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3 445b 0515275 9

OR NL-5

FLANGE: A Computer Program forthe Analysis of Flanged Jointswith Ring-Type Gaskets

E. C. RodabaughF. M. OHara, Jr.S. E. Moore

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Printed in the United States of America. Available f romNational Technical Informat ion Service

U.S. Department of Commerce5285 Port Royal Road, Springfield, Virginia 221 61Price: Printed Copy 7.75; Microfiche 2.25

This report was prepared as an account of work sponsored by the United StatesGovernment. Neither the United States nor the Energy Research and DevelopmentAdministration, nor any of their employees, nor any of their contractors,subcontractors, or their employees, makes any warranty, express or implied, orassumes any legal liability or responsibility for the accuracy, completeness orusefulness of any information, apparatus, product or process disclosed, or representsthat its use would not infringe privately owned rights.

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O R N L -5035YRC-1 , -5

Contract No. W-7405-eng-26

Re a c t o r Division

FLANGE: A COMPUTER PROGRAM FOR THE ANALYSISOF FLANGED JOINTS WITH RING-TYPE GASKETS

E . C . RodabaughBattel le-Columbus Laboratories

F . M. O'Hara, J r . S. E . MooreOak Ridge National Laboratory

Work funded by th e Nucle ar R egula tory Commissionunder 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 YOak Ridge, Tennessee 3 7 8 3 0Operated by

U N I O N C A R B I D E CORPORATIONf o r t h eU.S. E N E R G Y RESEARCH AND DEVELOPMENT ADMINISTRATION3 4456 0535275 9

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iii

CONTENTSPage

FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V1 . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1

Purpose and Scope . . . . . . . . . . . . . . . . . . . . . . . 1Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . 2

. . . . . . . . . . . . . . 4GENERAL DESCRIPTION OF THE ANALYSIS3 . FLANGE WITH A TAPERED-WALL H U B . . . . . . . . . . . . . . . . 7

Equations for the Annular Ring . . . . . . . . . . . . . . . . 7Equations for the Tapered Hub . . . . . . . . . . . . . . . . . 8Equations for the Pipe . . . . . . . . . . . . . . . . . . . . 11Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 11Boundary Equations . . . . . . . . . . . . . . . . . . . . . . 12Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Displacements . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 FLANGE WITH A STRAIGHT H U B . . . . . . . . . . . . . . . . . . 175 BLIND FLANGES . . . . . . . . . . . . . . . . . . . . . . . . . 20

Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . 20Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Displacements . . . . . . . . . . . . . . . . . . . . . . . . . 25

6 THERMAL GRADIENTS . . . . . . . . . . . . . . . . . . . . . . . 267 CHANGE IN BOLT LOAD WITH PRESSURE. TEMPERATURE.AND EXTERNAL MOMENTS . . . . . . . . . . . . . . . . . . . . . 27

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 28External Moment Loading . . . . . . . . . . . . . . . . . . . . 36

8 COMPUTER PROGRAM . . . . . . . . . . . . . . . . . . . . . . . 37Option Control Data Card . . . . . . . . . . . . . . . . . . . 37Input for Code-Compliance Calculations . . . . . . . . . . . . 39Output from Code-Compliance Calculations . . . . . . . . . . . 41Input for General Purpose Calculations . . . . . . . . . . . . 43Output from General Purpose Calculations . . . . . . . . . . . 47

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i v

Page

. . . . . . . . . . . . . . . . . . . . . . . . . .CKNOWLEDGMENT 52REFERENCES 52. . . . . . . . . . . . . . . . . . . . . . . . . . .APPENDIX A. Examples of Application of Computer ProgramFLANGE 53. . . . . . . . . . . . . . . . . . . . . . .APPENDIX B. Flowcharts and Listing of Computer ProgramFLANGE and Attendant Subroutines . . . . . . . . . . . 97

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V

FOREWORD

The work reported here was performed at Oak Ridge National Laboratoryand at Battelle-Columbus Laboratories under Union Carbide Corp., NuclearDivision, Subcontract No. 2913 as part of the ORNL Design Criteria forPiping and Nozzles Program, S. E. Moore, Manager. This program isfunded by the Division of Reactor Safety Research (RSR) of the U.S.Nuclear Regulatory Commission as part of a cooperative effort withindustry to develop and verify analytical methods for assessing thesafety of pressure-vessel and piping-system design. The cognizant RSRproject engineer is E. K. Lynn. The cooperative effort is coordinatedthrough the Pressure Vessel Research Committee of the Welding ResearchCouncil under the Subcommittee on Piping, Pumps, and Valves.

The study described in this report was conducted under the generaldirection of W. L. Greenstreet and S. E. Moore, Solid Mechanics Depart-ment, Reactor Division, ORNL, and is a continuation of work supported inprior 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, Investigationsof Piping Components, Valves, and Pumps to Provide Information forCode Writing Bodies, ASME Paper 68-WA/PTC-6, American Society ofMechanical Engineers, New York, Dec. 2, 1968.W. L. Greenstreet, S. E. Moore, and R. C. Gwaltney, Progress Reporton Studies in Applied Solid Mechanics, ORNL-TM-4576 (August 1970).E. C. Rodabaugh, Phase Report No. 11s-1 on Stress Indices for SmallBranch Connections w i t h ExternaZ Loadings, ORNL-TM-3014 (August1970).E. C. Rodabuagh and A. G . Pickett, Survey Report on Structural Designof Piping Systems and Components, TID-25553 (December 1970).E. C. Rodabaugh, Phase Report No. 1 1 5 - 8 , Stresses in Out-of-RoundPipe Due to Interna2 Pressure, ORNL-TM-3244 (January 1971).S. E. Bolt and W. L. Greenstreet, Experimental Determination ofPlastic 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 sof 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-InchTees, " 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 iso 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 AnnuaZProgress Report on Studies in Applied Solid Mechanics (NuclearS 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 sAnalys i s of Cyl inde r-to- Cyl inde r Sh el l Models and Comparisons wi thTh 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 lConference 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 so f B16.9 Tees by t h e F i n i t e Element Method," Paper No. F4/7, F i r s tIn t e rn a t io na l Conference on S t ru c t u r a l Mechanics i n Reac to rTechnology, 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 . 9Tees, Re se ar ch Re por t 71-9E7-PHOTO-R2, Wes ting house Re sea rchLaboratory (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 torsf o r Moment Loadings on Elbows and Curved Pipe, ORNL-TM-3658 (March1972).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 fORNL Thin-She22 Cy Iinder-to-Cy Zinder Model No. I , ORNL-4553 (October1972).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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vii19.

20.

21.

22

23.

24.

25.

26.

27.

28 .

29.

30.

31.

