ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules
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2010 SECTION VIII, DIVISION 2
4-375
c
c
o
a
a
ρ
= (4.18.156)
2
1
2
t
st
o
d
xN
a
⎛⎞
=−
⎜⎟
⎝⎠
(4.18.157)
2
2
1
2
tt
tt
o
dt
xN
a
⎛⎞
−
=−
⎜⎟
⎝⎠
(4.18.158)
b) STEP 2 – Calculate the shell and channel coefficients.
1) The shell coefficients for Configurations a, b and c.
()
()
0.25
2
0.5
12 1
s
s
sss
Dtt
ν
β
⎡⎤
−
⎣⎦
=
+⎡⎤
⎣⎦
(4.18.159)
()
3
2
61
s
ss
s
s
Et
k
β
ν
=
−
(4.18.160)
22
3
6
1
2
ss s
ss
Dk h
h
h
β
λβ
⎛⎞
=++
⎜⎟
⎝⎠
(4.18.161)
2
1
42
s
s
s
ss
D
Et
ν
δ
⎛⎞
=−
⎜⎟
⎝⎠
(4.18.162)
For Configurations d, e , f, A, B, C, and D,
0
ssss
k
β
λδ
=
===.
2) The channel coefficients for Configurations a, e, f, and A.
()
()
0.25
2
0.5
12 1
c
c
ccc
Dtt
ν
β
⎡⎤
−
⎣⎦
=
+
⎡⎤
⎣⎦
(4.18.163)
()
3
2
61
ccc
c
c
Et
k
β
ν
=
−
(4.18.164)
22
3
6
1
2
cc c
cc
Dk h
h
h
β
λβ
⎛⎞
=++
⎜⎟
⎝⎠
(4.18.165)
2
1
42
cc
c
cc
D
For a Cylinder
Et
ν
δ
⎛⎞
=−
⎜⎟
⎝⎠
(4.18.166)
2010 SECTION VIII, DIVISION 2
4-376
2
1
42
cc
c
cc
D
For a Hemispherical Head
Et
ν
δ
−
⎛⎞
=
⎜⎟
⎝⎠
(4.18.167)
For Configurations b, c, d, B, C, and D,
0
cccc
k
β
λδ
=
===.
c) STEP 3 – Calculate
hp. Determine *EE 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
⎡⎤
−−
⎢⎥
=
⎢⎥
⎢⎥
⎣⎦
(4.18.168)
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
=
(4.18.169)
()( )
1* ln
*
sc
EK
F
E
νλλ
−++
=
(4.18.170)
()
1*
F
ν
Φ= + (4.18.171)
1
1
1
s
v
m
Z
Q
Z
ρ
−−Φ
=
+Φ
(4.18.172)
e) STEP 5 – Calculate the following quantities.
1)
s
ω
, *
s
ω
,
c
ω
, and *
c
ω
.
()
s
1
ssss s
kh
ω
ρβδ β
=+ (4.18.173)
()
()
22
11
*
4
os s
s
s
a
ρρ
ω
ω
−−
=−
(4.18.174)
()
1
ccccc c
kh
ωρβδ β
=+ (4.18.175)
()
()
()
2
2
11
1
*
42
cc
s
co c
a
ρρ
ρ
ω
ω
⎡⎤
+−
−
⎢⎥
=−−
⎢⎥
⎣⎦
(4.18.176)
2)
b
γ
.
0.0 , ,
b
Configuration a A D
γ
=− (4.18.177)
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2010 SECTION VIII, DIVISION 2
4-377
,
c
b
o
GC
Configuration b B
D
γ
−
=−
(4.18.178)
1
,
c
b
o
GG
Configuration c C
D
γ
−
=−
(4.18.179)
cs
b
o
GG
Configuration d
D
γ
−
=−
(4.18.180)
s
b
o
CG
Configuration e
D
γ
−
=−
(4.18.181)
1 s
b
o
GG
Configuration f
D
γ
−
=−
(4.18.182)
f) STEP 6 – For each loading case, calculate the effective pressure
e
P .
1) For an exchanger with an immersed floating head (see Figure 4.18.10 Sketch (a)):
est
PPP=− (4.18.183)
2) For an exchanger with an externally sealed floating head (see Figure 4.18.10 Sketch (b)):
()
2
1
es s t
PP P
ρ
=−− (4.18.184)
3) For an exchanger with an internally sealed floating tubesheet (see Figure 4.18.10 Sketch (c)):
()
()
2
1
est s
PPP
ρ
=− − (4.18.185)
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
(4.18.186)
2) Calculate the tubesheet bending stress.
i) If
0
e
P ≠ , calculate
3
Q .
2
31
2
2
eo
Q
QQ
Pa
=+
(4.18.187)
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 maximum tubesheet bending stress.
