ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules
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2010 SECTION VIII, DIVISION 2
4-355
2) Configurations a, e and f – A cylindrical channel shall have a uniform thickness of
c
t for a minimum
length of
1.8
cc
Dt adjacent to the tubesheet. Calculate the axial membrane stress,
,cm
σ
, the
bending stress,
,cb
σ
, and total axial stress,
c
σ
, in the channel at its junction to the tubesheet.
()
2
,
4
ct
cm
ccc
DP
tD t
σ
=
+
(4.18.51)
()
()
2
,
23
61 *
6
1
*232
coco
cb c c t p s t
c
kDhD
PMPP
tEh
ν
β
σβδ
⎡⎤
−
⎛⎞
⎛⎞⎛ ⎞
=− ++−
⎢⎥
⎜⎟
⎜⎟⎜ ⎟
⎝⎠⎝ ⎠
⎝⎠
⎣⎦
(4.18.52)
,,ccmcb
σ
σσ
=+ (4.18.53)
3) Acceptance Criteria
i) Configuration a – If
1.5
s
s
S
σ
≤
and 1.5
cc
S
σ
≤
, the shell and channel designs are
acceptable and the calculation procedure is complete. Otherwise, proceed to STEP 11.
ii) Configurations b and c – If
1.5
s
s
S
σ
≤
, the shell design is acceptable and the calculation
procedure is complete. Otherwise, proceed to STEP 11.
iii) Configurations e and f – If
1.5
cc
S
σ
≤
, the channel design is acceptable and the calculation
procedure is complete. Otherwise, proceed to STEP 11.
k) STEP 11 – The design shall be reconsidered. One or a combination of the following three options may
be used.
1) Option 1 – Increase the assumed tubesheet thickness
h and return to STEP 1.
2) Option 2 – Increase the integral shell and/or channel thickness as follows, and return to STEP 2.
i) Configurations a, b and c – If
1.5
s
s
S
σ
> , increase the shell thickness
s
t .
ii) Configurations a, e and f – If
1.5
cc
S
σ
> , increase the channel thickness
c
t .
3) Option 3 –Perform a simplified elastic-plastic calculation for each applicable loading case by using a
reduced effective modulus for the integral shell and/or channel to reflect the anticipated load shift
resulting from plastic action at the integral shell and/or channel-to-tubesheet junction. This may
result in a higher tubesheet bending stress,
σ
. This option shall not be used at temperatures where
the time-dependent properties govern the allowable stress.
i) Configuration a – This option may only be used when
,
s
PS s
S
σ
≤
and
,cPSc
S
σ
≤ . In STEP
4, if
1.5
s
s
S
σ
> , replace
s
E with *1.5
s
sss
EE S
σ
= and recalculate
s
k and
s
λ
. If
1.5
cc
S
σ
> , replace
c
E with *1.5
cc cc
EE S
σ
= and recalculate
c
k and
c
λ
.
ii) Configurations b and c – This option may only be used when
,
s
PS s
S
σ
≤ . In STEP 4,
replace
s
E with *1.5
s
sss
EE S
σ
= and recalculate
s
k and
s
λ
.
2010 SECTION VIII, DIVISION 2
4-356
iii) Configurations e and f – This option may only be used when
,cPSc
S
σ
≤ . In STEP 4,
replace
c
E with *1.5
cc cc
EE S
σ
= and recalculate
c
k and
c
λ
.
After making the above changes, perform STEPs 5 and 7, and recalculate the tubesheet bending
stress
σ
given in STEP 8. If
2S
σ
≤
, the assumed tubesheet thickness
h
is acceptable and the
design is complete. Otherwise, the design shall be reconsidered by using Option 1 or 2.
4.18.7.5 Calculation Procedure for Simply Supported U-Tube Tubesheets
4.18.7.5.1 Scope
This procedure describes how to use the rules of paragraph 4.18.7.4 when the effect of the stiffness of the
integral channel and/or shell is not considered.
4.18.7.5.2 Conditions of Applicabiltiy
This calculation procedure applies only when the tubeheet is integral with the shell or channel (Configurations
a,b,c,e,and f).
4.18.7.5.3 Calculation Procedure
The calculation procedure outlined in 4.18.7.4 shall be performed accounting for the following modifications.
a) Perform STEPs 1 through 9.
b) Perform STEP 10 except as follows:
1) The shell (Configuration a,b,and c) is not required to meet a minimum length requirement.
