ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules
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2010 SECTION VIII, DIVISION 2
4-395
,
P
Sc
S allowable primary plus secondary stress evaluated using paragraph 5.5.6.1.d for channel
material at temperature
c
T
,
P
Ss
S allowable primary plus secondary stress evaluated using paragraph 5.5.6.1.dfor shell material
at temperature
s
T
,,1
P
Ss
S allowable primary plus secondary stress evaluated using paragraph 5.5.6.1.d for shell material
adjacent to the tubesheet at temperature
s
T
T tubesheet design temperature
a
T ambient temperature, 20°C (70°F)
c
T channel design temperature
s
T shell design temperature
t
T tube design temperature
,
s
m
T mean shell metal temperature along shell length
,tm
T mean tube metal temperature along tube length
'
T tubesheet metal temperature at the rim
'
c
T channel metal temperature at the tubesheet
'
s
T shell metal temperature at the tubesheet
c
t channel thickness
s
t shell thickness
,1
s
t shell thickness adjacent to the tubesheets
t
t nominal tube wall thickness
W flange design bolt load for the gasket seating condition (see paragraph 4.16)
t
W tube-to-tubesheet joint load
,
s
m
α
mean coefficient of thermal expansion of shell material at
,
s
m
T
,,1
s
m
α
mean coefficient of thermal expansion of shell material adjacent to the tubesheets at
,
s
m
T
,tm
α
mean coefficient of thermal expansion of tube material at
,tm
T
'
α
mean coefficient of thermal expansion of tubesheet material at
'
T
'
c
α
mean coefficient of thermal expansion of channel material at
'
c
T
'
s
α
mean coefficient of thermal expansion of shell material at
'
s
T
γ
axial differential thermal expansion between tubes and shell
ν
Poisson’s ratio of tubesheet material
c
ν
Poisson’s ratio of channel material
s
ν
Poisson’s ratio of shell material
t
ν
Poisson’s ratio of tube material
e) Nomenclature for tube-to-tubesheet welds (see paragraph 4.18.10)
c
a length of the combined weld legs measured parallel to the longitudinal axis of the tube at its
outside diameter
2010 SECTION VIII, DIVISION 2
4-396
f
a fillet weld leg
g
a groove weld leg
r
a minimum required length of the weld leg(s) under consideration
o
d nominal tube outside diameter
d
f
ratio of the design strength to the tube strength
f
f
ratio of the fillet weld strength to the design strength
w
f
weld strength factor
d
F design strength, but not greater than
t
F
f
F
fillet weld strength, but not greater than
t
F
g
F groove weld strength, but not greater than
t
F
t
F axial tube strength
max
L maximum allowable axial load in either direction on the tube-to-tubesheet joint
t nominal tube wall thickness
a
S allowable stress from Annex 3.A of the tube
t
S allowable stress from Annex 3.A of the material to which the tube is welded
w
S allowable stress in weld,
[
]
min ,
wat
SSS=
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2010 SECTION VIII, DIVISION 2
4-397
4.18.16 Tables
Table 4.18.1 – Effective Elastic Modulus And Poisson’s Ratio For A Perforated Plate With An
Equilateral Triangular Hole Pattern
h
p
0
A
1
A
2
A
3
A
4
A
0.10 0.0353 1.2502 -0.0491 0.3604 -0.6100
0.25 0.0135 0.9910 1.0080 -1.0498 0.0184
0.50 0.0054 0.5279 3.0461 -4.3657 1.9435
2.00 -0.0029 0.2126 3.9906 -6.1730 3.4307
h
p
0
B
1
B
2
B
3
B
4
B
0.10 -0.0958 0.6209 -0.8683 2.1099 -1.6831
0.15 0.8897 -9.0855 36.1435 -59.5425 35.8223
0.25 0.7439 -4.4989 12.5779 -14.2092 5.7822
0.50 0.9100 -4.8901 12.4325 -12.7039 4.4298
1.00 0.9923 -4.8759 12.3572 -13.7214 5.7629
2.00 0.9966 -4.1978 9.0478 -7.9955 2.2398
Notes:
1.
() () ()
234
01 2 3 4
*****EE A A A A A
μμμμ
=+ + + +
2.
() () ()
234
01 2 3 4
*****BB B B B
ν
μμ μ μ
=+ + + +
3. These coefficients are only valid for
0.1 * 0.6
μ
≤
≤ . Data for the range 0.1 * 1.0
μ
≤≤ is
provided in Part 5, Annex 5.E.
