the remaining relaxation factor (rather than the relaxation loss factor). Practically, the above
consideration can be implemented by the following modification to the preceding limits:
15
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
S y = the lesser of S ya or S yo
and
S yo = the greater of S yo 1.25 g  or S yo
Where
g
is the gasket relaxation factor from PCC-1 Appendix O (typically taken as 0.7 unless gasket test data
is available), S ya is the assembly (ambient) temperature yield of the flange material and S yo is the operating
temperature yield of the flange material.
a)
Longitudinal Hub Stress:
SH  2.0S y
b)
Tangential Stress at Hub/Flange Junction:
ST  1.5S y
c)
Tangential Stress at Hub/Shell Junction:
STO  1.0S y
d)
Combined Stress at Hub/Flange Junction:
e)
Combined Stress at Hub/Flange Junction:
f)
Combined Stress at Hub/Shell Junction:
 SH f  ST   3.0S y
 SR  ST   3.0S y
 SH  STO   3.0S y
g)
Radial Stress at Hub/Flange Junction :
S R  2.0S y
5
ELASTIC-PLASTIC FEA METHODS
The FEA that was performed to establish GPD limits for different flange configurations was based on
axisymmetric approximation of the flange geometry. The reduction in accuracy by assuming axisymmetric
behavior was more than offset by the reduction in assessment time, which was significant given the large number
of FEA assessments required. It should be noted at this point that a sensitivity study into such factors as the
element order, contact assumptions, and mesh density was performed subsequent to the finalization of the
results. It was found that, depending on the assumptions made, the answer for the point of GPD could be made
to vary by 2 to 3% between different identical geometry models. However, this variation, while significant from an
academic sense, was well within the accuracy of other factors that commonly occur in bolted joint practice.
Three such factors are:
a)
b)
c)
The effect of assembly method inaccuracy on achieved bolt load. This factor is well documented and
commonly the achieved accuracy for controlled joint assembly is within the ±10% to ±30% range.
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.
For standard piping flanges, the exact shape of the hub is not well defined in the B16.5 and B16.47
standards. 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.150
flange, Elastic-Plastic FEA demonstrated that the 45° hub had a maximum allowable assembly bolt load of
less than 30% of the full height hub geometry flange. Most suppliers tend to deliver flanges with hubs closer
to the full height condition. For this reason, it was assumed in the analysis conducted that the hub height
corresponded 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 many
variations of flange limits, for every different possible combination, that the end result would not be practical or
usable. The intent of the FEA work was, therefore, to provide a basis upon which an approximate code equation
method could be verified such that, if desired, other variables could be incorporated into the assessment on an
as-needs basis using the code equation method. The goal was to achieve agreement between the methods of
16
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
around ±10% in order to be satisfied that both methods resulted in an answer that would be sufficiently accurate
for the purposes of selecting an assembly bolt load.
The following FEA modeling simplifications/assumptions were made in order to facilitate the assessment and/or to
achieve as accurate as possible a result:
1)
The flange geometry was taken from the appropriate ASME standard, with the assumption that the hub
height was a full height hub. One half of the flange pair was modeled, with symmetry being assumed
through the central plane of the gasket.
2) The gasket sealing element geometry was taken as a spiral wound gasket in accordance with ASME
B16.20. The inner and outer rings were not modeled, so any possible contact between the flange and
those components was neglected.
3) The FEA models were constructed using first-order axisymmetric elements for the flange, first-order
plane stress elements for the bolts/nuts, and Abaqus gasket elements with normal direction behavior
only (GKAX4N) (See Fig. 3).
4) The gasket element elastic behavior was taken from flat-platen room temperature testing of a spiral
wound gasket (see Fig. 4).