2010 SECTION VIII, DIVISION 2
4-378
2
'
1.5 2
*
mo
e
g
Fa
P
hh
σ
μ
⎛⎞
⎛⎞
=
⎜⎟
⎜⎟
⎜⎟
−
⎝⎠
⎝⎠
(4.18.188)
ii) If
0
e
P = , calculate the maximum tubesheet bending stress.
(
)
2
2
6
*
g
Q
'
hh
σ
μ
=
−
(4.18.189)
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.
For Configurations a, b, c, d, e, and f, proceed to STEP 8. For Configuration A, proceed to STEP
10. For Configurations B, C, and D, the calculation is complete.
h) STEP 8 – For each loading case, check 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
⎛⎞
⎛⎞
=
⎜⎟
⎜⎟
⎝⎠
⎝⎠
(4.18.190)
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
⎛⎞
⎧⎫
⎛⎞
⎪⎪
=⋅
⎜⎟
⎨⎬
⎜⎟
⎜⎟
⎝⎠
⎪⎪
⎩⎭
⎝⎠
(4.18.191)
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 the 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
⎡⎤
=−−
⎣⎦
−
(4.18.192)
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2010 SECTION VIII, DIVISION 2
4-379
()
,2 ,max
1
tssttet
ts
Px Px PF
xx
σ
⎡⎤
=−−
⎣⎦
−
(4.18.193)
When
0
e
P =
()
2
,1 ,min
2
0
2
1
tssttt
ts
Q
Px Px F
xx a
σ
⎡⎤
=−−
⎢⎥
−
⎣⎦
(4.18.194)
()
2
,1 ,max
2
0
2
1
tssttt
ts
Q
Px Px F
xx a
σ
⎡⎤
=−−
⎢⎥
−
⎣⎦
(4.18.195)
ii) Determine
,maxt
σ
,max ,1 ,2
max ,
ttt
σσσ
⎡⎤
=
⎣⎦
(4.18.196)
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 design and return to STEP 1.
Otherwise, proceed to paragraph 4.18.9.4.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
=− (4.18.197)
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
4.18.9.4.i.4.
4) If
,1t
σ
or
,2t
σ
is negative, proceed to paragraph 4.18.9.4.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 .
2010 SECTION VIII, DIVISION 2
4-380
t
lkl= (4.18.198)
ii) Determine the maximum permissible buckling stress limit
tb
S for the tubes.
2
2
min ,
t
tb t t t
st
E
SS CF
FF
π
⎡⎤
⎧⎫
=≤
⎨⎬
⎢⎥
⎩⎭
⎣⎦
(4.18.199)
,
min 1 ,
2
yt
t
tb t t t
st
S
F
SSCF
FC
⎡⎤
⎧⎫
⎛⎞
⎪⎪
=− >
⎢⎥
⎨⎬
⎜⎟
⎪⎪
⎢⎥
⎝⎠
⎩⎭
⎣⎦
(4.18.200)
where
()
4
3
2
dva
q
Z
QZ X
F
+
=
(4.18.201)
2
,
2
t
t
yt
E
C
S
π
= (4.18.202)
t
t
t
l
F
r
=
(4.18.203)
()
2
2
2
4
ttt
t
dd t
r
+−
=
(4.18.204)
When
0
e
P ≠
()
()
{
}
4
3
min max 3.25 0.25 ,1.25 , 2.0
sdwa
FZQZX
⎡⎤
=−+
⎣⎦
(4.18.205)
When
0
e
P =
1.25
s
F = (4.18.206)
iii) Determine
,mint
σ
,min ,1 ,2
min ,
ttt
σσσ
⎡⎤
=
⎣⎦
(4.18.207)
iv) Acceptance criteria
If
,minttb
S
σ
> , reconsider the tube design and return to STEP 1.
If
,minttb
S
σ
≤ , the tube design is acceptable. Proceed to STEP 10.
j) STEP 10 – For each loading case, check the stresses in the shell and/or channel integral with the
tubesheet.
1) Configurations a, b and c – The shell shall have a uniform thickness of
s
t for a minimum length of
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2010 SECTION VIII, DIVISION 2
4-381
1.8
s
s
Dt adjacent to the tubesheet. Calculate the axial membrane stress,
,
s
m
σ
, the bending
stress,
,
s
b
σ
,and total axial stress,
s
σ
, in the shell at its junction to the tubesheet, where H is given
by Equation (4.18.122).
()
()
()
()
22
2
,
1
oe s s t
st
sm
s
ss s ss
aP PP
aP
Dtt Dtt
ρ
σ
⎡⎤
+− −
⎣⎦
=+
++
(4.18.208)
()
()
2
3
,
23
61 *
6
1
*2
sos
sb s s s
s
kah
PH
tEh
ν
β
σβδ
⎡⎤
−
⎛⎞
⎛⎞
⎢⎥
=+ +
⎜⎟
⎜⎟
⎢⎥
⎝⎠
⎝⎠
⎢⎥
⎣⎦
(4.18.209)
,,
s
sm sb
σ
σσ
=+ (4.18.210)
2) Configurations a, e, f, and A – 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, where
H is given by Equation (4.18.122).