W. G. Dodge and S. E, Moore, Stress Indices and Flexibility Factorsf o r Moment Loadings on Elbows and Curved Pipe, Welding ResearchCouncil 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 rSafeky) , ORNL-4821 (December 1972).W. G. Dodge and S. E. Moore, ELBQW: A Fortran Program f o r theCalculation of Stresses , S tr ess Indices , and Fle xi b i l i ty Factorsfor Elbows and Curved Pipe, ORNL-TM-4098 (April 1973).W. G. Dodge, Secondary Stress Indices f o r Integral StructuralAttachments t o Straig ht Pipe, ORNL-24-3476 (June 1973). A l s o inWelding Research Council Bu Zlet in 1 9 8 , September 1974.E. C. Rodabaugh, W. G. Dodge, and S. E. Moore, Stress Indices at LugSupports on Piping Systems, OKNL-'TM-4211 (May 1974). Also in WeldingResearch Council Bulletin 1 9 8 , September 1974.W. L. Greenstreet, S. E. Moore, and J. P. Callahan, Fourth AnnualProgress Report on St ud ie s i n Applied So li d Mechanics (PressureVessels 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, Universityof California, Berkeley (September 1974).R. C. Gwaltney, CURT-11 - A Computer Program fo r Anal yzi ng CurvedTubes or Elbows and At tached Pipes wi th Symmetric and UnsyrrunetricLoadings, ORNL-TM-4646 (October 1974) .E. C. Rodabaugh and S. E. Moore, Stress Indices and Flexib i l i tyFactors for Concentric Reducers, ORNL-TM-3795 (February 1975).D. R. Henley, Test Report on Experimental Stress AnalysisInch Diameter Tee (ORNL T - 1 3 ) , ORNL-Sub-3310-3 (CENC 1189bustion Engineering, Inc. (March 1975).D. R. Henley, T e s t Report on Experimental Stress AnalysisInch Dimeter Tee (ORNL T-12), ORNL-Sub-3310-4 (CENC 1237bustion 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 24Inch 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-CyZinderModel 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-ShellCplinder-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 1Standard 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 andFinite-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 designingbolted flange connections with ring-type gaskets based on a stressanalysis developed by Waters et a1.2graphs for calculating stresses due to a moment applied to the flangering. The Code rules, however, do not require that stresses due tointernal 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 thestresses due to moment loads on the flange ring but also stresses due tointernal pressure; stresses due to a temperature difference between thehub and ring; and stresses due to the variations in bolt load thatresult from pressure, hub-ring temperature gradient, and/or bolt-ringtemperature difference. The program FLANGE is applicable to tapered-hub, straight, and blind flanges. The analysis method is based on thedifferential equations for thin plates and shells rather than on thestrain-energy method used by Waters et al.2loading calculated by the two methods are essentially identical foridentical 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 remainderof this chapter.flanges used in the theoretical development of the computer code isprovided. The actual mathematical expressions for calculating stressesand displacements due to moment and pressure loads are derived inChapters 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 thisreport. Example calculations, listings, and flowcharts of the programand 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 rea = o u t s i d e r a d i u s of r i n gA = 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 aA = g a s k e t a r e agb = 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 gb = Be sse l f u n c t i o n of rln

c = b o l t - c i r c l e r a d i u sC = 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 nC = C. /b11 ID = ~ 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

EE

E = Eb6f = ASME Code design parameterF = 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 lf= 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 egl = 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 sG = 2g = g a s k e t c e n t e r l i n e d i a me te rh = l eng th of t ape red-wa l l hubK = a / b = A/B

R O = b o l t l e n g t hM = 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 11p = i n t e r n a l p r e ss u r eP . = s h e ar r e s u l t a n t s , l b / i n .1p * = - ( v / 2 ) b p = nondimensional pr es su re parameterg 0 Er = 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 thicknesstXu = radial displacement, hub

u, = radial displacement, pipeu = radial displacement, ringrV = ASME Code design parameterv o = undeformed gasket thicknessw = axial displacement, ring

W, = initial bolt load, lbW, = residual bolt load, lbx = axial coordinate, hub

x1 = axial coordinate, pipe0, = (g1 - g o ) / g o = p - 1 = nondimensional wall-thickness parameter

= [ 3 ( 1 - v2)/b2g:l1j4 = dimensional parameter used in the analysisy = [ 1 2 ( 1 - v2)/b2gi] 1/4 h) = dimensional parameter used in the analysih = 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 materialgn = 2 ~ ( 4 J / a ) ~ / ~nondimensional argument of the modified Bessel functiov = Poisson's ratio (0.3 used herein)5 = x/h = nondimensional distance parameterp = g,/g, = nondimensional wall-thickness parametero = stress, with subscripts:

1

R = longitudinal (pipe o r hub)c = circumferential (pipe or hub)t = tangential (ring)r = radial (ring)b = bendingm = membraneo = outside surface of the pipe or hub on the hub side of ringi = 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 inFig. 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-thicknesscylindrical shell with midsurface radius b. The hub is considered to bea linearly variable-wall-thickness ylindrical shell with midsurfaceradius 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 effectsof 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, themoment 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 usedin the ASME Code calculation meth0d.l

2. Internal pressure, acting radially on the pipe, hub, and ringand axially on an (assumed remote) end closure on the pipe.

3 . A temperature difference between the pipe and the ring. Thepipe 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 bedifferent 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 andloadings, and 12 integration constants are obtained, 4 for each part.These constants are evaluated by the usual discontinuity analysis methodof writing continuity equations at the junctures of the parts and at theboundaries.the algebraic equations provide the means for computing the stresses anddeflections. In the development of the equations for stresses, theassumption is made that the bolt load W does not change with pressure ortemperature. Later the analysis is modified to include changes in W asa function of these loadings. Because the relations are linear, it ispossible 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 urft

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6

of initial bolt loading, pressure, and temperature change. The modelused for straight-hub flanges is a simplification of the tapered-hubcase in that only two parts are involved, the pipe and the ring.

In common with all shell-type analyses, the analysis gives anomalousresults at points of abrupt thickness change or meridional directionchange. In particular, the stresses at the juncture of the hub to thering represent only the gross loading effect; detailed local stressesare not determined by the theory. Displacements, however, are representedfairly 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 thebasic shell/plate equations for the ring, the hub, and the pipe. Wethen inspect the boundary conditions, compute the constants, and calcu-late the stresses and displacements.

Equations for the Annular RingThe 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 andq = a uniformly distributed lateral load on the plate, D = Et3/12(l -u2) = the flexural rigidity of the plate, E = modulus of elasticity ofthe flange material, t = plate thickness, and u = Poissons ratio.Equation (1) can be integrated to give a relation for the displacementin terms of arbitrary constants:

where numerical values for the constants C7, . . . , C10 are establishedfrom boundary conditions. Derivatives of w, required i n the subsequentanalysis, are:

c9 r3qwdr_ - C7(2r in r + r) + 2C8r + - -r 16D

d2w c g 3r2qdr2 r2 16D- - - C7(2 Rn r + 3) + 2C8 - -

(3)

( 4 )

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8

and

- -3w i t ) + - + -C g 3rqL 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 dwd r 2 r d r )

M = - D ( + - - Irand

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 ac 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 byTimoshenko3 as X

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9

The solution of Eq. (10) can be shown* to be:

bP*(Clbl + C2b2 + C3b3 + C4b4) +u = - >1/2 1 + a ] D (5931t tand

0 = i 6 M / t 2 = IEtMr/[2(1 - w 2 ) ] D .r rA 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 rA t t h e g a s ke t ( r = g ) ,

M = - D { D , 2 [ 2 ( 1 + v ) ] + g2p(3 + v ) / 1 6 D } ,rand

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 onthe 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 p1 ceme n t sI 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) ac 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 eassumed 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 ei 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 ei 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 dependentupon 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 tand 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 ean 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 nTable 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 er 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 er 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 nTable 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 ofT 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 emater 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 byadding (*/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 ercolumn i n Table 3 [ E q s . (20-Sa) and (20- Sb)] . The analo gous term i sa l r e a d y i n c lu d ed i n T a bl e 6 .

f

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7 . CHANGE I N BOLT LOAD WITH PRESSURE, TEMPERATURE,A N D EXTERNAL MOMENTS

A flanged joint is a statically indeterminate structure. Thus, inorder to determine the residual bolt load in the joint, it is necessaryto calculate the relative displacements of the parts when the joint issubjected to (1) initial bolt loading, 2 ) moment loading, ( 3 ) internalpressure, and (4) thermal gradients.

