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ii

TABLE OF CONTENTS

FOREWORD INTRODUCTION . 1

NOMENCLATURE 3

IDENTICAL PAIR OF FLANGES 5

Regime Where 0 A > 0, hc - (A-C>/2 il

Regime Where 8 A - 0, hc < (A-Q/2 . 15

STRAIGHT HUB FLAKGE BOLTED TO A FLAT COVER 17

APPLICATION EXAMPLES 21

Flanged Joints Selected Eor Examples 21

Stresses and Allowable Pressures by Part A Rules 23

Identical Pair, Part B Rules 27,

Flange/Cover Joint, Reference (3) Theory 31

Discussion of Significant Aspects . . . 39

TEST DATA .

COMPUTER PROGRAMS . . . . . . . . . . . 69

Output Data, FLGB 49

Output Data, COVER B .50

RECOMMENDATIONS 53

ACKNOWLEDGEMENT 54

REFERENCES 5S

APPENDIX A COPY OF "AXISYMHETRIC, NONIDENTICAL, FLAT-FACE FLANGES WITH METAL-TO-METAL CONTACT BEYOND THE BOLT CIRCLE" BY WATERS AND SCHNEIDER . . . . A-1

APPENDIX B

LISTING OF COMPUTER PROGRAMS FLGB AND COVER B B-l

i l l

LIST OF TABLES

Page

TABLE I . PART B RULES 7

TABLE 2 , DIMENSIONS OF API-605 FLANGES USED IN IN APPLICATION EXAMPLES 22

TABU 3. PART A RULES, STRESSES (PSI ) AND ALLOWABLE PRESSURES (PS I ) FOR API-605 FLANGES 24

TABLE 4 . PART B RULES, VALUES OF S^, o b , H/Ab AND Z, IDENTICAL PAIR AS SHOWN IN FIGURE 1 28

TABLE 5 . PART B RULES, STRESSES (PSI ) FOR API-605 FLANGED JOINTS, IDENTICAL PAIR AS SHOWN IN FIGURE 1 30

TABLE 6 . FLANGE/COVER JOINT, VALUES OF S [ , C b , H/Ab AND 0 2 0 , JOINT AS SHOWN IN FIGURE 2 33

TABLE 7. FLANGE/COVER JOINT, STRESSES (PSI ) IN STRAIGHT-HUB FLANGE. API-605 FLANGED JOINTS, JOINT AS SHOWN IN FIGURE 2 35

TABLE 8 . FLANGE/COVER JOINT, STRESSES (PSI ) IN COVER FLANGE, API-605 FLANGED JOINTS AS SHOWN IN FIGURE 2 37

TABLE 9 . MAXIMUM PRESSURES IN PSI FOR Sb • 25,000 P S I , S f ® 20 ,000 PSI 41

TABLE 10. COMPARISON OF TEST DATA FROM REFERENCE (9 ) WITH CALCULATED RESULTS, ANSI B16.S, 12" - 300 CLASS WELDING NECK-TO-WELDING NECK, IDENTICAL PAIR; AND WELDING NECK-TO-BUND, FLANGE/COVER 48

TABLE 11. OUTPUT DATA IDENTIFICATION, COMPUTER PROGRAM FLGB . . . . . 51

TABLE 12. OUTPUT DATA IDENTIFICATION, COMPUTER PROGRAM COVER B . . . . 52

iv

LIST OF FIGURES

Page

FIGURE 1. CONFIGURATION OF IDENTICAL PAIR FLANGED JOINT 6

FIGURE 2. CONFIGURATION OF FLANGE/COVER FLANGED JOINT 18

FIGURE 3. LOCATIONS AND DIRECTIONS OF FLANGE STRESSES, PART A AND PART B RULES (IDENTICAL PAIR) AND STRAIGHT-HUB FLANGE OF FLANGE/COVER FLANGED JO.'NT 25

FIGURE 4. OPERATING BOLT STRESS, AS A FUNCTION OF INITIAL BOLT STRESS, S£. IDENTICAL PAIR, p = P 1 0 0 26

FIGURE 5. FLANGE STRESSES, oh AND orrC, AND FACE SEPARATION OF BORE, Z, AS A FUNCTION OF INITIAL BOLT STRESS, S IDENTICAL PAIR, 26" - 150 CLASS, p = P100 29

FIGURE 6. OPERATING BOLT STRESS, ob, AS A FUNCTION OF INITIAL BOLT STRESS, S^ FLANGE/COVER, p « P100 32

FIGURE 7. FLANGE STRESSES, oh AND CTrC, IN STRAIGHT HUB FLANGE AS A FUNCTION OF INITIAL BOLT STRESS, S^ FLANGE/COVER, P " P100 3 4

FIGURE 8« LOCATIONS AND DIRECTION OF STRESSES ON COVER 36

FIGURE 9. STRESSES, a r t, AND a r C, IN COVER AS A FUNCTION OF INITIAL BOLT STRESS, Si. FLANGE/COVER, p - P 1 Q 0 38

i

V

FOREWORD

The work r e p o r t e d here was performed f o r the Oak Ridge N a t i o n a l Laboratory a t Bat te l le -Columbus Labora tor ies under Union Carbide Corpora-

t i o n , Nuclear D i v i s i o n , Subcontract No. 2913 as p a r t of the ORNL Design

C r i t e r i a for P ip ing and Nozzles Program, S. E. Moore, Manager. This

program i s funded by the O f f i c e of Nuclear Regulatory Research of the

U. S. Nuclear Regulatory Commission, D i v i s i o n of Reactor Sa fe ty Research

(RSR) as par t of a coopera t ive e f f o r t w i t h indus t ry to develop and v e r i f y

a n a l y t i c a l methods f o r assessing the s a f e t y of nuc lear p r e s s u r e - v e s s e l

and p ip ing-sys tem design. The cooperat ive e f f o r t i s coordinated through

the Design D i v i s i o n , Pressure Vessel Research Committee, Welding Research

Counci l . The cognizant RSR-NRC p r o j e c t engineer i s E. K. Lynn.

The study of ASME - Par t B f langed j o i n t s descr ibed i n t h i s

repor t i s a p o r t i o n of a t h r e e - p a r t study of f langed p i p i n g j o i n t design

being conducted i n support o f codes and standards design r u l e s assess-

ment. Resul ts from t h i s study w i l l be used by a p p r o p r i a t e ASME Code

groups i n d r a f t i n g new and improved design r u l e s .

Other r e p o r t s i n t h i s s e r i e s a r e :

( 1 ) E. C. Rodabaugh, F. M. O 'Hara , J r . , and S. E. Moore, FLANGE: A Computer Program for the Analysis of Flanged Joints with Ring-Type Gaskets, ORNL-5035, January, 1976.

(2 ) E. C. Rodabaugh and F . M. O 'Hara , J r . , Evaluation of the Bolting and Flanges of ANSI B16.5 Flanged Joints— ASME Part A Rules (to be published).

BLANK

iS&tSSSEŜ MWauCTBcii jifra ntwwrrr-

INTRODUCTION

The ASME B o i l e r and Pressure Vessel Code, Sect ion V I I I , D i v i s i o n

h e r e i n a f t e r r e f e r r e d to as the Code*, g ives r u l e s which a r e subdivided i n t o

"Par t A" and "Par t B". Par t A covers f langed j o i n t s where contact between

f langes occurs through a gasket located ins ide the b o l t h o l e s . Par t B

covers f langed j o i n t s w i th contact outs ide the b o l t h o l e s .

The theory behind the F a r t B Code r u l e s i s developed and discussed

i n References ( 2 ) , ( 3 ) , ( 4 ) , and ( 5 ) . At p r e s e n t , the Code r u l e s cover on ly

j o i n t s c o n s i s t i n g of an i d e n t i c a l p a i r o f f langes used w i t h a s e l f - s e a l i n g

( e . g . , e lastoraer ic 0 - r i n g ) gasket . Revis ions to the Code r u l e s , however, a re

under c o n s i d e r a t i o n which are intended both to s i m p l i f y the present r u l e s and

to expand the coverage t o T ionident ica l f l anges .

The ASME B o i l e r and Pressure Vessel Code, Sec t ion I I I , D i v i s i o n

(Nuclear Power P l a n t Components) inc ludes both P a r t A and P a r t B r u l e s i n

subsect ion NA, Mandatory Appendix X I . However, subsect ion NB f o r Class 1 Com-

ponents does not appear to recognize the p o s s i b i l i t y o f f langed j o i n t s w i t h

contact ou ts ide the b o l t c i r c l e ; i . e . . P a r t B type . For example, NB-3231

requi res t h a t the b o l t a rea i s to be determined by the procedures o f Appendix

E but Appendix E i s a norutiandatory appendix a p p l i c a b l e to f l anged j o i n t s w i t h

contact i n s i d e the b o l t ho les ; i . e . , P a r t A type . Never the less , NB-3231

appears t o r e q u i r e i t s use regard less of whether the f l a n g e j o i n t i s designed

to P a r t A r u l e s or Par t B r u l e s . Examples presented i n t h i s r e p o r t suggest

tha t i t could be unconservat ive to design the b o l t i n g by Appendix E procedures

i f , i n f a c t , the f langed j o i n t i s P a r t B; i . e . , w i t h contact ou ts ide the b o l t

c i r c l e .

* I n t h i s r e p o r t , u n l i k e the m a j o r i t y of o ther repor ts of t h i s s e r i e s o f r e p o r t s , the terra "Code" r e f e r s to Sect ion V I I I , D i v i s i o n 1 ; not Sect ion I I I . Reference to Sect ion I I I o f the Code i s s p e c i f i c a l l y i n d i c a t e d where so in tended . Reference t o p o r t i o n s of e i t h e r the "Code" or the ASME Sect ion I I I Code are i d e n t i f i e d as i n those Codes; e . g . , UA-57 of the "Code" or NB-3231 of the ASME Sect ion I I I Code.

2

Subsections NC and ND for Class 2 and Class 3 Components of the ASHE

Sect ion I I I Code r e f e r d i r e c t l y to Appendix X I as a pe rmiss ib le f langed j o i n t

design procedure; see NC-3262.3 , NC-3362, and ND-3362.

Th is r e p o r t c o n s t i t u t e s the l a s t o f a s e r i e s of t h r e e repor ts on the

subject of b o l t e d - f l a n g e d j o i n t s . Reference (7) descr ibes the theory a p p l i c a b l e

to T a r t A f langed j o i n t s . Reference (8 ) examines the c a p a b i l i t i e s o f ANSI B16.5

f langed j o i n t s when used w i t h gaskets ins ide the b o l t h o l e s . This r e p o r t ( a )

summarizes the theory f o r P a r t B f l anged j o i n t s , (b) presents examples which

show the s i g n i f i c a n t d i f f e r e n c e s between P a r t A f langed j o i n t s and P a r t B

f langed j o i n t s , (c ) presents the a v a i l a b l e t e s t da ta r e l e v a n t to the c h a r a c t e r -

i s t i c s o f P a r t B f langed j o i n t s , (d) g ives l i s t i n g s of two computer programs

which can be used to eva lua te c h a r a c t e r i s t i c s of P a r t B f langed j o i n t s , and

(e ) g i v e s recommendations fo r Code r e v i s i o n s and other aspects of P a r t B f langed-

j o i n t des ign.