4. If
0.1hp< , use 0.1hp= .
5. If
2.0hp> , use 2.0hp= .
2010 SECTION VIII, DIVISION 2
4-398
Table 4.18.2 – Effective Elastic Modulus And Poisson’s Ratio For A Perforated Plate With A Square
Hole Pattern
h
p
0
A
1
A
2
A
3
A
4
A
0.10 0.0676 1.5756 -1.2119 1.7715 -1.2628
0.25 0.0250 1.9251 -3.5230 6.9830 -5.0017
0.50 0.0394 1.3024 -1.1041 2.8714 -2.3994
2.00 0.0372 1.0314 -0.6402 2.6201 -2.1929
h
p
0
B
1
B
2
B
3
B
4
B
0.10 -0.0791 0.6008 -0.3468 0.4858 -0.3606
0.15 0.3345 -2.8420 10.9709 -15.8994 8.3516
0.25 0.4296 -2.6350 8.6864 -11.5227 5.8544
0.50 0.3636 -0.8057 2.0463 -2.2902 1.1862
1.00 0.3527 -0.2842 0.4354 -0.0901 -0.1590
2.00 0.3341 0.1260 -0.6920 0.6877 -0.0600
Notes:
1.
() () ()
234
01 2 3 4
*****EE A A A A A
μμμμ
=+ + + +
2.
() () ()
234
01 2 3 4
*****BB B B B
ν
μμ μ μ
=+ + + +
3. These coefficients are only valid for
0.1 * 0.6
μ
≤
≤ . Data for the range 0.1 * 1.0
μ
≤≤ is
provided in Part 5, Annex 5.E.
4. If
0.1hp< , use 0.1hp= .
5. If
2.0hp> , use 2.0hp= .
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2010 SECTION VIII, DIVISION 2
4-399
Table 4.18.3 – Evaluation Of
a
Z
,
d
Z
,
v
Z
,
w
Z
,
m
Z
, And
m
F
Evaluation Of Kelvin Functions
ber , bei , 'ber and 'bei relative to
x
() ( )
()
()
()
()
()
()
()
()
44812
1
2222
0
2222
1 1 ...
2 ! 2! 4! 6!
n
nm
n
n
xxxx
ber x
n
=−
=
=− =− + − +
∑
() ( )
()
()
()
()
()
()
()
()
42 2 6 10
1
22 2 2
1
2222
1 ...
21! 1! 3! 5!
n
nm
n
n
xxxx
bei x
n
−
=
−
=
=− = − + −
−
∑
() ( )
()
()
()
()
()
()
()
()
41 3 7 11
2222
1
2 2 22 42 62
' 1 ...
2 ! 2! 4! 6!
n
nm
n
n
nx x x x
ber x
n
−
=
=
=− =− + − +
∑
() ( )
()
()
()
()
()
()
()
()
()
43 1 5 9
1
2222
1
21 2 2 32 52
' 1 ...
21! 1! 3! 5!
n
nm
n
n
nx x x x
bei x
n
−
=
−
=
−
=− = − + −
−
∑
Note: Use
42
a
mX=+ terms (rounded to the nearest integer) to obtain an adequate approximation of
the Kelvin Functions and their derivatives.
