FLANGE - A Computer Program for the Analysis of Flanged Joints With Ring-Type Gaskets

7/26/2019 FLANGE - A Computer Program for the Analysis of Flanged Joints With Ring-Type Gaskets

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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


2/149

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.


3/149

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


4/149


5/149

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


6/149

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


7/149

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.


8/149

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).


9/149

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


12/149

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


14/149

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,


15/149

5

- c r y

b

-

O R N L - DWG 75- 4299

PIPE

-

-90

---tu4

Ar W

0 ur

f

t


16/149

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.


17/149

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 )


18/149

8

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


19/149

9

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 ) .


35/149

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


36/149

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


37/149

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


38/149

28

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.


39/149

2 9

After application of loadings, the bolt length becomes

R2 =

v2

+ t2

+

t; - 6, -

6;

The basic displacement relationship

is

thus


40/149

30

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


41/149

31

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


42/149

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


43/149

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


44/149

34

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.


45/149

35

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).


46/149

36

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)

*


47/149

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 ,


48/149

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.


49/149

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.


50/149

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


51/149

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.


52/149

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,


53/149

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


54/149

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 .


55/149

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.


56/149

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


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,


57/149

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


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


58/149

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


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 ,


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,


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


59/149

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-

FLANGE - A Computer Program for the Analysis of Flanged Joints With Ring-Type Gaskets

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Transcript of FLANGE - A Computer Program for the Analysis of Flanged Joints With Ring-Type Gaskets