flange - a computer program for the analysis of flanged joints with ring-type gaskets
TRANSCRIPT
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3 445b 0515275 9
OR
NL-5
FLANGE:
A
Computer Program for
the Analysis of Flanged Joints
with Ring-Type Gaskets
E. C.
Rodabaugh
F. M.
OHara, Jr.
S.
E. Moore
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Printed in the United States of America. Available f rom
National Technical Informat ion Service
U.S. Department of Commerce
5285 Port Royal Road, Springfield, Virginia 221 61
Price: Printed Copy 7.75; Microfiche 2.25
This report was prepared
as
an account of work sponsored by the United States
Government. Neither the United States nor the Energy Research and Development
Administration, nor any
of
their employees, nor any
of
their contractors,
subcontractors, or their employees, makes any warranty, express or implied, or
assumes any legal liability or responsibility for the accuracy, completeness or
usefulness
of
any information, apparatus, product or process disclosed, or represents
that its use would not infringe privately owned rights.
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O R N L
-5035
YRC-1 ,
-5
Contract No. W-7405-eng-26
Re a c t o r
Division
FLANGE:
A COMPUTER PROGRAM FOR
THE
ANALYSIS
OF FLANGED JOINTS WITH
RING-TYPE
GASKETS
E .
C . Rodabaugh
Battel le-Columbus Laboratories
F .
M.
O'Hara,
J r .
S.
E .
Moore
Oak Ridge National Laboratory
Work
funded by th e Nucle ar R egula tory Commission
under Interagency Agreement 40-495-75
JANUARY 1976
( OR NL - Su bc on tr ac t No. 2913
]
f o r
OAK
R I D G E N A T I O N A L L A B O R A T O R Y
Oak Ridge, Tennessee
3 7 8 3 0
Operated by
U N I O N C A R B I D E CORPORATION
f o r t h e
U.S. E N E R G Y RESEARCH AND DEVELOPMENT ADMINISTRATION
3
4456
0535275
9
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iii
CONTENTS
Page
FOREWORD
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
V
1 . INTRODUCTION
. . . . . . . . . . . . . . . . . . . . . . . . .
1
Purpose and Scope
. . . . . . . . . . . . . . . . . . . . . . .
1
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . 2
. . . . . . . . . . . . . . 4
GENERAL DESCRIPTION
OF
THE ANALYSIS
3 . FLANGE WITH A TAPERED-WALL
H U B
. . . . . . . . . . . . . . . . 7
Equations
for
the Annular Ring
. . . . . . . . . . . . . . . .
7
Equations for the Tapered Hub . . . . . . . . . . . . . . . . . 8
Equations for the Pipe
. . . . . . . . . . . . . . . . . . . .
11
Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 11
Boundary Equations . . . . . . . . . . . . . . . . . . . . . . 12
Stresses
. . . . . . . . . . . . . . . . . . . . . . . . . . .
15
Displacements . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 FLANGE WITH A STRAIGHT
H U B
. . . . . . . . . . . . . . . . . . 17
5
BLIND FLANGES . . . . . . . . . . . . . . . . . . . . . . . . . 20
Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . 20
Stresses
. . . . . . . . . . . . . . . . . . . . . . . . . . .
24
Displacements . . . . . . . . . . . . . . . . . . . . . . . . . 25
6 THERMAL GRADIENTS . . . . . . . . . . . . . . . . . . . . . . . 26
7 CHANGE IN BOLT LOAD WITH PRESSURE. TEMPERATURE.
AND EXTERNAL MOMENTS
. . . . . . . . . . . . . . . . . . . . .
27
Analysis
. . . . . . . . . . . . . . . . . . . . . . . . . . .
28
External Moment Loading
. . . . . . . . . . . . . . . . . . . .
36
8 COMPUTER PROGRAM . . . . . . . . . . . . . . . . . . . . . . . 37
Option Control Data Card
. . . . . . . . . . . . . . . . . . .
37
Input for Code-Compliance Calculations . . . . . . . . . . . . 39
Output from Code-Compliance Calculations
. . . . . . . . . . .
41
Input for General Purpose Calculations
. . . . . . . . . . . . 43
Output from General Purpose Calculations
. . . . . . . . . . . 47
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i v
Page
. . . . . . . . . . . . . . . . . . . . . . . . . .
CKNOWLEDGMENT 52
REFERENCES
52
. . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX A.
Examples of Application of Computer Program
FLANGE
53
. . . . . . . . . . . . . . . . . . . . . . .
APPENDIX B. Flowcharts and Listing of Computer Program
FLANGE and Attendant Subroutines . . . . . . . . . . . 97
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V
FOREWORD
The work reported here was performed at Oak Ridge National Laboratory
and at Battelle-Columbus Laboratories under Union Carbide Corp., Nuclear
Division, Subcontract No.
2913 as part of the ORNL Design Criteria for
Piping and Nozzles Program, S. E. Moore, Manager. This program is
funded by the Division of Reactor Safety Research (RSR)
of
the
U.S.
Nuclear Regulatory Commission as part of a cooperative effort with
industry to develop and verify analytical methods for assessing the
safety of pressure-vessel and piping-system design. The cognizant
RSR
project engineer is
E. K.
Lynn. The cooperative effort is coordinated
through the Pressure Vessel Research Committee of the Welding Research
Council under the Subcommittee on Piping, Pumps, and Valves.
The study described in this report was conducted under the general
direction of
W.
L. Greenstreet and S. E. Moore, Solid Mechanics Depart-
ment, Reactor Division, ORNL, and is a continuation of work supported in
prior years by the Division of Reactor Research and Development,
U.S.
Energy Research and Development Administration (formerly the USAEC).
Prior reports and open-literature publications in this series are:
1.
2.
3.
4.
5.
6 .
W. L. Greenstreet, S.
E.
Moore, and
E.
C. Rodabaugh, Investigations
of Piping Components, Valves, and Pumps to Provide Information for
Code Writing Bodies, ASME Paper 68-WA/PTC-6, American Society of
Mechanical Engineers, New York, Dec. 2,
1968.
W. L. Greenstreet,
S.
E. Moore, and R. C. Gwaltney, Progress Report
on Studies
in
Applied Solid Mechanics,
ORNL-TM-4576 (August 1970).
E.
C. Rodabaugh,
Phase Report No. 11s-1 on Stress Indices for Small
Branch Connections
w i t h
ExternaZ
Loadings, ORNL-TM-3014 (August
1970).
E.
C. Rodabuagh and
A. G .
Pickett,
Survey Report on Structural Design
of Piping Systems and Components,
TID-25553 (December 1970).
E.
C. Rodabaugh,
Phase Report No. 1 1 5 - 8 , Stresses in Out-of-Round
Pipe Due
to
Interna2 Pressure,
ORNL-TM-3244 (January 1971).
S.
E. Bolt and W. L. Greenstreet, Experimental Determination of
Plastic Collapse Loads
f o r
Pipe Elbows, ASME Paper 71-PVP-37,
American Society of Mechanical Engineers, New York May 1971.
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v i
7.
8.
9.
10.
11.
1 2 .
13.
14.
15.
16.
17 .
18.
G . H. Powell , R . W . Clough, and A . N . Gan taya t , "S t r e s s Ana lysi s
of B16.9 Tees by t h e F i n i t e Element Method," ASME Paper 71-PVP-40,
American Society of Mechanical Engineers, N e w York, May 1971.
J .
K .
Hayes and B . Rober t s , "Exper imen ta l S t r e s s Ana lys i s
o f
24-Inch
Tees, " ASME Paper 71-PVP-28, American So ci et y of Mechanical Eng inee rs,
New York, May 1971.
J . M .
Corum
e t a l . ,
"Exper imental and F in i te Element St re ss Analys is
o f
a
Th in- She ll Cyl ind er- to- Cy li nde r Model," ASME Paper 71-PVP-36,
American So c i e t y of Mec hanical Eng in ee rs, New York, May 19 71.
W . L . G r e e n s t r e e t ,
S .
E . Moore, and J . P . Cal lahan , -Second
AnnuaZ
Progress Report on Studies in Applied Solid Mechanics (Nuclear
S a f e t y ) ,
ORNL-4693 ( J u l y 1971 ).
J . M. Corum and W .
L .
Greens t r ee t , "Exper imen ta l Elas t i c S t r e s s
Analys i s of Cyl inde r-to- Cyl inde r Sh el l Models and Comparisons wi th
Th eo ret ic al Pr ed ic t i ons , ' ' Paper No. G2/5, F i r s t I n t e r n a t i o n a l
Conference on St ru ct ur al Mechanics i n Reactor Technology, Be r l i n ,
Germany, Sept. 20-24, 1971.
R . W .
Clough, G . H. Powell, and A . N . Gan taya t , " S t r e s s Ana lys i s
o f
B16.9 Tees by t h e F i n i t e Element Method," Paper No.
F4/7, F i r s t
In t e rn a t io na l Conference on S t ru c t u r a l Mechanics i n Reac to r
Technology, Be rl i n, Germany, Se pt . 20-24, 1971.
R .
L . Johnson, Photo elastic Determination
o f
St re sse s
i n
ASA
B 1 6 . 9
Tees, Re se ar ch Re por t 71-9E7-PHOTO-R2, Wes ting house Re sea rch
Laboratory (November 1971).
E . C .
Rodabaugh and
S. E .
Moore, Phase Report No.
115-10
on
Com-
parisons
o f
Test Data
w i t h
Code
Methods
for Fatigue Evaluations,
ORNL-TM-3520 (November 1971).
W . G .
Dodge and S .
E .
Moore, Stre ss Indices and Fl ex i bi l i ty Fac tors
f o r
Moment Loadings
on
Elbows and Curved Pipe, ORNL-TM-3658 (March
1972).
J .
E .