5) The gasket element surfaces were tied to the flange raised face. Since the gasket elements used do
not allow tension or shear to be generated this has no effect in terms of overly restraining the joint, as
would 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 lateral
movement and the ability to separate after contact. This means that the reaction point between the nut
and the flange will move inward as the flange is loaded and rotates. In a very few cases, however, it
was necessary to tie the nut to the flange in order to achieve convergence. Those cases will slightly
under-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 bolt
diameter in order that the bending moment of inertia for the plane stress representation was identical to
the actual multiple cylindrical bolt cross-section. This bending is due to flange rotation and is significant
in 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 the
elements matched the total tensile area of the flange bolts. Note that root area was not used (as is
required in code calculations) as the tensile area is considered to be more appropriate in terms of actual
joint elastic interaction behavior. However, particularly in the larger size flanges, the two areas could be
interchanged without significant effect on the end result.
10) The bolt load was applied using the “*Pretension” command in Abaqus. This command reduces the
length of the elements across a plane on the bolt until the desired preload is established. The load was
applied 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 change
in flange rotation versus applied bolt load was greater than two times the initial elastic portion of the
slope (See Fig. 5).
12) The bolt-hole region of the flange was modeled using anisotropic elastic material properties. Since the
stress levels in that region did not typically approach yield, the use of elastic properties should not have
affected the obtained GPD value. The material properties (subscripts indicate direction, as per the code
equations) used were:

Tangential Young’s Modulus = Very Small Value (Negligible)

Radial and Longitudinal Young’s Modulus = E f



Radial/Longitudinal Shear Modulus = Radial and Longitudinal Young’s Modulus / 2.6
Other Shear Moduli = Very Small Value (Negligible)
where E f = Young’s Modulus, nb = number of bolts, d bh = diameter of bolt hole, C = bolt pitch

circle diameter
This results in the following values for each of the materials used in this study:
17
1   0.25 n
b
dbh C  
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
Material Young’s Modulus
Young’s Modulus (Tangential)
ET
ER and EH
Shear Modulus
GRH
GRT and GTH
SA-105
SA-182 F304
202,500 MPa
193,500 MPa
1 MPa
1 MPa
151,875 MPa
145,125 MPa
58,413 MPa
55,817 MPa
0.5 MPa
0.5 MPa
13) The Elastic-Plastic stress-strain behavior was taken from ASME II-D material properties for SA-105 and
SA-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 categories
of stress component limits and are provided for information only, since the actual GPD point was determined
purely 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
 STO  .
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
direction
 SH  .
combination of
 STO  and the other at the hub in the axial
The final example is a B16.47 Series A, NPS 46, cl. 300 flange, which shows failure due to the
 SH 
and
 ST  .
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 stress
that can be applied to flanged joints without damaging them. This is the case for both standard piping flanges and
custom 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 be
designed such that it is not possible to over-stress the gasket or flanges. This vastly improves the practicality of
the joint, in that it will therefore not be possible to overstress and permanently damage the joint during assembly
or operation. In addition, the method outlined is essential for determining the root cause of joint leakage, since
without knowledge as to which of the joint components, if any, are limiting, it is not possible to categorically
identify the root cause of joint leakage.
18
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
Figure 2 – Flange Stress Component Locations
First-order
Axisymmetric
Radial Stress
Hoop Stress
Axial Stress
Gasket
Elements
Plane
Stress
Elements
Figure 3 – FEA Model Plot (NPS 12, cl.300 flange)
19
First-order
Axisymmetric
Anisotropic
Properties
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
Gasket Stress (MPa)
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
Figure 4 – Gasket Mechanical Behavior
Flange Rotation (degrees)
0
-0.5
-1
-1.5
-2
Rotation (deg)
Normalised on Load
-2.5
-3
0
0.2
0.4
0.6
0.8
Bolt Stress / Yield
1
1.2
Figure 5 – Example Flange Rotation vs. Bolt Load Plot (NPS 16, cl.300)
20
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
500
450
400
Stress (MPa)
350
300
250
SA182 F304
200
SA105
150
100
50
0
0.00E+00
2.00E-02
4.00E-02
6.00E-02
8.00E-02
1.00E-01
Strain
Figure 6 – Flange Material Elastic-Plastic Properties
Strength
Limited by ST0
Sh
ST
SR
Sh
ST
SR
Figure 7 – 20in., cl.150, SA182-F304 FEA Results (MPa)
21
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
Strength Limited
by ST0
ST
Sh
ST
Sh
ST
Strength Limited
by ST0
ST
Strength
Limited By SH
Strength
Limited By SH
Sh
Sh
Figure 8 – 24in. Heat Exchanger FEA GPD Results (psi)
von Mises
Sh
Sh
Strength
Limited By
(SH + ST)
Figure 9 – 46in., Cll.300, SA182-F304 FEA Results (MPa)
22
ST
ST
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
7
REFERENCES
1.