The object of the analysis is to determine the residual bolt loadW2 in terms of (1) the loadings W1, p, A , and A'; (2) the componenttemperatures 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 coversonly the effect of initial bolt loading and part of the influence ofinternal pressure; the remaining influence from the internal pressure isdiscussed by Rodabaugh.7 The extension of the analysis to cover thermalgradients is relatively simple and is covered below.

The nomenclature used in this development is:A = cross-sectional area of bolts or gasketB = inside diameter of ringC = bolt-circle diameterE = modulus of elasticitygo = wall thickness of pipe

G = gasket centerline diameterR = bolt lengthp = internal pressure

p* = equivalent pressure for external moment loadingq = elastic deformation coefficientst = ring thicknessT = final-state temperature (initial-state temperature is defined as

zero)v = gasket thicknessW = bolt load

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6 = relative axial displacement between the gasket centerline andthe bolt circle

E = coefficient of thermal expansionA = 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 tothe bolts, gasket, and flange, respectively.are for one of the flanges in a pair (e.g., T; refers to the temperatureof the right-hand flange in Fig. 3); quantities without a prime are forthe other flange.

Quantities with a prime I )

AnalysisFigure 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 deformedbolt 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 modeof deformation.

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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 nhe 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 g2Eys. (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 ai 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 ln i t moment l oa d, qPpr 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 ta 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 rt 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 lc 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 lcondi 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 ei 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 nomenclatureu 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.lThe 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 ed 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 cend 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 , hi 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), hfrom 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 ld 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 , andp 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 nDi s t h e r a d i a l d i s t a n c e i n i nc he sG

TSymbols, 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>

71H D 2 = - B2p , (f>

(h 1T= - ( G 2 - B 2 ) p ,HT2 4

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M = W h = H h ( R )

(m)1 i G G I G '

M = HD2hD+ HT2hT + H G 2hG '

M i = H'2h ' H+2h+ HG2hG *

2and

(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 eu 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 gW, on t h e l e f t g i v e s :

+ h 29 ' > w = (qbl + q g l + h 2 q 'fi 12(qb2 qg2 h G q f2 G f 2 23 2 )T E V + T E ~T ' E ' ~ ' T E Lg g o f f 0 f f o b b o qg2CHD2

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and2 2Q, = qb2 + qg2 h~qf2 hGqi2

D, H i , HT, and H, Eq. (75) becomesnd using the given definitions of H r '1

+ T'E't' - T E R )f f o b b oT E v + TfEftOQ, 1 42 g g oQ,= - w

hG- qpQ2 + q')p - hG qtA + q;c') . (76)P Q2In order to compute the flange stresses under the various loading

conditions, it is necessary to compute the flange moment MFrom Eq. (73m) and the definitions in E q s . (73a-k),

or Mi.2

7M, = 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 0The residual bolt load, after internal pressure (acting in an axialdirection) has transferred the bolt load on the gasket to a tensile loadon 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 thelever arms and the radial effect of pressure acting on the integralflangeis) and/or on the inside surface of a blind flange is given by:

The residual bolt load due to a temperature difference between the huband the ring is given by:

A slight modification of the above is required for the case of ablind flange. If we designate the blind flange as that with the primednomenclature, then all* of Eqs. (7Oa-9,) are valid except Eqs. (70fand 9, for 6; and 6;.

*For v2 it should be noted that H D 2 - HT2 = nG2p/4; hence, thisequation is valid for blind flanges.

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For blind flanges, W is used rather than M as the loading parameterbecause the relationship M = W(a - b) is not valid for the blind-flangeanalysis. For blind-flange analysis, E q . (65) gives a value of w . hereC '-w is the equivalent of -w + w in Eq. (72) because w f 0 in theblind-flange analysis. c g gFor blind flanges we define

where (-w ) is the axial displacement per unit total bolt load W. Theequation for W2 for a blind flanged joint is then:c w

Ql 1W = - 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 GP Q2+ q'lp - - A

G- qpQ2 ( 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 thelever arms, the residual bolt load for the case where a blind flange isused is

It should be noted that q;A' does not exist for an integral flange matedto a blind flange.

The combined effect of all of the above is also obtained from thecomputer 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 . Forf 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 hedp 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 er 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 ea 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 mwhere 8 = ang l e a round t he c i rcumference ( e = 0 a t t h e po i nt of maximumt 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 sr 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 eb 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 sof 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 tw 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 san 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 ewhich 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 externalmoment.

MM m

bThe 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 lmoment. 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 p2bwith 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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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 yo 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 displacementsf 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 dt 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 ecompliance wit h t h e ASME Boi ler and Pre ss ure Vessel Code. The programa 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 Codev 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 hecu rv es gi ve n i n Code Fi g s . UA-51.2, UA-51.3, and UA-51.6. Loose hubbedflanges, which a r e covered by t h e Code, however, a r e not covered by t h ecomputer 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 ndo 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 . Formore 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 eexamples 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 APIStanda 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 gramo 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 sof 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 ef 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 aand program ou tpu t f o r Code compliance cal cu la t i on s and f o r more ge ner alc a l c u l a t i o n s are d i sc usse d .

ODtion Control Data CardThe 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 mo 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 ga 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. Thesespe 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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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 datacard.

Different types of flanges and different types of calculations havedifferent input data requirements. These data and their formats arediscussed in the following sections.

Input for Code-Compliance CalculationsSince the ASME Code calculation procedures consider only one flange

at a time, the input data requirements for the computer program arequite simple and straightforward.by the three data cards illustrated in Table 9. The nomenclature is thesame as that used in the Code.

Input data are completely prescribed

The first card is the option control card discussed in the previoussections. 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 zeroat x = h, as specified by the Code.always be 2 and will therefore cause the program to compute the stressesin accordance with Code paragraph UA-50 for straight or tapered-hubflanges o r paragraph UG-34(~)(2) for blind flanges. The last variableMATE will always be 1 for Code-compliance calculations. This variableessentially controls the bolt-load-change calculations made by theprogram.determining compliance, when MATE = 1 these calculations are not per-formed

The next variable IBgNDrThe 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 ofthe flange being analyzed, as shown in Table 9. These dimensions arethe outside and inside diameters of the flange ring A and B , the ringthickness 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, andthe internal pressure. All dimensions are expressed in inches; thepressure 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 di n ASME Code, Secti on VII I, Div ision 1 , Appendix I 1Option-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 71-80Flange Flangeou ter inne r Ring Pipe- wall Hub Hubdiameter diameter th ickness th ickness th ickness length diamete r Pressure

B o lt - c i r c l eCA B t g0 g 1 h P

XA X B TH G O G1 H L C PRESS

Column number

Quant i ty

Variable

d0-10 11-20 21-30 31-40 41-50 51-60 61-70e 7 2 d 73-80Minimum A 1 lowable Allowable Basicde 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 tG 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 hIY GO Gi b a %XM Y GOUT G I N SB SA A B INBO BO

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The third card inputs other physical data, including the gasketfactor my the minimum-design seating stress y, the outside diameter ofthe gasket Go, the inside diameter of the gasket Gstress at design temperature S the allowable bolt stress at ambienttemperature S the total cross-sectional area of the bolts A anoption-selecting variable I, and the basic gasket-seating width b . Theoption variable I controls the calculation o f b and G.

the allowable bolti'b y

a' b'0

Output for Code-Compliance CalculationsFor Code-compliance calculations, all of the output for each flange

being analyzed is printed on a single page (e.g., see examples 1 and 2of Appendix A).effective gasket seating width b and the loads, bolt stresses, andmoments identified under the headings shown in Table 10. For compliancewith Code criteria, the value of SB1 must not exceed the allowable boltstress at design temperature, and the value of SB2 must not exceed theallowable bolt stress at atmospheric* temperature.