L a t e r i n t h i s r e p o r t , we w i l l be g i v i n g examples of the a p p l i c a t i o n

of the theory which invo lves both the C o d e ^ r u l e s f o r P a r t B f l a n g e s ; for

i d e n t i c a l p a i r s , and the theory of Reference (3 ) f o r a f l ange b o l t e d to a f l a t

cover . I t i s p e r t i n e n t t o note t h a t the bas ic t h e o r e t i c a l approaches used i n

these two re ferences a re cons is ten t w i t h each o t h e r ; hence cross-comparisons

between the two kinds o f j o i n t s are on a cons is tent b a s i s .

3

NOMENCLATURE

A " outs ide diameter of f l ange

A^ n t o t a l cross sec t ion root area of b o l t s

A ® t o t a l required cross s e c t i o n a l l.oot area of b o l t s m

- W H1 / S b a - (A + C ) / 2 B 1

B i n s i d e diameter o f f l ange

B r B + 8 o

b « e f f e c t i v e gasket s e a t i n g width

C a b o l t c i r c l e diameter

D =• diameter of b o l t hole

E = modulus of e l a s t i c i t y

Ef « modulus of e l a s t i c i t y o f f l ange m a t e r i a l

E^ » modulus of e l a s t i c i t y o f b o l t m a t e r i a l

G « mean diameter of gasket

g « thickness of hub ° 2 H « 0 ,785 G p

H c - (Mp + M s ) / h c

H d - 0 .785 B2p Hp = gasket s e a l i n g force, ( t aken as zero h e r e i n )

h =» r a d i a l d is tance from b o l t c i r c l e to f l a n g e - f l a n g e bear ing c i r c l e

where the slope of the f l a n g e i s ca lcu la ted to be z a r o .

hcmax - ( A ~ C > / 2 h D = ( C - B - g o ) / 2

h G - ( C - G ) / 2

h T = (2C-B-G) /4

j = 0 .550 ( g Q / t ) » 'B 1 /g o

K = A./B

k = 2 [ ( K 2 + 1 ) / ( K 2 - 1 ) + 0 . 3 ] / ( B ^ / g Q )

I = e f f e c t i v e b o l t l e n g t h = 2 t + ( 1 / 2 ) nominal b o l t diameter f o r each threaded end

M^ = moment a c t i n g on end of hub, p ipe or s h e l l a t i t s j u n c t u r e w i t h back

face of f l ange r i n g

4

Np - V d + H T h T + HGhG = M J J + Qt /2

N = number of b o l t s

p = pressure

- a l lowable pressure us l i m i t e d by b o l t s t r e s s

P^ = a l lowab le pressure as l i m i t e d by f l ange or cover s t ress

PlOO = ra ted pressure a t 10Q F .

Q shear f o r c e between f l a n g e r i n g and end of hub, p i p e , or s h e l l

r_ = b o l t - h o l e f l e x i b i l i t y f a c t o r

r = E^/E^ ( taken as u n i t y here in )

r g = 1 - S i / o b (Code: 1 - S ± / S b )

S^ = a l lowable b o l t s t ress a t design temperature

S^ = a l lowab le f l a n g e s t r e s s a t design temperature

S^ = i n i t i a l b o l t s t r e s s ( b o l t p r e s t r e s s )

S' = i n i t i a l b o l t s t r e s s such t h a t h = ( A - C ) / 2 and E6 = 0 , fo r i d e n t i c a l p a i r j o i n t s X C A

= i n i t i a l b o l t s t r e s s f o r t a n g e n t i a l contact at d i a . A, f o r f l ange /cover j o i n t s

t = f l ange r i n g thickness

t = cover th ickness c Z = f l ange face a x i a l separa t ion a t bore

0 = (C + B 1 ) / 2 B 1 9 = f l ange or cover r o t a t i o n

= r o t a t i o n a t ou ts ide d iameter , A

0g = Rota t ion a t b o r e , B

v = Poisson's r a t i o ( taken as 0 . 3 h e r e i n )

o^h = ca lcu la ted b o l t s t r e s s , Par t A r u l e s

o^ = operat ing b o l t s t ress

o c - c o n t r o l l i n g f l a n g e s t ress o o o, , o „ , o „ = f l ange s t resses , see F igure 3 r o , to , n rc. rfl a , a , a , a , a = cover s t resses , see F igure 8

tan

5

IDENTICAL PAIR OF FLANGES

Rules for analysis of an identical, pair of flanges are given in the Code, Appendix II, Part B. The type of bolted-flanged joint under con-sideration is shown in Figure 1. A significant portion of the text of the Code rules is included herein as Table 1. The rules given in UA-57 and UA-58 are difficult to understand and follow. The reasons for this are discussed in the following, where we identify Code equations with a prefix "C".

First, we note that S. is defined in UA-47 as "Allowable bolt stress (4) at design temperature". According to Waters ? theoretically, this is not

the correct quantity for use in Equation (C13) or in the definition of r in s UA-47. We will define the quantity o^ as the "operating bolt stress", and use it in place of S^ in Equation (C13) and in the definition of rg; which is in accordance with the basic theory behind the Code rules. The intent of the Code in using S, for a, will be discussed later herein. h b

Second, we note that Equation (C-13) in Table 1 contains four "unknowns", h , S.(in r = 1-S./a,),a, and M . The Code states that M can c' i s i b b s s be neglected in Equations (C13) and (C14), but this doesn't help very much because these equations still contain four unknowns: h^, S^, ff^, and There are at least two unknowns in each of Equations (C13) through (C28), except Equations (C21) through (C24).

After some study, the Code user will find that there is an explicit solution in the Code rules provided that he

(a) Starts with Equation (C27) and works backwards through the equations given in the Code, and

(b) Assumes a value of h or E0.. If he assumes h < (A-C)/2 C A C

then E6A =0. If he assumes > 0, then hc = (A-C)/2.

The details of this explicit solution are given later herein. At this point, it is pertinent to note that the basic theory is

applicable to a pair of identical flanges of given dimensions and material properties (v and E), loaded with

(a) Internal pressure, p, and (b) An initial bolt stress, S .

.N-bolt holes, Diam. D

J=L

B C

O-ring groove and gasket

FIGURE 1. CONFIGURATION OF IDENTICAL PAIR FLANGED JOINT

7

TABLE 1: PART B RULES, FROM CODE(1\ SHEET 1 OF 4

PART B—FLAT FACE FLANGES WITH METAL-TO-METAL CONTACT OUTSIDE

THE BOLT CIRCLE The rules in Part B apply specifically to bolted

flanged connections where the flanges are flat faced and bolted together directly or separated by a metal spacer such that there is metal-to-metal contact. It is assumed that a self-sealing gasket is used approxi-mately in-line with the wall of attached pipe or vessel. The rules provide for hydrostatic end loads only and assume that the gasket seating loads are small and may in most cases be neglected. It is also assumed that the seal generates a negligible axial load under operating conditions. If such is not the case, allow-ance shall be made for a gasket load Ha, dependent on the size and configuration of the seal and design pressure.

Proper allowance shall be made if connections are subject to external forces other than external pres-sure, and if gasket seatingrequirements are significant.

The flange design methods outlined in UA-57 through UA-59 are applicable to circular flanges under internal pressure, and designed to operate in identical pairs. As with flanges with ring type gas-kets, the stress in the bolts may vary appreciably with pressure. There is an additional stress increase due to a prying effect; that is, each bolt acts as a fulcrum with hc as the lever arm. As a result, fatigue of the bolts and other parts comprising the flanged connection may require consideration (sec UG-22) and controlled prctensioning of the bolts may be necessary. It is important to note that the operating bolt stress is relatively insensitive to change in pre-tightening stress up to a certain point. Thereafter, the two stresses arc essentially the same.

The formula for the calculated strain length I of the bolts is generally applicable. However, variations in the thickness of material actually clamped by each bolt, such as sleeves, collars, or multiple washers placed between a flange arid the bolt heads or nuts, or by countcrboring, must be considered in fixing a value for I for use in the design formulas. A large iricreasc in I may cause undesirable flexibility in the entire flange assembly and, as a result, the stresses may be under or overestimated.

UA-57 Bolt Loads (a) Flange Thickness. The following approximate

formula may be used for obtaining the necessary flange thickness to resist bending at the bolt circle. It is based on a loading due to hydrostatic end force only, with no compensation of a moment, either fa-vorable or unfavorable, due to continuity with a hub or shell; allowance is made for removal of metal at the bolt holes, equivalent to 40 percent of the total bolt circle circumference.

(b) Required Bolt Load. The flange bolt load used in calculating the required cross-sectional area of bolts shall be determined as follows:

(1) The required bolt load for the operating condition, W,„„ shall be sufficient to resist the sum of the hydrostatic end force, H, exerted by the maximum allowable working pressure on the area bounded by the diameter of the gasket reaction, and the contact force H c exerted by the mating flange on the annular area where the flange faces are in contact. To this shall be added the gasket load H„ for those de-signs where gasket seating requirements arc significant.

(2) Before the contact force Hc can be deter-mined, it is necessary to obtain a value for its mo-ment arm hc. Due to the interrelation between bolt elongation and flange defection, h c involves the flange thickness, t, operating bolt stress Sb, initial bolt pre-stress factor ra and calculated strain length I, elasticity factor rE, and total moment loading on the flange Mp+Ms- The relation between these quanti-ties is expressed by Formula (13) , provided that the resulting solution for hc is not greater than ( A - C ) / 2, in which case dA, the slope of the flange face at its

8

TABLE 1: (CONTINUED), SHEET 2 OF 4

outside diameter, equals zero. Note that the moment arms for MP are given in Table UA-50.

he = 0.929 y j i at*lrErsSbBx

Mp + Ms (13)

If the value of h c calculated by Formula (13) exceeds (A — C)/2, the actual value of ho is to be taken as hcttmx = (A—C)/2, and the face of the flange then has a slope at its outside diameter equal to 9a radians, as expressed by Formula (14) .

E 0 A = r J p M - 0 . 2 9 0 ^ (14) A — C BfQt For loose type and optional type flanges without hubs, the moment Ms in Formulas (13) and (14) equals zero. For all other flanges, Ms in these two formulas may be neglected, provided that a final check calculation is made to establish the adequacy of the bolting and flange stresses. For calculation of Mh, see UA-58.

(3) The contact force Hc is determined by For-mula (15a) for loose type and optional type calcu-lated as loose type flanges without hubs, and by Formula (15b) for all integral type flanges, and hubbed flanges of the loose or optional type where advantage may be taken of significant interaction between flange and hub.

(15a) (15b)

(4) The required bolt load for operating con-ditions is determined in accordance with Formula (16).

W,„=H+HC+H0 (16) (c) Total Required and Actual Bolt Areas, and

Flange Design Bolt Load. The total required cross-sectional area of bolts, A„„ equals Wmt/Sb. A selec-tion of bolts to be used shall be made such that the actual total cross-sectional area of bolts A t , will not be less than A,„. The flange design bolt load W shall be taken equal to WM1.

