ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules
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2010 SECTION VIII, DIVISION 2
4-235
Table 4.12.10 – Stress Calculations And Acceptance Criteria For Type 9 Noncircular Vessels
(Obround Cross Section)
Acceptance Criteria – Critical Locations of Maximum Stress
cB
m
SS≤
1.5
cB cB
mbi
SS S+≤
1.5
cB cB
mbo
SS S+≤
cC
m
SS≤
1.5
cC cC
mbi
SS S+≤
1.5
cC cC
mbo
SS S+≤
l
m
SS
≤
1.5
llA
mbi
SS S+≤
1.5
llA
mbo
SS S+≤
1.5
llB
mbi
SS S+≤
1.5
llB
mbo
SS S+≤
Acceptance Criteria – Defined Locations for Stress Calculation
Not Applicable
1.5
llY
mbi
SS S+≤
1.5
llY
mbo
SS S+≤
Nomenclature For Stress Results
cB
m
S membrane stress in the circular arc at point B.
,
cB cB
bi bo
SS bending stress in the circular arc at point B on the inside and outside surfaces,
respectively.
cC
m
S membrane stress in the circular arc at point C.
,
cC cC
bi bo
SS bending stress in the circular arc at point C on the inside and outside surfaces,
respectively.
l
m
S membrane stress in the long side.
,
lB lB
bi bo
SS
bending stress in the long side at point B on the inside and outside surfaces,
respectively.
,
lA lA
bi bo
SS bending stress in the long side at point A on the inside and outside surfaces,
respectively.
,
lY lY
bi bo
SS bending stress in the long side at a point defined by
Y
on the inside and outside
surfaces, respectively.
s
t
m
S membrane stress in stay bar or plate, as applicable.
2010 SECTION VIII, DIVISION 2
4-236
Table 4.12.11 – Stress Calculations And Acceptance Criteria For Type 10 Noncircular Vessels
(Reinforced Obround Cross Section)
Membrane And Bending Stresses – Critical Locations of Maximum Stress
()
11
cB
m
m
PRp
S
AptE
=
+
2
2
2
11 3
3
6
cc
cB cB
ii
bi bo
c
ob
cPpLc
C
SS L
cIE A
⎛⎞ ⎡ ⎤
=− = −
⎜⎟
⎢⎥
⎝⎠ ⎣ ⎦
()
()
2
11
cC
m
m
PR L p
S
AptE
+
=
+
()
2
2
2
11 3
32
6
cc
cC cC
ii
bi bo
c
ob
cPpLc
C
SS Lr
cIE A
⎛⎞ ⎡ ⎤
=− = + −
⎜⎟
⎢⎥
⎝⎠ ⎣ ⎦
()
11
l
m
m
PRp
S
AptE
=
+
2
2
11 3
6
ll
lA lA
ii
bi bo
l
ob
cPLpc
C
SS
cIEA
⎛⎞ ⎡ ⎤
−
=− =
⎜⎟
⎢⎥
⎝⎠ ⎣ ⎦
2
2
2
11 3
3
6
ll
lB lB
ii
bi bo
l
ob
cPLpc
C
SS L
cIE A
⎛⎞ ⎡ ⎤
=− = −
⎜⎟
⎢⎥
⎝⎠ ⎣ ⎦
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2010 SECTION VIII, DIVISION 2
4-237
Table 4.12.11 – Stress Calculations And Acceptance Criteria For Type 10 Noncircular Vessels
(Reinforced Obround Cross Section)
Membrane And Bending Stresses – Defined Locations for Stress Calculation
2
22
11 3
62
ll
lY lY
ii
bi bo
l
ob
cPpc
LC
Y
SS
cIE A
⎛⎞ ⎡ ⎤
−
=− = +
⎜⎟
⎢⎥
⎝⎠ ⎣ ⎦
Equation Constants
2
3
2
L
Ar
r
π
⎡⎤
⎛⎞
=+
⎜⎟
⎢⎥
⎝⎠
⎣⎦
2
2
22
2
23 12
LL
Cr
rr
π
⎡
⎤
⎛⎞ ⎛⎞
=++
⎢
⎥
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
⎢
⎥
⎣
⎦
Acceptance Criteria – Critical Locations of Maximum Stress
cB
m
SS≤
1.5
cB cB
mbi
SS S+≤
1.5
cB cB
mbo
SS S+≤
cC
m
SS≤
1.5
cC cC
mbi
SS S+≤
1.5
cC cC
mbo
SS S+≤
l
m
SS
≤
1.5
llA
mbi
SS S+≤
1.5
llA
mbo
SS S+≤
1.5
llB
mbi
SS S+≤
1.5
llB
mbo
SS S+≤
Acceptance Criteria – Defined Locations for Stress Calculation
Not Applicable
1.5
llY
mbi
SS S+≤
1.5
llY
mbo
SS S+≤
Nomenclature For Stress Results
2010 SECTION VIII, DIVISION 2
4-238
Table 4.12.11 – Stress Calculations And Acceptance Criteria For Type 10 Noncircular Vessels
(Reinforced Obround Cross Section)
cB
m
S
membrane stress in the circular arc at point B.