The program prints the input data followed by the0

Immediately below, the program prints the flange stresses neededfor comparison with the ASME Code criteria.hub flanges (ITYPE = 1 or 2), the program prints five stresses under thetwo headings ASME FLANGE STRESSES AT OPERATING MOMENT, MOP and ASMEFLANGE STRESSES AT GASKET SEATING MOMENT. The stresses are identifiedas follows:

For tapered-hub and straight-

2 / 3 ( S H ) = two-thirds of the longitudinal stress on the outsidesurface 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 wordatmospheric is used as it is used in the Code.

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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 Programsymbola symbol Desc r pt iona

BO

H WM11wM12W M 1SB1

'm 1

WM 2SB2

'm2

(e) MOP( d ) MG S

MGS 1

bSee 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 / 42~bGmp-irG2p/4 + 21~bGmpB ol t s t r e s s ,TbGyB 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 rITYPE = 3(B1 in df 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 printedunder the first heading must not exceed the allowable stress for theflange material at the design temperature.second heading must not exceed the allowable stress for the flangematerial at atmospheric temperature.

The values printed under the

For blind flanges ( IT Y PE = 3 ) , the program prints the followingfive 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 =mirG2p/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 WSGS = the stress at gasket-seating conditions.

= nbGy, andm2

For Code compliance, SOP must not exceed the allowable stress for theflange material at design temperature, and SGS must not exceed theallowable stress at atmospheric temperature.

Innut for General PurDose CalculationsWhen the computer program is used for general purpose calculations,

(i.e., when it is used for calculating displacements and stresses otherthan those needed specifically for checking Code compliance), the usermay select almost any combination of admissible values for the fourvariables ITYPE, I B g N D , ICPDE, and MATE coded in the option control datacard. The only specific requirement is that the variable I C O E must beless than two for other than Code-compliance calculations.the input data are structured somewhat differently than those describedin the previous section.

In this case

When I C a D E = 0 and MATE = 1, ( i . e . , only one flange is to beanalyzed and the user does not wish to obtain bolt load changes), threedata cards a r e needed as shown in Table 11. These are the option-controlcard (for which ITYPE may be 1, 2 , or 3 and T B g N D may be 0 or 2) and twophysical-property data cards.

When I C g D E = 0 and MATE = 2 , 3 , . . . 6, the program will analyze apair of flanges mated together and give bolt load changes. If MATE = 2,the program performs the calculations f o r a pair of identical flangesmated together. The input data requirements include the data cardsshown in Table 11 plus the three cards shown in Table 12.three cards contain data on the physical properties of the bolts andgasket, 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 ea 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 et h i c k n e s s l e n g t h d i a m e t e r

h CG 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 eP

PRESS

I C ~ D E MATE'Column numberV a r i a b l eV 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 0olumn numberT 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 fa 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 yf 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 fVar 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 tc e n t e r l i n ed 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 lt h i c k n ess

goGOa'

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

21-30Boltc o e f f i c i e n tof thermalexpansion

'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 lbol t Out s id e Ins ide root a reatempera ture diamete r diamete r of a l lof gaske t of gaske t bol t sTb

Column number

Quantity Nominaldiamete r

Column number

Variable

11-20

0- 10 11-20 21-30 31-40 41 -50 51-60In i t i a l s t a t e ; G as ke t Equ iva le n tg 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 reGasket 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 PBET 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 moduluso f e l a s t i c i t yEb

Column number

Q ua n t i t y

Variable

0-10 11-20 21-30 31-40 41-50 51-60 61-70F i n a l s t a t ei 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 eI 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 tbo1t 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 ofload 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

EI T f 2 T i 2 E f 2 E ;2 EbW 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. Identification1

2l6

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 calculationsfor a pair of nonidentical flanges, neither of which, however, isblind ( 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 withMATE = 4.data requirements.nonidentical flanges (neither of which is blind) consists of the follow-ing nine cards.

Data forData for

The three cards described in Table 12 will then complete theThe complete input data set for analyzing a pair of

Card No. Identification

1

32 l4

6

Option-control card, ITYPE # 3 , ICgDE = 0, MATE = 3Data cards per Table 11 for first flange of pair

Option-control card, ITYPE # 3, ICgDE = 0, MATE = 4Data 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 calculationsfor 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 flangeis designated as the second with MATE = 6.set is completed by using the data cards described in Table 12. Thecomplete input data set for this case consists of the following ninecards.

A s befo re , the input data

Card No. Identification1 Option-control card, ITYPE = 3 , 1CP)DE = 0, MATE = 5

32 l Data cards per Table 11 f o r blind flange4 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 12Output 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 inturn 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 loadingonly (the bolt load for blind flanges), pressure loading only, andtemperature-gradient (hub to ring) loading only (except for blindflanges); 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. Thefirst page gives (1) the input data and (2) the parameters involved inthe bolt-load-change calculations. The second page gives (1) theloadings, (2) the residual bolt loads, and ( 3 ) the initial and residualmoments. The symbols used in the first and second page of printout areexplained 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 ionTheory ProgramSymbol symbol Descr ip t ion

u a r = or t u r = gru r = gt u r = cra t , r = ca r = at & C

SLSOQSLSPSCSOascs UsL L OS L L I

SCLOSCLISTHSTFSRHSRFZ GzcQFHGY OY 1THETA

SORTSGRSGTSCRSCTSATzc

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 eSt r es s long i tud ina l , smal l end of hub , in s id eS 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 aceo u t s i d e s u r f a c ei 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 eS 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 esur f aceS 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 ei 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 = bS 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 = bS 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 = bS 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 = gAxial displacement a t r = c- 6 + 6Radial displacement , small end of hubRadia l d i sp lacement , l a r ge end of hubRota t ion of r in g a t r = b

c g

bS 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 lS t r e s s , r = g r a d i a lS 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 lS t r e s s , r = c , t a n g e n t i a lS t r e s s , r = a , t a n g e n t i a lAxial 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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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 6Theory Programsymbol symbol Descr ip t ion

QFHG Axial d isplacement from C t o G , u n i t moment l oad f l h GqP 1 G QPHG Axial displacement from C t o G , u n i t p r e ss u r eload

Q T H G ~ Axial d isplacement from C t o G , u n i t DELTA t l h G2b In si de diameter

