ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules
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2010 SECTION VIII, DIVISION 2
4-115
()
2
2
23 2
3
0.78
,
n
npr nn
n
Hpr
t
A t L t R t for VariableThickness Openings
t
where L L t
⎛⎞
=++
⎜⎟
⎝⎠
>+
(4.5.20)
2
3
,
,
nH
Hpr
A t L forVariableThickness Openings
where L L t
or forUniformThickness Openings
=
≤+
(4.5.21)
3 nI
AtL= (4.5.22)
2
41 41
0.5AL= (4.5.23)
2
42 42
0.5
A
L=
(4.5.24)
2
43 43
0.5AL= (4.5.25)
5ae
AWt= (4.5.26)
5
=
bRe
A L t for nozzles inserted through the vessel wall (4.5.27)
()
5bRne
A L t t for nozzles abutting thevessel wall=− (4.5.28)
[
]
555
min ,
ab
A
AA=
(4.5.29)
n
rn
S
f
S
=
(4.5.30)
p
rp
S
f
S
=
(4.5.31)
e) STEP 5 – Determine the effective radius of the shell as follows:
1) For cylindrical shells:
0.5=
eff i
R
D (4.5.32)
2) For conical shells
eff
R
is the inside radius of the conical shell at the nozzle centerline to cone
junction. The radius is measured normal to the longitudinal axis of the conical shell
f) STEP 6 – Determine the effective shell thickness for nozzles in cylindrical or conical shells as follows:
5Rrp
eff
R
tL A f
tt
tL
+
⎛⎞
=
⎜⎟
⎝⎠
(4.5.33)
2010 SECTION VIII, DIVISION 2
4-116
g) STEP 7 – Determine the applicable forces:
()
NxnH
f
PR L t=− (4.5.34)
()
SxsRn
f
PR L t=+ (4.5.35)
Yxsnc
f
PR R= (4.5.36)
ln
n
xn
nn
n
t
R
R
t
R
=
⎡⎤
+
⎢⎥
⎣⎦
(4.5.37)
ln
eff
xs
eff eff
eff
t
R
R
t
R
=
⎡⎤
+
⎢⎥
⎢⎥
⎣⎦
(4.5.38)
h) STEP 8 – Determine the average local primary membrane stress and the general primary membrane
stress in the vessel:
()
NSY
avg
T
f
ff
A
σ
++
=
(4.5.39)
x
s
circ
eff
PR
t
σ
=
(4.5.40)
i) STEP 9 – Determine the maximum local primary membrane stress at the nozzle intersection:
()
max 2 ,
L avg circ circ
P
σσ σ
⎡⎤
=−
⎣⎦
(4.5.41)
j) STEP 10 – The calculated maximum local primary membrane stress should satisfy Equation (4.5.42). If
the nozzle is subjected to internal pressure, then the allowable stress,
allow
S , is given by Equation
(4.5.43). If the nozzle is subjected to external pressure, then the allowable stress is given by Equation
(4.5.44) where
ha
F is evaluated in paragraph 4.4 for the shell geometry being evaluated (e.g. cylinder,
spherical shell, or formed head).
L allow
PS≤ (4.5.42)
where,
1.5
allow
S SE for internal pressure= (4.5.43)
allow ha
S F for external pressure= (4.5.44)
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2010 SECTION VIII, DIVISION 2
4-117
k) STEP 11 – Determine the maximum allowable working pressure of the nozzle:
max1
2
allow
p
x
s
Teff
S
P
A
R
At
=
−
(4.5.45)
max 2
x
s
t
PS
R
⎛⎞
=
⎜⎟
⎝⎠
(4.5.46)
[
]
max max1 max 2
min ,PPP= (4.5.47)
where,
()( )
pxnH xsRnnc
A
RL t RL t R=−+++ (4.5.48)
4.5.5.2 If the nozzle is subject to external forces and moments from supplemental loads as defined in
paragraph 4.1, then the local stresses at the nozzle-to-shell intersection shall be evaluated in accordance
with paragraph 4.5.15.