2) The channel (Configurations a,e,and f) is not required to meet a minimum length requirements.
3) Acceptance Criteria
i) Configuration a: If
,
s
PS s
S
σ
≤ and
,cPSc
S
σ
≤
, then the shell and channel are acceptable.
Otherwise increase the thickness of the overstressed component(s) (shell and/or channel)
and return to STEP 1.
ii) Configuration b and c : If
,
s
PS s
S
σ
≤
then the shell is acceptable. Otherwise increase the
thickness of the shell and return to STEP 1.
iii) Configuration e and f : If
,cPSc
S
σ
≤
then the channel is acceptable. Otherwise increase the
thickness of the channel and return to STEP 1.
c) Do not perform STEP 11
d) Repeat STEPs 1 - 8 with the following changes until the tubesheet criteria have been met:
1) STEP 4
i) Configurations a, b, and c:
0, 0, 0, 0
ssss
k
β
λδ
=
===.
ii) Configurations a, e, and f:
0, 0, 0, 0
cccc
k
β
λδ
=
===.
2) STEP 7
o
M
M=
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2010 SECTION VIII, DIVISION 2
4-357
4.18.8 Rules for the Design of Fixed Tubesheets
4.18.8.1 Scope
These rules cover the design of tubesheets for fixed tubesheet heat exchangers. The tubesheets may have
one of the four configurations shown in Figure 4.18.5.
a) Configuration a – tubesheet integral with shell and channel.
b) Configuration b – tubesheet integral with shell and gasketed with channel, extended as a flange.
c) Configuration c – tubesheet integral with shell and gasketed with channel, not extended as a flange.
d) Configuration d – tubesheet gasketed with shell and channel, extended or not extended as a flange.
4.18.8.2 Conditions of Applicability
The two tubesheets shall have the same thickness, material and edge conditions.
4.18.8.3 Design Considerations
a) It is generally not possible to determine, by observation, the most severe condition of coincident
pressure, temperature and differential thermal expansion. Thus, it is necessary to evaluate all the
anticipated loading conditions to ensure that the worst load combination has been considered in the
design. The various loading conditions to be considered shall include the normal operating conditions,
the startup conditions, the shutdown conditions, and the upset conditions, which may govern the design
of the main components of the heat exchanger (i.e., tubesheets, tubes, shell, channel, tube-to-
tubesheet joint).
1) For each of these conditions, the following loading cases shall be considered to determine the
effective pressure
e
P to be used in the design equations:
i) Loading Case 1 – Tube side pressure
t
P acting only
(
)
0
s
P
=
without differential thermal
expansion.
ii) Loading Case 2 – Shell side pressure
s
P acting only
(
)
0
t
P
=
without differential thermal
expansion.
iii) Loading Case 3 – Tube side pressure
t
P and shell side pressure
s
P acting simultaneously,
without differential thermal expansion.
iv) Loading Case 4 – Differential thermal expansion acting only
(
)
0
s
P = and
()
0
t
P
=
.
v) Loading Case 5 – Tube side pressure
t
P acting only
(
)
0
s
P
=
with differential thermal
expansion.
vi) Loading Case 6 – Shell side pressure
s
P acting only
(
)
0
t
P
=
with differential thermal
expansion.
vii) Loading Case 7 – Tube side pressure
t
P and shell side pressure
s
P acting simultaneously,
with differential thermal expansion.
2) When vacuum exists, each loading case shall be considered with and without the vacuum.
3) When differential design pressure is specified by the user, the design shall be based only on
Loading Cases 3, 4, and 7. If the tube side is the higher-pressure side,
t
P shall be the tube side
2010 SECTION VIII, DIVISION 2
4-358
design pressure and
s
P shall be
t
P less the differential design pressure. If the shell side is the
higher-pressure side,
s
P shall be the shell side design pressure and
t
P shall be
s
P less the
differential design pressure.
4) The designer should take appropriate consideration of the stresses resulting from the pressure test
required by paragraph 4.1.6.2 and Part 8.
b) Elastic moduli, yield strengths, and allowable stresses shall be taken at design temperatures. However
for cases involving thermal loading (Loading Cases 4, 5, 6, and 7), it is permitted to use the operating
temperatures instead of the design temperatures.
c) As the calculation procedure is iterative, a value
h shall be assumed for the tubesheet thickness to
calculate and check that the maximum stresses in tubesheet, tubes, shell, and channel are within the
maximum permissible stress limits and that the resulting tube-to-tubesheet joint load is acceptable.
d) Because any increase of tubesheet thickness may lead to overstresses in the tubes, shell, channel, or
tube-to-tubesheet joint, a final check shall be performed, using in the equations the nominal thickness
of tubesheet, tubes, shell, and channel, in both corroded and uncorroded conditions.
e) The designer shall consider the following:
1) The effect of deflections in the tubesheet design, especially when the tubesheet thickness
h is less
than the tube diameter.