,
cB cB
bi bo
SS bending stress in the circular arc at point B on the inside and outside surfaces,
respectively.
cC
m
S membrane stress in the circular arc at point C.
,
cC cC
bi bo
SS bending stress in the circular arc at point C on the inside and outside surfaces,
respectively.
l
m
S membrane stress in the long side.
,
lB lB
bi bo
SS bending stress in the long side at point B on the inside and outside surfaces,
respectively.
,
lA lA
bi bo
SS bending stress in the long side at point A on the inside and outside surfaces,
respectively.
,
lY lY
bi bo
SS bending stress in the long side at a point defined by Y on the inside and outside
surfaces, respectively.
s
t
m
S membrane stress in stay bar or plate, as applicable.
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2010 SECTION VIII, DIVISION 2
4-239
Table 4.12.12 – Stress Calculations And Acceptance Criteria For Type 11 Noncircular Vessels
(Obround Cross Section With Single Stay Plate Or Multiple Bars)
Membrane And Bending Stresses - Defined Locations for Stress Calculation
1
cB
m
m
PR
S
tE
=
()
2
1
22
1
23
⎛⎞
⎡⎤
=− = − − +
⎜⎟
⎢⎥
⎣⎦
⎝⎠
cB cB
ii
bi bo
ob
cPbLc
C
SS FBAL AL
cIAE
()
22
1
2
2
cC
m
m
P
SRLLF
tE
⎡⎤
=+−
⎣⎦
()()
2
1
22
1
2
23
⎛⎞
⎡
⎤
=− = − − − + +
⎜⎟
⎢
⎥
⎣
⎦
⎝⎠
cC cC
ii
bi bo
ob
cPbLc
C
S S F B AL AR A L R
cIAE
2
l
m
m
PR
S
tE
=
2
1
2
23
⎛⎞
⎡⎤
=− = −
⎜⎟
⎢⎥
⎣⎦
⎝⎠
lA lA
ii
bi bo
ob
cPbLc
C
SS BF
cIAE
()
2
1
22
2
23
⎛⎞
⎡⎤
=− = − − +
⎜⎟
⎢⎥
⎣⎦
⎝⎠
lB lB
ii
bi bo
ob
cPbLc
C
S S F B AL AL
cIAE
2
3
st
m
st
PL F
S For A Stay Plate
tE
=
2
2
3
4
st
m
st
PL Fp
S For Stay Bars
tE
π
=
2010 SECTION VIII, DIVISION 2
4-240
Table 4.12.12 – Stress Calculations And Acceptance Criteria For Type 11 Noncircular Vessels
(Obround Cross Section With Single Stay Plate Or Multiple Bars)
Equation Constants
3
1
1
12
bt
I =
3
2
2
12
bt
I =
22
1
2
LI
AR
R
I
π
⎡⎤
⎛⎞
⎛⎞
=+
⎢⎥
⎜⎟
⎜⎟
⎝⎠
⎝⎠
⎣⎦
2
2
2222
11
2
LLII
BR
R
RI I
π
⎡⎤
⎛⎞ ⎛⎞
⎛⎞ ⎛⎞
=+ +
⎢⎥
⎜⎟ ⎜⎟
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
⎢⎥
⎝⎠ ⎝⎠
⎣⎦
2
2
2222
1
11
23 12
LLII
CR
R
RI I
π
⎡⎤
⎛⎞ ⎛⎞
⎛⎞ ⎛⎞
=+ +
⎢⎥
⎜⎟ ⎜⎟
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
⎢⎥
⎝⎠ ⎝⎠
⎣⎦
(
)
()
11
2
1
32
6
AD BC
F
AE B
−
=
−
32
222
1
3
1
22 2
11
2
12 2
LLI
RRI
DR
LI I
RI I
π
π
⎡
⎤
⎛⎞
⎛⎞ ⎛⎞
+
+
⎢
⎥
⎜⎟
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
⎝⎠
⎢
⎥
=
⎢
⎥
⎛⎞ ⎛⎞
⎛⎞
⎢
⎥
+
⎜⎟ ⎜⎟
⎜⎟
⎢
⎥
⎝⎠
⎝⎠ ⎝⎠
⎣
⎦
32
222
1
3
1
22 2
11
46
24 3
LLI
RRI
ER
LI I
RI I
π
π
⎡
⎤
⎛⎞
⎛⎞ ⎛⎞
+
+
⎢
⎥
⎜⎟
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
⎝⎠
⎢
⎥
=
⎢
⎥
⎛⎞ ⎛⎞
⎛⎞
⎢
⎥
+
⎜⎟ ⎜⎟
⎜⎟
⎢
⎥
⎝⎠
⎝⎠ ⎝⎠
⎣
⎦
Acceptance Criteria - Critical Locations of Maximum Stress
cB
m
SS≤
1.5
cB cB
mbi
SS S+≤
1.5
cB cB
mbo
SS S+≤
cC
m
SS≤
1.5
cC cC
mbi
SS S+≤
1.5
cC cC
mbo
