ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules
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2010 SECTION VIII, DIVISION 2
4-155
4.7.3.2 The flange thickness of the head for a Type B Head Configuration shall be determined by the
following equations where the flange moments
o
M
and
g
M
for the operating and gasket seating conditions,
respectively, are determined from paragraph 4.16.
a) Flange thickness for a ring gasket
max ,
g
o
TTT
⎡⎤
=
⎣⎦
(4.7.3)
where
g
g
fg
M
AB
T
SB A B
+
⎛⎞
=
⎜⎟
−
⎝⎠
(4.7.4)
o
o
fo
M
AB
T
SB A B
+
⎛⎞
=
⎜⎟
−
⎝⎠
(4.7.5)
b) Flange thickness for a full face gasket
()()
0.6
fo
B
ABCB
P
T
SAB
⎛⎞
+−
=
⎜⎟
−
⎝⎠
(4.7.6)
4.7.3.3 A Type B head may only be used if both of the requirements in paragraph 4.7.2.3 are satisfied.
4.7.4 Type C Head Thickness Requirements
4.7.4.1 The thickness of the head for a Type C Head Configuration (see Figure 4.7.3) shall be
determined by the following equations.
a) Internal pressure (pressure on the concave side) – the head thickness shall be determined using
Equation (4.7.2).
b) External pressure (pressure on the convex side) – the head thickness shall be determined in accordance
with the rules in paragraph 4.4.
4.7.4.2 The flange thickness of the head for a Type C Head Configuration shall be determined by the
following equations where the flange moments
o
M
and
g
M
for the operating and gasket seating conditions,
respectively, are determined from paragraph 4.16.
a) Flange thickness for a ring gasket for heads with round bolting holes
max ,
g
o
TTT
⎡⎤
=
⎣⎦
(4.7.7)
where
1.875
75
g
g
fg
M
CB
T
SB C B
+
⎛⎞
=
⎜⎟
−
⎝⎠
(4.7.8)
1.875
75
o
o
fo
M
CB
TQ
SB C B
+
⎛⎞
=+
⎜⎟
−
⎝⎠
(4.7.9)
2010 SECTION VIII, DIVISION 2
4-156
475
fo
PL
CB
Q
SCB
+
⎛⎞
=
⎜⎟
−
⎝⎠
(4.7.10)
b) Flange thickness for ring gasket for heads with bolting holes slotted through the edge of the head
max ,
g
o
TTT
⎡⎤
=
⎣⎦
(4.7.11)
where
1.875
3
g
g
fg
M
CB
T
SB C B
+
⎛⎞
=
⎜⎟
−
⎝⎠
(4.7.12)
1.875
3
o
o
fo
M
CB
TQ
SB C B
+
⎛⎞
=+
⎜⎟
−
⎝⎠
(4.7.13)
43
fo
PL
CB
Q
SCB
+
⎛⎞
=
⎜⎟
−
⎝⎠
(4.7.14)
c) Flange thickness for full-face gasket for heads with round bolting holes
()
2
3
B
QC B
TQ Q
L
−
=+ +
(4.7.15)
The parameter Q is given by Equation (4.7.10).
d) Flange thickness for full-face gasket for heads with bolting holes slotted through the edge of the head
()
2
3
B
QC B
TQ Q
L
−
=+ +
(4.7.16)
The parameter Q is given by Equation (4.7.14).
4.7.5 Type D Head Thickness Requirements
4.7.5.1 The thickness of the head for a Type D Head Configuration (see Figure 4.7.4) shall be
determined by the following equations.
a) Internal pressure (pressure on the concave side) – the head thickness shall be determined using
Equation (4.7.2).
b) External pressure (pressure on the convex side) – the head thickness shall be determined in accordance
with the rules in paragraph 4.4.