Brown, W., 2004, “Efficient Assembly of Pressure Vessel Bolted Joints” Proceedings of the ASME PVP
2004, ASME, San Diego, USA
2.
Brown, W., Reeves, D., 2006, “Considerations for Selecting the Optimum Bolt Assembly Stress For Piping
Flanges”, 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 of
Mechanical Engineers, NY, USA
4.
Brown, W., Reeves, D.., 2007, “An Update on Selecting the Optimum Bolt Assembly Stress For Piping
Flanges”, 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 Flange
Load Limit”, ASME PVP Conference, Chicago, IL, PVP2008-61709
6.
Brown, W., 2008, “Selecting the Optimum Bolt Assembly Stress: Influence of Flange Type on Flange Load
Limit”, ASME PVP Conference, Chicago, IL, PVP2008-61708
7.
Brown, W., 2010, “Background on the New ASME PCC-1-2010 Appendices D & O Guidelines for Allowable
Gasket Contact Surface Flatness and Defect Depth &Assembly Bolt Load Selection”, ASME PVP
Conference, Bellevue, WA, PVP2010-25766
8.
ASME PCC-1-2010 “Guidelines for Assembly of Pressure Boundary Bolted Joints”, ASME, NY, 2010
23
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
8
APPENDICES
8.1
Appendix A – ASME PCC-1-2010 Appendix O Errata
Errata #1 – Usage of the flange rotation limit (gmax) is not consistent throughout the appendix. The definition
implies that the limit is associated with the sum of the mating flange rotations, but the limits listed in O-4.1(a) are
for single flanges and the flange rotation levels listed in the Tables (O-3, O-5, and O-7) are for single flanges. The
limit definition and references throughout the Appendix should be changed to ensure it is clear that the limit
applies to single flange rotation. Therefore, for a flange pair, the gasket will see the combined rotation of both
flanges, 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 (WRC
538).
Errata #3 – The incorrect method was used to determine if the reduction in flange material yield should be
accounted 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 flange
stress limits defined in this document, are as follows:
Table O-4M Replacement
150
300
2
450
310
2.5
576
284
3
724
394
4
445
561
5
402
724
6
541
593
8
724
614
10
503
639
12
712
607
14
583
454
16
563
398
18
614
472
20
568
451
24
479
365
26
218
242
28
193
264
30
228
290
32
173
272
34
160
296
36
207
261
38
211
557
40
199
536
42
218
581
44
221
676
46
238
724
48
222
524
600
515
388
545
633
663
630
657
566
563
513
508
594
482
450
359
354
447
396
463
404
623
634
626
638
687
605
900
332
377
517
417
468
543
463
444
494
526
532
534
545
546
448
399
465
460
418
436
551
532
585
570
563
625
1500
413
441
432
492
528
605
576
627
554
485
487
521
501
481
Table O-4 Replacement
150
2
65
2.5
83
3
105
4
65
5
58
6
78
8
105
10
73
12
103
14
84
16
82
18
89
20
82
24
69
26
32
28
28
30
33
32
25
34
23
36
30
38
31
40
29
42
32
44
32
46
35
48
32
2500
447
496
531
454
501
535
557
543
594
24
300
45
41
57
81
105
86
89
93
88
66
58
69
65
53
35
38
42
40
43
38
81
78
84
98
105
76
600
75
56
79
92
96
91
95
82
82
74
74
86
70
65
52
51
65
58
67
59
90
92
91
93
100
88
900
48
55
75
61
68
79
67
64
72
76
77
77
79
79
65
58
67
67
61
63
80
77
85
83
82
91
1500
60
64
63
71
77
88
83
91
80
70
71
76
73
70
2500
65
72
77
66
73
78
81
79
86
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
8.2
Appendix B – Graphical Representation of f and f2
h/(sqrt(B.g 0)
0.05
0.1
f (longitudinal stress factor)
0.2
0.3
10
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
1
1
2
3
g1/g0
25
4
5
h/(B*g0)
0.5
h/(B*g0)
0.5
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
2.5
h/(sqrt(B.g 0)
0.05
0.1
0.2
0.3
0.35
0.4
f2 (hoop factor)
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0.25
1
2
3
g1/g0
26
4
5
h/(B*g0)
0.5
h/(B*g0)
0.5
WRC Bulletin 538
Determination of Pressure Boundary Joint Assembly Bolt Loads
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. They
are calculated using a flange yield stress of 345 MPa.