UA-58 Flange-Hub Moments, Shear, Dcflcction and Slope of Flange Face

(a) For loose type and optional type calculated as loose type flanges, without hubs, the interaction moment Ms, hub moment M„, and shear Q are as-sumed to be nonexistent. The slope and deflection at the flange i.d. are computed by Formulas (27) and (28) .

Hc=Mr/hc Hc=(MP+MB)/hc

(b) For all flanges with hubs, including flanges integral with or welded to pipe or shell as in Fig, UA-57(3) , (4 ) , (4a), (5 ) , (5a), or (5b); the inter-action moment MH, hub moment Mu, shear Q, slope at flange-hub junction 0tl, and internal pressure P arc interrelated in accordance with these formulas:

M „ = - ( j - y J ,EOj , t>+J ,Pty( fy (17)

Q=-(j-)SJ>E0Bp+Jtpr/(fy (18)

MB=M„ + Qt/2 (19)

E{8»-0A)V=JM>,+hMf, (20)

If the flange contact distance h c is less than ht mai, 9A=0. Otherwise, there is an additional relation between M« and 0* given by Formula (14) . How-ever, a good approximation for OA may be obtained by using Formula (14) with Ms assumed equal to zero.

The symbols / , , / 3 , , . , h represent the dimen-sional characteristics of flange and hub, and contain the ratio factors / and k for all types of hub, with Ci, c.„ Cj, etc. for tapered hubs and hubs of loose type flanges. See UA-47 for j and k, also Fig. UA-58 for j, k, and applicable c factors.

A = 0 . 9 5 1 C { £ ^ + C , / ] (21 ,

, ^ = 5 A 9 i , [ £ ! l T S r + l A 0 0 C i ] ( 2 2 )

U 9 0 1 i u t M ( 2 3 )

/ — 1 fi -iQC'i*(C4~~k) 7 , - 1 0 . 3 8 l + g J k (24)

/ . « / . - 1 . 7 3 8 ^ - (26)

(c) Allocation of c factors. For loose type flanges with constant thickness hubs, sec Fig. UA-58(3) for c„ c„ and c3. h and 3, equal zero.

For loose type flanges with tapered hubs, sec Fig. UA-58(9) , (10 ) , and (11) for c„ cu and c,. J* and /< equal zero.

For integral flanges with constant thickness hubs, c,, c2, and c 3 = l , c 1 =0.85, c 6 = 0 .

For integral flanges with tapered hubs, see Fig. UA-58(4) , (5 ) , (6 ) , ( 7 ) , and (8) for c„ c„ ca, c„ and cs.

(d) The slope of the flange face at its inside diani-

9

TABLE 1: (CONTINUED), SHEET 2 OF 4

cter is given by Formula (27), derived from the preceding formulas (17), (13), (19), and (20). This formula is applicable to .ill types of flange, with or without hubs.

E0„ = 7 — « (27) 1 + / » ( / , + Vi Ja)

The value of EQ„ as found from Formula (27), is substituted in Formulas (17), (18), and (20) to obtain the values of hub moment Mu, shear Q, and interaction moment Ms-

For loose type flanges without hubs or with hubs for which credit is not taken for their reinforcing value, the factors / „ J„ h, and / , equal zero In all

preceding formulas. For loose type flanges with hubs for which credit is taken, but internal pressure has no barreling effect, the factors 7, and /« are taken as equal to zero.

(e) The axial separation of two identical mating flanges at their inside diameter is given by Formula (28), and applies to all types of flanges.

1 2 ( 1 - ^ ) z= rCEt3 O'C + M2 - ho(^hc +

+*Chur0 J + =

+ 2 ( / I c + M < > a (28)

10

TABLE 1 (CONTINUED), SHEET 4 OF 4

UA-59 Calculation of Flange Stresses

(a) Before calculating the flange stresses, the as-sumed operating and initial bolt stresses shall be verified or corrected to the actual design values by means of Figs. UA-59.1 or UA-59.2. In using this figure, proceed as follows:

(}) Compute the value of x2 and mark it on the vertical scale.

(2) Compute the value of ? . / i c / ( " - B , ) or 2hCmtx/(C—Bl), as may be applicable, and mark it on the curve.

( j ) With a straightedge on these two points, mark the value of where the straightedge cuts the horizontal scale.

(4) From this value of *„ compute the design value of the initial bolt stress.

NOTE: If Ma = 0 and A, is not significantly greater than Am, the foregoing procedure may be omitted,

(b) The flange stresses shall be determined in accordance with the following formulas:

(]) For loose type ring flanges (including op-tional type calculated as loose type) having a rectan-gular cross section:

® u (29) t2 ( 3 . 1 4 C - n D )

5 « = 0 at inside diameter

at bolt circle

(30)

*ST= ± 5A6Mi

Bt2

E9At M S M & H

+ — - (see Fig. UA-59.3 ) (31)

(2) For loose type flanges with hubs (including optional type calculated as loose type); the hubs considered as reinforcement (see Fig. UA-57 (4a), (5) , (5a),and (5b): Radial, at bolt circle

e _ 6(Mp+Ma) S"-* r-(rC-nD) ( 3 2 )

Radial, in flange adjacent to hub 6Ma • c = J 2

* wBtt - 7rBxt* Circumferential, in flange adjacent to hub

_ QZ , (EtQ„ 1.8 Af , \

Longitudinal, in hub adjacent to flange

6Mu ; / i= i -

(33)

(34)

(35)

Circumferential, in hub adjacent to flange EtO„ t I AM,, (36)

*B,t T B, ±nB,g," (3) For flanges integral with pipe, shell or

tapered hub (sec Fig. UA-57(4)):

Radial, at bolt circle

Sn-~6 (M,.+Ma) t'inC-nD)

Radial, in flange adjacent to hub

Circumferential, in flange adjacent to hub

Longitudinal, in hub adjacent to flange *o _ P B l , 6 Mn ^"Tf^lSS?

Circumferential, in hub adjacent to flange

+ 0.075 81 irBtgf

Longitudinal, at small end of tapered hub Sut= (In preparation)

Circumferential, at small end of tapered hub Sm = (In preparation)

(37)

(38)

(39)

(40)

(41)

(42)

(43)

* Use -f- sign for contact face of flange or inside of hub, — sign for back face of flange or outside of hub.

(c) The flange stresses calculated by the formulas in UA-59 (b) shall not exceed the following values:

(1) Longitudinal hub-stress Su not greater than S, for cast iron 1 and except as otherwise limited by ( l ) ( a ) and ( l ) ( b ) , not greater than 1.5 St for mate-rials other than cast iron.

(a) Longitudinal hub-stress Su not greater than the smaller of 1.5 Sf or 1.5 S„ for optional type flanges designed as integral (Fig. UA-57 (4a), (5 ) , (5a) , and (5b), also integral type (Fig. UA-57 (4)) where the neck material constitutes the hub of the flange.

(b) Longitudinal hub-stress not greater than the smaller of 1.5 Sf or 2.5 S„ for integral type flanges with hub welded to the neck, pipe or vessel wall.

(2). Radial flange stress Su not greater than St. (3) Tangential flange stress ST not greater than

Sr.

(4) A l s o , n o t g r e a t e r than .9/and S " + S r

not greater than 5/.

1 When the flange material is cast iron, particular care should be taken when tightening the bolts to avoid excessive slress that may break the flange; an attempt should be made to apply no greater wrenching effort than is needed to assure tightness in Ihe hydrostatic test.

11

The p ressure , p , shows up e x p l i c i t l y i n the Code e q u a t i o n The other load

which the Code user can s p e c i f y f o r f i e l d i n s t a l l a t i o n 1 x n i t i a l b o l t

s t r e s s , S^. When the user assumes a v a l u e o f h c or E0 A , he i s i m p l i c i t l y

assuming some unknown v a l u e of S^. However, i t i s not p r a c t i c a l to s p e c i f y

h o r E0 f o r c o n t r o l o f f i e l d i n s t a l l a t i o n . A c c o r d i n g l y , the Code user C A

e v e n t u a l l y must convert h or E0A to a v a l u e of S^ which w i l l y i e l d the

v a l u e assumed o r i g i n a l l y f o r h c or E8^. I t would seem more u s e f u l i f

the Code equat ions were mod i f i ed so t h a t the Code user would assume

( s p e c i f y ) a va lue of S^.

As i n t i m a t e d above, the r u l e s must be d i v i d e d i n t o two regimes

of a p p l i c a b i l i t y , ( 1 ) where h = ( A - C ) / 2 , 0 > 0 , and (2) where h c 0 , h = ( A - C ) / 2

We w i l l consider as an independent v a r i a b l e and f i n d E6g, M g ,

S i and as func t ions of EG^. Equat ion (C27) g ives

£ 6 b = A x + A 2 E 9 A , ( 1 )

where

J 5 ( J 2 + J A / 2 ) p / ( g 0 / t ) + J 6 M p / t 3

1 1 + J 5 ( J l + J 3 / 2 ) ( g { j / t ) 2

l_ 2 1 + J 5 ( J L + J 3 / 2 ) ( g o / r ) 2

12

The va lues of A^ and A2 are known q u a n t i t i e s ; i n p a r t i c u l a r , J,. and Jg are

known because h c i s known to equal ( A - C ) / 2 ,

Equat ion (1 ) can be s u b s t i t u t e d i n Equation (C20) to g i v e :

( A 1 + A 2 E 9 A - E 6 A ) t = J5Mg + J6Mp _ (2)

Solving Equat ion (2 ) f o r M : s

M = A , + A.E6. , s 3 4 A ' (3 )

where

A 3 = J

A, t - J ,M 1 6 p

( A , - l ) t -A 4 = — J — ~

Equation (016) g i v e s :

W . , f M + M I

s M h c G (4 )

Using Equat ion ( 3 ) to d e f i n e M as a f u n c t i o n of E 6 . , Equat ion (4 ) can be 8 A

w r i t t e n as

a b - A 5 + A 6 E 6 A ( 5 )

where

A os 5 *b t [ " + 3 t

+ A. h + ^G

13

Equation (C14) , using Equations (3) and (5 ) to de f ine M and a, as funct ions S D of E6„, becomes A

r_,(A + A,E6. - S . ) £ 0 .29(A-C)(M^ + A_ + A ,E0 . ) r?a _ a 3 O A x E -J H A

B l . t 3 ' W >

Equation (6) can be w r i t t e n i n the form

S± = A? + A8E6A , (7)

where 0.29 x 4 . x h 2

A = A £ - ( M + A ) ' * B . a t r I P J

1 E

2h 0 .29 x 4 x h 2 » _ A — — A

8 6 ~ r 2. ~ _ 3 . x A 4 r B , a t r i 1 E

Equations ( 1 ) , ( 3 ) , ( 5 ) , and (7) e s t a b l i s h values of E6_, M , a. , U S D

and S i f o r use i n Equations (C17) , (C18) , (C28) and (C37) through (C41) .

Using S^ = 0 as the lower l i m i t on S^ leads , by Equation ( 7 ) , to the upper

bound l i m i t on E0. of A

E0A = - A ? / A 8 ; ( a t S± = 0 ) . (8 )

The lower bound l i m i t on E6. i s 0 .