4.7.5.2 The flange thickness of the head for a Type D Head Configuration shall be determined by the
following equations.
max ,
g
o
TTT
⎡⎤
=
⎣⎦
(4.7.17)
where
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2010 SECTION VIII, DIVISION 2
4-157
g
g
fg
M
AB
T
SB A B
+
⎛⎞
=
⎜⎟
−
⎝⎠
(4.7.18)
2
o
o
fo
M
AB
TQ Q
SB A B
+
⎛⎞
=+ +
⎜⎟
−
⎝⎠
(4.7.19)
()
22
4
8
fo
PB L B
Q
SAB
−
=
−
(4.7.20)
When determining the flange design moment for the design condition,
o
M
, using paragraph 4.16, the
following modifications shall be made. The moment arm,
D
h , shall be computed using Equation (4.7.21). An
additional moment term,
r
M
, computed using Equation (4.7.22) shall be added to
o
M
as defined paragraph
4.16. The term
oe
M
in the equation for
o
M
as defined paragraph 4.16 shall be set to zero in this calculation.
Note that this term may be positive or negative depending on the orientation of
,,
vR
tRA.
()
0.5
D
hCB=− (4.7.21)
[
]
()
2
0.785 cot
rr
M
BP h
β
= (4.7.22)
where
arcsin
2
B
Lt
β
⎡⎤
=
⎢⎥
+
⎣⎦
(4.7.23)
4.7.5.3 As an alternative to the rules in paragraphs 4.7.5.1 and 4.7.5.2, the following procedure can be
used to determine the required head and flange thickness of a Type D head. This procedure accounts for the
continuity between the flange ring and the head, and represents a more accurate method of analysis.
a) STEP 1 – Determine the design pressure and temperature of the flange joint. If the pressure is negative,
a negative value must be used for
P in all of the equations of this procedure, and
0.0
e
P for internal pressure= (4.7.24)
e
P P for external pressure= (4.7.25)
b) STEP 2 – Determine an initial Type D head configuration geometry (see Figure 4.7.5). The following
geometry parameters are required:
1) The flange bore,
B
2) The bolt circle diameter,
C
3) The outside diameter of the flange,
A
4) Flange thickness,
T
5) Mean head radius,
R
6) Head thickness,
t
2010 SECTION VIII, DIVISION 2
4-158
7) Inside depth of flange to the base of the head,
q
c) STEP 3 – Select a gasket configuration and determine the location of the gasket reaction,
G , and the
design bolt loads for the gasket seating,
g
W
, and operating conditions,
o
W , using the rules of paragraph
4.16.
d) STEP 4 – Determine the geometry parameters.
()
1
2
CG
h
−
=
(4.7.26)
()
2
2
GB
h
−
=
(4.7.27)
()
2
AB
d
−
=
(4.7.28)
T
n
t
=
(4.7.29)
A
K
B
= (4.7.30)
arcsin
2
B
R
φ
⎡⎤
=
⎢⎥
⎣⎦
(4.7.31)
[]
1
2cot
t
eq T
φ
⎛⎞
=− −
⎜⎟
⎜⎟
⎝⎠
(4.7.32)
[]
1
12
1cot
2
k
ν
φ
λ
−
⎛⎞
=−
⎜⎟
⎝⎠
(4.7.33)
[]
2
12
1cot
2
k
ν
φ
λ
+
⎛⎞
=−
⎜⎟
⎝⎠
(4.7.34)
()
0.25
2
2
31
R
t
λν
⎡⎤
⎛⎞
=−
⎢⎥
⎜⎟
⎝⎠
⎢⎥
⎣⎦
(4.7.35)
e) STEP 5 – Determine the shell discontinuity geometry factors.
[
]
3
1
1
0.275 lnnt K
Ce
k
⋅
=−
(4.7.36)
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2010 SECTION VIII, DIVISION 2
4-159
[
]
3
2
1
1.1 ln
1
nt K
C
Bk
λ
⋅
=+
(4.7.37)
[
]
42
11
sin
11.65
24
B
e
Ck
kndtk
λφ
⎛⎞
=+++
⎜⎟
⎝⎠
(4.7.38)
5
1
1.65 4
1
e
C
tk B
λ
⎛⎞
=+
⎜⎟
⎝⎠
(4.7.39)
f) STEP 6 – Determine the shell discontinuity load factors for the operating and gasket conditions.
[]
(
)
2
321
2
cot
4
oo
qT q
BP
Ce hWh
B
π
φ
⎛⎞
−
=⋅+ −−
⎜⎟
⎝⎠
(4.7.40)
[
]
[]
2
6
4cot
0.35
44 sin
o
qB
BP
C
nd
φ
π
φ
⎛⎞
−⋅
=−
⎜⎟
⎜⎟
⎝⎠
(4.7.41)
31gg
CWh=− (4.7.42)
6
0.0
g
C = (4.7.43)
g) STEP 7 – Determine the shell discontinuity force and moment for the operating and gasket conditions.