Brock, Ela st i c Buckling of Heated, Straight-Line Piping Con-
f igura t ions , ORNL-TM-3607 (March 1972).
J .
M .
Corum e t a l . , Theoret ical and Experhental Stress Analysis o f
ORNL
Thin-She22 Cy Iinder-to-Cy Zinder Model No.
I ,
ORNL-4553 (October
1972).
W . G . Dodge and J . E . Smith, A Diagnostic Procedure for the Eval-
uation
of
St ra in Data from a Linear Ela sti c Te st, ORNL-TM-3415
(November 1972).
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vii
19.
20.
21.
22
23.
24.
25.
26.
27.
28 .
29.
30.
31.
W. G. Dodge and S. E, Moore, Stress Indices and Flexibility Factors
f o r Moment Loadings on Elbows and Curved Pipe,
Welding Research
Council Bulletin 1 7 9 ,
December 1972.
W. L. Greenstreet, S. E. Moore, and
J.
P. Callahan, Third Annua%
Progress Report on Studies i n Applied Sol id Mechanics (flu clea r
Safeky) ,
ORNL-4821 (December 1972).
W. G. Dodge and S. E. Moore, ELBQW: A Fortran Program
f o r
the
Calculation of Stresses , S tr ess Indices , and Fle xi b i l i ty Factors
for Elbows and Curved Pipe, ORNL-TM-4098 (April 1973).
W. G. Dodge, Secondary Stress Indices f o r Integral Structural
Attachments t o Straig ht Pipe,
ORNL-24-3476 (June 1973). A l s o in
Welding Research Council Bu Zlet in 1 9 8 ,
September 1974.
E. C. Rodabaugh, W. G. Dodge, and S. E. Moore, Stress Indices at Lug
Supports
on
Piping Systems, OKNL-'TM-4211 (May 1974). Also in Welding
Research Council Bulletin
1 9 8 ,
September 1974.
W. L. Greenstreet, S. E. Moore, and J. P. Callahan, Fourth Annual
Progress Report
on
St ud ie s i n Applied So li d Mechanics (Pressure
Vessels and Piping System Components), ORNL-4925 (July 1974).
G. H. Powell, Finite Element Analysis of Elastic-Plastic Tee Joints,
ORNL-Sub-3193-2 (UC-SESM 74-14), College of Engineering, University
of California, Berkeley (September 1974).
R. C. Gwaltney,
CURT-11
-
A
Computer Program fo r Anal yzi ng Curved
Tubes or Elbows and At tached Pipes wi th Symmetric and Unsyrrunetric
Loadings,
ORNL-TM-4646 (October 1974)
.
E. C. Rodabaugh and S.
E.
Moore, Stress Indices and Flexib i l i ty
Factors for Concentric Reducers,
ORNL-TM-3795 (February 1975).
D.
R.
Henley, Test Report
on
Experimental Stress Analysis
Inch Diameter Tee (ORNL T - 1 3 ) , ORNL-Sub-3310-3
(CENC
1189
bustion Engineering, Inc. (March 1975).
D.
R.
Henley, T e s t
Report on Experimental Stress Analysis
Inch Dimeter Tee (ORNL
T-12),
ORNL-Sub-3310-4 (CENC 1237
bustion Engineering, Inc. (April 1975).
of a 24
,
C o m -
o f a 2 4
, Com-
D. R. Henley, Test Report
on
Experimental Stress Analysis
of
a 24
Inch Diameter Tee
(ORNL
T - 2 6 ) , ORNL-Sub-3310-5 (CENC 1239), Com-
bustion Engineering, Inc. (June 1975).
R. C. Gwaltney,
S.
E. Bolt, and J. W . Bryson, Theoretical and Experi-
mental St re ss Analysis of ORNL Thin-Shell Cylinder-to-CyZinder
Model
4 ,
ORNL-5019 (June 1975).
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v i i i
32. R . C. Gwaltney, S . E . Bo l t , J . M . Corm, and J . W . Bryson,
Theoretical and Experimental St re ss Analysi s of
ORNL
Thin-Shell
Cplinder-to-Cylinder Model
3,
ORNL-5020 (June 1975) .
3 3 .
E .
C . Rodabaugh and
S .
E . Moore, Stress Indices for A N S I
B 1 6 . 1 1
Standard Socket- Wel d i n g Fit t ings , ORNL-TM- 929 (August 1975) .
3 4 . R . C . Gwaltney,
J .
W . Bryson, and S . E . Bo l t , Experimental and
Finite-Element
Analysis o f
ORNL Thin-Shell Model
No.
2 ,
O R N L -
5021 (October 1975).
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1. INTRODUCTION
Purpose and Scope
The
ASME
Boiler
and
Pressure Vessel Codel
gives rules for designing
bolted flange connections with ring-type gaskets based
on
a stress
analysis developed by Waters et a1.2
graphs for calculating stresses due to a moment applied to the flange
ring. The Code rules, however, do not require that stresses due to
internal pressure be taken into account, although Ref. 2 briefly dis-
cusses such stresses.
These rules give formulas and
The computer program FLANGE was written to calculate not only the
stresses due to moment loads on the flange ring but also stresses due to
internal pressure;
stresses due to a temperature difference between the
hub and ring; and stresses due to the variations in bolt load that
result from pressure, hub-ring temperature gradient, and/or bolt-ring
temperature difference. The program FLANGE is applicable to tapered-
hub, straight, and blind flanges. The analysis method is based on the
differential equations for thin plates and shells rather than on the
strain-energy method used by Waters et al.2
loading calculated by the two methods are essentially identical for
identical boundary conditions. The analysis provided herein also in-
cludes
a
different, and perhaps more realistic, set of boundary con-
ditions than those used in Ref. 2 .
The stresses due to moment
The nomenclature used in this
r e por t
is
identified
in the remainder
of this chapter.
flanges used in the theoretical development of the computer code is
provided. The actual mathematical expressions for calculating stresses
and displacements due to moment
and pressure loads are derived in
Chapters 3 ,
4,
and 5 for tapered-hub, straight hub, and blind flanges,
respectively.
include the effects of thermal gradients and variations in bolt loads.
The computer program FLANGE is described in the last chapter of this
report. Example calculations, listings, and flowcharts of the program
and
its
subroutines are included as appendices.
In Chapter 2 a description of the general model
of
In Chapters
6
and
7,
these expressions are extended to
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2
Nomenc1 t u re
a =
o u t s i d e r a d i u s of r i n g
A
= 2a = o u t s i d e d ia m e te r o f r i n g
%
=
c r o s s - s e c t i o n a l b o l t a r e a
A = g a s k e t a r e a
g
b = i n s i de rad ius of r i ng and mean
B
= 2b
=
i n s i d e d i am e t er o f r i n g
b
= Be sse l f u n c t i o n
of rl
n
c = b o l t - c i r c l e r a d i u s
C =
2c
= b o l t - c i r c l e d i a m e t e r
C . = c o n s t a n t
o f
i n t e g r a t i o n
C =
C. /b
1
1 I
D = ~ t 3 / 1 2 ( 1 ~ 2 )
r a d i u s
of
p ipe
= c o n s t a n t s o f i n t e g r a t i o n ( b l i n d - f l a n g e a n a l y s i s )
' i j
E
E
E = E
b
6
f = ASME Code design parameter
F =
ASME Code design parameter
=
modulus
of
e l a s t i c i t y
of
f l a n g e mate r i a l
f
=
m od ulu s o f e l a s t i c i t y of b o l t m a t e r i a l
= m od ulu s o f e l a s t i c i t y o f g a s k e t mate r i a l
go
= wal l
t h i c k n e s s
of
p i p e
gl
= wall
t h i c k n e s s o f hub a t i n t e r s e c t i o n w i th r i n g
g = g a s k e t c e n t e r l i n e r a d i u s
G = 2g =
g a s k e t c e n t e r l i n e d i a me te r
h = l eng th of t ape red-wa l l hub
K = a / b = A/B
R O
=
b o l t l e n g t h
M = t o t a l moment a p p l i e d t o r i n g , i n . - l b
M .
o r
M . .
= m o m e n t r e su l t a n t s , i n . - l b / i n .
1 11
p = i n t e r n a l p r e ss u r e
P .
=
s h e ar r e s u l t a n t s , l b / i n .
1
p *
=
- ( v / 2 ) b p = nondimensional pr es su re parameter
g 0 E
r = r a d i a l c o o r d i n at e , r i n g
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3
t
= ring thickness
= hub thickness
tX
u = radial displacement, hub
u,
=
radial displacement, pipe
u
= radial displacement, ring
r
V =
ASME
Code design parameter
v o = undeformed gasket thickness
w = axial displacement, ring
W, = initial bolt load, lb
W, =
residual bolt load, lb
x = axial coordinate, hub
x1 = axial coordinate, pipe
0,
=
(g1
-
g o ) / g o
=
p
-
1
=
nondimensional wall-thickness parameter
= [ 3 ( 1 - v2)/b2g:l1j4 = dimensional parameter used in the analysis
y =
[ 1 2 ( 1
- v2)/b2gi]
1/4
h)
=
dimensional parameter used in the analysi
h
= temperature difference between hub/pipe and ring
6 .
=
axial displacement of ring
= coefficient of thermal expansion, flange material
= coefficient of thermal expansion, bolt material
'
E =
coefficient of thermal expansion, gasket material
g
n = 2 ~ ( 4 J / a ) ~ / ~
nondimensional argument of the modified Bessel functio
v = Poisson's ratio (0.3 used herein)
5 = x/h = nondimensional distance parameter
p = g,/g, = nondimensional wall-thickness parameter
o = stress, with subscripts:
1
R
= longitudinal (pipe
o r
hub)
c = circumferential (pipe or hub)
t =
tangential (ring)
r
=
radial (ring)
b
=
bending
m = membrane
o =
outside surface of the pipe or hub on the hub side of ring
i = inside surface of the pipe or hub on the gasket-face side of ri
J
=
5 + (l/a) = nondimensional parameter
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4
2. GENERAL DESCRIPTION OF THE
ANALYSIS
The model used for the analysis of tapered-hub flanges is shown in
Fig. 1. The three parts involved are the pipe, hub, and ring, respec-
tively.
plates and shells. The pipe is considered to be a uniform-wall-thickness
cylindrical shell with midsurface radius b. The hub is considered to be
a linearly variable-wall-thickness ylindrical shell with midsurface
radius b.