The other independent parameter which we wish to use i s the i n t e r -

n a l pressure, p . I f H^ i s assumed to be zero (e las tomet r ic 0 - r i n g gasket)

then Mp i s p ropor t iona l t o p and A^, A^, A^, and A^ are also p ropor t iona l to p.

Accordingly, Equations ( 1 ) , ( 3 ) , ( 5 ) , and (7) can be w r i t t e n i n the form

1 4

(9)

(10)

(11)

(12)

where

A^ = A^p, A^ = A^/p, etc.

The constants A^, k^ •••• Ag depend only upon the dimensions of the flanged joint and the material properties. Accordingly, Equations (9) through (12) give a set of linear relations'-ips between the independent variables E6

Pi and p and the dependent variables E9„, M , a, , and S.. Therefore, it becomes o S D 1 very simple to use S^ rather than E9A as the independent variable, i.e., from Equation (12)

E9b - Ajp + A2E9a

M s . A J P + A 4 E 8 a

a b = A ; P + A 6 E 9 a

E0a - ( S r A7p)/Ag . (13)

By using E6a from Equation (13) for E6A in Equations (9), (10), and (11) , we

obtain a set of equations with independent variables S^ and p and dependent

variables E8_, M , a, , and E0.. D S D A Using Equations (9) through (12), the stresses by Fquations (C37)

through (C41) can be written in the form

o. - C P + D E0A ; j = 1,2, . . . 10 . (14)

15

where

°j = any one of the 10 flange stresses Cj and D̂. arc constants that depend only on the flanged joint dimensions and material property, v.

The independent variable ES^ can be changed to S^ by use of Equation (13). To obtain the allowable pressure, P , permitted for a specific max

flanged joint, the stress limits given in the Code must be met. These are

V S T * Sf

(15)

(16)

SH1' SH2» SH3' SH4 - 1 , 5 Sf ( 1 7 )

(SH1 + SR ) / 2' (SH1 + ST ) / 2 - Sf»

16

(20)

(21)

(22)

However, A ' , A i , A ! , and A' are now funct ions of h because J_ and J , are 1 J 5 7 c 5 o funct ions of h^. The dependent v a r i a b l e s and a l l s t resses are s t i l l propor -

t i o n a l to the i n t e r n a l p ressure , p.

The constants A^, A^, and A^, however, a re not l i n e a r func t ions

of h . Note , f o r example, i n the d e f i n i t i o n of A7 under Equation (7) tha t there i s an h - term. Indeed, A7 turns out to be a f i f t h order polynominal c / i n h^ and S^. A r e l a t i v e l y e f f i c i e n t way to handle t h i s , which i s incorporated

i n the computer program FLGB ( l i s t e d i n Appendix B ) , i s to s t a r t w i t h h £ =

(A -C ) /2 and decrease i t i n steps u n t i l the computed va lue of S^ matches the

input v a l u e of S^; t h i s r e q u i r e s a smal l f r a c t i o n of a second of computer

t ime. Having obtained the va lue of h c which corresponds to the input va lue

of S^, the remaining a n a l y s i s uses Equations (19) through (21) f o r E0g, M g ,

and 0, ; and Equat ion (14) w i t h E9. = 0 f o r the s t resses .

2

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STRAIGHT HUB FL.-.NGE BOLTED TO A FLAT COVER

The type of bolted-flanged joint under consideration is shown in C3)

Figure 2. The basic theory is given by Waters and Schneider- ; a copy of which is included herein as Appendix A. Nomenclature in this portion of the report is that used by Waters and Schneider . The solution to the analysis is given in the form of three equations which must be solved simultaneously for the unknowns Mi» M2, and Q. The pressure load is explicitly included in the equations. The initial bolt stress is implicitly contained in the assumed value for b or 03f.

The three equations to be solved for M^, M̂ ,, and Q are

8 . + 0 ' + 8 . lc c 3c 3 ( l - v ) R

m

E t 3 c c (FR - 4M,) m 1 (23)

0.. ^ + 0 ; + if f 3f 2R2 g2 4R2 B3

- f i r ( Q ) - - f i r

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'N- bolt holes, Diam. D

_CL

- G

- B - C

- h

O-ring groove and gasket

\

FIGURE 2. CONFIGURATION OF FLANGE/COVER FLANGED JOINT

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The above relationships introduce other quantities which can be expressed in terms of the unknowns by other equations from Ref. (3):

Equation in Ouantitv Reference (3)

Mlb (5)

Mlu (7)

H2b (6)

M2U (4) and (7)

Using the relationships indicated above, Equations (23), (24), and (25) reduce to a set of equations in the unknowns M^, and Q and the selected independent variable (which is indirectly the initial bolt load parameter) b or The user may assume that the independent variable is:

(1) 9, > 0 for b = b : or v ' 3f max (2) 6,, = 0 for b < b o . ^ ' 3f max

The value of b is involved through its use in Equations (9) and (14) of Reference (3). Subsequently, the initial bolt stress, Ŝ ,, required to satisfy the value assumed for the independent variable b or 0 ^ is calcu-lated from an equation which expresses equality between bolt elongation and separation of the flanges at the bolt circle.

Having obtained Mj, ll̂ , and Q, the values of bolt stresses and flange stresses are obtained from Equations (35) through (48) of Reference (3). The values of other "unknowns" used in these Equations are obtained as follows:

Equation in Unknown Reference (3)

M l b (5) (Note that SMĵ = M ^

^ b

Mlu

^ u

6 63f " °> b < bmax

20

6 (27) 0 „ > 0, b = b 3£ max B (30) 6--. = 0, b < b v ' 3f ' max B < 3 1 ) 63f > 0, b = b max

The loading parameters b or 0gf are not readily "controllable" in field installation, hence, it would be desirable to use the intial bolt stress S^ as the independent variable along with the pressure. The relation-ship between S^ and b or 0 ^ is given by Reference (3) Equations (29) and either (25), for b < b , or by (27), for 0,- > 0. For 0,, > 0, it is mEX j t j r possible to express the solution as a linear set of three equations with unknowns M^, l^, and Q, and with Ŝ . as the independent variable. However, for 0 ^ ~ 0 (and b < h m a x) use of S^ instead of b as the independent variable leads to a set of three nonlinear equations.

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APPLICATION EXAMPLES

The purpose of this part of the report is to give the reader an indication of the characteristics of Part B flanged joints by means of specific examples. It is deemed informative to select, as examples, flanges which are designed for use as Part A flange joints. These flanges will have a certain pressure rating according to the Part A Code rules. The reader can then see how the pressure rating is changed when the same flanges are used except with full-face contact and an 0-ring gasket.

Flanged Joints Selected for Examples

The particular flanges selected for examples are taken from API Standard 605, "Large-Diameter Carbon Steel Flanges". This standard covers 26 inc.h to 60 inch sizes with nominal pressure ratings (class) of 75 , 150 and 300 pounds. We have selected the smallest (26 inch) and largest (60 inch) of each class to serve as examples herein, a total of six flanges. The dimensions of the flanges are shown in Table 2.

Three sets of calculations were made..

(1) Straight-hub flange using Part A Code rules (gasket inside the bolt holes) with an asbestos gasket; gasket factors m = 2.75, y = 3700.

(2) Identical pair of flanges as shown in Figure 1, using Part B rules. An elastometric 0-ring gasket was assumed, giving H_ = 0. The gasket (j diameter G used in these calculations

was the same as shown in Table 2. (3) Straight-hub flange bolted to a cover as shown in Figure 2. Calculations

were based on the theory as given in Reference (3). An elastomeric 0-ring gasket was assumed, giving Ĥ , = 0. As in Reference (3), the gasket was assumed to be in line with the shell wall, hence G = 2R . ' m

Calculations were made for pressures equal to the API-605 rated pressures at 100 F for the three classes noted below:

100 F Rated Class Pressure, psi

75 140 150 275 300 720

TABLE 2: DIMENSIONS OF API-605 FLANGES USED IN APPLICATION EXAMPLES

Class

Nom. Size,

D , in. o A, in. B, in. (1)

g , in-t, in.

t , in. h ) C, in. N v i n - 2

G, in. (4)

Bolt Diam. in.

(5)

75 26 30.000 25.5 .562 1.312 1.192 28.5 36 7.272 27.138 5/8 60 66.000 59.5 .812 2.188 2.672 63.875 44 24.244 61.750 1

150 26 30.938 25.5 .719 1.625 1.719 29.312 36 10.872 27.339 3/4 60 67.938 59.057 1.378 3.000 3.837 65.438 52 48.308 62.171 1-1/4

300 26 34.125 24.930 1.348 3.500 3.000 31.625 32 29.728 28.171 1-1/4 60 73.938 57.531 2.703 5.938 6.587 69.438 40 136.920 63.910 2-1/4

(1) B = D q - 2 tg, where T = P 1 Q 0 D q / ( I . 7 5 X 20,000), P1()0 = rated pressure at 100 F; tg >_ 0.25". (2) gQ = (X - B)/2, where X = diameter of hub at base. (3) t = C v 0.25 P..«.720,000 , see ASME Code Section VIII, Division 1, par. UG-34.

C 1UU (4) G - effective gasket diameter by Part A rules for a gasket with O.D. = API-605 R-dimension

(O.D. of raised face) and with I.D. = Dq + 0.25". (5) Bolt hole diameters are 1/8" larger than bolt diameters.

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Allowable stresses were .issumcd to be* the same chose cited in API-605, i.e., Sb» 25,000 psi for the bolt material and Sf» 20,000 psi for the flange material.

Stresses and Allowable Pressures by Part A Rules

Table 3 shows the t:;i lcul.uctl stresses ;ind allowable pressures for the flanges with raised faces, i.e., Code Part A calculations.

Locations of the calculated scresst's arc shown in Figure 3. !*«rt A rules define a "controlling stress", as shown in footnote (2) of Table 3. The allowable pressure, P p as controlled by flange stresses, is Sf/°c* We are using SF » 20,000 psi and, since o was calculated for a rated pressure at 100 F of PJQQ, and c c is proportional to p, the value of Pf is {20,000/^1 x pi00"

Hie allowable pressure, P^, as controlled by bolt strength, is W c a r e u 8* n® ®b ™ 2S»QOO P8* an

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TABLE 3: PART A RULES, STRESSES (PSI) for p= P 1 0 Q AND ALLOWABLE PRESSURES (PSI) FOR API-605 FLANGES

°rB

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Stresses are shown on "Out" surfaces.

Code Part B Equation

Ref. (3) Equation

Symbol

37 4 2 °>C

3 8 4 0 °"r B

39 4 1 °"tB

40 3 7 °h

FIGURE 3. LOCATIONS AND DIRECTIONS OF FLANGE STRESSES, PART A AND PART B RULES (IDENTICAL PAIR) AND STRAIGHT-HUB FLANGE OF FLANGE/COVER FLANGED JOINT

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FIGURE 4. OPERATING BOLT STRESS, ab AS A FUNCTION OF INITIAL BOLT STRESS, Si (IDENTICAL PAIR, p = P 1 0 Q)

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as S4. Values of S^ are shown ln Table 4. For S^ < Sj, ob Is a linear function of S^. For S^ > S^, ob is almost a linear function of S.̂ and is slightly larger than S^. In Figure 4, for S^ > S^, the difference between S^ and cannot be seen with the scales used.