26 3 5
24 15
oo
do
CC C C
V
CC CC
−
=
−
(4.7.44)
16 3 4
24 15
oo
do
CC C C
M
CC CC
−
=
−
(4.7.45)
26 3 5
24 15
gg
dg
CC C C
V
CC CC
−
=
−
(4.7.46)
16 3 4
24 15
gg
dg
CC C C
M
CC CC
−
=
−
(4.7.47)
h) STEP 8 – Calculate the stresses in the head and at the head-to-flange junction using Table 4.7.1 and
check the stress acceptance criteria. If the stress criteria are satisfied, then the design is complete. If
the stress criteria are not satisfied, then re-proportion the bolted head dimensions and go to STEP 3.
2010 SECTION VIII, DIVISION 2
4-160
4.7.6 Nomenclature
A flange outside diameter.
B
flange inside diameter.
β
angle formed by the tangent to the center line of the dished cover thickness at its point of
intersection with the flange ring, and a line perpendicular to the axis of the dished cover
C bolt circle diameter.
1
C shell discontinuity geometry parameter for the Type D head alternative design procedure.
2
C shell discontinuity geometry parameter for the Type D head alternative design procedure.
3
g
C shell discontinuity load factor for the gasket seating condition for the Type D head alternative
design procedure.
3o
C shell discontinuity load factor for the design operating condition for the Type D head
alternative design procedure.
4
C shell discontinuity geometry parameter for the Type D head alternative design procedure.
5
C shell discontinuity geometry parameter for the Type D head alternative design procedure.
6
g
C shell discontinuity load factor for the gasket seating condition for the Type D head alternative
design procedure.
6o
C shell discontinuity load factor for the design operating condition for the Type D head
alternative design procedure.
e geometry parameter for the Type D head alternative design procedure.
r
h
moment arm of the head reaction force.
1
h geometry parameter for the Type D head alternative design procedure.
2
h geometry parameter for the Type D head alternative design procedure.
1
k geometry parameter for the Type D head alternative design procedure.
2
k geometry parameter for the Type D head alternative design procedure.
K geometry parameter for the Type D head alternative design procedure.
L
inside crown radius.
λ
geometry parameter for the Type D head alternative design procedure.
dg
M
shell discontinuity moment for the gasket seating condition.
do
M
shell discontinuity moment for design operating condition.
g
M
flange design moment for the gasket seating condition determined using paragraph 4.16.
o
M
flange design moment for the design condition determined using paragraph 4.16 (see
paragraph 4.7.5.2 for exception)
r
M
moment from the head reaction force.
n geometry parameter for the Type D head alternative design procedure.
ν
is Poisson’s ratio.
P
design pressure.
e
P
pressure factor to adjust the design rules for external pressure.
φ
one-half central angle of the head for the Type D head alternative design procedure.
q
inside depth of the flange to the base of the head.
R
mean radius of a Type D head.
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2010 SECTION VIII, DIVISION 2
4-161
r
inside knuckle radius.
f
g
S allowable stress from Annex 3.A for the flange evaluated at the
gasket seating condition.
f
m
S membrane stress in the flange.
f
mbi
S
membrane plus bending stress on the inside surface of the flange.
f
mbo
S membrane plus bending stress on the outside surface of the flange.
f
o
S allowable stress from Annex 3.A for the flange evaluated at the design temperature.
hb
S bending stress at the head-to-flange junction.
hg
S allowable stress from Annex 3.A for the head evaluated at the gasket seating condition.
hm
S head membrane stress.
hl
S local membrane stress at the head-to-flange junction.
hlbi
S local membrane plus bending stress at the head-to-flange junction on the inside surface of
the head.
hlbo
S local membrane plus bending stress at the head-to-flange junction on the outside surface of
the head.
ho
S allowable stress from Annex 3.A for the head evaluated at the design temperature.
yT
S yield strength from Annex 3.D evaluated at the design temperature.
u
S minimum specified ultimate tensile strength from Annex 3.D.