The ring is considered to be a flat annular plate with con-
stant thickness t, inside radius b y and outside radius a. The effects
of
the bolt holes are neglected.
The analysis presented here is based on the theory of thin
Three different types of loadings on bolted flanges are considered:
1.
Bolt load, represented
by
W in Fig. 1. In application, the
moment
M
applied to the flange ring is converted into an equivalent bolt
load by the relationship W(a
-
b)
=
M. This is the same approach used
in the ASME Code calculation meth0d.l
2. Internal pressure, acting radially on the pipe, hub, and ring
and axially on an (assumed remote) end closure
on
the pipe.
3 . A temperature difference between the pipe and the ring.
The
pipe and the hub are assumed to be at the same uniform temperature.
ring is also assumed to b e at a uniform temperature, which may be
different from that of the pipe
o r
hub.
The
Upon integration of the shell and plate differential equations,
algebraic equations in terms of dimensions, materials properties and
loadings, and 12 integration constants are obtained,
4
for each part.
These constants are evaluated by the usual discontinuity analysis method
of writing continuity equations at the junctures of the parts and at the
boundaries.
the algebraic equations provide the means for computing the stresses and
deflections. In the development of the equations for stresses, the
assumption is made that the bolt load W does not change with pressure or
temperature. Later the analysis is modified to include changes in W as
a function of these loadings. Because the relations are linear, it is
possible to determine the stresses
(o r stress range) due to combinations
After numerical values are determined for the constants,
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5
- c r y
b
-
O R N L - DWG 75- 4299
PIPE
-
-90
---tu4
Ar W
0 ur
f
t
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6
of initial bolt loading, pressure, and temperature change. The model
used for straight-hub flanges
is a simplification of the tapered-hub
case in that only two parts are involved, the pipe and the ring.
In common with all shell-type analyses, the analysis gives anomalous
results at points of abrupt thickness change or meridional direction
change. In particular, the stresses at the juncture of the hub to the
ring represent only the gross loading effect; detailed local stresses
are not determined by the theory. Displacements, however, are represented
fairly accurately.
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7
3 .
FLANGE
WITH A
TAPERED-WALL
H U B
The first step in deriving the stress equations is to state the
basic shell/plate equations for the ring, the hub, and the pipe. We
then inspect the boundary conditions, compute the constants, and calcu-
late the stresses and displacements.
Equations for the Annular Ring
The basic differential equation for the displacement w of a circular
plate given by Timoshenko3 is
where the coordinate r and displacement w are illustrated in Fig.
1 and
q = a uniformly distributed lateral load on the plate, D = Et3/12(l
-
u2)
=
the flexural rigidity of the plate, E
=
modulus
of
elasticity
of
the flange material, t
=
plate thickness, and u
=
Poissons ratio.
Equation
(1)
can be integrated to give a relation for the displacement
in terms of arbitrary constants:
where numerical values for the constants C7, . . . , C10 are established
from boundary conditions. Derivatives of w, required
i n
the subsequent
analysis, are:
c9
r3q
w
dr
_
- C7(2r in r + r)
+
2C8r
+
- -
r 16D
d2w c g 3r2q
dr2 r2 16D
- -
-
C7(2 Rn r + 3)
+
2C8
-
-
(3)
( 4 )
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and
- -3w
i t ) + - + -C g
3rq
L r r 3 8~
r
- c7
I n t h e s u b se qu e nt a n a l y s i s t h e d i s t r i b u t e d l o ad q
i s
taken
as
zero .
The radia l and tangent ia l moments a re g i v e n 3 by t h e e q u a t i o n s :
d2w v dw
d r 2 r d r )
M
= - D ( + - - I
r
and
Using Eqs. (3) and ( 4 ) , t h es e moments can be exp resse d
as
C7[2(1 + v ) Rn r + (3 + v ) ] + C 8 [ 2 ( l + v ) ]
r
and
C 7 [ 2 ( l + v ) Rn r + (1 + 3 v ) l
+
C8[2( l
+
v ) ]
Eaua tion s f o r t h e TaDered Hub
The b a s i c d i f f e r e n t i a l e q u a t i on f o r t h e r a d i a l d i sp l ac e me n t u
of
a
c y l i n d r i c a l s h e l l w it h
a
l i n e a r l y v a r i a b l e
w a l l
t h i c k n e s s t i s given by
Timoshenko3
as
X
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The solution of Eq.
(10)
can be shown* to be:
bP*
(Clbl + C2b2 + C3b3
+
C4b4)
+
u = -
>
1/2 1 +
a ] D (5931
t t
and
0
=
i 6 M
/ t 2 = IEtMr/[2(1 -
w 2 ) ] D
.
r r
A t t h e c e n t e r of t h e f l a n g e ( r = 0 ) ,
M
=
M
=
- D I D , 2 [ 2 ( 1
+
v ) ] >
.
t r
A t t h e g a s ke t ( r = g ) ,
M = - D { D , 2 [ 2 ( 1 + v ) ] + g2p(3 + v ) / 1 6 D }
,
r
and
A t
t h e b o l t c i r c l e
( r
=
c ) ,
and
In a l l of t he above ,
a
posi t ive moment produces
a
t e n s i l e s t r e s s on
the back
of
t h e f l a n g e
( p o s i t i v e w s i d e o f
F i g .
2 ) .
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2 5
Di p
1
ceme n t s
I n t h e t h i r d and s i x t h b ou nd ary c o n d i t i o n s l i s t e d i n Ta bl e 7 , t h e
ax ia l d i sp lacemen t
a t
t h e
g a s k e t
h as be en a r b i t r a r i l y s e t e qu al t o z e ro .
The r e la t ive d i sp lacemen t of t h e b o l t c i r c l e t o t h e g a sk e t i s t h e r e f o r e
w
= D32c2 +
D 3 3
Rn
c
+ D34
.
(65)
C
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2 6
6. THERMAL
GRADIENTS
Two kind s of therm al gr ad ie nt s are i n cl u de d i n t h e a n a l y s i s :
(1)
a
c o n s t a n t t e m p e r a tu re i n t h e p ip e an d hub t h a t may be d i f f e r e n t fro m th e
assumed cons tan t t empera tu re i n th e r i ng and ( 2 ) a c o n s t a n t t e m p e ra tu r e
i n t h e b o l t s t h a t may b e d i f f e r e n t f ro m th e a ssum ed c o n s t a n t t e m p e ra tu r e
i n t h e r i n g .
T h e s i g n i f i c a n c e
o f
t h e b o l t - t o - r i n g t he rm al g r a d i e n t s
i s
dependent
upon t h e d im e ns io na l a nd m a t e r i a l c h a r a c t e r i s t i c s o f t h e f l a n g e d j o i n t
and
i s
c ov e re d l a t e r i n Ch a pt e r 7 .
The p ipe /hub - to - r ing tempera tu re g ra d ie n t i s i n cl u de d i n t h e
an a l ys i s by an app r op r i a te change i n the " load ing paramete r s" shown i n
Table
3 .
p ipe/hub and th e r i ng ;
A i s
p o s i t i v e i f t h e p i pe /h ub
i s
h o t t e r t ha n t h e
r i n g . The r a d i a l e xp a ns ion o f t h e t a p e r e d h u b a t
i t s
j u n c t u re w i t h t h e
r i n g
i s
then :
We d e f i n e
A
as
t h e d i f f e r e n c e i n t e m p e r atu r e be tw ee n t h e
where b i s t h e p i p e r a d i u s ;
b
terms are t h e B e s se l f u n c t i o n s d e f i n e d i n
Table
1
e v a l u a t e d
a t x
=
h ,
n
=
2yp1/'/a,
as
i n d i c a t e d
i n
f o o tn o t e
e
of
T a b l e
3 ;
and
i s
t h e c o e f f i c i e n t o f t h er m al e x p an sion of t h e f l a n g e
mater ia l .
1
The e f f e c t s o f such
a
t h e r m a l g r a d i e n t
are
t a k e n i n t o a c c ou n t
by
adding
(*/b)
(bE A ) t o t h e e x i s t i n g t er ms i n t h e l oa di ng -p a ra m et er
column i n Table
3 [ E q s .
(20-Sa) and (20- Sb)] . The analo gous term
i s
a l r e a d y i n c lu d ed i n T a bl e 6 .
f
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2 7
7 .
CHANGE I N
BOLT
LOAD
WITH
PRESSURE, TEMPERATURE,
A N D EXTERNAL MOMENTS
A
flanged joint is a statically indeterminate structure. Thus, in
order to determine the residual bolt load in the joint, it is necessary
to calculate the relative displacements of the parts when the joint is
subjected to
(1)
initial bolt loading, 2 ) moment loading, ( 3 ) internal
pressure, and (4) thermal gradients.
The object of the analysis is to determine the residual bolt load
W2 in terms of (1) the loadings W1, p,
A ,
and A'; (2) the component
temperatures
T
(4) the material properties.
T
Tf, and Ti;
(3)
the flanged-joint dimensions; and
The basic analysis is given by Wesstrom and BerghY6 and we follow
b '
g'
their nomenclature, with additions as necessary. Reference 6 covers
only the effect
of
initial bolt loading and part of the influence of
internal pressure; the remaining influence from the internal pressure
is
discussed
by
Rodabaugh.7 The extension of the analysis to cover thermal
gradients is relatively simple and is covered below.