The variation of a, and a _ for the 26 inch - 150 class joint are h r e shown in Figure 5. Stresses for all six joints are shown in Table 5. It can be seen in Table 5 that Figure 5 is typical for all of the six joints. The value of o, goes down with increasing S, j all other stresses increase with increasing S^. Stresses are linear with S.̂ up to S^. Above S^, the flange stresses are nonlinear with S ^ but change only slightly with increase in S ^

The face separation at the flange bore (Z) is also shown in Figure 5. Values of Z at S i = 0 and Ŝ ^ = S^ are shown in Table 4. The face separation decreases by an order of magnitude as S^ is increased from zero to S^. Above S^, the separation decreases very slightly with increasing S^.

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TABLE 4: PART B RULES, VALUES OF Sj , ob> H/A^ AND Z, FOR p - P i n n > IDENTICAL PAIR AS SHOWN IN FIGURE 1

Class Size

>

Si

psi Cl)

ob (psi) for S ± (psi) s

H

Z (Mils) for Sĵ (psi) =

Class Size

>

Si

psi Cl) 0 °b H/Ab 25000

ab H/Afa

H 0 (2)

i Si (2)

75 26 29160 18620 1.67 27920 2.51 11130 5.41 0.48 60 48180 30980 1.79 40050 2.32 17290 15.05 0.76

150 26 42510 24310 1,64 35230 2.37 14850 9.56 0.94 60 52120 27070 1.57 39230 2.27 17280 19.78 1.47

300 26 46790 17920 1.06 33440 2.21 15100 15.35 1.29 60 49710 22290 1.32 36220 2.15 16870 31.91 3.09

(1) S ± = initial bolt stress at which hc = (A-C)/2 and E 8 A » 0 , p = P (2) Z = separation between flange faces at bore. E = 30,000,000 psi.

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22 - = flonge stress, outside surfoce of hub

= flange stress, radial, at bolt circle

= face separation at bore

FIGURE 5. FLANGE STRESSES, ah AND a r C AND FACE SEPARATION OF BORE, Z, AS A FUNCTION OF INITIAL BOLT STRESS, S± (IDENTICAL PAIR, 26" - 150 CLASS, p = P...)

30

TABLE 5: PART B RULES, STRESSES (PSI) FOR p = p FOR API-605

FLANGED JOINTS, IDENTICAL PAIR AS SHOWN IN FIGURE 1

Class Size Si

Radial Tangential^ Hub (1 )

Class Size Si

Eq. 37

arC

Eq. 38 Out °rB

Eq. 38 In

°rB

Eq. 39 Out °tB

Eq. 39 In

°tB

Eq. 40 Out ah

Eq. 40 In ah

75 26 0 2280 2430 - 2 3 8 0 2590 - 2 9 7 0 11990 - 8 7 5 0 25000 5100 100 - 4 0 0 1720 400 3110 130

60 0 2930 2590 - 2 5 6 0 3450 - 3 8 5 0 17830 - 1 2 6 4 0 25000 4860 930 - 1 1 2 0 2910 - 7 5 0 9110 - 3 9 2 0

150 26 0 3140 4600 - 4 4 4 0 4580 - 5 5 0 0 20230 - 1 5 2 2 0 25000 6750 1700 - 2 0 2 0 3420 - 1 5 0 0 10220 - 5 2 0 0

60 0 2940 5290 - 5 1 6 0 4810 - 6 0 0 0 22880 - 1 6 8 5 0 25000 6590 2520 - 2 7 7 0 4100 - 1 9 7 0 13420 - 7 3 9 0

300 26 0 930 6480 - 6 3 5 0 9110 - 9 6 0 0 30940 - 2 3 9 2 0 25000 6040 2610 - 3 3 7 0 6460 - 3 4 8 0 16840 - 9 8 2 0

60 0 2310 8000 - 7 9 0 0 8710 - 9 1 9 0 31260 - 2 3 2 4 0 25000 8240 3740 - 4 4 5 0 6830 - 3 3 1 0 18490 - 1 0 4 7 0

(1) See Figure 3 for locations and directions of stresses. Stresses are also identified in this table by Code equation numbers; see Table 1.

31

Flange/Cover Joint. Reference (3) Theory

Figure 6 shows the variation of a^ as a function of S^. The variation of a, with S. is similar to that for the identical pairs (Figure 4) b i i.e., linear up to S^ and essentially o^ = S^ for Sj > S^. Values of S^ are shown in Table 6. By comparing Table 4 with Table 6, it can be seen that S^ is much higher for the flange/cover joint.

The variation of a, and a - for the 26-inch-150 class joint are h re shown in Figure 7, along with the stresses for an identical pair. It can be seen that stress o^ has changed sign for the flange/cover joint as S^ is increased from zero to 40,000 psi. This indicates that, at high values of Si> the flange is forced to rotate with the cover and the cover bends the flange over backward. Values of the rotation at the bore of the flange (^Q) are shown in Table 6, indicating this effect in terms of rotations.

Stresses in the flanges of flange/cover joints are shown in Table 7. Because of the "reversing effect", in some joints, the maximum stress in the flange occurs at high initial bolt stresses, e.g.; the 26-inch-75 class.

Locations and directions of stresses in the cover are shown in Figure 8. Stresses in the covers of flange/cover joints are shown in Table 8 and the values of o ^ and a for the 26-inch-150 class are plotted in Figure 9. The stress at the center of the cover is usually the maximum stress in the cover for S^ up to 40,000 psi; however, in the 26-inch-300 class a r C is the highest. The value of crrt is relatively insensitive to changes in S^.

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S-,, ksi

FIGURE 6. OPERATING BOLT STRESS, Cfb, AS A FUNCTION OF INITIAL BOLT STRESS, Si, FLANGE/COVER, p = P n

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TABLE 6: FLANGE/COVER JOINT, VALUES OF S^ , ab> H/A^ AND 0„n, FOR p = JOINT AS SHOWN IN FIGURE 2

Class Size

o b (psi) for Si (psi) = e20^10 3 r a d'^ f o r Si

psi _ % _ 0 Si (1) 0 H/Ajj 25000 H ^ Afa (2) (2)

75 26 48510 33070 3.36 41420 4.21 9830 0.16 -1.51 60 81800 46040 2.57 57110 3.56 16060 1.36 -3.46

150 26 60860 33860 2.62 45190 3.50 12920 1.40 -0.98 60 82320 37050 2.33 50920 3.27 15590 2.24 -1.68

300 26 53140 21660 1.83 36620 3.10 11820 1.52 -0.09 60 61800 25440 1.86 40290 2.95 13670 2.08 -0.28

initial bolt stress at which tangential contact occurs at diameter A

rotation of flange ring at bore, E = 30,000,000 psi.

(1) S± = (2) e 2 0 =

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S j , ks i

FIGURE 7. FLANGE STRESSES, Oh AND O r C, IN STRAIGHT HUB FLANGE AS A FUNCTION OF INITIAL BOLT STRESS, Si, FLANGE/COVER,

35

TABLE 7: FLANGE/COVER JOINT, STRESSES (PSI)FOR p - P 1 0 Q IN STRAIGHT-FLANGE (API-605 FLANGED JOINTS, JOINT AS SHOWN IN FIGURE 2)

Radial Tangential Hub S1, Eq. 42 Eq. 40 Eq. 41 Eq. 41 Eq. 37 Eq. 37

Class worn. Size psi °rC °rB

In °tB

Out CTtB

In °h

Out °h

75 26 0 6840 310 1440 780 2340 830 25000 9380 2290 1650 2450 10450 -7280

60 0 6240 -970 2150 -280 -3640 8770 25000 8600 930 2410 2100 7010 -1880

150 26 0 6700 -3000 2030 -1520 -9490 14370 25000 10460 -150 2220 700 1132 3750

60 0 6230 -4550 1890 -2210 -14360 20250 25000 10400 -1525 2550 260 -3360 9270

300 26 0 3120 -5410 4940 -4660 -19640 26300 25000 7990 -2070 3940 -1250 -6130 12790

60 0 4750 -7790 3910 -4280 -22570 30230 25000 11080 -3480 3890 -970 -8540 16200

(1) See Figure 3 for location and direction of stresses. Stresses are also identified in this table by Ref. (3) equation numbers; see Appendix A.

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'

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TABLE 8: FLANGE/COVER JOINT, STRESSES (PSI) FOR p = P IN COVER FLANGE, API-605 FLANGED JOINTS AS SHOWN IN FIGURE 2

Class Nom. Size

Si psi

Radial (1) Tangential^ Center^

Class Nom. Size

Si psi

Eq. 46 °rC

Eq. 44 arB

Eq. 47 ° t c

Eq. 45 atB

Eq. 48 ° r t

75 26 0 8750 1520 8850 7800 18300 25000 11820 3910 8050 6840 15900

60 0 4510 180 9640 9050 21330 25000 6100 1470 9200 8530 20030

150 26 0 6450 -1410 9570 8510 20140 25000 9810 1120 8750 7500 17620

60 0 4210 -1710 10040 9240 21870 25000 6750 120 9500 8500 20040

300 26 0 4500 -6610 10460 9170 21990 25000 11230 -1760 9000 7230 17140

60 0 436G -4960 10370 9190 21950 25000 9500 -1460 9380 9010 18460

(1) See Figure 8 for location and direction of stresses. Stresses are also • identified in this table by Ref. (3) equation numbers; see Appendix A.

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Sj, ksi

FIGURE 9. STRESSES,arc, AND C r C, IN COVER AS A FUNCTION OF INITIAL BOLT STRESS, Si5 FLANGE/COVER, p = P 1 0 0

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Discussion of Significant Aspects

Hydrostatic End Load Versus Operating Bolt Stress

In looking at Figure 1 or Figure 2, and considering force equilibrium in the axial direction, many analysts might jump to the conclusion that the strength of the bolts is sufficient if the bolt material yield strength is something greater than H/A^ defined as:

JL „ SiIA}£e . ( 2 6 )

In at least one Type B flanged joint in a missile casing with an elastomeric O-ring seal, the assumption that Equation (26) actually represented the stress in the bolts was made. The bolts used in the joint had a very high strength and ultimate strength only slightly higher than the yield strength. The bolt area was designed to withstand the test pressure end load, H, with what was thought to be a comfortable margin on yield strength of the bolt material. The intended test pressure wasn't reached because the bolts snapped off at a lower pressure.

The theory described herein shows the fallacy in assuming that Equation (26) actually represents the total load on the bolts. Table 4 shows examples of ratios of a^/(H/A^) up to 1.79 while Table 6 shows ratios up to 3.36. These are ratios at S^ = 0. Accordingly, even for the limited range of examples covered herein, we find cases where Equation (26) is unconservative by factors of up to 3.36. However, with respect to the API-605 flanged joints, the calculations do not indicate any need for concern about the static (non-fatigue) strength of the bolts; even if such flanges are used with full-face contact with O-ring seals and are used in identical pairs or with covers of thickness as required by Code Section VIII-Division 1, Paragraph UG-34. The reason for this is that API-605 states that "The flange ratings are based on use of ASTM A193, Grade B7, allow steel stud bolts...". This bolt material has a minimum specified yield strength of 105,000 psi. The worst case is the 60"-75 class joint as shown in Figure 4. It can be seen that for any credible

40

value of Si (e.g., St = 45000/v^"= 45000 psi; d = bolt diameter = 1.00" for the 60"-75 class) the value of is well below 105000 psi. While it is true that o^ may greatly exceed the allowable volt stress of 25000 psi given in ASME Code Section VIII-Div. 1, the bolts would not be expected to yield.