2) The effect of radial differential thermal expansion between the tubesheet and integral shell or
channel (Configurations a, b, and c) in accordance with paragraph 4.18.8.7.
f) The designer may consider the tubesheet as simply supported in accordance with 4.18.8.8.
4.18.8.4 Calculation Procedure
a) STEP 1 – Determine
o
D ,
μ
, *
μ
, and
g
'
h
from paragraph 4.18.6.4.a. For Loading Cases 4, 5, 6, and
7,
0.
g
'
h =
Calculate the following quantities.
2
o
o
D
a
= (4.18.54)
2
c
c
D
a Configuration a=−
(4.18.55)
,,
2
c
c
G
a Configurations b c d=−
(4.18.56)
,,
2
s
s
D
a Configurations a b c=−
(4.18.57)
2
s
s
G
a Configuration d=−
(4.18.58)
s
s
o
a
a
ρ
= (4.18.59)
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2010 SECTION VIII, DIVISION 2
4-359
c
c
o
a
a
ρ
= (4.18.60)
2
1
2
t
st
o
d
xN
a
⎛⎞
=−
⎜⎟
⎝⎠
(4.18.61)
2
2
1
2
tt
tt
o
dt
xN
a
⎛⎞
−
=−
⎜⎟
⎝⎠
(4.18.62)
b) STEP 2 – Calculate the following parameters.
1) The shell axial stiffness and the tube axial stiffness.
()
s
sss
s
tD tE
K
L
π
+
=
(4.18.63)
(
)
tt t t
t
td tE
K
L
π
−
=
(4.18.64)
2) The stiffness factors.
,
s
st
tt
K
K
NK
=
(4.18.65)
J
J
S
K
J
KK
=
+
(4.18.66)
3) The shell coefficients for Configurations a, b and c.
()
()
0.25
2
0.5
12 1
s
s
sss
Dtt
ν
β
⎡⎤
−
⎣⎦
=
+
⎡⎤
⎣⎦
(4.18.67)
()
3
2
61
s
ss
s
s
Et
k
β
ν
=
−
(4.18.68)
22
3
6
1
2
ss s
ss
Dk h
h
h
β
λβ
⎛⎞
=++
⎜⎟
⎝⎠
(4.18.69)
2
1
4 2
s
s
s
ss
D
Et
ν
δ
⎛⎞
=−
⎜⎟
⎝⎠
(4.18.70)
For Configuration d,
0
ssss
k
β
λδ
====.
2010 SECTION VIII, DIVISION 2
4-360
4) The channel coefficients for Configuration a.
()
()
0.25
2
0.5
12 1
c
c
ccc
Dtt
ν
β
⎡⎤
−
⎣⎦
=
+⎡⎤
⎣⎦
(4.18.71)
()
3
2
61
ccc
c
c
Et
k
β
ν
=
−
(4.18.72)
22
3
6
1
2
cc c
cc
Dk h
h
h
β
λβ
⎛⎞
=++
⎜⎟
⎝⎠
(4.18.73)
2
1
4 2
cc
c
cc
D
For a Cylinder
Et
ν
δ
⎛⎞
=−
⎜⎟
⎝⎠
(4.18.74)
2
1
4 2
cc
c
cc
D
For a Hemispherical Head
Et
ν
δ
−
⎛⎞
=
⎜⎟
⎝⎠
(4.18.75)
For Configurations b, c, and d,
0
cccc
k
β
λδ
=
===.
c) STEP 3 – Calculate
hp. Determine *
E
E and *
ν
using paragraph 4.18.6.4.b. Calculate
a
X
.