The nomenclature used in this development is:
A
= cross-sectional area
of
bolts or gasket
B = inside diameter of ring
C
=
bolt-circle diameter
E
= modulus of elasticity
go = wall thickness of pipe
G = gasket centerline diameter
R = bolt length
p = internal pressure
p* = equivalent pressure for external moment loading
q
= elastic deformation coefficients
t =
ring thickness
T
= final-state temperature (initial-state temperature is defined as
zero)
v
=
gasket thickness
W = bolt load
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6
= relative axial displacement between the gasket centerline and
the bolt circle
E = coefficient of thermal expansion
A =
temperature between hub/pipe and ring
The subscripts 0,
1,
and
2
refer to the undeformed, initial deformed,
and final deformed states, respectively; subscripts b, g, and
f
refer to
the bolts, gasket, and flange, respectively.
are for one of the flanges in a pair (e.g., T; refers to the temperature
of the right-hand flange in Fig.
3); quantities without a prime are for
the other flange.
Quantities with a prime I )
Analysis
Figure 3 shows
a
schematic illustration of the general case of two
dissimilar flanges and their mode of deformation.
initially tightened to make up the joint, the resulting initial deformed
bolt length is
When the bolts are
R 1 = v1 + tl
+
t; -
6 ,
- 6 ;
ORNL-
D W G 75-
297
Fig. 3 .
General case of two dissimilar flanges and their mode
of deformation.
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2 9
After application of loadings, the bolt length becomes
R2 =
v2
+ t2
+
t; - 6, -
6;
The basic displacement relationship
is
thus
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and q i n
he e l a s t i c d e fo rm at io n c o e f f i c i e n t s q b l q g l q b2
g2
Eys.
(70a--R) ar e fu r t he r def ined a s
0
-RO
-
qb2
V O
In Eqs. (70a-R), th e term q f l i s
a
r o t a t i o n o f t h e f l a n g e due t o
a
i s a r o t a t i o n o f t h e f l a n g e d ue t o
a
u n i t i n t e r n a l
n i t moment l oa d, q
P
pr es su re ) and qt i s
a
r o t a t i o n o f t h e f l a n g e d ue t o
a
u n i t t e m p e r a t u r e
gra d ie n t be tween th e hub and th e r in g .
The q u a n t i t i e s q f l , q p , and q t
a r e o b t a i n e d fr om t h e f u n c t i o n a l
e x p r e s s i o n
where hG
=
(C
-
G)/2, C i s t h e b o l t - c i r c l e d i a m e t e r, a nd G
i s
t h e g a s k e t -
c e n t e r l i n e d i am e te r .
obt a in ed from Eqs.
(46)
and (47) w i t h t h e a p p r o p r i a t e u n i t v a l u e s f o r
t h e l o ad s A , P , and M .
f l
Values f o r th e displacemen ts wc(L) and
w
g (L) a re
For
q t h e mod ulus o f e l a s t i c i t y u sed i s t h a t f o r t he i n i t i a l
c o n d i t i o n . For
q
a nd q t h e m od ul i u sed a r e t h o se f o r t h e f i n a l
condi t ion . The
term
q f 2 i s o b t a in e d fro m q f l a nd t h e r a t i o o f t h e
i n i t i a l and f i n a l e l a s t i c m od ul i; t h u s:
P t
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The moments and loa ds a r e de fi ne d by Eqs. (73a-n).
The nomenclature
u se d i n t h e s e e q u a t i on s
i s
a na log ou s t o t h a t u s e d i n t h e ASME C0de.l
The symbol
H
r e p r e s e n t s
a
l o a d , h r e p r e s e n t s a le ve r arm, and M r e p r e -
s e n t s
a
moment.
t h e a r e a i n s i d e t h e f l a n g e , HG i s th e gaske t load i n pounds,
HT i s
t h e
d i f f e r e n c e b etwe en t h e t o t a l h y d r o s t a t i c end f o r c e and t h e h y d r o s t a t i c
end f o r c e on t h e a r e a i n s id e t h e f l a n g e , h
i n ch e s f rom t h e b o l t c i r c l e t o t h e c i r c l e on which HD a c t s ( a s p r e -
s c r i b e d i n T a bl e UA-50 of t he Code), h
from t h e g a s ke t -l o ad r e a c t i o n t o t h e b o l t c i r c l e , and hT
i s
t h e r a d i a l
d i s t a n c e i n i n c he s from t h e b o l t c i r c l e t o t h e c i r c l e on which H a c t s
( a s p r e s c r i b e d i n Ta b l e U A - 5 0 ) .
e a r l i e r i n t h i s c ha pt er .
de fo rmed s ta te ,
a
s u b s c r i p t
2
r e f e r s t o t h e f i n a l deform ed s t a t e , and
p r im e d q u a n t i t i e s r e f e r
t o
t h e m a ting f l a n g e .
The term
%
i s
th e hyd ros ta t i c end fo r ce ( i n pounds) on
i s t h e r a d i a l d i s t a n c e i n
D
i s
t h e r a d i a l d i s t a n c e i n i nc he s
G
T
Symbols,
C , B , G ,
g o , and p a r e d e f i n e d
Again,
a
s u b s c r i p t
1
r e f e r s t o t h e i n i t i a l
hT
= [C -
(G
+
B)/2] /2
,
(c)
h +
=
[C
-
( G
+
B1 ) /2 ] /2
,
(d)
hG = ( C - G ) / 2 ,
( e>
71
H D 2
= - B2p ,
(
f>
(h 1
T
=
-
( G 2 - B 2 ) p ,
HT2 4
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3 2
M
= W h = H h
( R )
(m)
1
i G G I G '
M
= HD2hD+ HT2hT
+
H
G 2h
G
'
M i = H'2h '
H+2h+
HG2hG *
2
and
(n)
Su bs ti tu t i n g Eqs. (70a--R) i n t o Eq. (69) g i v e s
Tb~bLO qb2W2 - qblW1 = TgEgv0 - 'g2('2 - 'D2 - HT2)
I n o r d e r t o e l i m i n a t e M , and M 2 from Eq. (7 4) ' Eqs. ( 7 3 L and m ) a r e
u se d; t h e s i x t h term on t h e r ig h t - ha n d s i d e of Eq. (74) then becomes
The l a s t term i n Eq. (74)
i s
t r e a t e d s i m i l a r l y . C o l l e c ti n g terms c o n t a i n i n g
W,
on
t h e
l e f t
g i v e s :
+ h 29 ' > w
=
(qbl
+
q g l
+
h 2 q 'fi 1
2
(qb2 qg2 h G q f2 G f 2
2
3 2 )
T E V + T E ~
T ' E ' ~ '
T E L
g g o f f 0 f f o b b o qg2CHD2
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3 3
and
2 2
Q,
= qb2 + qg2 h~qf2 hGqi2
D, H i , HT,
and
H,
Eq. (75) becomes
nd using the given definitions of
H
r '
1
+
T'E't'
-
T E
R )
f f o b b o
T E
v
+
TfEftO
Q, 1 42
g g o
Q,
= - w
hG
-
qp
Q2
+
q')p - hG
qtA
+
q;c')
.
(76)
P Q2
In order to compute the flange stresses under the various loading
conditions, it is necessary to compute the flange moment M
From Eq. (73m) and the definitions in
E q s .
(73a-k),
or
Mi.
2
7
M, = 4
P[B 2 h D + ( G 2
-
B2)hT
- G 2 h G ]
+ W2hG
.
And similarly for the mating flange,
M i
=
t
p
{(B'I2h;
+
[G2
-
(B')2]h+
-
G2hG
+
W,hG
.
The computer program was written to separately evaluate the various
effects involved in bolt-load changes. The residual bolt load due to
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temperature differences that produce differential axial strain is
(78)
1
= W 1 + - ( T v
+ T E ~ T ' E ' ~ ' - T E R ) .
'2a
Q, g g o f f 0
f f o b b 0
The residual bolt load, after internal pressure (acting in an axial
direction) has transferred the bolt load on the gasket to a tensile load
on the attached pipes due to a shift in
lever arms, is given by:
The total effect of internal pressure due
to
both the shift in the
lever arms and the radial effect of pressure acting on the integral
flangeis) and/or on the inside surface of a blind flange is given by:
The residual bolt load due to a temperature difference between the hub
and the ring is given by:
A
slight modification of the above is required for the case of a
blind flange. If we designate the blind flange as that with the primed
nomenclature, then all* of Eqs. (7Oa-9,) are valid except Eqs. (70f
and
9,
for 6; and
6;.
*For
v2 it should be noted that
H D 2 -
HT2
=
nG2p/4; hence, this
equation
is valid for blind flanges.
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For blind flanges, W is used rather than M as the loading parameter
because the relationship M = W(a - b) is not valid for the blind-flange
analysis. For blind-flange analysis,
E q . (65)
gives
a
value of w
.
here
C '
-w is the equivalent of -w + w in Eq.
(72)
because
w f 0
in the
blind-flange analysis.
c g
g
For blind flanges we define
where (-w
)
is the axial displacement per unit total bolt load W. The
equation for W2 for a blind flanged joint is then:
c w
Ql 1
W = - W ,
+ - ( T E V
+ T E
t
+ T ' E ' ~ '
T E E )
42 42 g g ~ f O f f o b b o
h G
P Q2
+ q'lp - - A
G
- qp
Q2
( 8 3
In E q .
83) the primed values refer to properties of the blind flange.
After the internal pressure has transferred the bolt load on the
gasket to a tensile
load on the attached pipe due to a shift in the
lever arms, the residual bolt load for the case where a blind flange is
used is
It
should be noted that q;A' does not exist for an integral flange mated
to a blind flange.