Another significant aspect of the value of H/Aĵ is that, if it is not equal to or less than the operating bolt stress a, , the calculation is b not valid. This condition did not arise in any of the examples cited herein, but was encountered when checking identical pairs of ANSI B16.5 flanged joints of the higher pressure classes; specifically the 16"-900 class, 8", and 16" and 24"-1500 class and 4", 8" and 12"-2500 class. The assumptions inherent in the general application of beam theory to describe the flexural behavior of the flanges can lead to a force at A which keeps the edges in contact. Since the force cannot exist, the solution is invalid when a^ < (H/A^), how-ever, the method of analysis is only capable of indicating that such a problem of separation exists when it is the result of a large flange-hub interaction moment. The general problem, however, is associated with low values of S^ and flanges which are stiff with respect to the bolting. The problem of flange separation is touched on in Reference (5).

Conditions at S. = 0 1

An initial bolt stress of zero is significant because in some appli-cations of elastomeric 0-ring joints in flanged joints, the design is motivated by the fact that it is not necessary to tighten the bolts to high stress levels in order to obtain a leak-tight joint. Accordingly, during installation, the nuts on the bolts may be "finger tightened"; corresponding to Ŝ ^ = 0. Further, the user of Code design procedure normally seeks a minimum-cost design which meets the Code rules. In terms of the examples given herein, the user may want to use the flanged joints at the highest possible pressure permitted by the Code rules. This highest possible pressure will depend upon both the strength of the bolts and the strength of the flanges.

With respect to the bolts, Part B Rules require that ab not exceed It is apparent from Figures 4 and 6 that the smallest value of is

obtained for S. = 0. Values of P, , the maximum pressure as limited by the i b bolts, are shown in Table 9.

TABLE 9: MAXIMUM PRESSURES IN PSI FOR S = 25,000 PSI, S = 20,000 PSI

Type A Type B Nom. Identical Pair Flange Cover

Class (1)

Size Si' psi Pb Pf >„(2) Ff V2) Flange Pf Cover Pf

75 26 0 252 241 188 350 106 409 153 (140) 25000 252 241 118 454 70.5 357 171

60 0 179 152 113 236 76.0 373 131 25000 179 152 71.2 304 42.4 396 140

150 26 0 366 311 283 408 203 574 273 (275) 25000 366 311 159 545 111 612 307

60 0 347 314 254 361 186 407 251 25000 347 314 130 474 82.6 486 274

300 26 0 901 814 1004 698 831 821 655 (720) 25000 901 814 381 1026 333 1190 814

60 0 899 694 808 • 691 708 715 656 25000 899 694 358 985 287 982 771

(1) Value in parenthesis is P-j^g. t h e API-605 rating at 100 F. (2) For S, = 25000 psi, the value of P, is such that S. = S! = a

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With respect to the flanges, Part B Rules require that the control-ling stress not exceed S^. The controlling stress is defined as the largest of (2/3) S , S , S„, (S + S, )/2 and (S„ + S, )/2. For the examples herein, h r t r h t h at S^ = 0, the controlling stress is always (2/3) S^. Values of P^, the maximum pressure as limited by the flanges, are also shown in Table 9.

For the 75 and 150 classes, it can be seen in Table 9 that the maximum pressure is limited by the bolts and not by the flanges. Accordingly, for these flanges, the Code user is implicitly encouraged to use S^ = 0 be-cause it gives the maximum pressure for a given flanged joint. In the 300 class, he may obtain a higher allowable pressure by using S^ > 0; as discussed later herein.

However, if S^ = 0, some potential problems arise. As indicated by Figure 4, each full pressure application will increase the bolt stress from zero to and, if there are many full-pressure cycles, fatigue of the bolts might occur. Similarly, as indicated by Figure 5, the stress o^ will vary from zero to a relatively large value with each pressure cycle. Finally, as indicated in Figure 5 and Table 4, the separation at the bore (Z) might be sufficient to permit partial extrusion of the 0-ring with subsequent "nibbling" of the 0-ring with each pressure cycle. In most applications, the number of pressure cycles would not be sufficient to make these potential problems be-come "real" problems. Nevertheless, these aspects do indicate some motivation for using a high initial bolt stress.

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Conditions at S. > 0 1

It can be seen in Table 9 that, for the 300-class flanged joints at S^ = 0, the maximum pressure is limited by the flange strength rather than the bolt strength. Noting that the controlling flange stress (which is (2/3)0^ at S^ = 0) decreases with increasing S^, a higher maximum pressure is permissible at some nonzero value of S^. Because of the linear nature of the solution between S^ = 0 and S^ = S^ the highest permissible pressure can be found from the data given in Tables 4 and 5. It turns out that, for the 26-inch 300-class identical pair, the highest pressure is obtained at S^ = 8050 psi, at which both P^ and P^ = 804. For the 60-inch 300-class identical pair, the highest pressure is obtained at Si = 3920 psi at which both and P f = 737 psi.

It is apparent that there is not much motivation in the Part B Rules to use high initial bolt stresses for the examples selected. However, it is informative to consider the maximum pressure for the maximum values of a. b permitted by the Code, i.e., a^ = S^. These values are shown in Table 9 for the specific bolt material, SA-193 Grade B7, with = 25,000 psi at 100 F. The value of P, in Table 9 is such that S. = S!, hence, S. = a, = 25,000 psi b x i x t>

Comparison of Type A with Type B, Identical Pair

Comparisons in terms of allowable pressures are also shown in Table 9.

(1) The allowable pressures of the flanges considered as Type A confirm the 100 F rating pressure given in API-605. That is, the calculated allowable pressures are essentially equal to or exceed the rated pres-sure of 140 psi, 275 psi, and 720 psi for the 75, 150, and 300 class, respectively.

(2) The maximum allowable pressures of the flanged joints, if they are considered as Type B, are lower than when they are considered as Type A, usually because of the bolt strength limitation, At S i = 25,000 psi, the values of P^ average about one-half of the P^QQ rated pressures. Accordingly, the bolt area must be approximately doubled to obtain the same pressure rating as given to the flanges under Type A rules.

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(3) For the 26-inch 300-class identical pair at S.̂ = 0, it can be seen in Table 9 that Pf is higher for Type A than for Type B; i.e., 814 psi versus 698 psi. For both types, the controlling stress is (2/3)0^. This appears to indicate that the "full-face" edge restraint increases rather than decreases the flange rotation. However, the major part of this anomaly is due to that fact that Part A rules ignore the average longitudinal hub stress due to pressure, whereas, Part B rules add the average longitudinal hub stress; pB^/(4gQ) to the hub-bending stress.

Comparisons of Type A, Type B, Identical Pair and Type B, Flange/Cover

Comparisons in terms of allowable pressures are shown in Table 9.

(1) The allowable pressures for the flange/cover joint, with the exceptions of the 300 class at S^ = 0, are controlled by the bolt strength as indicated by P^. Values of P^ for the flange/cover joint are lower than for the identical pairs joint and, in the worst case (60-inch 150 class flange/cover at S i = 25,000 psi), the allowable pressure is only 0.3 of the Type A rated pressure at 100 F.

(2) The covers, with thickness as required by the Code for pressure equal to ]?100 (see footnote (3) of Table 2), in some cases have values of P^ < Thus, if Reference (3) theory were introduced into the Code, there would be a contradiction in the Code for design of flat covers.

(3) The values of P^ for a flange used as an identical pair and the same flange bolted to a cover are not the same. As can be seen by comparing Table 5 with Table 7, the stresses are quite different.

The Code Limit of a, < S, and S. < S, b — b I — b

As remarked earlier, the Code uses S, (the allowable bolt stress) D in place of a^ (the theoretical operatng bolt stress). Accordingly, the Code places an upper limit on o^ of S^. This is analogous to the design rules for Part A flanges. However, Part B rules place an explicit restriction on the

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initial bolt stress, S^. Part A rules do not place an explicit restriction on S^ and, indeed, Appendix S of the Code states that "... it is evident that an initial bolt stress higher than the design value may and, in some cases, must be developed in the tightening operation, ....". A more explicit limit on S^ is given the ASME Boiler Code, Section III, Nuclear Power Plant Components, wherein Paragraph NB-3232.1 states that the maximum value of service stress, averaged across the bolt-cross section, shall not exceed two times the allowable bolt stress.

In examining the API flanges as examples, it is apparent.that, if S^ and 0, are both limited to S, , major increases in bolt areas would be required in b b using such flanges as Part B flanges with elastomeric O-ring gaskets. It is not apparent that such large increases in bolt area are really necessary. In Part A rules, the effect of internal pressure on bolt stresses is ignored whereas in Part B rules, the effect of internal pressure on bolt stresses is directly incorporated into the rules. Accordingly, it is not apparent that the same design bolt stress limit needs to be imposed in both Part A and Part B rules. It appears that the Part B rules could incorporate limit a of a, < 2 S, with adequate conservatism. For design purposes, this would auto-

D — D

matically limit S^ since S^ is always less than In practice, however, the Code has not and probably will not control S^. Accordingly, the design rules should be such that for any feasible value of S^, such as realized by ordinary wrenching techniques, the flanged joint will be satisfactory.

46

TEST DATA

The only available test is that reported some 20 years ago by (9)

Schuster and Rupe.x ' Tests were run on 12-inch 150 class ANSI B16.5 flanged joints with the raised face on the flanges removed for the purpose of determining if the pressure capacity of ANSI B16.5 standard flanges could be increased by the use of elastomeric O-ring gaskets. Two types of joints were tests:

(1) Welding-neck flange bolted to a welding neck flange. Pipe with 0.5-inch nominal wall thickness, about 12 inches long, was welded to each welding neck flange and closed with a cap.

(2) Welding flange (and its attached pipe) bolted to a blind flange.

The gasket was an 0-ring with 13.53 inches inside diameter. No further details are given about either the 0-ring or the 0-ring groove.

Tests consisted of prestressing the bolts to S^, then introducing pressure into the test assembly (through a small connection provided in the attached pipe) and determining the bolt stress, a^, under pressure. Bolt stresses were determined by measuring the bolt elongation. Reference (9) does not describe just how this measurement was made but, unless extreme care were taken, it is unlikely that the elongation measurements are more accurate than + 0.001 inch. The effective bolt length (two-flange thickness plus one-bolt diameter) is 5.125 inches. Assuming a modulus of elasticity of the bolt material of 30,000,000 psi, the reported bolt stresses are subject to an un-certainly of + 30,000,000 x 0.001/5.125 = 5800 psi.