GOa Pipe wall t h i c k n e s st 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 ef1YF2C 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 ef

f E F~ Coe ff i c ie n t o f thermal expans ion of f l a n g em 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 rrrp. 11aFor 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 lb 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 dvg 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 eunprimed 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) .eInput 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 aTheory Programsymbol symbol aD e s c r i p t i o n

R

*bC

Eb1Eb2'bVO

EE

g18 2gE

w 1

Tf 2TLTb

TAA 'P

g

X LBA BCY BY B 2E BvoX GOX G IY GY G 2EGw1TBTFT F PTGDELTADELTAPPRESS

E f f e c t i v e b o l t l e n g thC 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 sB o l t - c i r c l e d i a m e t e rModulus 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 eModulus 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 eCo e f f i c i en t of t h e rma l ex pan s io n , b o l t sGasket th icknessOuts ide d iameter o f gaske tIn s id e d i am e ter o f g a s k e tModulus 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 eModulus 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 eCo 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 sI n i t i a l t o t a l b o l t l oa dT em pe ra tur e o f b o l t s , f i n a l s t a t eT 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 eT 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 eT em pe ra tu re o f g a s k e t , f i n a l s t a t eT 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 eT 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 twoI 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 eequat 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

aTheory Prog r a msymbol 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 tf 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 eW 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 ast 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 oi 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 ecor 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 op 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 ft 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 lmoment 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 heresidual 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 pageso 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 ewhen 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 sar 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 of 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 ttwo 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 ecase when MATE = 2 .

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5 2

Acknowledgment

1.

2 .

3.

4.

5.

6.

7.8.

The authors gratefully acknowledge the assistance of 0. W. Russof the Computer Sciences Division for converting the CDC 7700 Fortranprogram written at Battelle-Columbus Laboratories to double precisionfor operation on the ORNL IBM 360 computers.

ReferencesASME Bo il er and Pressure Ve ss el Code, Section VIII-1971, NuclearPower Plant Components, American Society of Mechanical Engineers,New York, July 1, 1971.E. 0. Waters et al., Formulas for Stresses in Bolted FlangedConnections 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 ofFlanged 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 nth e Bo lt in g and Flanges of B 1 6 . 5 Flanged Jo in ts wi th Metal-to-MetalContact Outside the Bolt Circle (in preparation).D. B. Wesstrom and S. E. Bei-gh, Effect of Internal Pressure onStresses and Strains in Bolted-Flanged Connections, Trans ASME73, 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 ) , APIStandard 605, 1st Ed., American Petroleum Institute, New York,1967.

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A P P E N D I X AE 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 ACONTENTS

Page57. . . . . . . . . . . . . . . . . . . . . . . . . .NTRODUCTION . . . . . . . . . . . . 59ETAILS OF THE FLANGE USED I N THE EXAMPLES

. . . . . . . . . . . . . 62SME C O D E CALCULATIONS, EXAMPLES 1 A N D 2. . . . 6 7

Inpu t Data 67O u t p u t D a t a 70

7 0esidual Bolt LoadsBlind Flange St re ss es , Example 3(a) 80Tapered-Hub Flang e S tr es se s, Example 3(a ) 81Blin d and Tapered-Hub S t r e s s e s , Example 3(b) 83Disp 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 8484

. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .es idua l Bolt Loads. . . . . . . . . . . . . . . . . . . . .l a n ge S t r e s s e s 93

Displacements 94. . . . . . . . . . . . . . . . . . . . .96OMPUTER TIME . . . . . . . . . . . . . . . . . . . . . . . . . . .

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INTRODUCTION

Several examples have been selected to illustrate the input/outputdata 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-hub flange.bolt stresses and flange stresses are close to the upper limits set in

This particular flange represents a design in which the

API-605.Six examples are included:

1. A Code stress calculation is performed for a tapered-hub flange atits rated pressure of 720 psi at 100F. The results show that thisparticular flange does indeed meet the criteria given in API-605 at720 psi and 100F.A Code stress calculation is performed for a blind flange to matchthe 60-in., 300-lb API-605 tapered-hub flange. The thickness of theblind flange was selected so that its maximum stress was the allow-able flange stress of 17,500 psi used in API-605.A blind flange bolted to a tapered-hub flange under pressure loadingonly is analyzed.(a) For an initial bolt stress equal to the API-605 allowable

stress for the bolting material of 20,000 p s i , the resultsindicate that the flanged joint will probably leak at itsrated pressure of 720 psi at 100F.

(b) For an initial bolt stress of 44,300 psi, the results indicatethat the flanged joint will pass a hydrostatic test of 1.5 x720 psi at ambient temperature.

4 . A tapered-hub flange bolted to an identical tapered-hub flange withan initial bolt stress of 46,100 psi is analyzed.

*Large-Diameter Carbon S t e e l Flanges ( S i z e : 26 Inches to 30 Inches,Inclusive, Nominal Pressure R a t i n g : 75, 1 5 0 , and 300 Zb), API Standard605, 1st Ed., American Petroleum Inst., New York, 1967.

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(a) For pressure loading o n l y , the results indicate that theflanged joint w i l l hold a hydrostatic test pressure of1.5 x 720 psi.

(b) For pressure loading of 300 p s i ( A P I - 6 0 5 rated pressure at850F) plus an external bending moment that produces an axialstress in the attached p i p e of 7500 psi, the results indicatethat the flanged joint i s adequate to carry these loads.

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59

DETAILS OF THE FLANGE USED I N THE EXAMPLES

A s k e t c h o f t h e t a p e re d - hu b f l a n g e i s shown i n Fi g . A . l . Thedimensions are as sp ec i f ie d i n API -605 .s i o n s B (and th e re fo re g and g ) a r e n o t s p e c i f i e d i n AP I-605. F or t h epu rpose o f check ing r a t i ng s , th e fo l lowing equa t io n g iven i n API-605was u se d t o e s t a b l i s h B :

The i ns id e d i ame ter and dimen-0 1

B = D - 2 t ,0 P ( A . 11

whereD o = nomina l ou ts i de d iamete r o f p ipe , in . ;t = p D /2 (0 .875 )S (bu t no t l e s s t h a n 0 . 2 5 ) , i n . ;p, = r a t e d p r e s s u re a t 100"F , p s i ;

0.875 = assumed p ipe -wa ll to le ra nc e; andP 1 0

S = 2 0, 00 0 p s i , t h e a l l o w a b le s t r e s s a t 100'F.The d e f i n i t i o n o f t with D o = 60 i n . and p = 720 p s i , l e a d s t o t =P' 1 P= 1 .2343 in . Equa t ion (A . l ) g ive s B = 57.5314 i n . and g = ( X - B ) / 2 =12.7030 in .