The combined effect of all of the above is also obtained from the
computer program
by
calculating W2 from Eqs.
(76)
and (83).
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External Moment Loading
Up t o t h i s p o i n t , a l l loa ds conside red have been axisymmetric . For
f l an g ed j o i n t s i n p i pe l i n e s , t h e r e
i s
o ne o t h e r s i g n i f i c a n t l o a di n g ;
t h a t
i s ,
th e bending moment imposed on th e f lang ed j o i n t by th e at tac hed
p i p e . T o d i s t i n g u i s h t h i s f rom t h e l o c a l moments a p p l i e d t o t h e f l a n g e
r i n g , t h e bending moment
w i l l
be de sign ate d a s an l le xte rna l" moment.
The external moment
c an be r e p r e s e n te d by a d i s t r i b u t e d a x i a l e d ge f o r c e
a c t i n g on t h e a t t a c h e d p i p e :
F
( e ) =
F
COS e ,
M m
where
8
= ang l e a round t he c i rcumference ( e =
0
a t t h e po i nt of maximum
t e n s i l e
s t r e s s
i n t h e p i p e du e t o t h e e x t e r n a l moment). S i n c e t h i s
r e p o r t d e a l s o n l y w it h cases i n which a l l c o n t a c t o c c u rs w i t h i n t h e
b o l t - h o l e
c i r c l e ,
a reasonably good f i r s t a pp r ox im a ti on f o r t h e e f f e c t s
of the external moment
lo ad in g can b e o b t a in ed by r ep l a c in g t h e d i s -
t r i b u t e d a x i a l f o r ce
F
( e ) w i t h t h e axisymmetric t e n s i l e f o rc e
Fm =
F (max). Then, si nc e F i s axisymmetric, t h e r e i s some pr es su re p* th a t
w i l l p ro du ce t h e same a x i a l f o r c e i n t h e p ip e ; o r a l t e r n a t e l y , t h e r e
i s
an e q u i v a l e n t p r e s s u r e p* t h a t w i l l p ro d u ce an ax i a l s t r e s s i n t h e p ip e
which
i s
e qu al t o t h e
maximum
t e n s i l e
s t r e s s
S
produced by an external
moment.
M
M m
b
The r e l a t i o n between p* and Sb is g i v e n by
where S i s th e bend ing s t r e s s i n t h e a t t a c h ed p i p e due t o t h e e x t e r n a l
moment. The change i n b o l t load W i s t h en o b t a in ed b y r ep l ac in g p
2b
with p
+
p* i n Eqs. (79) and
( 8 4 ) .
I t s h o ul d b e no te d t h a t t h i s e qu iv -
a l e n t p r e s s u re
i s
i n c lu d ed o n l y i n Eqs . (79) and
(84)
an d n o t i n
E q .
b
(80)
*
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3 7
8 .
COMPUTER
PROGRAM
A
Fortran computer program named
FLANGE
h a s bee n w r i t t e n t o c a r r y
o u t t h e c a l c u l a t i o n s a c co rd i ng t o t h e a n al y s e s d e sc r ib e d i n t h i s r e p o r t .
The progra m c a lc u la t e s a ppr opr i a t e loa d s , s t r e s s e s , and displacements
f o r t h e f l a n g e s , b o l t s , and g a s k e t s when t h e fl a n g e d j o i n t i s s u b j e c t e d
t o in t e r na l p r e s su r e , m oment, a nd /o r ther m al g r a d ie n t loa d ings ; t hus ,
t h e program
i s
much more gen eral tha n t h at needed onl y t o determin e
compliance wit h t h e ASME Boi ler and Pre ss ure
Vessel
Code. The program
a l so ha s t he a dva n tage o f in t e r n a l ly comput ing th e va lu e s o f th e Code
v a r i a b l e s F ,
V ,
and f t h a t m us t o the r wise be e x t r a c t e d m a nua l ly fr om t he
cu rv es gi ve n i n Code Fi g s . UA-51.2, UA-51.3, and UA-51.6. Loose hubbed
flanges, which
a r e
covered by t h e Code, however,
a r e
not covered by t h e
computer program.
The m ain f unc t ion o f t h i s c ha p te r i s t o d e s c r i b e t h e i n p u t a nd
o u t p u t f o r t h e v a r i o u s c o mp u ta ti o na l o p t i o n s a v a i l a b l e t o t h e u s e r . For
more de t a i l e d in f o r m a t ion , t he r e a de r i s u rg ed t o c a r e f u l l y s t ud y t h e
examples given
i n Appendix A where a f l a nge d j o i n t , s e l e c t e d f rom API
Standa rd 605 (Ref .
8), i s
analyz ed. Sev era l sample problems a r e worked,
and t h e da ta i npu t and program out put a r e g i v e n f o r t h e v a r i o u s p ro gram
o p t i o n s a l on g w i t h a d i s c u s s i o n o f t h e r e s u l t s . F l ow c ha rt s a nd l i s t i n g s
of t h e program and
i t s
subr ou t ine s a r e g ive n i n Appendix
B .
I n t h e
f o ll o w in g s e c t i o n s , t h e i n p u t d a t a f o r o p t i on c o n t r o l a nd t h e i n p u t d a t a
and program ou tpu t f o r Code compliance cal cu la t i on s and f o r more ge ner al
c a l c u l a t i o n s are d i sc usse d .
ODtion Control
Data
Card
The f i r s t c a r d
of
e ac h d a t a s e t , h e r e i n c a l l e d t h e o p t i o n c o n t r o l
c a r d , c on ta ins c on t r o l i n f o r m a t ion f o r e xe c u t ion o f t he va r ious pr ogra m
o p t i o n s . I t c o n t a i n s i n fo r m a ti o n s p e c i f y i n g t h e t y p e o f f l a n g e b e in g
a na ly ze d, t h e boundary c on di t i on p la ce d on t h e d is pl ace me nt ( u ~ ) ~ =
t h e
s t r e s s e s
a nd o t h e r v a r i a b l e s t o be c a l c u l a t e d , an d t h e j o i n t c on-
f i g u r a t i o n and wh ich f l a n g e ( of t h e p a i r )
i s
t o be ana lyzed. These
spe c i f i c a t io ns a r e under c on t r o l o f th e f ou r va r i a b le s ITYPE, I B Q ) N D ,
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3 8
ICgDE, and
MATE.
The a d m i s s i b l e v a l u e s a nd t h e i r s i g n i f i c a n c e a r e as
fo l lows .
ITYPE ( in di ca te s the typ e of f la ng e being analyzed)
1
f o r a t ape red-h u b f l an g e
2
f o r a s t r a i g h t - h u b f l a ng e
3 f o r
a
bl ind hub
IBOND ( s p e c if i e s th e displac emen t u a t x = h)
r
0 f o r ( u ~ ) ~ = ~
0
t o conform with th e ASME Code ba si s
1
( s e e f o o t n o t e ) *
2 fo r (u r Ix zh # 0 [see Eq. ( 2 0 - 6 ) o f t h i s r e p o r t ]
ICgDE (c on tr ol s t h e amount of ou tput d at a )
0
f o r a wide v a r i e t y o f s t r e s s e s , moments, and l o ad s f o r s p ec i f i e d
moment, pressure, and
AT
1
( s e e f o o t n o t e ) *
2 f o r a s e l e c t
l i s t f o r checking Code compliance i n accordance
wi th Sec t i o n
V I I I ,
Div.
1
of t h e ASME Code
MATE ( s p e c i f i e s t h e j o i n t c o n f i g u r a t i o n and t h e f l a n g e t o be a n a ly z ed )
1 fo r o n ly o ne f l a n g e t o b e ana lyzed (T hi s i s t h e s i t u a t i o n f o r
ASME-Code re la te d ca lc ul at io ns . )
2
f o r t wo i d e n t i c a l f l a n g e s m ated t o g e t h e r
3 f o r t h e
f i r s t
o f two f l a n g e s t h a t a r e n o t i d e n t i c a l , n e i t h e r of
which
i s
a b l i n d f l a n g e
4 fo r t h e s eco n d of two f l a n ge s t h a t a r e no t i d e n t i c a l , n e i t h e r
of which i s a b l i n d f l a n g e
5 f o r a b l i n d f l a n g e
6 f o r a f l a n ge t h a t
i s
mated with
a b l i n d f l a n g e .
The da ta card wi th the above in fo rmat ion
i s
fo ll o wed by o th e r d a t a ca r d s
c o n t ai n i ng p h y si c a l -p r o pe r t y d a t a , e t c . , f o r t h e p a r t i c u l a r f l a n g e b ei ng
analyzed.
Si nce th e program can be used t o ana lyz e any number of f l an ge s
*
In t he o r ig in a l concept ion of th e program, IBgND and I C g D E were
e n v is i on e d a s c o n t r o l l i n g a d d i t i o n a l c a l c u l a t i o n s t h a t w ere n o t i mp le -
m ented i n t h e p re s en t v e r s i o n . A s i t i s now wr i t te n , th e program does
n o t d i s t i n g h i s h be tween v a lu es o f 0 o r
1
nor between 2 and numbers
g r e a t e r t h a n 2 f o r e i t h e r IBgND or 1CQ)DE.
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39
or flanged joints sequentially
(as done in the examples of Appendix A),
the data card set for each flange must start with an option-control data
card.
Different types
of
flanges and different types of calculations have
different input data requirements. These data and their formats are
discussed in the following sections.
Input for Code-Compliance Calculations
Since the ASME Code calculation procedures consider only one flange
at a time, the input data requirements for the computer program are
quite simple and straightforward.
by the three data cards illustrated in Table
9.
The nomenclature is the
same as that used in the Code.