()
()
()
0.25
2
2
3
24 1 *
*
ttt t t o
a
NEtd ta
X
ELh
ν
⎡⎤
−−
⎢⎥
=
⎢⎥
⎢⎥
⎣⎦
(4.18.76)
Using the calculated value of
a
X
enter either Table 4.18.3 or Figure 4.18.6 to determine
d
Z
,
v
Z
,
w
Z
,
and
m
Z
.
d) STEP 4 – Calculate the following parameters
o
A
K
D
=
(4.18.77)
()( )
1* ln
*
sc
EK
F
E
νλλ
−++
=
(4.18.78)
()
1*F
ν
Φ= + (4.18.79)
1
1
1
s
v
m
Z
Q
Z
ρ
−−Φ
=
+Φ
(4.18.80)
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2010 SECTION VIII, DIVISION 2
4-361
()
4
1
1
2
dwa
Z
Z
QZ X
Q
+
=
(4.18.81)
()
4
1
2
2
vma
Z
Z
QZ X
Q
+
=
(4.18.82)
()
4
1
1
ws ma
m
Z
ZX
U
Z
ρ
+−
⎡⎤
⎣⎦
=
+Φ
(4.18.83)
e) STEP 5 – Calculate the following quantities.
1)
γ
for Loading Cases 4, 5, 6, and 7. For Loading Cases 1, 2, and 3, 0
γ
= .
()()
,, , ,tm tm a sm sm a
TT TTL
γα α
⎡⎤
=−−−
⎣⎦
(4.18.84)
2)
s
ω
, *
s
ω
,
c
ω
, and *
c
ω
.
()
s
1
ssss s
kh
ωρβ
δ
β
=+
(4.18.85)
()
()
22
11
*
4
os s
s
s
a
ρρ
ω
ω
−−
=−
(4.18.86)
()
1
ccccc c
kh
ωρβδ β
=+ (4.18.87)
()
()
()
2
2
11
1
*
42
cc
s
co c
a
ρρ
ρ
ω
ω
⎡⎤
+−
−
⎢⎥
=−−
⎢⎥
⎣⎦
(4.18.88)
3)
b
γ
0
b
Configuration a
γ
=− (4.18.89)
c
b
o
GC
Configuration b
D
γ
−
=−
(4.18.90)
1c
b
o
GG
Configuration c
D
γ
−
=−
(4.18.91)
cs
b
o
GG
Configuration d
D
γ
−
=−
(4.18.92)
2010 SECTION VIII, DIVISION 2
4-362
f) STEP 6 – For each loading case, calculate the effective pressure.
(
)
()
,rim
,1 2
11
st s t W
e
st Z s Z
''
JK P P P P P
P
JK Q Q
γ
ρ
−++ +
=
++−⎡⎤
⎣⎦
(4.18.93)
where
()
()
2
22
2
2
, , ,
1
1
2
21
2
Js
ss
s
sst s s
st o st st o
DD
J
D
'
Px x P
K D JK JK D
ρ
νν
⎛⎞
⎡⎤
−
−
⎛⎞
−
⎣⎦
⎜⎟
=+− + − −
⎜⎟
⎜⎟
⎝⎠
⎝⎠
(4.18.94)
()
,
1
21
tt tt t
st
'
Px x P
JK
ν
⎛
⎞
=+− +
⎜
⎟
⎟
⎜
⎠
⎝
(4.18.95)
2
tt
o
NK
P
a
γ
γ
π
= (4.18.96)
2
2
b
W
o
UW
P
a
γ
π
=−
(4.18.97)
()
rim
2
**
ss ct
o
UP P
P
a
ωω
−
=−
(4.18.98)
g) STEP 7 – For each loading case check the bending stress.
1) Calculate
2
Q
()
2
**
2
1
b
ss ct
m
W
PP
Q
Z
γ
ωω
π
−+
=
+Φ
(4.18.99)
2) Calculate the tubesheet bending stress
i) If
0
e
P ≠ , calculate
3
Q
2
31
2
2
eo
Q
QQ
Pa
=+
(4.18.100)
For each loading case, determine coefficient
m
F from either Table 4.18.3 or Figures 4.18.7 and
4.18.8. Calculate the tubesheet maximum bending stress
2
'
1.5 2
*
mo
e
g
Fa
P
hh
σ
μ
⎛⎞
⎛⎞
=
⎜⎟
⎜⎟
⎜⎟
−
⎝⎠
⎝⎠
(4.18.101)
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2010 SECTION VIII, DIVISION 2
4-363
ii) If
0
e
P = , calculate the tubesheet maximum bending stress
()
2
2
*'
6
g
Q
hh
σ
μ
=
−
(4.18.102)
3) Acceptance criteria
For Loading Cases 1, 2, and 3, if
1.5S
σ
≤ , and for Loading Cases 4, 5, 6, and 7, if
PS
S
σ
≤ , the
assumed tubesheet thickness is acceptable for bending. Otherwise, increase the assumed
tubesheet thickness
h
and return to STEP 1.
h) STEP 8 – For each loading case, calculate the average shear stress in the tubesheet at the outer edge
of the perforated region.