T flange thickness.
*T flange thickness for a Type C Head.
g
T required flange thickness for the gasket seating condition.
o
T required flange thickness for design operating condition.
t required head thickness.
dg
V shell discontinuity shear force for the gasket seating condition.
do
V shell discontinuity shear force for design operating condition.
g
W
bolt load for the gasket seating condition.
o
W bolt load for design operating condition.
2010 SECTION VIII, DIVISION 2
4-162
4.7.7 Tables
Table 4.7.1 – Junction Stress Equations and Acceptance Criteria for a Type D Head
Operating Conditions Gasket Seating Conditions
2
hm e
PR
SP
t
=+
[
]
cos
2
do
hl e
V
PR
SP
tBt
φ
π
=+ +
2
6
do
hb
M
S
B
t
π
=
hlbi hl hb
SSS=+
hlbo hl hb
SSS=−
[]
22
2
14 1
cot
41
f
mdoe
BP q K
SVP
BT B K
π
φ
π
⎛⎞⎛⎞
+
⎛⎞
=−−+
⎜⎟⎜⎟
⎜⎟
−
⎝⎠
⎝⎠⎝⎠
1
4
0.525
do
fb do
M
n
SV
Btk B
λ
⎛⎞
=−
⎜⎟
⎝⎠
f
mbo fm fb
SSS=−
f
mbi fm fb
SSS=+
0.0
hm
S
=
[
]
cos
dg
hl
V
S
B
t
φ
π
=
2
6
dg
hb
M
S
B
t
π
=
hlbi hl hb
SSS
=
+
hlbo hl hb
SSS
=
−
()
2
2
11
1
fm dg
K
SV
BT K
π
⎛⎞
+
=−
⎜⎟
−
⎝⎠
1
4
0.525
dg
fb dg
M
n
SV
Btk B
λ
⎛⎞
=−
⎜⎟
⎝⎠
f
mbo fm fb
SSS
=
−
f
mbi fm fb
SSS
=
+
Acceptance Criteria
hm ho
SS≤
1.5
hl ho
SS≤
1.5
hlbi ho
SS≤
1.5
hlbo ho
SS≤
f
mfo
SS≤
1.5
f
mbo fo
SS≤
1.5
f
mbi fo
SS≤
hm hg
SS
≤
1.5
hl hg
SS
≤
1.5
hlbi hg
SS
≤
1.5
hlbo hg
SS
≤
f
mfg
SS
≤
1.5
f
mbo fg
SS
≤
1.5
f
mbi fg
SS
≤
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2010 SECTION VIII, DIVISION 2
4-163
4.7.8 Figures
Tangent Line
Tangent Line
Edge of Weld
Shall Not Overlap
Knuckle
t
Gasket
Knuckle
Radius
(a) Loose Flange Type
L
Not Less Than
2t and In No
Case Less Than
13 mm (1/2 in.)
Gasket
Knuckle
Radius
(b) Integral Flange Type
L
Ellipsoidal or
Torispherical Head
Toriconical Head
Hemispherical
Head
Flange
Skirt
t
t
Toriconical Head
Hemispherical
Head
t
Ellipsoidal or
Torispherical Head
Skirt
t
t
Note: See Table 4.2.5, Details 2 and 3 for transition requirements for a head and skirt with different
thicknesses
Figure 4.7.1 – Type A Dished Cover with a Bolting Flange
L
1/2A
1/2C
Preferably
2t Min.
1/2B
Ring Gasket
Shown
t
0.7t Min.
T
t
Figure 4.7.2 – Type B Spherically Dished Cover with a Bolting Flange
2010 SECTION VIII, DIVISION 2
4-164
1/2B
Ring Gasket
Shown
t
L
1/2C
T*
T* = T > t
Preferably
2t Min.
Figure 4.7.3 – Type C Spherically Dished Cover with a Bolting Flange
h
r
T
1/2B
1/2C
Use Any Suitable
Type of Gasket
Centroid
1/2A
1/4 (A + B)
Point of H
D
Action
Full Penetration
Weld
t
L
Smooth As Welded.
Smooth Weld Both Sides
H
D
H
r
β
1
Figure 4.7.4 – Type D Spherically Dished Cover with a Bolting Flange
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