4.5.6 Hillside Nozzle in a Cylindrical Shell
For a hillside nozzle in a cylindrical shell (see Figure 4.5.4), the design procedure in paragraph 4.5.5 shall be
used with the following substitution.
max ,
2
ncl
nc n
R
R
R
⎡⎤
⎛⎞
=
⎜⎟
⎢⎥
⎝⎠
⎣⎦
(4.5.49)
where,
()
12ncl eff
RR
θ
θ
=−
(4.5.50)
1
1
cos
X
eff
D
R
θ
−
⎡⎤
=
⎢⎥
⎢⎥
⎣⎦
(4.5.51)
1
2
cos
Xn
eff
DR
R
θ
−
⎡⎤
+
=
⎢⎥
⎢⎥
⎣⎦
(4.5.52)
4.5.7 Nozzle in a Cylindrical Shell Oriented at an Angle from the Longitudinal Axis
For a nozzle in a cylindrical shell oriented at an angle from the longitudinal axis, the design procedure in
paragraph 4.5.5 shall be used with the following substitution (see Figure 4.5.5):
[]
sin
n
nc
R
R
θ
= (4.5.53)
2010 SECTION VIII, DIVISION 2
4-118
4.5.8 Radial Nozzle in a Conical Shell
For a radial nozzle in a conical shell (see Figure 4.5.6), the design procedure in paragraph 4.5.5 shall be
used with the following substitutions.
[]
[]
()
sin
cos 2
c
Seff Rn
L
P
f
RLt
α
α
⎛⎞
=+ +
⎜⎟
⎝⎠
(4.5.54)
[]
[]
sin
2
cos
nc
eff nc
Y
R
PR R
f
α
α
⎛⎞
+
⎜⎟
⎝⎠
=
(4.5.55)
[
]
()
[]
sin
cos
eff c
circ
eff
PR L
t
α
σ
α
+
=
(4.5.56)
[]
[]
max
2sin
cos
allow
peffc
Teff
S
P
AR L
At
α
α
=
+
−
(4.5.57)
()
[]
[]
[
]
(
)
[]
0.5 sin
sin
2cos cos
α
α
αα
⎡⎤
+
⎛⎞
+
⎛⎞
⎢⎥
=−++ +
⎜⎟
⎜⎟
⎜⎟
⎝⎠
⎢⎥
⎝⎠
⎣⎦
nc eff nc
cRn
pxnH eff
RR R
LLt
ARLtR
(4.5.58)
cRnnc
LLtR=++ (4.5.59)
4.5.9 Nozzle in a Conical Shell
4.5.9.1 If a nozzle in a conical shell is oriented perpendicular to the longitudinal axis (see Figure 4.5.7),
then the design procedure in paragraph 4.5.8 shall be used with the following substitution.
[]
cos
n
nc
R
R
α
=
(4.5.60)
4.5.9.2 If a nozzle in a conical shell is oriented parallel to the longitudinal axis (see Figure 4.5.8), then the
design procedure in paragraph 4.5.8 shall be used with the following substitution.
[]
sin
n
nc
R
R
α
=
(4.5.61)
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2010 SECTION VIII, DIVISION 2
4-119
4.5.10 Radial Nozzle in a Spherical Shell or Formed Head
4.5.10.1 The procedure to design a radial nozzle in a spherical shell or formed head subject to pressure
loading is shown below. The parameters used in this design procedure are shown in Figure 4.5.9.
a) STEP 1 – Determine the effective radius of the shell or formed head as follows.
1) For spherical shells:
0.5=
eff i
R
D (4.5.62)
2) For ellipsoidal heads:
2
0.9
2
62
ii
eff
DD
R
h
⎡⎤
⎛⎞
=+
⎢⎥
⎜⎟
⎝⎠
⎢⎥
⎣⎦
(4.5.63)
3) For torispherical heads:
eff
R
L= (4.5.64)
b) STEP 2 – Calculate the limit of reinforcement along the vessel wall.
1) For integrally reinforced nozzles in spherical shells and ellipsoidal heads:
min , 2
Reffn
LRtR
⎡
⎤
=
⎣
⎦
(4.5.65)
2) For integrally reinforced nozzles in torispherical heads:
()
1
2
i
RRnn
D
LDRt=− ++
(4.5.66)
2
min , 2
Reffn
LRtR
⎡⎤
=
⎣⎦
(4.5.67)
[
]
12
min ,
RRR
L
LL=
(4.5.68)
3) For pad reinforced nozzles:
1Reff
LRtW=+ (4.5.69)
()
()
2Reff e
L R ttt=++ (4.5.70)
3
2
Rn
LR= (4.5.71)
[
]
123
min , ,
RRRR
L
LLL=
(4.5.72)
c) STEP 3 – Calculate the limit of reinforcement along the nozzle wall projecting outside the vessel surface.