Calculations were made of values of a, for the given values of S., b x using the theory described herein. The only description of the flanges in Reference (9) is that they were "ASA 300-12-inch flanges", hence, nominal dimensions of ANSI B16.5 flanges were used; including the assumption that the bolting consisted of sixteen, 1-1/8-inch nominal size, 8-thread series, root area per bolt of 0.728 square inch. Because the computer programs are not developed to handle variable thickness hubs, the actual welding neck hub, which varies from a thickness of 1.375 inches at the base to 0.500 inch at

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the attached pipe, was simulated by a uniform hub thickness of 1.000 inch. This is deemed to be a fairly good simulation of the actual variable hub thickness. Calculations were also run for uniform hub thicknesses of 1.375 inches and 0.75 inch; with relatively minor effect on the calculated value of a. . b

Measured and calculated values of a^ at the test pressure are shown in Table 10. An informative way to compare the test results with the calcu-lated results is to compare the values of a^/(H/A^). If there were no "prying effect" due to contact outside the bolt circle, a^ would simple equal H/A^ by equilibrium in the axial direction. The test data consistently give a lower value of than the calculated results. This indicates that the theory is conservative, but the tests are not sufficiently well defined to conclude that this is always true. In addition to uncertainties of dimen-sions and measured bolt stresses, the machining accuracy in removing the raised face for the tests could significantly affect the test results. Tests aimed specifically at evaluating the validity of the theory are needed.

TABLE 10: COMPARISON OF TEST DATA FROM REFERENCE ( 9 ) W I T H CALCULATED RESULTS, ANSI B16.5, 12" - 300 CLASS WELDING NECK-TO-WELDING NECK, IDENTICAL PAIR; AND WELDING NECK-TO-BLIND, FLANGE/COVER

Joint

Si> psi (1)

P» psi (2)

°b , psi

H / V psi

ab/ (H/A^

Joint

Si> psi (1)

P» psi (2)

Test (1)

Calc. sn = i.oo" ° (3)

H / V psi Test Calc.

g = 1.00" ° (3)

Calc. g = 1.375" ° (4)

Calc. g = .75" ° (4)

Identical Pair 10200 3500 51800 75590 43200 1.20 1.75 1.41 2.08 26900 3500 62000 81180 43200 1.44 1.88 1.57 2.18

Flange/Cover 11360 3500 49700 73370 43200 1.15 1.70 1.59 1.81 24200 3600 66740 79440 44430 1.50 1.79 1.69 1.90

(1) Test data on S^ and a^ . Subject to uncertainty of about + 5800 psi. (2) Test pressure at which o^ was measured. (3) Calculated based on uniform-wall hub, gQ = 1.00" is best estimated of "equivalent" hub. (4) Calculated based on different values of g to indicate effect of this dimension.

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COMPUTER PROGRAMS

In order to carry out the evaluations discussed herein, two computer programs were written:

(1) FLGB, which performs the calculations for an identical pair of integral, constant thickness hub flanges using Part B rules of the Code; Table 1 herein.*

(2) COVER B, which performs the calculations involved in Reference (3) for a constant thickness hub flange bolted to a flat cover.

The listings of these two programs are included herein as Appendix B. The input data is described by "comment" cards at the beginning

of each program. The output data is described in the following.

Output Data, FLGB

The program prints out the input data followed by three sets of data for:

(1) S ± = 0

(2) S = S» (E0. = 0 and h = (A-C)/2) 1 1 A C (3) The specific input value of S ^

The first two sets of data provide a simple way to obtain the dependent variables for any values of Si between zero and S^. The variables are all given by an equation of the form:

* The Part B rules of the Code provide rules for other types of flanged joints; i.e., loose type flanges with constant thickness hubs, loose type with tapered hubs, and integral flanges with tapered hubs. These types differ in the values of c^, C2> c„, c^, and c,.. The computer program FLGB can be modified to Include these other types By (a) removing the three cards which set c^ = c_ = c„ = 1.; c^ = 0.85 and c,. = 0.0; and (b) expanding the READ statement to read in these five constants. Values of the constants are identified in UA-58(c) of the Code. Minor changes in stress calculations would also be needed as shown in UA-59 of the Code.

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V - Cx P + C 2 S ± , (27)

where V is any variable (e.g., o^, a ny flange stress) C^ and C^ are constants.

The third set of data represents any input value of S., either i i f

less than or greater than S^. If the input value of S^ is greater than S^, an additional line of data is printed out as indicated in Table 11. If the input value of S^ is so high that hc is less than 0.1 (A-C)/2, the program aborts and prints out a message: SHC LESS THAN .1 * SHCMAX, NO ANSWER.

The output symbols are defined in Table 11. In addition, flange stresses are identified by the equation number used in the Code; see Table 1 herein.

Output Data, COVER B

The program prints out the input data followed by three sets of data for

(1) S. = S'. (b = b and 9__ = 0) i i max 3f (2) S± = 0

(3) The specific input values of b and Sgf The program does not use S^ as input.

The first two sets of data provide a simple way to obtain dependent variables for S^ between zero and S^; using an equation of the form shown by Equation (27). It may be noted that the second set of data, labeled FOR SI = 0, prints out a value of SI which is not exactly zero. The program uses linear interpolation to find the value of S^ from trial values of such that S is essentially but not exactly zero.

The third set of data represents any input value of b (except zero) with 0 3 f = 0 or any value of ©3f with b = (A-C)/2. This input can be used for values of S ^ either less than or greater than S^.

The output symbols are defined in Table 12. In addition, flange stresses and cover stresses are identified by the equation number used in Reference (3), Appendix A.

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TABLE 11: OUTPUT DATA IDENTIFICATION, COMPUTER PROGRAM FLGB

Program Symbol Definition

S I

SB CMS

ETHA

ETHB ZETA

SHCM SHC XSI SI

*

*

*

*

S^ = initial bolt stress o^ = operating bolt stress M g = total moment on flange ring due to continuity with hub, pipe,

or shell, = M„ + Qt/2 rl E = modulus of elasticity times rotation of flange ring at out-

side of ring E 9 = modulus of elasticity times rotation of flange ring at bore D Z = axial separation between flanges at bore, Code equation (C28),

see Table 1 h = (A-C)/2 cmax value of hc to approximately give input S^ value of Si corresponding to SHC. input value of S^.

* These are printed out under "FOR INPUT VALUE OF SI" only if Si > S^. The program uses an iteration to determine a value of h£ (SHC) which gives, to a close approximation, the input value of S^. Comparison of XSI with SI indicates accuracy of the solution.

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TABLE 12i OUTPUT DATA IDENTIFICATION, COMPUTER PROGRAM COVER B

Program Symbol

Ref. (3) Symbol

See App. A Note No. Notes

Ml M1 (1) (1) M^, M^, and Q are obtained by solution of equations (23), (24), and (25) of this report.

M2 M2 (1) (2) Rotations of cover at flange bore:

Q Q (1) 0, + e ' + 0 , =0.„ lc c 3c 13

TIC 61C (2) Equation (R13) is Ref. (3) Eq. 13

TCP 0' c (2) (3) Rotations of flange at flange bore

T13 0 by Eq. (R13) (2)

TIF

53

RECOMMENDATIONS

Part B Rules of the Code should be simplified and made more consistent with Part A Rules. In the simplified form, the value of initial bolt stress should not appear as a design parameter. The simplified method should be formulated so that the flanged joint is adequate for any credible value of S^. The computer programs included in this report could be used to check the validity of simplified methods over an appropriate range of variables.

Consideration should be given to increasing the allowable bolt stress for Part B flanged joints.

A simplified method is deemed suitable for the Code; i.e., Section VII-Division 1. Such a simplified method would also be suitable for Class 2 and Class 3 components under the Nuclear Power Plant Components, ASME Code Section III. However, the more complete theory should be retained for Class 1 components under ASME Code Section III.

Tests on two or more Part B flanged joints should be conducted to evaluate the validity of the theory.

54

ACKNOWLEDGEMENT

The authors wish to express their appreciation to Mr. R. W. Schneider, Gulf and Western, Energy Products Group, Bonney Forge Division, for his review of a draft of this report. Mr. Schneider's comments and suggestions contributed significantly to the report.

Table 1 and Appendix A are copyrighted material published by the American Society of Mechanical Engineers. Permission for inclusion herein was granted by the American Society of Mechanical Engineers.

55

REFERENCES

(1) ASME Boiler and Pressure Vessel Code, Section VIII, Division 1, "Pressure Vessels", 1974 Edition. Published by the American Society of Mechanical Engineers, 345 E. 4th St., New York, New York 10017.

(2) Schneider, R. W., "Flat Face Flanges with Metal-to-Metal Contact Beyond the Bolt Circle", J. of Engineering for Power, Trans, of ASME, Vol. 90, Series A., No. 1, January, 1968, pp 82-88.

(3) Waters, E. 0. and Schneider, R. W., "Axisymmetric, Nonidentical, Flat Face Flanges with Metal-to-Metal Contact Beyond the Bolt Circle", J. of Engineering for Industry, Trans, of ASME, Vol. 91, Series B., No. 3, August, 1969, pp 615-622.

(4) Waters, E. 0., "Derivation of Code Formulas for Part B Flanges", Welding Research Council Bulletin No. 166, October, 1971.

(5) Schneider, R. W. and Waters, E. 0., "Some Considerations Regarding the Analysis of Part BT Code Flanges - 1974", ASME Paper No. 75-PVP-48.

(6) ASME Boiler and Pressure Vessel Code, Section III, Division 1, "Nuclear Power Plant Components", 1974 Edition. Published by the American Society of Mechanical Engineers, 345 E. 47th St., New York, New York 10017.

(7) Rodabaugh, 0'Hara and Moore, "FLANGE, A Computer Program for the Analysis of Flanged Joints With Ring-Type Gaskets", 0RNL-5035, January, 1976.

(8) Rodabaugh, E. C., and O'Hara, Jr., F. M., "Evaluation of the Bolting and Flanges of ANSI B16.5 Flanged Joints—ASME Part A Rules" (to be published).

(9) Schuster, E. C., and Rupe, V. L., "Getting the Most for Your Flange Dollar Using 0-Rings", Pipe Line Industry, October, 1955.

APPENDIX A

"AXISYMMETRIC. NONIDENTICAL, FLAT FACE FLANGES WITH METAL-TO-METAL CONTACT BEYOND THE BOLT CIRCLE"

BY E, 0, WATERS AND R. W. SCHNEIDER. Journal of Engineering for Industry, August 1969

Reference (3) Herein

A-1

E. 0 . WATERS Professor Emeritus,

Yale University, New Haven, Conn.

Mem. ASME

R. W. SCHNEIDER Manager of Engineering,

Bonriey Forge Division, Bonney Forge and Foundry, Inc.

Allentown, Pa. Mem. ASME

Axisymmetric, Nonidentical, Flat Face Flanges With Metal-to-Metal Contact Beyond the Bolt Circle A method of analyzing a pair nf nonidentical, axisymmetric flat face flanges with metal-to-metal conflict beyond the boll circle is described. The design method lakes into ac-count interaction between opposing flanges in u bolted closure and provides for com-patibility of deformations of all elements comprising the closure. The case of a blind enter to an integral flange having a hub of uniform thickness is described in detail. Ihnueier, the same analytical approach can be extended to cover a tapered, htibbcd flange or the general situation where a reducing flange is substituted for the blind cover.