1) Calculate the average shear stress. The shear stress may be conservatively calculated using the
following equation.
1
2
o
e
a
P
h
τ
μ
⎛⎞
⎛⎞
=
⎜⎟
⎜⎟
⎝⎠
⎝⎠
(4.18.103)
If
3.2
e
o
Sh
P
D
μ
> , the shear stress may be more accurately calculated by the following equation.
4
11
4
p
e
p
A
P
hC
τ
μ
⎛⎞
⎧⎫
⎛⎞
⎪⎪
=⋅
⎜⎟
⎨⎬
⎜⎟
⎜⎟
⎝⎠
⎪⎪
⎩⎭
⎝⎠
(4.18.104)
2) Acceptance criteria
If
0.8S
τ
≤ , the assumed tubesheet thickness is acceptable for shear. Otherwise, increase the
assumed tubesheet thickness
h and return to STEP 1.
i) STEP 9 – Check the tube stress and tube-to-tubesheet joint design for each loading case.
1) Check the axial tube stress.
i) For each loading case, determine coefficients
,mint
F and
,maxt
F from Table 4.18.4 and
calculate the two extreme values of tube stress,
,1t
σ
and
,2t
σ
.
,1t
σ
and
,2t
σ
may be
positive or negative.
When
0
e
P ≠
()
,1 ,min
1
tssttet
ts
Px Px PF
xx
σ
⎡⎤
=−−
⎣⎦
−
(4.18.105)
()
,2 ,max
1
tssttet
ts
Px Px PF
xx
σ
⎡⎤
=−−
⎣⎦
−
(4.18.106)
When
0
e
P =
()
2
,1 ,min
2
0
21
tssttt
ts
Q
Px Px F
xx a
σ
⎡⎤
=−−
⎢⎥
−
⎣⎦
(4.18.107)
2010 SECTION VIII, DIVISION 2
4-364
()
2
,1 ,max
2
0
2
1
tssttt
ts
Q
Px Px F
xx a
σ
⎡⎤
=−−
⎢⎥
−
⎣⎦
(4.18.108)
ii) Determine
,maxt
σ
,max ,1 ,2
max ,
ttt
σσσ
⎡⎤
=
⎣⎦
(4.18.109)
2) Acceptance criteria
For Loading Cases 1, 2, and 3, if
,maxtt
S
σ
> , and for Loading Cases 4, 5, 6, and 7, if
,max
2
tt
S
σ
> ,
reconsider the tube design and return to STEP 1.
Otherwise, proceed to paragraph 4.18.8.4.i.3.
3) Check the tube-to-tubesheet joint design.
i) Calculate the largest tube-to-tubesheet joint load,
t
W
()
,maxtt ttt
Wdtt
σπ
=− (4.18.110)
ii) Determine the maximum allowable load for the tube-to-tubesheet joint design,
max
L . For
tube-to-tubesheet joints with full strength welds.
max
L shall be determined in accordance
with 4.18.10. For tube-to-tubesheet joints with partial strength welds,
max
L shall be
determined in accordance with 4.18.10 or Annex 4.C, as applicable. For all other tube
joints,
max
L shall be determined in accordance with Annex 4.C.
iii) Acceptance criteria
If
maxt
WL> , tube-to-tubesheet joint design shall be reconsidered.
If
maxt
WL≤ , tube-to-tubesheet joint design is acceptable. Proceed to paragraph
4.18.8.4.i.4.
4) If
,1t
σ
or
,2t
σ
is negative, proceed to paragraph 4.18.8.4.i.6.
5) If
,1t
σ
and
,2t
σ
are positive, the tube design is acceptable. Proceed to STEP 10.
6) Check the tubes for buckling.
i) Calculate the largest equivalent unsupported buckling length of the tube
t
l considering the
unsupported tube spans
l and their corresponding method of support defined by the
parameter
k .
t
lkl= (4.18.111)
ii) Determine the maximum permissible buckling stress limit for the tubes.
2
2
min ,
t
tb t t t
st
E
SS CF
FF
π
⎡⎤
⎧⎫
=≤
⎨⎬
⎢⎥
⎩⎭
⎣⎦
(4.18.112)
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