CALCULATIONS IN ACCORDANCE WITH ASME VIII, Div.1, APPENDIX Y.
FLAT-FACE FLANGES WITH METAL-TO-METAL CONTACT OUTSIDE THE BOLT CIRCLE. SoG-1050i-375p-DF450 add test
Although the Support Rings could be classified as "Loose Flanges", this
definition/classification is only valid for Appendix 2 - Lap Joint Flanges.
Hence:- By ref. to Table Y-6.1 and by comparison with the drawings in this appendix, our method of construction gives a Class 1, Category 1 Assembly.
Thus we must take go = g1 = 0.25"
SYMBOLS USED:
A = Outside Diameter B = Inside Diameter
C = Pitch Circle Diameter D = Dia. of Bolt clearance Hole
G = Dia. at center of "Seal"ing point
n = No. of Bolts
tg = Flange Thickness - Gas End Separate Gas and Liquid end thicknesses
tl = Flange Thicknss - Liquid End are only applicable to "FLo" products.
Pd = Design Pressure
db = Bolt Diameter
dbr = Bolt Root Diameter
ts = Spacer Thickness - This parameter usually proves to be irrelevant
go = "Thickness of hub at small end (weld prep) of flange" This most nearly
equates to the side of our dome in our design
g1 = "Thickness of hub at back of flange" This most nearly equates to
thickness of our dome immediately after the return knuckle radius.
db = nominal bolt diameter dbr = bolt thread root diameter
For our design, as go = g1, so we can establish:-

MODIFYING FACTORS for flange stresses

2-7.2: g1/go=1
F=0.908920

2-7.3 Integral Factor:
g1/go=1 V=0.550103

From Appendix 2-7.2:

From Appendix 2-7.3:

2-7.6: Hub stress
correction hubs of uniform
thickness g1/go=1 f=1

From Appendix 2-7.6:

PARAMETERS:64

Thus:

(From BS 6104) a
Standard which states
thread root diameters.

Note 1: All dimensions used in calculations are in inches.
Dimensions given in mm are derived from the inch dimensions.
Note 2: Equations are given the same numbers as in ASME.
The other equations that ASME does not number, are given numbers following on from those in ASME.

Preliminary examination:

HydThr - Hydrostatic thrust

So:

For Bolts to DIN Metric Grade 10.9, U.T.S. = 142,000 psi.By analogy with Sub-section C, Tables UCS-23/UHA-23, and using
a Safety Factor of 5.6, we get Allowable Stress:

So:

RnCp - retention capability

So:

Hence, HydThr < RnCp, therefore THE DESIGN COULD BE SATISFACTORY.

The holding power ratio HdPw is:

So:

EQUATION (7) - FLANGE MOMENT DUE TO FLANGE-HUB INTERACTION If ARbar = AR, then we have:-
Equation (45):- Note: In code AR has an over
score or bar over it, Hence "ARBar"

Equation (46):-

So:

Equation (47):-

So:

Equation (48):-

So:

Equation (49):-

So:

Equation (50):-

So:

Equation (51):-

So:

Equation (52):-

(from Table 2-6)

So:

Equation (53):-

So:

Equation (54):-

So:

Equation (55):-

So:

Equation (56):-

So:

Equation (57):-

So:

Equation (58):-

So:

Equation (59):-

So:

Equation (60):-

So:

Equation (61):-
MP = HD*hD + HT*hT + HG*hG
As the load required to compress the sealing bead of the Diaphragm can be exerted by only hand-tightening of the Bolts, then the design comes within the ambit of Y-1(b).

Therefore:-
HG = 0
The equation, therefore, becomes:-

So:

Equation (62):-

So:

EQUATION (7) - FLANGE MOMENT DUE TO FLANGE-HUB INTERACTION:-

So:

EQUATION (8) - SLOPE OF FLANGE AT INSIDE DIAMETER TIMES E:-

So:

EQUATION (9) - CONTACT FORCE BETWEEN FLANGES AT hC:-

So:

EQUATION (10) - BOLT LOAD AT OPERATING CONDITIONS:- Note:-

From (61)

So:

Equation (63):-

So:

Square ins.

EQUATION (11) - OPERATING BOLT STRESS:-

So:

Equation (64):-

Note:-

So:

Equation (65):-

Modulus of Elasticity of Flange Material

rE = Elasticity Factor = ----------------------------------------

Modulus of Elasticity of Bolt Material

Figures to be taken from Table UF-27.For both Straight Chromium
Steels and Carbon-Moly Steels,E = 28,500 at 200 Deg.F; so,

EQUATION (12) - DESIGN PRE-STRESS IN BOLTS:-

Let Si1 = Si

So:

EQUATION (13) - RADIAL FLANGE STRESS AT BOLT CIRCLE:-

Let:- SR1 = SR for this particulat Equation; hence:-

So:

EQUATION (14a) - RADIAL FLANGE STRESS AT INSIDE DIAMETER:-

Let:- SR2 = SR for this particular Equation; hence:-

So:

Equation (66)

From Fig. 2-7.1 we have:-

Hence,

Therefore, from the Graph,

So:

EQUATION (15a) - TANGENTIAL FLANGE STRESS AT INSIDE DIAMETER:-

So:

EQUATION (16a) - LONGITUDINAL HUB STRESS:-

So:

Y-7 ALLOWABLE FLANGE DESIGN STRESSES.

Y-7(a)

From Equation (11),

If you remember:

Hence,

< Sb, therefore THE DESIGN IS SATISFACTORY.

In this case holding power ratio HdPw1 is:

that is:

Y-7(b)(1)From Equation (16a)

Flange, Table UHA-23, Spec SA516 gr70 so:

Shell, Table UNF-23.3, Spec SB127 -400 so:

26250

should be SA 240 Gr.
316/316L Sn 18000

Therefore:

Hence, SH < 1.5*Sf, therefore THE DESIGN IS SATISFACTORY.

Y-7(c)

From Equation (14a)

From Table UHA-23:

17500

Hence, SR2 < Sf, therefore THE DESIGN IS SATISFACTORY.

Y-7(d)

From Equation (15a)

Is less than

From Table UHA-23:

17500

Hence, ST < Sf, therefore THE DESIGN IS SATISFACTORY.

Y-7(e)

17500

Is less than

17500

and

Hence the conditions:- (SH + SR2)/2 < Sf and:- (SH + ST)/2 < Sf
ARE BOTH SATISFIED.
CONCLUSION:
THE DESIGN MEETS ALL THE REQUIREMENTS OF APPENDIX Y.