F or t h e pu r po s e o f c h e c k in g r a t i n g s , t h e hub l e n g th h was c a l c u l a t e dby t h e e qua t ion g iven i n APi -605 :

h = Y - t + O . 1 7 6 g 0 + 0.469 .Dimensions Y and t a r e shown i n Fi g . A . l . F or t h i s f l a n g e :

h = 10.6875 - 5.9375 + 0.176(1.2343) + 0.469 = 5.4362 in .The APL-605 st an da rd s t a t e s t h a t f l a n g e r a t i n g s were based on use

o f a 1 /16 - in . - th ick , compressed -asbes to s , f l a t r i n g - s h a p e d g a s k e t , w i tha n i n s id e d i a m e te r 1 / 4 i n . l a r g e r t h a n t h e o u t s i d e d i am e t e r of t h e p i p eand wi th an ou ts ide d iamete r equa l t o t h e r a i s e d - f ac e d i am e t er .6 0 - in . , 3 00 -lb f l a n g e , t h e g a s k e t i n s id e d i a m e ter i s 6 0 . 2 5 i n . ; i t s

F o r t h e

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6 0O R N L - D W G 75-4296

TDIMENSIONS IN INCHES

r = 62.9375t-0 = 57.5314

Fig . A . l . Dimensions ( in inches) o f 60 - in . , 300- lb API-605 t a p e r e d -hub f l ange . The terms B y R , C y D o , X , and A are d i a m e t er s e x p r es se d i ni n c h e s .

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6 1

o u t s id e d i a m e te r i s 6 5 i n .t h i c k a s b e s t o s g a s k e t , m = 2.75, and y = 3700 p s i .

According to t he ASME Code, for a 1 /1 6 - in . -

The 60 - in . , 300 - lb f lang e has fo r t y 2 -1 /4 -in . -diam. bo l t s . For an8 - pi t c h t h r e a d, t h e r o o t a r e a p e r b o l t i s 3.423 i n . 2 , g iv in g a t o t a lb o l t r o o t a r e a of 136.92 i n . 2 .

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62

ASME CODE CALCULATIONS, EXAMPLES 1 AND 2

The input data for examples 1 and 2 ar e shown i n Table A . l . Theso u r c e o f a l l i n p u t f o r Ca r d s 2 a nd 3 a r e c o n ta i n ed i n t h e p r e v i o u ss e c t i o n on f l a n g e d e t a i l s , e xc ep t t h a t t h e t h i c k n e s s o f t h e b l i n d f l a n g ewas s e l e c t e d * s o t h a t t h e c o n t r o l l i n g f l a n g e s t r e s s i s 17,500 p s i . Notetha t Card 2 i s i d e n t i c a l f o r e x a m p l e s 1 and 2 e x ce p t f o r t h e v a l u e o f t ;however, B , g o , g , , and h a r e not used f o r example 2 ( b l i n d f l a n g e ) , andany number ( in c lu din g zero) can be ente red f o r the se dimensions.

Example 1 i s a Code s t r e s s c a l c u l a t i o n f o r t h e 6 0 - i n . , 3 00 -l bAPI-605 tapered-hub flange a t i t s ra t e d press ure o f 720 p s i a t 100 'F.The out put d a t a a re shown in Table A . 2 .i s t h e c o n t r o l l i n g b o l t s t re s s , which e s se n t i a l l y m ee ts t h e API c r i t e r i o nv a l u e o f a b o l t s t r e s s n o t g r e a t e r t ha n 20,000 p s i .(SH + S T ) / 2 = 17, 293 p s i und er t h e h ead ing "ASME FLANGE STRESSES ATOPERATING MOMENT, MOP" i s t h e c o n t r o l l i n g f l a n g e s t r e s s a nd meets t h eAPI-605 c r i t e r i o n of a c o n t r o l l i n g f l a n ge s t r e s s n o t g r e a t e r t h a n1 7, 50 0 p s i . The r e su l t s , t h e r e f o r e , c o nf ir m t h a t t h e 6 0 - i n . , 3 0 0- lbAPI-6 05 t a pe re d- hu b f l a n g e me et s t h e s t a t e d c r i t e r i a .

'The value of SB1 = 20 ,033 ps i

The value of

The reader who i s accus tomed t o us i ng hand ca l cu la t io ns f o r check ingf l an ge des igns accord ing t o Code ru l e s w i l l n o t e t h a t t h e p ro gra m i n p u td oes n ot r e q u i r e e i t h e r t h e f a c t o r s T , U, Y , Z from Code Fig. UA-51.1,o r F , V , and f from Code Fi gs . UA-51.2, UA-51.3, and UA-51.6, r e sp e c -t i ve ly . These fa c t or s a r e ca l cu la t ed by th e compute r p rogram. Ina d d i t i o n t o s i m p l i f yi n g t h e i n p u t , t h e program a c c u r a t e l y c a l c u l a t e s F ,V , and f v a l u e s f o r a ny v a l u e s o f h / ht h e r a n ge o f t h e Code f i g u r e s .

and g l /g , , i nc lud ing those beyond0Example 2 i s a Code s t r e s s c a l c u l a t i o n f o r a b l i n d f l a n g e t o m atch

th e 60 - in . , 300-lb API-605 tapered-hub f l an ge . The ca lc ul a t io n methodi s t h a t gi ven i n UG-34 [Eq. ( 2 ) ] , with C = 0 .3 . The ou tpu t da t a a r eshown i n Table A .3 . The co n t ro l l i ng f l ang e s t re s s i s SOP = 1 7, 50 0 p s i ;

*API-605 does no t g ive b l in d- f l an ge th i ck nes ses .

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3ccm

vc.rwc3ucvv0kwvQaU 44

2vdkrcwca+ac

Qaecb

akcuwvk.diLkae

c\1

cc

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Table A . 2 . Output data f o r example 1, ASME Code ana l ys is of a tape red-hub f lange

F L A N G E P L A RG E F L A N G E P I P E H U B A T H U B E C LT P R E S S U R E .O . D . . A I. D . ,B T H I C K . ,T Y A L L ,G O B A S E , G l L E N G T H ,H C1RCLE.C P7 3 . 9 3 7 5 0 5 7 . 5 3 1 4 0 5 . 9 3 7 5 0 1 . 2 3 4 3 0 2 .7 0 3 0 0 5 . 4 3 6 2 0 6 9 . 4 3 7 5 0 7 2 0 . 0 0 0

n Y G OU T G I N S B SA AB2 . 7 5 0 0 0 3 7 0 0 . 0 0 0 0 0 6 5 . 0 0 000 6 0 . 2 5000 20000 . o o o o o 2 0 0 0 0 . 0 0 0 0 0 1 3 6 . 9 2 0 0 0BO wnt 1 Y R 1 2 wn1 SB wn2 SB22 . 9 5 6 3 D 0 3. 0 4 7 7 D 0 5. 0 0 3 3 D 0 4. 1 8 7 5 D 0 0 2 . 3 0 9 7 D 0 6 4 . 3 32 2 D 05 2 . 7 4 3 0 D 06nop MGS RGS 11 . 1 7 1 9 D 0 7 7 . 5 7 4 2 1) 06 1 . 1 1 8 6 D 0 6

A S M E F L d N G E S T R E S S E S AT O P E R A T I N G M O H EN T, H O P

(2/3)*SH= 1 . 5 6 0 8 D 04 S T = 1 . 1 1 7 4 D 04 SB = 8 . 4 4 0 2 D 0 3 ( S H + S T ) / 2 = 1 . 7 2 9 3 0 0 4 (SH+SR ) / 2 = 1 . 5 92 8 D 04

A S U E F L A N G E S T R E S S E S A T G A S K ET S E A T I N G R O C IE NT , PlGS

( 2 / 3) * S H = 1 . 0 0 8 7 D 04 ST = 7 . 2 2 1 6 D 03 SR = 5 . 0 5 76 D 0 3 ( S H + S T ) / 2 = 1 . 1 1 7 6 D 04 (SH+SR ) / 2 = 1 . 0 2 9 4C 0 4