SS S+≤
st
m
SS
≤
l
m
SS
≤
1.5
llA
mbi
SS S+≤
1.5
llA
mbo
SS S+≤
1.5
llB
mbi
SS S+≤
1.5
llB
mbo
SS S+≤
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2010 SECTION VIII, DIVISION 2
4-241
Table 4.12.12 – Stress Calculations And Acceptance Criteria For Type 11 Noncircular Vessels
(Obround Cross Section With Single Stay Plate Or Multiple Bars)
Nomenclature For Stress Results
cB
m
S
membrane stress in the circular arc at point B.
,
cB cB
bi bo
SS bending stress in the circular arc at point B on the inside and outside surfaces,
respectively.
cC
m
S membrane stress in the circular arc at point C.
,
cC cC
bi bo
SS bending stress in the circular arc at point C on the inside and outside surfaces,
respectively.
l
m
S membrane stress in the long side.
,
lB lB
bi bo
SS bending stress in the long side at point B on the inside and outside surfaces,
respectively.
,
lA lA
bi bo
SS bending stress in the long side at point A on the inside and outside surfaces,
respectively.
,
lY lY
bi bo
SS bending stress in the long side at a point defined by Y on the inside and outside
surfaces, respectively.
s
t
m
S membrane stress in stay bar or plate, as applicable.
2010 SECTION VIII, DIVISION 2
4-242
Table 4.12.13 – Stress Calculations And Acceptance Criteria For Type 12 Noncircular Vessels
(Circular Cross Section With Single Stay Plate)
Membrane And Bending Stresses – Critical Locations of Maximum Stress
Equal Pressure Unequal Pressure
1
1
m
m
PR
S
tE
=
()
2
11
2
1
2
38
ii
bi bo
ob
cbc
Pt
SS
cIE
π
⎡⎤
⎛⎞
⎢⎥
=− =
⎜⎟
−
⎢⎥
⎝⎠
⎣⎦
()
2
11
2
3
2
38
st
m
m
Pt
S
R
tE
π
π
=
−
1
m
m
PR
S
tE
=
()
2
2
12
1
1
3
2
1
3
1
3
2
38
6
ii
bi bo
ob
R
PP
cbc
t
SS P
cIE
t
t
π
⎡
⎤
⎢
⎥
−
⎛⎞
⎛⎞
⎢
⎥
=− = +
⎜⎟
⎜⎟
⎢
⎥
−
⎛⎞
⎝⎠
⎝⎠
⎢
⎥
+
⎜⎟
⎢
⎥
⎝⎠
⎣
⎦
(
)
()
2
11 2
2
3
38
st
m
m
tPP
S
R
tE
π
π
+
=
−
(
)
2
11 2
1
3
2
vi
st st
i
bi bo
ob
JP PLbc
c
SS ForLR
cIE
−
⎛⎞
=− = ≤
⎜⎟
⎝⎠
(
)
2
11 2
1
3
4
2
i
st st
i
bi bo
ob
JP P Rbc
c
SS ForLR
cIE
−
⎛⎞
=− = >
⎜⎟
⎝⎠
Equation Constants
3
1
1
12
bt
I =
3
3
3
12
bt
I =
() ()
() ()
2
1
34
-0.055314 0.14237 - 0.041311
min , 5.0
0.0050644 - 0.00021145
hh
hh
RR
J
RR
⎡
⎤
⎛⎞
++
⎢
⎥
⎜⎟
=
⎜⎟
⎢
⎥
⎝⎠
⎣
⎦
2
max ,
2
v
h
v
L
R
R
R
L
⎡
⎤
=
⎢
⎥
⎣
⎦
Acceptance Criteria - Critical Locations of Maximum Stress
Equal Pressure Unequal Pressure
m
SS≤
1.5
mbi
SS S+≤
1.5
mbo
SS S+≤
st
m
SS≤
m
SS
≤
1.5
mbi
SS S
+
≤
1.5
mbo
SS S
+
≤
st
m
SS
≤
1.5
st st
mbi
SS S+≤
1.5
st st
mbo
SS S+≤
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2010 SECTION VIII, DIVISION 2
4-243
Table 4.12.13 – Stress Calculations And Acceptance Criteria For Type 12 Noncircular Vessels
(Circular Cross Section With Single Stay Plate)
Nomenclature For Stress Results
m
S
membrane stress in the pipe.