2010 SECTION VIII, DIVISION 2
4-120
1
min ,
Hepnnpr
L t t F R t L t for nozzles inserted through
thevessel wall
⎡⎤
=++ +
⎣⎦
(4.5.73)
1
min ,
Hepnnpr
L t t F R t L for nozzles abutting the
vessel wall
⎡⎤
=++
⎣⎦
(4.5.74)
For ellipsoidal and torispherical heads,
min , 0.35
pnp oi
FCC forXD
⎡⎤
=>
⎣⎦
(4.5.75)
0.35
pn o i
FC forX D=≤ (4.5.76)
0.35
exp
16
io
p
DX
C for ellipsoidal heads
t
−
⎡⎤
=
⎢⎥
⎣⎦
(4.5.77)
0.35
exp
8
io
p
DX
C for torispherical heads
t
−
⎡⎤
=
⎢⎥
⎣⎦
(4.5.78)
=++
oRnn
X
DRt (4.5.79)
For spherical shells and heads,
=
pn
FC (4.5.80)
The parameter
n
C is given by Equation (4.5.81).
0.35
min , 1.0
e
n
n
tt
C
t
⎡⎤
⎛⎞
+
⎢⎥
=
⎜⎟
⎢⎥
⎝⎠
⎣⎦
(4.5.81)
d) STEP 4 – Calculate the limit of reinforcement along the nozzle wall projecting inside the vessel surface,
if applicable.
2
min ,
⎡⎤
=
⎣⎦
Ipnnpr
LFRtL (4.5.82)
e) STEP 5 – Determine the total available area near the nozzle opening (see Figure 4.5.1) where
rn
f
and
rp
f
are given by Equations (4.5.30) and (4.5.31), respectively.
1234142435
()
Trn rp
AAfAA AA A fA=+ + + + + + (4.5.83)
1 R
AtL= (4.5.84)
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2010 SECTION VIII, DIVISION 2
4-121
()
2
2
23 2
3
0.78
,
n
npr nn
n
Hpr
t
A t L t R t for VariableThickness Openings
t
where L L t
⎛⎞
=++
⎜⎟
⎝⎠
>+
(4.5.85)
2
3
,
,
nH
Hpr
A t L forVariableThickness Openings
where L L t
or forUniformThickness Openings
=
≤+
(4.5.86)
3 nI
AtL= (4.5.87)
2
41 41
0.5AL= (4.5.88)
2
42 42
0.5
A
L=
(4.5.89)
2
43 43
0.5AL= (4.5.90)
5ae
AWt= (4.5.91)
5
=
bRe
A L t for nozzles inserted through the vessel wall (4.5.92)
()
5
=−
bRne
A L t t for nozzles abutting thevessel wall (4.5.93)
[
]
555
min ,=
ab
A
AA
(4.5.94)
f) STEP 6 – Determine the applicable forces.
()
NxnH
f
PR L t=−
(4.5.95)
()
2
x
sR n
S
PR L t
f
+
=
(4.5.96)
2
x
snc
Y
PR R
f =
(4.5.97)
ln
n
xn
nn
n
t
R
R
t
R
=
⎡⎤
+
⎢⎥
⎣⎦
(4.5.98)
ln
eff
xs
eff eff
eff
t
R
R
t
R
=
⎡⎤
+
⎢⎥
⎢⎥
⎣⎦
(4.5.99)
2010 SECTION VIII, DIVISION 2
4-122
g) STEP 7 – Determine the effective thickness for nozzles in spherical shells or ellipsoidal or torispherical
heads as follows.
5Rrp
eff
R
tL A f
tt
tL
+
⎛⎞
=
⎜⎟
⎝⎠
(4.5.100)
h) STEP 8 – Determine the average local primary membrane stress and the general primary membrane
stress in the vessel.
()
NSY
avg
T
f
ff
A
σ
++
=
(4.5.101)
2
x
s
circ
eff
PR
t
σ
=
(4.5.102)
i) STEP 9 – Determine the maximum local primary membrane stress at the nozzle intersection.
{
}
max 2 ,
L avg circ circ
P
σσ σ
⎡⎤
=−
⎣⎦
(4.5.103)
j) STEP 10 – The calculated maximum local primary membrane stress should satisfy Equation (4.5.104). If
the nozzle is subjected to internal pressure, then the allowable stress,
allow
S , is given by Equation
(4.5.43). If the nozzle is subjected to external pressure, then the allowable stress is given by Equation
(4.5.44).
L allow
PS≤ (4.5.104)
k) STEP 11 – Determine the maximum allowable working pressure of the nozzle.
max1
2
2
allow
p
x
s
Teff
S
P
A
R
At
=
−
(4.5.105)
max 2
2
x
s
t
PS
R
⎛⎞
=
⎜⎟
⎝⎠
(4.5.106)
[
]
max max1 max 2
min ,PPP= (4.5.107)
where,
()
()
2
x
sR n nc
pxnH
R
LtR
ARLt
++
=−+
(4.5.108)
4.5.10.2 If the nozzle is subject to external forces and moments from supplemental loads as defined in
paragraph 4.1, then the local stresses at the nozzle-to-shell intersection shall be evaluated in accordance
with paragraph 4.5.15.