Input data are completely prescribed
The first card is the option control card discussed in the previous
sections. The first variable ITYPE may be equal to 1, 2 , or 3 , de-
pending on the type of flange being analyzed.
will always be 0, in which case the displacement u will be equal to zero
at x
=
h, as specified by the Code.
always be
2
and will therefore cause the program to compute the stresses
in accordance with Code paragraph
UA-50
for straight or tapered-hub
flanges
o r
paragraph UG-34(~)(2) for blind flanges. The last variable
MATE will always be 1 for Code-compliance calculations. This variable
essentially controls the bolt-load-change calculations made by the
program.
determining compliance, when MATE =
1
these calculations are not per-
formed
The next variable IBgND
r
The third variable ICgDE will
Since the ASME Code does not consider bolt-load changes in
The second card in the data set enters the physical dimensions of
the flange being analyzed, as shown in Table
9.
These dimensions are
the outside and inside diameters of the flange ring A and
B ,
the ring
thickness
t,
the pipe-wall thickness go, the hub thickness at the hub-
to-ring juncture g,, the hub length h, the bolt-circle diameter C, and
the internal pressure. All dimensions are expressed in inches; the
pressure is in pounds per square inch.
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l a h l e 9.
Inpu t da t a fo r ASME bo l t a nd f l a nge s t r e s s c a l c u l a t i o n , u s i ng s ym bo ls de f i ne d
i n
ASME
Code, Secti on VII I, Div ision 1 , Appendix
I 1
Option-Control Card (Read-in i n FLANGE)
Column number
Quant i ty
V a r i a b l e
0-10 11-20 21-30 31-40
4 1 - 5 0
51-60 61-70 71-80
Flange Flange
ou ter inne r Ring Pipe- wall Hub Hub
diameter diameter th ickness th ickness th ickness length diamete r Pressure
B o lt - c i r c l e
C
A
B t g0 g 1 h P
XA X B TH
G O
G1 H L
C
PRESS
Column number
Quant i ty
Variable
d
0-10 11-20 21-30 31-40 41-50 51-60 61-70e 7 2 d 73-80
Minimum A 1 lowable Allowable Basic
de s i gn G as ke t G a ske t bo l t s t r e s s bo l t s t re s s Bol t gaske t
G a ske t s e a t i ng ou t e r i nne r a t de s i gn a t a t m os pher i c c ro s s - s e c t i ona l s e a t
f a c t o r s t r e s s d i am e t er d i a m e t er t e m pe rat u re t e m pe rat u re a re a O p ti on w i dt h
I
Y
GO
Gi b a %
XM
Y GOUT
G I N SB
SA A B INBO
BO
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41
The third card inputs other physical data, including the gasket
factor my
the minimum-design seating stress y, the outside diameter of
the gasket Go, the inside diameter of the gasket G
stress at design temperature
S
the allowable bolt stress at ambient
temperature S the total cross-sectional area of the bolts A an
option-selecting variable I, and the basic gasket-seating width b
.
The
option variable I controls the calculation o f b and G.
the allowable bolt
i'
b y
a'
b'
0
Output for Code-Compliance Calculations
For Code-compliance calculations, all of the output for each flange
being analyzed is printed on a single page (e.g., see examples
1
and
2
of Appendix A).
effective gasket seating width b and the loads, bolt stresses, and
moments identified under the headings shown in Table 10. For compliance
with Code criteria, the value of SB1 must not exceed the allowable bolt
stress at design temperature, and the value of SB2 must not exceed the
allowable bolt stress at atmospheric* temperature.
The program prints the input data followed by the
0
Immediately below, the program prints the flange stresses needed
for comparison with the ASME Code criteria.
hub flanges (ITYPE =
1
or 2), the program prints five stresses under the
two headings ASME FLANGE STRESSES AT OPERATING MOMENT, MOP and ASME
FLANGE STRESSES AT GASKET SEATING MOMENT. The stresses are identified
as follows:
For tapered-hub and straight-
2 / 3 ( S H )
= two-thirds
of
the longitudinal stress on the outside
surface at the small end of the hub,
ST = the tangential stress on the hub side of the ring,
SR = the radial stress on the hub side of the ring,
(SH
+
ST)/2 = the average
of SH
and
ST,
and
(SR + ST)/2 = the average of SR and
ST.
*
Although ambient would probably be a better term here,
the word
atmospheric is used as it is used in the Code.
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4 2
T a b le 1 0 . Ou tp u t d a t a i d e n t i f i c a t i o n , ICgDE
= 2 ,
(ASME Code s t r e s s e s )
ASME Code Program
symbola symbol
Desc r p
t
iona
BO
H WM11
wM12
W M 1
SB1
'm 1
WM 2
SB2
'm2
(e)
MOP
( d )
MG S
MGS 1
b
See ASME Code, Ta bl e UA-49.2.
(Th is
w i l l
b e i n p u t d a t a f o r I = 2 . )
~ G ~ p / 4
2~bGmp
-irG2p/4 + 21~bGmp
B ol t s t r e s s ,
TbGy
B ol t s t r e s s ,
W m 2 /
H ~ h ~
% h ~
H ~ h ~
[(Am + A, ) S a /2 ]
x
[ (C - G)/2]
'm i / %
E x c e p t f o r
ITYPE =
3
(B1 in d
f l a n g e s )
x
[(C - G ) / 2 1
'rn2
A l l s ym b ol s a r e d e f in e d i n t h e ASME B o i l e r C od e, S e c t i o n
V I I I ,
bSee Foo tno te d of T a b le
9 .
e
dMGS
i s
t h e g a s k e t s e a t i n g moment
as
def in ed by t h e ASME Code.
Div. 1 (1971), Appendix 11.
MOP
i s
the opera t ing moment
as
de fi ne d by t h e ASME Code.
For compliance with the Code Criteria, each of the above values printed
under the first heading must not exceed the allowable stress for the
flange material at the design temperature.
second heading must not exceed the allowable stress for the flange
material at atmospheric temperature.
The values printed under the
For blind flanges ( IT Y PE = 3 ) , the program prints the following
five quantities under the heading ASME CODE STRESSES FOR BLIND FLANGE :
SP = the stress due to pressure loading only,
SW1 = the stress due to the bolt load Wml only, where W
=
mi
rG2p/4 + 2~rbGmp,
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4 3
SOP = the stress at operating conditions,
SW2
=
the stress due to the bolt load Wm2, where W
SGS = the stress at gasket-seating conditions.
=
nbGy, and
m2
For Code compliance, SOP must not exceed the allowable stress for the
flange material at design temperature, and
SGS
must not exceed the
allowable stress at atmospheric temperature.
Innut for General PurDose Calculations
When the computer program is used for general purpose calculations,
(i.e., when it is used for calculating displacements and stresses other
than those needed specifically for checking Code compliance), the user
may select almost any combination of admissible values for the four
variables ITYPE,
I B g N D ,
ICPDE, and MATE coded in the option control data
card. The only specific requirement is that the variable I C O E must be
less than two for other than Code-compliance calculations.
the input data are structured somewhat differently than those described
in the previous section.
In this case
When I C a D E
= 0
and MATE = 1, ( i . e . , only one flange is to be
analyzed and the user does not wish to obtain bolt load changes), three
data cards
a r e
needed as shown in Table 11. These are the option-control
card (for which ITYPE may be 1, 2 , or
3
and T B g N D may be 0 or 2) and two
physical-property data cards.
When
I C g D E
=
0
and MATE = 2 , 3 , . . . 6, the program will analyze a
pair
of
flanges mated together and give bolt load changes.
If
MATE
=
2,
the program performs the calculations
f o r
a pair of identical flanges
mated together. The input data requirements include the data cards
shown in Table 11
plus
the three cards shown in Table 12.
three cards
contain data on the physical properties of the bolts and
gasket,
supplemental data on the initial and final state of the flange,
and other conditions. For this case, the six cards listed below com-
plete the input data set when MATE =
2 .
These last
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T a b l e
11.
I n p ut d a t a f o r t h e g e n e r a l p u rp o se a n a l y s i s o f a s i n g l e f l a n g e
a nd p a r t i a l d a t a f o r p a i r e d f l a n g e s
41-50 51-60 61-70
Hub
Hub B o l t - c i r c l e
t h i c k n e s s
l e n g t h d i a m e t e r
h
C
G l a j b HL, C
g l
O p t i o n - C o n t r o l C a r d :
[FgRMAT (415) re ad - i n i n
FLANGE]
71-80
P r e s s u r e
P
PRESS
I C ~ D E
MATE'
Column number
V a r i a b l e
V a l u e
1, 2 ,
o r 3
0
o
2
1 o r
( 2 )
0-10
11-20 21-30 3 1 - 4 0
olumn number
T h e r m a l
M o m e n t C o e f f i c i e n t
g r a d i e n t M o du lu s o f
a p p l i e d t o o f t h e r m a l
p i p e o r h ub e l a s t i c i t y
f l a n g e r i n g e x p a n s io n t o r i n g f l a n ge
Q u a n t i t y
A E
f
Var i
b
1 X M O A ~ E F ~ DELT ^ YM
S e c o n d C a r d :
[FgRMAT (8E10 .5 ) ; r ea d - in i n
TAPHUB,
STHUB, o r BLIND]
41-50
G a s k e t
c e n t e r l i n e
d i me
t
er
2g
G
F l a n g e
F
1 n g e
Column number
Q u a n t i t y
o u t e r i n n e r R in g
V a r i a b l e
31-40
P i p e - w a l l
t h i c k n es
s
go
GOa'
T h i r d C a r d : [FgRMAT ( 5 E1 0 .5 ) ; r e a d - i n i n TAPHUB, STHUB, o r BLIND]
% h e n ITYPE
= 2 , GO
m u s t b e e n t e r e d ;
G 1
a n d
HL
a r e n o t u s e d .
bWhen
ITYPE
= 3 ,
X B ,
G O ,
G 1 ,
HL, E F ,
and
DELTA are
n o t u s ed ; t h e v a l u e f o r
XMOA i s
t h e t o t a l b o l t l o a d
W
When
MATE = 2 ,
a d d i t i o n a l d a t a a s d e s c r i b e d i n T a b l e
1 2
a r e a l s o r e q u i r e d .