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Table A . 3 . O u tp u t da ta for example 2 , ASME Code a n a l y s i s of a b l i n d f l a n g e

FLANGE FLANGE FLANGE PIPE H U B AT H U B BCLT PRESSURE,O.D. ,A I . D . , E T H I C K . , T WALL,GO BASE,G1 LEN G TH ,H C I R C L E , C P73.93750 0 . 0 7.90440 0.0 0.0 0 .o 6 9.4375 0 720.000Y GOUT G I N SB SA h B2.75000 3 700.0000 0 65.00000 60.25000 20000 . o o o o o 20000.00000 136.92000

BO wu11 WH12 u n 1 SB 1 UH2 S B 22.0033D 0 4 4.0477D 0 5 2.9563D 0 3. 1875D 0 0 2.30971) 06 4 . 3322D 0 5 2.7430D 06ASUE CODE STRESSES FOR B L I N D FLANGE

SP SWl SOP sw2 SGS1.4121D 0 4 3.37921) 03 1.75 00~104 4.9865D 02 3.3763D 03

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6 6

the flange thickness of 7.9044 in. was selected to obtain this result.This example was included to illustrate that a blind flange may have tobe considerably thicker than a mating flange in order for both to meetthe Code stress limitations.

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B L I N D - T O - T A P E R E D - H U B FLANGED J O I N T , EXAMPLES 3(a). AND 3 ( b )

Input Data

The inpu t da ta f o r examples 3 (a ) and 3(b) a r e shown i n T abl e A.4.I n a d d it i o n t o t h e b a s i c p ur po se of i l l u s t r a t i n g i n p u t /o u t p u t d a t a f o rthe program FLANGE, t h i s p a i r o f e xa mp le s was se le c t ed t o show how t heprogram can be used t o est imate r eq ui re d i n i t i a l b o l t s t r e s s e s . Inad d it io n , example 3( a) shows how th e gen er al purp ose op ti on (ICODE # 2 )g i v e s s t r e s s e s a s o b t a i n e d f rom Code c a l c u l a t i o n s p l u s d e f o r m a ti o n d a t aa n d a d d i t o n a l s t r e s s e s ,

Examples 3(a) and (b) do n o t i n v o lv e t e m pe r at u re g r a d i e n t s o rt e m p e r a t u r e s o t h e r t h a n am bi en t; h en ce , t h e m od ulu s o f e l a s t i c i t y i s t h esame f o r t h e i n i t i a l a nd f i n a l s t a t e s . V a l ue s of t e m p e r a t u r es f o r t h ef l a ng e s , b o l t s , and g a s k et s i n t h e f i n a l s t a t e h av e been e n t e r e d a sz e ro . The i n i t i a l - s t a t e r e f e r e n c e t e mp e r at u re i s zero ; hence, a z e r o i nt h e f i n a l s t a t e d en ote s a ze ro the rmal g r ad i en t . However, t he va lu e o fDELTA ( t h e h u b - t o - r i n g t h er m a l g r a d i e n t ) c a n no t b e e n t e r e d as ze row i t h o u t c a u s i n g a d i v i d e - c h e c k e r r o r , s o a v a l u e of 0 .01 was used. Asm al l e r va lu e cou ld be used (e . g . , 0 .001 o r O.OOOl), bu t t h e ou t pu t da tashows that DELTA = 0 .01 i s s u f f i c i e n t l y small so t h a t i t s i n f l u e n c e i sn e g l i g i b l e . A c o e f f i c i e n t o f t h e r m al e x p a n si o n o f 6 x has beene n t e r e d b u t i s n o t s i g n i f i c a n t i n t h e s e ex am pl es .

The value of FACE, which i s i n t e nd e d t o p e r m it u s e of a b o l t l e n g t hThe modulust h e r t h a n L o = TH + THP + VO + BSIZE, was e n t e r e d a s z e r o .

o f e l a s t i c i t y f o r b o t h t h e f l a n g e s a nd t h e b o l t s w a s assumed t o be3 x l o 7 p s i .ga sk et was assumed t o be 3 x lo6 p s i .

The m odulus o f e l a s t i c i t y f o r t h e 1 / 1 6 - in . - t hi c k a s b e s t o s

Some comments on t h e u s e o f a modulus of e l a s t i c i t y o f 3 x l o 6 f o ra 1 / 1 6 - i n. a sb e s t o s g a sk e t may b e a p p r o p r i a t e . The s t r e s s - s t r a i n re-l a t i o n s h i p f o r s uch a gasket , which i s c o n f i n ed b et we en t h e two r i g i df l a n g e f a c e s , i s h i g h l y n o n l i n e a r a n d b o t h time and h i s to ry dependent .S t a r t i n g o u t w i t h a new gaske t , t he f i r s t i n c r e m e n t o f b o l t s t r e s s t oproduce a g a sk e t s t r e s s o f 1 00 0 p s i mi gh t d e c r e a se t h e g a sk e t t h i c k n e s s

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68

aTable A . 4 . Input data for blind-to-tapered-hub flanged joint, examples 3a and 3bCard ReadNo. Variables and numerical values format1 ITYPE I OND ICODE MATE

3 0 0 5 4152 A B t go gl h C P

73.9375 57.5314 7.9044 1.2343 2.7030 5.4362 69.4375 720. 8E10.5(1080.)

3 X M O A ~ EF DELTA' YM G2.7430D+6 6. D-6 .O1 3. D+7 62.625(6.0656D+6)

4 ITYPE I OND ICODE MATE1 0 0 6

5E10.5

4155 A B t go gl h C P

73.9375 57.5314 5.9375 1.2343 2.7030 5.4362 69.4375 720. 8E10.5( 1 0 8 0 . )

6 XMOA EF DELTA' YM G1.1719D+7 6. D-6 . 0 1 3. D+7 62.625(2.0661D+7)

7 BS ZE YB EB TB XGO XG I AB2.25 3. D+7 6. D-6 0 65. 60.25 136.92

8 vo YG EG TG FACE P E.0625 3. D+6 6. D- 6 0 0 0

9 w 1 TF TF YF2 YFP2 YB2 YG22.7430D+6 0 0 3. D+7 3. D+7 3. D+7 3. D+6(6.06561)+6)

5E10.5

7E10.5

6E10.5

7E10.5

abInitial bolt load is used here since ITYPE = 3; see footnote b t o Table 11 in the text.e .Since DELTA cannot be entered as zero, 0.01 was used as a satisfactorily small value.Values in parentheses are for example 3b.