Introduction T a n Suico.MMiTTEE on Bolted Flanged Connections

(Pressure Vessel Research Commit tee of the Welding Iteseurch Council) and the Task Group 011 Full Face Flanges (ASME Sub-group on Openings and At tachments ) are cooperatively develop-ing informal ion for the rational design of flat face flanges with metal- to-metal contact beyond the bolt circle. T h e research lopic was projHtsed by AKME Special Commit tee t o Review Code Stress Basis as a result of inquiries from indust ry to the ASM IS Boiler and Pressure Vessel Commit tee . It is designated Topic U —Stresj.es in Bolted Flanged Connections [SI.1 A design basis was presented in a recent, paper [2]; however, it is limited to the special case of symmetr ical configurations where t he flanges com-prising a "Insure are identical in all respects. Such n system of

1 Numbers in bracket.-, dcnigmitc Keferciici's at end of paper. Contributed by the Pressure Vessels and 1'ipiiiK Division for presen-

tation lit the Winter Aiinuul Meeting, New York, Deceinl>er 1-5. 1908 iif THE A.VKUICAN SOCIETV OK MKCII.\N-IC.\I. ENOIXKKKS. Manu-script received at ASM 10 Headquarters, Julv 2,'i. 19(>K. Pap®1" N"-

A-2

Fig. 1 Examples of symmetrical configurations

considered essential to approach the problem in this manner since il. is a prime goal of I he cooperating commit tees to develop u single me I hud of analyzing flat face flanges—irrespective of whether they are symmetrical or imsyiiinietrical configurations.

Subscripts c and / are used to indicate cover and shell flange, respectively; c is also used to denote a circumferential stress, e.g., a,. Letters » and ft, as subscripts, denote unbalanced and balanced moments, respectively.

I I J — V H 0

Fig. 2 O n * type c l nonfdentical flanges to wh ich th« analysis applies

Design Review of Symmetrical Configurations. I n t h e c a s e of a p a i r of

identical flanges, such as illustrated in Fig. 1, it was shown that PI:

1 Kl.it face flanges behave differently than so-called "con-ventional" flanges.

2 Flexural behavior of a flange can lie described using licain theory considering the flanges to be composed of discrete, radial beams.

.'! The discrete, trapezoidal elements can be modified to equivalent elements uniformly a in. wide from the holt circle to the outside diameter and r in. wide from the bore to the boll circle for a beam of unit width at /',„.

•t Under internal pressure, the flanges bear against each ol her beyond the bolt circle. The location of the centroid of the reac-tive forces can be calculated by using beam theory and assuming that line contact occurs where (he slope of a beam is calculated to be zero under the imposed loads.

A typical free-body diagram of such a flange is shown in Fig. •i. Since the mating flange is a duplicate in ali respects, it will be acted upon by the same xysteru of forces. It is nbviors that Mich a structure is in static, equilibrium and it is equally obvious that the Minimal inn »f moments mast equal zero in order lo use-beam analogy to represent the behavior of the flanges. There-fore, in the case of a pair of uonidenlical flanges, when —.1/ ^ II,

-Nomenclature-

shell-flange which includes Qlr/'2 term, lb in/in. (positive its shown in Fig. 4(a))

A" = number of bolts/in. of circumference of bolt circle, i n . - '

.V = number ol bolts/beam =» .\(/{,„ + i")//,',„ I ' = design pressure, psig Q = shear force a t flange-shell junction, lb/in. (positive

>.LS shown in Fig. 5) It,,, = radius to midthiekuess of shell, in.

S — ratio, Afi/Afi, dimensioiiless If = thickness of shell flange, in. /,. = thickness of cover flange, iu. in = total outward radial deflection of shell tlange at

= I

A-3

'mo*

O R N L - D W G 6 6 - 1 0 2 9 4 B F

o —

B /tf

. M

~P

HE- 'm

I d

b—J

F

~F

s - 0

- P

R

Fig. 3 Free-body diagram of one flanga of an identical pair (tymmofrical configuration)

Anon

t 4

ff f—b—"

1

T

(•DIRECTION)

(•DIRECTION)

B F

e F

T i = L

))

tu B F

Fig. 4 Foe-body diagram of an unrymmelrical configuration

it is necessary lo implement, beam analogy to account, for the presence of unbalanced moments .

Untymmetrical Configuration where ISM yl 0. Fig. 4(a) is a free-body diagram on unsymmelrical conriguration which cannot, be treated by beam analogy alone since Mi ^ Mi . If Aft = M 2 and //,„ of one flange equals R,„ of the other, theory presently avail-able [2J would suffice notwithstanding ihat the flanges differ in thickness. However, since /i the total elongation of the bolts must be apport ioned between the flanges in such a manner as lo match the deflection of each flange at the bolt, circle.

The problem created b y Mi & Mi can lie solved by considering Mi lo be comprised of two moments Mu, and'/Wi,,. I n a similar manner , M t is comprised of A fit, and iWJl4. These changes are reflected in Fig. 4(6). Beam analogy 12] can be used t o calculate the effects of Mu, and ilty, if it is required t h a t Mu, — Ma. T h e unbalanced portion of each moment. ( M u and M«„) can be con-sidered as producing rigid-body rotat ions only. If t he unbalanced momoii 's are apport ioned correctly, each flange will undergo the same amount, of rigid body rotation in the same direction which means that, the bolt stress and the flange-flange contact circle are determined by Mu,, Mu,, and F. Thus, maximum use can be made of existing theory [2]. The following equat ions can be wri t ten:

Mtl, + Mi„ = Mi

•U,.„ + = M,

Mi = SMi

A - 4

itiul the outward radial ili'lleeiiun is |.">|:

W—Q ) V.. -Otf/2 y /

Mlb-Ot,/?• *iy » Ut - Of,/2

Fig. 3 Frm-body diagram of blind cevtr lo thall-flang* combination

Or' = — : 5.21 J{,„M,„

fcV.»loKl„| Utm + L)/BJ

Therefore, I lie slope of I he cover flange al I!„, becomes;

(]:

.•.21/i,„1.l/..„

Continuity Equation!. ICquatiiins ( I I ) or (12 )and t Ki) arc equated to express rotnlional conlimiity of the cover at. radius /«*,„. Similarly, equal ions (10) or (17) and (20) arc equated to show slope compatibil i ty of the shell-flange and shell. Finally, sel l ing equal ion (IS) or (III) equal to equation (21) shows that Ihe shell and its flange undergo identical, radial displacements.

Before the set of equat ions can be solved, all balanced and unbalanced moments must be expressed in terms of .1/, (or .!//) using equat ions (Ij), (.V/, (li), (7), and (S). T h e resulting three equat ions will contain four unknowns, namely, .l/i (or Mj) , .S\ Q, and b. When the flanges pivot about their O.I) , , b is known (b = /;„,„«) and 0.i, and 0.1/ replace it as an unknown. The equa-tions can lie solved simply by assuming a value of h, or values of 0.v and 0i/ whe II f' — 'fiimxt which eliminates the extra unknown. When the flanges have the same O.D., which is usually the case, Oar and 0.1/ must he in I he rat io B*. '0, / = E j l ^ / E . I S since I lie balanced moments are equal (,Uih = A/•_>,.'). Subsequently, it will be necessary to calculate Ihe amount Ihe bolts must be pre-stressed in order lo sat isfy the assumption regarding b or Os.

A parameter s tudy may be made by performing a set of calcu-lations for numerous values of h and Ox, f rom which the general relation between prestress and operating bolt load is rcadib -

obtained. This is explained in detail in the two sections of Ihe paper which follow.

Required PrejtroM in Bolli. The theory presently available for analyzing a "matched set - ' of flanges [21 can be used for calcu-lating the amount of prestress required to yield Ihe value as-sumed for b or Br.. It is necessary to modify the calculations slightly, however, since the theory applies lo a pair of identical flanges where the elongation of the bolls is evenly distributed between both llanges. When the flanges are different, their relative stillness determines how ihe total elongation of a boll is apport ioncd.

Consider two llanges l r and l t having the same 0.1) . with Mih and Mj>, acting al radius IIm ; for example, the assembly shown in Kig. .*>. T h e total separation of Ihe (langes at the bolt circle must equal the total bolt elongation, or:

!lr + .'// = - « (22)

where \ir is the upward deflection of the cover flange anil /// Ihe downward delleetinn of the other linage, be t t ing x be the frac-tion of Ihe total boll elongation required to match the dcllfctioii of Ihe cover flange:

(I".)

(1G)

(17)

An examination of equations (4), (10) and (15) will show thai B/' = —6C' which, b y the s t a t ed sign convention, represents equal rig'd body rotat ions in the same direction.

The outward radinl deflection of the shell flange where it joins the shell is [2 | :

= K, + K„Q + (0„ + 0/)f,/2: b R 4A' *B* 0 ~ mP «?) - Wi - Qtj/2) (20)

x(MK - 5) = 2/),.'( I - f')(-!/„, + F(J

Er'il.3 ' (. - x) , » / * _ 6) = hjitl/

where J is simply / / £ , / ( / / £ , + lrzEr). ICqiitttions (23) and ('24), respectively, reduce to :

//',y _ ^ e^S r _ (A-6 - E)bc/n \ ' f ) 2/v7J(l - /•' + Mu,/( J (b,\ = (I - _ (KS - P)bj/t~\ \l) 2A'f"(l - V-) L + J

CM)

(24)

(25)

(2(1)

When h > !>,„.,I lie flanges have a .slope of ftv and fli/ al A',,, + ( + Ii due to the balanced loa

A-5

iu, v = V r ) 2A7'"(V- Vv

x j - , _ |A"«5 + ftA ,mJ(t — CJK)

Si net; h, •= lif ~ b, either equation (2.">) or (20) cim be used for calculating & when b < b„Ml; equation (27) or (2K) is applicable wlien b > b„„„ Tlie equal ions may tie solved graphically using Fig. II. Counecl the proper value on the ordinate for the cover (or flange) and the appropriate value oil the curve marked b/C; extend llie line and extract 8 from the number rend off the ab-scissa foi' the cover (or llange). The required p res tress in the bolts becomes:

Kb A'~M (20)

and this amount of preslress will yield the value assumed for b or ftt iviid ft/.

Dalerminlng Operating Bolt Load. T h e o p e r a t i n g bol t l o a d / b e a m is found using the free-body diagram of Fig. •"> and taking moments about H. Ei ther flange can be used since the unbalanced momenta Mi„ and M tu cause equal amounts of rigid-body rotation in the same direction and thus do not affect the operating bolt load and Mib = Mih. The equations for li become:

n = F + 0 + AU b <

« = /-•(i + , - - ) + AU(,--); '> > i>"

(30)

(:ti)

rTTt.8.:.

-. i « i - i :

f M : !/;

- p . . p - i I

I I I i i

b/J OR bmot/J WHEN b>bm

I l

^ . u i U P 1.3 i - r •

1 ' I . i i 1

-t.z- .—1 —I . - t .. I

-1.0- j-

—/—-08 • -/- 0.7 -f = bc, due to the definition of x following equation (24), and the faet that — Mtb. Having foun