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2010 SECTION VIII, DIVISION 2
4-123
4.5.11 Hillside or Perpendicular Nozzle in a Formed Head
4.5.11.1 If a hillside or perpendicular nozzle is located in an ellipsoidal head (see Figure 4.5.10), the
design procedure in paragraph 4.5.10 shall be used with the following substitution.
2
2
1
2
i
T
R
D
D
D
h
=−
(4.5.109)
4.5.11.2 If a hillside or perpendicular nozzle is located in a head type that is not an ellipsoidal heads (see
Figure 4.5.10), the design procedure in paragraph 4.5.10 shall be used with the following substitution.
()
12nc eff
RR
θ
θ
=− (4.5.110)
1
1
cos
R
eff
D
R
θ
−
⎡⎤
=
⎢⎥
⎢⎥
⎣⎦
(4.5.111)
1
2
cos
Rn
eff
DR
R
θ
−
⎡⎤
+
=
⎢⎥
⎢⎥
⎣⎦
(4.5.112)
4.5.12 Circular Nozzles in a Flat Head
4.5.12.1 The procedure to design a nozzle in a flat head subject to pressure loading is shown below. The
parameters used in this design procedure are shown in Figures 4.5.9. As an alternative, a central nozzle in
an integral flat head may be designed using the procedure in paragraph 4.6.3.
a) STEP 1 – Calculate the maximum unit moment at the nozzle intersection.
()
4
2
6
rf
o
pe
St
M
tCt
=
+
(4.5.113)
42
(0.5)
min , 0.6
⎡⎤
⎧⎫
+
=
⎨⎬
⎢⎥
⎩⎭
⎣⎦
e
p
n
wLt
C
Rt
(4.5.114)
b) STEP 2 – Calculate the nozzle parameters.
nnm
n
tR
285.1
=
λ
(4.5.115)
[
]
[
]
22
1
sinh sin
L
L
CCC=+ (4.5.116)
[
]
[
]
22
2
sinh sin
LL
CCC=− (4.5.117)
()
{
}
12
min , 6.0
L n pr pr
CLtL
λ
⎡⎤
=++
⎣⎦
(4.5.118)
2010 SECTION VIII, DIVISION 2
4-124
()
1
3
1
12
min ,
λ
−
+
=
⎡⎤
++
⎣⎦
pr
pr n pr
Lt
C
Lt L
(4.5.119)
0.5=+
nm n n
R
Rt (4.5.120)
ln
n
xn
nn
n
t
R
R
t
R
=
⎡⎤
+
⎢⎥
⎣⎦
(4.5.121)
()
41 43
0.5
λ
=+++
tne
x
t t L L for nozzles inserted through
the vessel wall
(4.5.122)
()
41
0.5
λ
=+
tne
x
t L for nozzles abutting the
vessel wall
(4.5.123)
[
]
exp=−
tt
Cx (4.5.124)
c) STEP 3 – Determine the maximum local primary membrane stress in the nozzle at the intersection.
2
13
2
2
on nm t xn
L
nn
M
RCCC PR
P
tC t
λ
=+ (4.5.125)
d) STEP 4 – The maximum local primary membrane stress at the nozzle intersection shall satisfy Equation
(4.5.126). If the nozzle is subjected to internal pressure, then the allowable stress,
allow
S , is given by
Equation (4.5.43). If the nozzle is subjected to external pressure, then the allowable stress is given by
Equation (4.5.44).
L allow
PS≤ (4.5.126)
4.5.12.2 If the nozzle is subject to external forces and moments from supplemental loads as defined in
paragraph 4.1, then the local stresses at the nozzle-to-shell intersection shall be evaluated in accordance
with paragraph 4.5.15.
4.5.13 Spacing Requirements for Nozzles
4.5.13.1 If the limits of reinforcement determined in accordance with paragraph 4.5.5 for nozzles in
cylindrical or conical shells or paragraph 4.5.10 for nozzles in spherical or formed heads, do not overlap, no
additional analysis is required. If the limits of reinforcement overlap, the following procedure shall be used or
the design shall be evaluated in accordance with the design by analysis rules of Part 5.
4.5.13.2 The maximum local primary membrane stress and the nozzle maximum allowable working
pressure shall be determined following paragraphs 4.5.5 or 4.5.10, for each individual nozzle with the value of
R
L determined as follows.
a) For two openings with overlapping limits of reinforcement (see Figure 4.5.11):
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