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Table
1 2 .
Last three input da ta ca rds f or th e genera l purpose ana lys is of pa i re d f l a nge s
21-30
Bolt
c o e f f i c i e n t
of thermal
expansion
'b
Card
No. 4
o r 7 : a
[FORMAT
(7E10.5); read-in in FLGDW]
31-40 41-50 51-60 61-70
F i na l s t a t e ; C ros s- s e ct i ona l
bol t Out s id e Ins ide root a rea
tempera ture diamete r diamete r of a l l
of gaske t of gaske t bol t s
Tb
Column number
Quantity Nominal
diamete r
Column number
Variable
11-20
0- 10 11-20 21-30 31-40 41 -50 51-60
In i t i a l s t a t e ; G as ke t Equ iva le n t
g a s ke t c o e f f i c i e n t F i n al s t a t e ; A f r e e p re s s u re
Gasket modulus of
of thermal gasket
bo lt see Eq. (86)
t h i c k n e s s e l a s t i c i t y expans ion tempera ture
length of text
V
5
VO YG E G TG F A C E b PBE
T v a r i a b l e
P*
g g R
d
I n i t i a l s t a t e ;
bolt modulus
o f e l a s t i c i t y
E
b
Column number
Q ua n t i t y
Variable
0-10 11-20 21-30 31-40 41-50 51-60 61-70
F i n a l s t a t e
i n al s t a t e F i n a l s t a t e F i n al s t a t e F in a l s t a t e
I n i t i a l
temperature temperature fla nge modulus
fla nge modulus
F i na l s t a t e ga s ke t
bo1t of
flange , of f lange ,
of
e l a s t i c i t y , o f e l a s t i c i t y , bo lt modulus modulus of
load s i d e one si de two si de one sid e two
o f e l a s t i c i t y e l a s t i c i t y
E
I
T f 2
T i 2 E f 2
E
;2 Eb
W l T F ~
T F P ~ YF2
Y F P 2
Y B 2 Y G Z
Card K O .
5
o r 8: [FONIAT (6E 10. 5); re ad -i n i n FLGDW]
Quant i ty
a .
bThe
e f fe c t i v e bo l t l oa d i s c a l c u l a t e d
as
Lo = X L B =
TH
+
THP +
VO + BSIZE
+
FACE.
F i r s t card number applies when MATE =
2 ; second number applies when MATE
=
3 and 4 or 5 and 6.
'Values fo r
G I
and
A
a re c a l c u l a te d u s i ng i npu t va r i a b l e s
X G O
and XGI.
n'-
. *
>
g
-initial-state t empera tures a re de rlneo as zero.
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46
Card No. Identification
1
2l
6
Option control card with MATE
= 2
Data cards per Table
11
Data cards per Table
12
When ICgDE
=
0 and MATE
= 3 ,
the program performs the calculations
for a pair of nonidentical flanges, neither of which, however, is
blind
( i . e . ,
ITYPE
= 1
or 2 # 3
on
the option-control card).
the first flange of the pair follows the option-control card.
the second flange in the pair will follow an option-control card with
MATE = 4.
data requirements.
nonidentical flanges
(neither of which is blind) consists of the follow-
ing nine cards.
Data for
Data for
The three cards described in Table 12 will
then complete the
The complete input data set for analyzing a pair
of
Card No.
Identification
1
32 l
4
6
Option-control card,
ITYPE
#
3 ,
ICgDE
=
0,
MATE
=
3
Data cards per Table 11 for first flange of pair
Option-control card, ITYPE # 3, ICgDE = 0, MATE = 4
Data cards per Table 11
for
second flange
of
pair
Data cards per Table 12
When
IC@DE
= 0 and MATE
=
5, the program performs the calculations
for a flanged joint that is closed with a blind flange. For this option,
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47
the blind flange is designated as the first flange and the mating flange
is designated
as
the second with MATE =
6.
set is completed
by
using the data cards described in Table
12.
The
complete input data set for this case consists of the following nine
cards.
A s befo re , the input data
Card No. Identification
1
Option-control card, ITYPE
=
3 , 1CP)DE =
0,
MATE = 5
32 l
Data cards per Table 11 f o r blind flange
4 Option-control card, ITYPE
=
1 or 2, ICgDE
=
0, MATE
=
6
Data cards per Table 11 for second flange
9"i
Data cards per Table 12
Output from General Purpose Calculations
The amount and format of the data printed out
are
determined pre-
dominantly by the number and types of flanges being analyzed, which in
turn are determined by the value of the option-control variable MATE.
When
MATE = 1,
the output consists of one page
of
printout, which gives
(1) the input data; ( 2 ) the three sets of stresses for moment loading
only (the bolt load for blind flanges), pressure loading only, and
temperature-gradient (hub to ring) loading only (except for blind
flanges); and
( 3 )
the displacements produced by the calculated stresses.
The symbols used on the printout are explained in Tables 1 3 and 14.
When MATE
= 2,
the output consists
of
three pages
of
printout. The
first page gives
(1)
the input data and (2) the parameters involved in
the bolt-load-change calculations. The second page gives
(1)
the
loadings, (2) the residual bolt loads, and ( 3 ) the initial and residual
moments. The symbols used in the first and second page of printout are
explained in Tables 15 and
16.
The third page gives the stresses and
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4 8
Table 13. O ut pu t d a t a i d e n t i f i c a t i o n , s t r e s s e s ,
disp lacements , and ro ta t ion
Theory Program
Symbol symbol
Descr ip t ion
u
a
r = o
r t
u
r = g
r
u r = g
t
u
r = c
r
a t , r
=
c
a r = a
t
& C
SLSOQ
SLSP
SCSOa
sc
s U
s
L L O
S L L I
SCLO
SCL
I
STH
STF
SRH
SRF
Z G
zc
QFHG
Y O
Y 1
THETA
SORT
SGR
SGT
SCR
SCT
SAT
zc
S t r e s s , l o n g i t u d i n a l , small end of hub,
o u t s i d e s u r f a c e
St r es s long i tud ina l , smal l end of hub , in s id e
S t r e s s , c i r c u m fe r e n t ia l , small end of hub,
S t r e s s , c i r c u m fe r e n t ia l , small end of hub,
s u r f
ace
o u t s i d e s u r f a c e
i n s i d e s u r f a c e
St re s s , long i tud ina l , l a r ge end of hub ,
o u t s i d e s u r f a c e
S t r e s s , l o n g i t u d i n a l , l a r g e end o f hu b, i n s i d e
sur f ace
S t r e s s , c i r c u m f e r e n t i a l , l a r g e e nd of hub,
S t r es s , c i r cu mferen t i a l , l a rge end of hub,
o u t s i d e s u r f a c e
i n s i d e s u r f a c e
S t r e s s , t a n g e n t i a l , hub s i d e of r i n g, a t r = b
S t r e s s , t a n g e n t i a l , f a c e s i d e o f r i n g ,
a t r
= b
S t r e s s , r a d i a l , h ub s i d e o f r i n g , a t
r
= b
S t r e s s , r a d i a l ,
f a c e s i d e of r i n g , a t r = b
( 6
E
0
a t r = b)
Axial displacement a t r = g
Axial displacement a t r = c
- 6
+
6
Radial displacement , small end of hub
Radia l d i sp lacement , l a r ge end of hub
Rota t ion of r in g a t
r =
b
c g
b
S t r e s s , r =
0 ,
r a d i a l a n d t a n g e n t i a l
S t r e s s , r = g r a d i a l
S t r e s s , r = g , t a n g e n t i a l
For
b l i n d f l a n g e s
S t r e s s , r = c , r a d i a l
S t r e s s , r = c , t a n g e n t i a l
S t r e s s , r =
a ,
t a n g e n t i a l
Axial displacement a t r = c
( 6
F
0
a t r =
g )
For Straight Hub Flange, these
are a t
j u n c t u r e
of
hub with r ing.
b A l l
s t r e s s e s
are
f o r t h e s i d e
of
t h e f l a n g e o p p o s i t e t h e p r e s s u re -
b e a r i n g s i d e .
r e v e r s e d s i g n s .
S t r e s s e s on t h e p r e s s u r i z e d s i d e o f t h e f l a n g e h av e
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49
Table 1 4 . Outpu t d a t a i d en t i f i ca t i o n when
MATE = 2 ,
3 and 4 ,
o r 5 and 6
Theory
Program
symbol
symbol
Descr ip t ion
QFHG Axial d isplacement from
C
t o G , u n i t moment l oad
f l h G
qP 1 G
QPHG
Axial displacement from C t o G , u n i t p r e ss u r e
load
Q T H G ~
Axial d isplacement from C t o
G ,
u n i t
DELTA
t l h G
2b In si de diameter
GOa Pipe
wall
t h i c k n e s s
t
TH
Ring th ickness
Modulus o f e l a s t i c i t y of f l a n g e m a t e r i a l , i n i t i a lYM
s t a t e
f
1
YF2C Modulus of e l a s t i c i t y o f f l a n g e m a t e r i a l , f i n a l
s t a t e
f
f
E
F~
Coe ff i c ie n t o f thermal expans ion
of
f l a n g e
m a t e r i a1
( 1
(
> p The above nine symbols with a prime m a r k I ) on
t h e t h eo ry s ym bo ls a r e f o r t h e m a ting f l an g e .
The program symbol has th e added f i n a l l e t t e r
rrp.