i
ψ
Functions For Determination of
a
Z
,
d
Z
,
v
Z
,
w
Z
,
m
Z
, and
m
F relative to
x
() () ()
1
1*
'
v
x
bei x ber x
x
ψ
−
⎛⎞
=+
⎜⎟
⎝⎠
() () ()
2
1*
'
v
x
ber x bei x
x
ψ
−
⎛⎞
=−
⎜⎟
⎝⎠
Evaluation Of
a
Z
,
d
Z
,
v
Z
,
w
Z
,
m
Z
at
a
X
()() ()
(
)
21
3
aa aa
d
aa
ber X X bei X X
Z
XZ
ψψ
+
=
()() ()
(
)
21
2
''
aa aa
v
aa
ber X X bei X X
Z
XZ
ψψ
+
=
() () ()
(
)
2
''
aa aa
w
aa
ber X ber X bei X bei X
Z
XZ
+
=
() ()
22
''
aa
m
aa
ber X bei X
Z
XZ
+
⎡⎤⎡⎤
⎣⎦⎣⎦
=
where
()() ()
(
)
21
''
aaa aa
Z
bei X X ber X X
ψψ
=−
Evaluation Of
m
F from 0
a
X
→
Calculate the functions
()
(
)
mv
Q x and Q x relative to
x
:
2010 SECTION VIII, DIVISION 2
4-400
Table 4.18.3 – Evaluation Of
a
Z
,
d
Z
,
v
Z
,
w
Z
,
m
Z
, And
m
F
()
()() ()
(
)
21
''
aa
m
a
bei X x ber X x
Qx
Z
ψψ
−
=
()
()() ()
(
)
12 21aa
v
aa
X
xXx
Qx
XZ
ψψ ψψ
−
=
For each loading case (note that
3
Q is a dependent on the load case being evaluated), calculate
(
)
m
F
x
relative to
x
:
()
() ()
3
2
vm
m
Qx QQ x
Fx
+⋅
=
m
F is the maximum of the absolute value of
(
)
m
F
x as
x
varies from 0
a
X
→ such that 0
a
x
X≤≤
()
max
mm
FFx
⎡⎤
=
⎣⎦
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2010 SECTION VIII, DIVISION 2
4-401
Table 4.18.4 – Evaluation Of
,mint
F
and
,maxt
F
Formulas For The Determination of
,mint
F
and
,maxt
F
Calculate the Kelvin functions, the
i
ψ
functions and
a
Z
from Table 4.18.3
Caclulate functions
()
d
Z
x and ()
w
Z
x relative to
x
:
(
)
(
)
(
)
(
)
21
3
()
aa
d
aa
X
ber x X bei x
Zx
XZ
ψψ
⋅+ ⋅
=
⋅
(
)
(
)
(
)
(
)
2
''
()
aa
w
aa
ber X ber x bei X bei x
Zx
XZ
⋅+ ⋅
=
⋅
For each loading case, calculate
()
t
Fx relative to
x
:
When
0
e
P ≠
() ()
4
3
()
2
a
td w
X
Fx Z x Q Z x=+⋅⋅
⎡⎤
⎣⎦
When
0
e
P =
()
4
()
2
a
tw
X
Fx Z x
=
⋅
Calculate the minimum and maximum values,
,mint
F and
,maxt
F , of ()
t
Fx as
x
varies 0
a
X
→ such that
0
a
x
X≤≤ .
,mint
F and
,maxt
F may be positive or negative.
[
]
,min
min ( )
tt
FFx=
[
]
,max
max ( )
tt
FFx=
2010 SECTION VIII, DIVISION 2
4-402
4.18.17 Figures
(a) U-Tube Heat Exchanger
(c) Floating Tubesheet Heat Exchanger
(b) Fixed Tubesheet Heat Exchanger
1
235 78 9
46
235 715 1682
9
21 3 5 7 8 9 10 11 12
13 14
64
Parts:
1 Channel Cover (Bolted Flat Cover) 9 Baffles or Support Plates
2 Channel 10 Floating Head Backing Device
3 Channel Flange 11 Floating Tubesheet
4 Pass Partition 12 Floating Head
5 Stationary Tubesheet 13 Floating Head Flange
6 Shell Flange 14 Shell Cover
7 Tubes 15 Expansion Joint
8 Shell 16 Distribution or Vapor Belt
Figure 4.18.1 – Terminology of Heat Exchanger Components
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2010 SECTION VIII, DIVISION 2
4-403
r
o
p
D
o
h
g
h
d
t
t
t
h
tx
(a) Tubesheet Layout
(b) Expanded Tube Joint
(c) Tube Side Pass Partition Groove Depth
ι
(d) Tubes Welded To Backside Of Tubesheet
Note: d
t
- 2t
t
< d < d
t
h
t
t
d
t
d
Figure 4.18.2 – Tubesheet Geometry
2010 SECTION VIII, DIVISION 2
4-404
L
L1
U
L1
(b) Two Lanes
L
L2
= L
L1
- U
L1
A
L
= U
L1
L
L1
+ U
L2
L
L2
D
o
U
L2
(a) One Lane
A
L
= U
L1
L
L1
U
L1
L
L1
D
o
(c) Three Lanes
A
L
= U
L1
L
L1
+ U
L2
L
L2
+ U
L3
L
L3
U
L1
L
L1
D
o
L
L2
L
L3
U
L2
U
L3
Figure 4.18.3 – Typical Untubed Lane Configurations
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