()
2
,
ct
cm
ccc
aP
Dtt
σ
=
+
(4.18.211)
()
()
2
3
,
23
61 *
6
1
* 2
coc
cb c c t
c
kah
PH
tEh
ν
β
σβδ
⎡⎤
−
⎛⎞
⎛⎞
⎢⎥
=− +
⎜⎟
⎜⎟
⎢⎥
⎝⎠
⎝⎠
⎢⎥
⎣⎦
(4.18.212)
,,ccmcb
σ
σσ
=+ (4.18.213)
3) Acceptance Criteria
i) Configuration a – For Loading Cases 1, 2, and 3, if
1.5
s
s
S
σ
≤
and 1.5
cc
S
σ
≤ , and for
Loading Cases 4, 5, 6, and 7, if
,
s
PS s
S
σ
≤
and
,cPSc
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 – For Loading Cases 1, 2, and 3, if
1.5
s
s
S
σ
≤ , and for Loading
Cases 4, 5, 6, and 7, if
,
s
PS s
S
σ
≤
, the shell design is acceptable and the calculation
procedure is complete. Otherwise, proceed to STEP 11.
iii) Configurations e, f, and A – For Loading Cases 1, 2, and 3, if
1.5
cc
S
σ
≤ , and for Loading
Cases 4, 5, 6, and 7, if
,cPSc
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.
2010 SECTION VIII, DIVISION 2
4-382
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 and return to STEP 1.
i) Configurations a, b and c – If 1.5
s
s
S
σ
> , increase the shell thickness
s
t .
ii) Configurations a, e, f and A – If 1.5
cc
S
σ
> , increase the channel thickness
c
t .
3) Option 3 - Perform the elastic-plastic calculation procedure as defined in 4.18.9.6 only when the
conditions of applicability stated in 4.18.9.6.b are satisfied.
4.18.9.5 Calculation Procedure for Effect of Plasticity at Tubesheet/Channel or Shell Joint
a) Scope – This procedure describes how to use the rules of paragraph 4.18.9.4 when the effect of
plasticity at the shell-tubesheet and/or channel-tubesheet joint is to be considered.
1) When the calculated tubesheet stresses are within the allowable stress limits, but either or both of
the calculated shell or channel total stresses exceed their allowable stress limits, an additional
“elastic-plastic solution” calculation may be performed.
2) This calculation permits a reduction of the shell and/or channel modulus of elasticity, where it
affects the rotation of the joint, to reflect the anticipated load shift resulting from plastic action at the
joint. The reduced effective modulus has the effect of reducing the shell and/or channel stresses in
the elastic-plastic calculation; however, due to load shifting this usually leads to an increase in the
tubesheet stress. In most cases, an elastic-plastic calculation using the appropriate reduced shell or
channel modulus of elasticity results in a design where the calculated tubesheet stresses are within
the allowable stress limits.
b) Conditions of Applicability
1) This procedure shall not be used at temperatures where the time-dependent properties govern the
allowable stress.
2) This procedure applies only for Loading Cases 1, 2, and 3.
3) This procedure applies to Configuration a when
,
s
PS s
S
σ
≤
and
,cPSc
S
σ
≤
.
4) This procedure applies to Configurations b and c when
,
s
PS s
S
σ
≤
.
5) This procedure applies to Configurations e, f, and A when
,cPSc
S
σ
≤
.
6) This procedure may only be used once for each iteration of tubesheet, shell, and channel thickness
and change of materials.
c) Calculation Procedure – After the calculation procedure given in paragraph 4.18.9.4 (STEP 1 through
10) has been performed for the elastic solution, an elastic-plastic calculation using the referenced steps
from paragraph 4.18.8.4 shall be performed in accordance with the following procedure for each
applicable loading case. Except for those quantities modified below, the quantities to be used for the
elastic-plastic calculation shall be the same as those calculated for the corresponding elastic loading
case.
1) Define the maximum permissible bending stress limit in the shell and channel.
,
,
*min , ,,
2
PS s
sys
S
S S Configurations a b c
⎡⎤
⎛⎞
=−
⎢⎥
⎜⎟
⎝⎠
⎣⎦
(4.18.214)
,
,
*min , ,,
2
PS c
cyc
S
S S Configurations a e f and A
⎡⎤
⎛⎞
=−
⎢⎥
⎜⎟
⎝⎠
⎣⎦
(4.18.215)
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2010 SECTION VIII, DIVISION 2
4-383
2) Using bending stresses
,
s
b
σ
and
,cb
σ
calculated in STEP 10 for the elastic solution, determine
s
f
act and
c
f
act as follows.