Flange Size
Flange Class
Flange Spec
Pipe Outside Diameter (mm)
Pipe Wall Thickness (mm)
Flange Bore (mm)
Flange Outside Diameter (mm)
Hub Outside Diameter (mm)
Hub Thickness at Flange Ring (mm)
Flange Thickness (mm)
Hub Height (mm)
Bolt Circle Diameter (mm)
Bolt Diameter (mm)
Bolt Area (mm²)
Number of Bolts
Gasket Inner Diameter (mm)
Gasket Outer Diameter (mm)
Flange Young's Modulus (MPa)
Poisson’s Ratio
Hub Thickness Ratio
Hub Length Ratio
Axial Stress Hub Factor
Hoop Stress Hub Factor
Basic Gasket Width (mm)
Effective Gasket Width (mm)
Gasket Reaction Diameter (mm)
Gasket Moment Arm (mm)
Bolt Stress (MPa)
Bolt Load (N)
Axial Stress (MPa)
Radial Stress (MPa)
Tangential Stress at hub/flange (MPa)
Tangential Stress at hub/shell (MPa)
Flange Rotation @ W
NPS
Class
ASME
Pipe OD
g0
B
A
X
g1
t
h
C
b
Ab
nb
Gask ID
Gask OD
E
Poisson’s
g1/g0
h/ho
f
f2
b0
b
G
hG
Sb
W
SH
SR
ST
STO
f
27
44
150
B16.47A
1117.6
9.5
1098.5
1405.0
1145.0
23.2
100.4
76.0
1314.0
38.1
906.5
40
1124.0
1165.2
202500
0.3
2.4
0.7
1.00
0.59
10.3
8.1
1149.0
82.5
221
8025408
418
45
295
245
0.9
16
300
B16.5
406.4
7.9
390.6
647.7
483.0
46.2
55.6
88.8
571.5
31.8
599.3
20
422.4
463.6
202500
0.3
5.8
1.6
1.00
0.79
10.3
8.1
447.4
62.0
399
4785057
312
370
194
245
0.4
24
300
B16.5
609.6
14.3
581.1
914.4
701.0
60.0
68.3
98.1
812.8
38.1
906.5
24
628.7
685.8
202500
0.3
4.2
1.1
1.42
0.93
14.3
9.5
666.8
73.0
365
7950404
374
335
165
245
0.4
12
900
B16.5
323.9
17.5
288.9
609.6
419.0
65.0
79.2
120.8
533.4
34.9
745.2
20
323.9
368.3
202500
0.3
3.7
1.7
1.00
0.27
11.1
8.4
351.5
90.9
494
7368113
393
490
246
107
0.2
INTENTIONALLY LEFT BLANK
28
WRC PVRC
MPC
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The Welding Research Council brings together science and
engineering specialists in developing the solutions to problems
in welding and pressure vessel technology. They exchange
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