11
a
For b l i n d f l a n g e s , t h e s e v a l ue s a r e n ot s i g n i f i c a n t ; an a r t i f i c i a l
b The se v a l u e s a r e i n p u t d a t a f o r f l a n g e s i d e o ne , i n p u t c a r d s
2
and
v a lu e o f -1.0000 i s p r i n t e d o u t .
3
( s ee T abl e 1 1 ) . For MATE
=
2 , t h e s e v a l u e s , a lo ng w it h c a l c u l a t e d
vg lues of
QFHG,
QPHG, and
QTHG,
a r e u sed fo r s i d e one and s i d e two ( i . e . ,
an i d e n t i c a l p a i r ) . I f MATE
= 3
o r 5 , t h e p rim ed v a l u e s a r e s t o r e d ; t h e
unprimed values
are
r e a d i n by i n p u t c a r d s
5
and
6 ,
and values of QFHGP,
QPHGP,
and QTHGP a r e c a l c u l a t e d.
and 6 (see Tab le 11) .
e
Input from card 6 f o r MATE
=
2 , card
9
f o r
MATE =
3 and 4 o r 5
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Table 15.
O utp ut d a t a i d e n t i f i c a t i o n , MATE = 2 , 3 and 4 ,
or 5 and 6 , b o l t s , g a s k e t , a nd lo a d in g s d a t a
Theory Program
symbol symbol
a
D e s c r i p t i o n
R
*b
C
Eb1
Eb2
'b
VO
E
E
g1
8 2
g
E
w 1
Tf 2
TL
Tb
T
A
A '
P
g
X LB
A B
C
Y B
Y B 2
E B
vo
X
GO
X G I
Y G
Y G 2
EG
w1
TB
TF
T F P
TG
DELTA
DELTAP
PRESS
E f f e c t i v e b o l t l e n g th
C r o s s - s e c t i o n a l r o o t area o f a l l b o l t s
B o l t - c i r c l e d i a m e t e r
Modulus of e l a s t i c i t y , b o l t s , i n i t i a l s t a t e
Modulus of e l a s t i c i t y , b o l t s , f i n a l s t a t e
Co e f f i c i en t of t h e rma l ex pan s io n , b o l t s
Gasket th ickness
Outs ide d iameter o f gaske t
In s id e d i am e ter o f g a s k e t
Modulus of e l a s t i c i t y o f g a s k e t , i n i t i a l s t a t e
Modulus of e l a s t i c i t y o f g a s k e t , f i n a l s t a t e
Co e f f i c i en t of t h e rm a l ex p an sio n , g a s k e t s
I n i t i a l t o t a l b o l t l oa d
T em pe ra tur e o f b o l t s , f i n a l s t a t e
T em pe ra tur e o f f l a n g e r i n g , s i d e on e, f i n a l s t a t e
T em pe ra tu re of f l a n g e r i n g , s i d e t wo , f i n a l s t a t e
T em pe ra tu re o f g a s k e t , f i n a l s t a t e
T herm al g ra d i e n t , p ip e/h u b t o r i n g , s i d e on e
T he rm al g ra d i e n t , p ip e /h ub t o r i n g , s i d e two
I n t e r n a l p r e s s u r e
A l l
v a l u e s a r e i n p u t d a t a , e x ce p t
X L B
which
i s
c a l c u l a t e d by t h e
equat ion :
X L B
= TH + THP + VO
+
B S I Z E
+
FACE.
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T a bl e 1 6. O ut pu t d a t a i d e n t i f i c a t i o n , MATE
2 , 3
and
4 ,
or 5 and
6 ,
res idua l bol t loads and moments
a
Theory Prog r a m
symbol symbol Ef fe ct inc lud ed
W2A R e l a t i v e ch an ge i n t em p e ra t u re o f b o l t s , g a s k e t
f l a n g e (AXIAL THERMAL)
W2B
Change i n moment arms (MOMENT SHIFT)
W2C T o t a l p r e s s u r e
W 2 D Thermal gr ad ie nt , pip e/hub t o r i n g (DELTA
2a
'2b
w
W 2 C
' d THERMAL)
W2 A l l of th e above , p l us change i n modulus of
e l
as
t i c i y (COMBINED)
W2
? ' h e c h an ge i n b o l t l oa d ( e . g . ,
W 1
- W2A) and r a t i o of re s i du a l t o
i n i t i a l bo l t load (e .g . , W2A/W1) are a l s o p r i n t e d o u t , a lo ng wi t h t h e
cor responding va lu es of th e i n i t i a l moment (Ml) and re s i du a l moments ,
M2A, . . . , M2P. The r e s i d u a l moment i d e n t i f i e r s w i th f i n a l l e t t e r P ( f o
p ri me) a r e f o r t h e f i r s t e n t e re d of a p a i r o f n o n i d e n ti c a l f l a n g e s . I f
t h e p a i r o f f l a n g es a r e i d e n t i c a l , t he n M2B
=
M 2 B P , e t c . The r e s i d u a l
moment values a r e n o t s i g n i f i c a n t f o r b l i n d f l a n g e s , ITYPE
=
3 ; t h e r e -
f o r e , r e s i d u a l b o l t l o ad s a re u se d f o r b l i n d f l a n g e s .
d isp lacements as f o r t he c a se when MATE = 1 p l u s t h e s t r e s s e s and d i s -
p lacements fo r combined loading . The heading inc lud es th e va l ue of t he
residual moments
M 2 =
M2P
u s e d f o r
t h e com bined-loa ding c a l c u la t ion s .
When MATE =
3
and 4 o r 5 a nd 6 , t he ou tp u t c on s i s t s o f f ou r pages
o f p r i n t o u t . The f i r s t two pages have the
same
format as f o r t h e c a s e
when MATE =
2 ,
e x ce p t i n p u t d a t a f o r b o th o f t h e ( n o n i d e n t i c a l ) f l a n g e s
ar e pr in te d . The re s i du a l moments on t h e l a s t l i n e of pa ge 2 a p p l y t o
f l a n ge one; tho se on th e p r e c e d ing l i n e app ly t o f l a nge two. The
l a s t
two pa ges o f p r in to u t are f o r f l a n g e o ne and f l a n g e t wo, r e s p e c t i v e l y ,
and a r e i d e n t i c a l i n form at t o t h e t h i r d p age of t h e p r i n t o u t f o r t h e
case when MATE
=
2 .
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Acknowledgment
1.
2 .
3.
4.
5.
6.
7.
8.
The authors gratefully acknowledge the assistance of
0.
W. Russ
of the Computer Sciences Division for converting the CDC 7700 Fortran
program written at Battelle-Columbus Laboratories to double precision
for operation on the ORNL
IBM 360 computers.
References
ASME Bo il er and Pressure Ve ss el Code, Section VIII-1971, Nuclear
Power Plant Components, American Society of Mechanical Engineers,
New York, July 1, 1971.
E.
0.
Waters et al., Formulas for Stresses in Bolted Flanged
Connections
I Trans.
ASME 59, 161-69
(1937)
S. Timoshenko, Theory
of
Plates and Shells , 1st ed., McGraw-Hill,
New York, 1940.
E.
C. Rodabaugh, F. M. O'Hara, Jr., and S. E. Moore, Analysis of
Flanged Jo in ts w it h Ring-Type Gaskets (in preparation).
E. C. Rodabaugh, F. M. O'Hara, Jr., and
S.
E. Moore, S t re s se s i n
th e Bo lt in g and Flanges
of
B 1 6 . 5 Flanged Jo in ts wi th Metal-to-Metal
Contact Outside the Bolt Circle
(in preparation).
D.
B. Wesstrom and S. E. Bei-gh, Effect of Internal Pressure on
Stresses and Strains
in Bolted-Flanged Connections, Trans ASME
73,
553-68
(1951).
E. C. Rodabaugh, Discussion Section of Ref. 6.
Large-Diameter Carbon S t e e l Flanges (S i ze :
26
Inches to
30
Inches,
Inclusive, Ngminal Pressure Rating: 7 5 , 1 5 0 , and
300
l b ) ,
API
Standard 605, 1st Ed., American Petroleum Institute, New York,
1967.
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A P P E N D I X A
E X A M P L E S OF A P P L I C A T I O N OF C O M P U T E R P R O G R A M F L A N G E
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APPENDIX
A
CONTENTS
Page
57
. . . . . . . . . . . . . . . . . . . . . . . . . .
NTRODUCTION
. . . . . . . . . . . .
59
ETAILS
OF THE FLANGE
USED
I N
THE EXAMPLES
. . . . . . . . . . . . .
62
SME C O D E CALCULATIONS, EXAMPLES
1
A N D 2
. . . .
6 7
Inpu t Data 67
O u t p u t D a t a 70
7 0
esidual Bolt Loads
Blind Flange St re ss es , Example 3(a) 80
Tapered-Hub Flang e S tr es se s, Example 3(a ) 81
Blin d and Tapered-Hub S t r e s s e s , Example 3(b) 83
Disp lacements 83
BLIND-TO-TAPERED-HUB FLANGED
J O I N T , EXAMPLES 3(a) and 3(b)
. . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . .
. . . . . .
. . . . . . . . . . . . . . . . . . . . . .
. . .
DENTICAL PAIR OF
TAPERED-HUB
FLANGES, EXAMPLES
4 ( a ) A N D
4(b) 84
. . . . . . . . . . . . . . . . . . . . . . . . . .
npu t Data 84
Output Data 84
84
. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .es idua l Bolt Loads
. . . . . . . . . . . . . . . . . . . . .
l a n ge S t r e s s e s 93
Displacements 94
. . . . . . . . . . . . . . . . . . . . .
96
OMPUTER TIME . . . . . . . . . . . . . . . . . . . . . . . . . . .
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INTRODUCTION
Several examples have been selected to illustrate the input/output
data of the computer program FLANGE and the significance of the results.
The flange selected for analysis is one included in API Standard 60.5.
The particular size and rating selected was the 60-in., 300-lb tapered-