,
0.4
min 1.4 , 1.0 , ,
*
sb
s
s
f
act Configurations a b c
S
σ
⎡⎤
⎛⎞
⎢⎥
=− −
⎜⎟
⎜⎟
⎢⎥
⎝⎠
⎣⎦
(4.18.216)
,
0.4
min 1.4 , 1.0 , ,
*
cb
c
c
f
act Configurations a e f and A
S
σ
⎡⎤
⎛⎞
⎢⎥
=− −
⎜⎟
⎜⎟
⎢⎥
⎝⎠
⎣⎦
(4.18.217)
3) For Configuration a, if 1.0
s
fact
=
and 1.0
c
fact
=
, the design is acceptable, and the calculation
procedure is complete. Otherwise, proceed to paragraph 4.18.9.6.c.4. For Configurations b and c,
if
1.0
s
fact = , the design is acceptable, and the calculation procedure is complete. Otherwise,
proceed to paragraph 4.18.8.6.c.4.
4) Calculate reduced values of
s
E and
c
E as follows:
*,,
ss s
E E fact Configurations a b c=⋅ − (4.18.218)
*,,
cc c
E E fact Configurations a e f and A=⋅ − (4.18.219)
5) In STEP 2, recalculate
s
k and
s
λ
by replacing
s
E with *
s
E , and
c
k and
c
λ
by replacing
c
E with
*
c
E .
6) In STEP 4, recalculate F , Φ , and
1
Q .
7) In STEP 7, recalculate
2
Q ,
3
Q ,
m
F , as applicable, and the tubesheet bending stress
σ
. If
1.5S
σ
≤ , the design is acceptable and the calculation procedure is complete. Otherwise, the unit
geometry shall be reconsidered.
4.18.9.6 Calculation Procedure for Effect of Radial Differential Thermal Expansion Adjacent to the
Tubesheet
a) Scope
1) This procedure describes how to use the rules of paragraph 4.18.9.4 when the effect of radial
differential thermal expansion between the tubesheet and integral shell or channel is to be
considered.
2) This procedure shall be used when cyclic or dynamic reactions due to pressure or thermal
variations are specified.
3) This procedure shall be used when specified by the user. The user shall provide the Manufacturer
with the data necessary to determine the required tubesheet, channel, and shell metal
temperatures.
4) Optionally, the designer may use this procedure to consider the effect of radial differential thermal
expansion even when it is not required by paragraphs 4.18.9.5.a.2 or 4.18.9.5.a.3.
b) Conditions of Applicability – This calculation procedure applies only when the tubesheet is integral with
the shell or channel (Configurations a, b, c, e, f and A).
2010 SECTION VIII, DIVISION 2
4-384
c) Calculation Procedure – The calculation procedure outlined in paragraph 4.18.9.4 shall be performed
only for Loading Cases 4, 5, 6 and 7, accounting for the following modifications.
1) Determine the average temperature of the unperforated rim
r
T .
'''
3
sc
r
TTT
T Configuration a
++
=−
(4.18.220)
''
,
2
s
r
TT
T Configurations b c
+
=−
(4.18.221)
''
,,
2
c
r
TT
T Configurations e f A
+
=−
(4.18.222)
For conservative values of
*
s
P and *
c
P ,
'
r
TT
=
may be used.
2) Determine the average temperature of the shell
*
s
T and channel *
c
T at their junction to the
tubesheet using the equations shown below.
'
*,,
2
sr
s
TT
T Configurations a b c
+
=−
(4.18.223)
'
*,,,
2
cr
c
TT
T Configurations a e f A
+
=−
(4.18.224)
For conservative values of
*
s
P and *
c
P ,
'
*
s
s
TT
=
and
'
*
cc
TT
=
may be used.
3) Calculate
s
*
P
and
c
*
P
.
()
(
)
''
*
*,,
ss s s a r a
s
s
Et T T T T
P Configurations a b c
a
αα
⎡⎤
−− −
⎣⎦
=−
(4.18.225)
*0 ,,
s
P Configurations e f A=− (4.18.226)
()
(
)
''
c
*
*,,,
cc c a r a
c
c
Et T T T T
P Configurations a e f A
a
αα
⎡⎤
−− −
⎣⎦
=−
(4.18.227)
*0 ,
c
P Configurations b c=− (4.18.228)
4) In STEP 7, replace the equation for
2
Q with:
()()
2
** **
2
1
b
ss ct ss cc
m
W
PP PP
Q
Z
γ
ωω ωω
π
−−−+
=
+Φ
(4.18.229)
5) In STEP 10, replace the equations for
,
s
b
σ
and
,cb
σ
with the following equations, where H is
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