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6 9

by 2 0 % , s o t ha t th e modulus would be 1000/(0 .2 x 0.0625) = 8 x l o 4 p s i .C rude o b s e r v a t i o n s i n d i c a t e t h a t , a t a b o l t s t ress t h a t p ro d u ces ag a s k e t s t r e s s of 40 ,0 00 p s i , t h e g a s k e t t h i c k n e s s i s about one-ha lf ofi t s o r i g i n a l t h i c k n e s s , s o t h a t t h e a v e ra g e modulus up t o t h i s s t r e s s i s40,000/0.03125 = 1.28 x l o 6 p s i .r a t i o o f w id th t o t h i c k ne s s of t h e g a s k e t and t h e time under s t r e s s ,p a r t i c u l a r l y fo r low g as k e t s t r e s s . However, f o r t h e f l a n g e d - j o in ta n a l y s i s , w e a r e n ot i n t e r e s t e d i n t h e g a s ke t s t r e s s - s t r a i n c h a r ac t e r-i s t i c s when t h e b o l t l oa d i s a p p l i e d b u t r a t h e r i n t h e g a sk e t s t r e s s -s t r a i n c h a r a c t e r i s t i c s when t h e g a s k e t s t r e s s i s decreased a f t e r t h egask e t has been under bo l t load f o r s ev er al days o r many months. Noda ta on t h e "sp r ing-back" of a s b e s t o s g a s k e t s a re a v a i l a b l e , b u t i n mostf l a n g e d j o i n t s u s i n g 1 / 1 6 - i n . - t h i c k a s b e s t o s g a s k e t s, t h e assumedmodulus o f e l a s t i c i t y o f t h e g a s k et i s n o t v e r y s i g n i f i c a n t p r o v i d e d i ti s n o t u n re a l i s t i ca l l y l ow. T h i s can b e shown f o r example 3 by notingth a t t h e ch an g e i n th e b o l t load depends upon the sum of t h e load-d i s p l a c e m e n t c h a r a c t e r i s t i c s of t h e b o l t s , t h e f l a n g e s , a nd t h e g a s k e t .The displacements for a u n i t b o l t l oa d a r e -

These numbers ar e dependent upon t he

16.15136.92 x 3 x l o 7 =

3.93 x 10-9 ,Of o r b o l t s : -AbEb

f o r f l a ng e s : 2 x QFHG = Z(1.197 x = 2.40 x lo- ' ,and

0.0625 1.34 x-0 - -E G67.26 x EGo r g a s k et : -A ~ E ~

A s Ev a r i e s as f o l l o w s :v a r i e s f ro m l o 5 t o l o 7 , t h e sum o f t h e s e t h re e d is p lacemen t sG

E GSum of d i s p l a c e -

ments (x109 i n

i o 5 3 x 105 106 3 106 i o 77.67 6.78 6.46 6.37 6.341

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7 0

From t h e abov e, i t can be seen t h a t changing th e gas ke t modulus by twoor de rs of magnitude changes th e sum of th e d i sp lacement by on ly 17%.

The i n i t i a l b o l t s t r e s s u se d i n e xam ple 3 ( a ) i s 2 0, 03 3 p s i , g i v i n gan i n i t i a l b o l t lo ad of W 1 = SbAb = 20,033 x 136.92 = 2.743 x l o 6 l b ;W 1 i s e n t e r e d i n p l a c e of XMOA on card 6 (see fo o tn o te b t o T ab le 11 oft e x t ) .i n . - l b . T h e i n i t i a l b o l t s t r e s s u sed i n examp le 3 (b ) i s 4 4 , 3 0 0 p s i ,g i v i ng an i n i t i a l b o l t l oa d o f W 1 = 6.0656 x l o 6 l b .XM OA, used i n example 3(b) i s 2.0661 x l o 7 i n . - l b .u s i ng t h e s e p a r t i c u l a r v a l u es o f W 1 and XMOA a r e d i s c us s e d i n connect ionwi th t h e o u tp u t d a t a f o r t h e s e examp les.

The i n i t i a l moment, XM OA, used i n example 3(a) i s 1.1719 x l o 7The i n i t i a l moment,

T h e r ea s o n s fo r

OutDut Data

Re si du al Bo 1 LoadsThe ou tpu t da ta fo r example 3(a ) are shown i n Tab le A.5. The

o u t p u t s t a r t s with a p r i n t o u t o f a l l i n p ut d a t a on t h e f i r s t pa ge(Table A.Sa).* The parameters involved i n t h e b o l t - lo ad -ch ang e ca l cu -l a t i o n s a re t h en p r i n t ed , fo l lo wed by r e s id u a l b o l t l o ad s an d moments,a l l on th e second page (Tab le A.5b). The i n i t i a l bo l t load under"LOADINGS" i s 2.743 x l o 6 l b ; t h e r e s i d u a l b o l t l oa d a f t e r a p p l i c a t i o no f t h e p re s s u re of 720 p s i i s given fo l lowing 'COMBINED" as W2 = 1.0948 xl o 6 l b .and t h e r a t i o of r e s i d u a l t o i n i t i a l b o l t l oa d i s given by W 2 / W 1 =0.39911.hub f lange a re p r in t e d on t h e t h i r d and fo u r th p ages (T abl e s A .5 c an dA .5 d, r e s p e c t i v e l y ) . T he se a r e d i s c u s s e d l a t e r .

The l o s s i n b o l t l oa d i s give n by W 1 - W2 = 1.6482 x l o 6 l b ,C a l c u la t e d s t r e s s e s f o r t h e b l i n d f l a n g e a nd f o r t h e t a p e r e d -

* For convenience i n r e f e r r i n g t o s p e c i f i c pa ge s o f m ul ti pa g e t a b l e s ,we have used a lpha bet ic su f f i xe s on ta b l e numbers . For example, th ef i r s t p ag e o f T a b le A.5 i s des i gnat ed Tab le A.5a; th e second page i sT ab le A .5 b, t h e t h i r d i s Table A.5c , e tc .

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Table A.5a. g u tp u t d a t a f o r ex am ple 3 ( a ) , b l i n d f l a n g e b o l t e d t o at ap er ed -h ub f l a n g e , w i th i n i t i a l b o l t s t r e s s = 2 0 , 0 3 3 p s i*PIPE H U B AT H U B BCLT PRESSURE,LANGE FLANGE FLANGEO . D . , A I . D . , B THICK.,T WALL,GO BASE,Gl LENGTH,H C 1 R C L E . C P73.93750 57.53140 7.90440 1.23430 2.70300 5.43620 69.43750 720.000

BOLT COEFF. OF nELTA N O D . OF H E A N GASKET ITYPE I E C N D ICODE HATE2.743D 06 6.000D-06 1.000D-02 3.000D 07 6.263D 0 1 3 0 0 5LO A D THERHAL EXP. ELAS TICITY DIANETER

FLANGZ FLANGE FLANGE P I P E H O B AT H U B BCLT PRESSURE,O . D . , A I . D . , E THICK.,T WALL,GO BASE,Gl LENG'fH,H CIRCLE,C P73.93750 57.53140 5.93750 1.23430 2.70300 5.43620 69.43750 720.000f lO f lEN T COEFF. OF D E L T A N O D . OF H E A N GASKET I T Y F E I E C N D I C O D E U A T E

1.172D 0 7 6.OCOD-06 1.000D-02 3.000D 0 7 6.263D 0 1 1 0 0 6THEREAL EXP. ELASTICITY DIAFlETER

B S I Z E Y D EB TB X GO X G I AB2.2500D O C 3.0000D 0 7 6.0000D-06 0 . 0 6.50000 0 1 6.0250D 01 1.3692D 0 26.25OOD-02 3.0000D 0 6 6.0000D-06 0 . 0 0 .0 0.02.7430D O F 0 .0 0 . 0 3.0000D 0 7 3.0000D 07 3.0000D 07 3.0000D 06

vo Y G E G TG FACE PEEw1 T F TFP YF 2 YFP2 YB2 YG2

FLANGE J