,
bi bo
SS bending stress in the pipe.
s
t
m
S membrane stress in stay plate, as applicable.
,
s
tst
bi bo
SS bending stress in the stay plate on the inside and outside surfaces, respectively.
Table 4.12.14 – Effective Width Coefficient
Material
Effective Width Coefficient
Δ
p
si
kPa
Carbon Steel 6000 15754
Austenitic Stainless Steel 5840 15334
Ni-Cr-Fe 6180 16229
Ni-Fe-Cr 6030 15834
Aluminum 3560 9348
Nickel Copper 5720 15021
Unalloyed Titanium 4490 11789
2010 SECTION VIII, DIVISION 2
4-244
Table 4.12.15 – Compressive Stress Calculations
Short Side Plates Long Side Plates End Plates
()
12
2
e
mA
PhH
S
tH th
=
+
1
2
e
mB
Ph
S
t
=
()
2
2
*
1
2
12 1
y
crA A
E
t
SK
H
π
ν
⎛⎞
=
⎜⎟
−
⎝⎠
2
**
*
4
y
crA y
crA
S
SS
S
=−
()
2
2
*
1
2
12 1
y
crB B
v
E
t
SK
L
π
ν
⎛⎞
=
⎜⎟
−
⎝⎠
2
**
*
4
y
crB y
crB
S
SS
S
=−
v
AA
L
KKx
H
⎛⎞
==
⎜⎟
⎝⎠
BB
v
H
KKx
L
⎛⎞
==
⎜⎟
⎝⎠
()
12
2
e
mA
PhH
S
tH th
=
+
2
2
=
e
mB
PH
S
t
()
2
2
*
2
2
12 1
y
crA A
E
t
SK
h
π
ν
⎛⎞
=
⎜⎟
−
⎝⎠
2
**
*
4
y
crA y
crA
S
SS
S
=−
()
2
2
*
2
2
12 1
y
crB B
v
E
t
SK
L
π
ν
⎛⎞
=
⎜⎟
−
⎝⎠
2
**
*
4
y
crB y
crB
S
SS
S
=−
v
AA
L
KKx
h
⎛⎞
==
⎜⎟
⎝⎠
BB
v
h
KKx
L
⎛⎞
==
⎜⎟
⎝⎠
()
25
2
ev
mA
v
PHL
S
tL tH
=
+
()
15
2
ev
mB
v
PhL
S
tL th
=
+
()
2
2
*
5
2
12 1
y
crA A
E
t
SK
H
π
ν
⎛⎞
=
⎜⎟
−
⎝⎠
2
**
*
4
y
crA y
crA
S
SS
S
=−
()
2
2
*
5
2
12 1
y
crB B
E
t
SK
h
π
ν
⎛⎞
=
⎜⎟
−
⎝⎠
2
**
*
4
y
crB y
crB
S
SS
S
=−
AA
h
KKx
H
⎛⎞
==
⎜⎟
⎝⎠
BB
H
KKx
h
⎛⎞
==
⎜⎟
⎝⎠
Nomenclature For Stress Results
mA
S compressive stress applied to the short edge of the side panels due to external pressure
on the end plates.
mB
S compressive stress applied to the long edge of the side panels due to external pressure
on the end plates.
crA
S plate buckling stress when the panel is subjected to stress on the short edge.
crB
S plate buckling stress when the panel is subjected to stress on the long edge.
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