ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules
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2010 SECTION VIII, DIVISION 2
5-129
Table 5.E.17 – Stress Factor
x
y
K – Square Hole Pattern
*
μ
1
C
2
C
3
C
4
C
5
C
0.05 4.10628E-04 -1.03092E+00 -2.60562E-02 1.42763E-02 -1.13154E-03
0.1 -1.82830E-04 -4.93550E-01 -1.94314E-02 4.90571E-03 -2.95940E-04
0.15 -5.94810E-05 -3.51560E-01 -4.36757E-03 1.34861E-03 -5.37530E-05
0.2 5.45892E-04 -2.81094E-01 1.23677E-02 -2.05420E-04 1.14121E-06
0.25 1.32829E-05 -2.22708E-01 -2.00720E-04 2.29490E-04 1.05088E-06
0.3 6.15483E-06 -1.89244E-01 2.07521E-04 9.47928E-05 5.03027E-06
0.4 1.66864E-06 -1.48510E-01 4.61787E-05 6.25567E-05 9.48205E-07
0.5 -1.20220E-06 -1.28243E-01 2.58038E-03 -2.56740E-05 1.42611E-07
0.6 -4.63660E-06 -1.19644E-01 -3.38840E-05 3.23761E-05 -2.36380E-07
0.7 4.34520E-06 -1.18318E-01 3.89048E-05 1.89838E-05 4.09430E-07
0.8 6.30422E-06 -1.21221E-01 1.89750E-06 2.05803E-05 4.80584E-07
0.9 -4.40310E-07 -1.28514E-01 9.10516E-05 1.44325E-05 7.77422E-07
1 -5.06060E-06 -1.39930E-01 7.41931E-05 2.11002E-05 3.89961E-07
*
μ
6
C
7
C
8
C
9
C
10
C
0.05 4.58608E-05 -1.11640E-06 1.69499E-08 -1.57290E-10 8.16374E-13
0.1 9.90563E-06 -2.11290E-07 2.94076E-09 -2.59170E-11 1.31470E-13
0.15 1.01724E-06 -1.01090E-08 3.65386E-11 2.29882E-13 -2.45460E-15
0.2 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.25 -3.33450E-07 9.60689E-09 -1.41310E-10 1.24782E-12 -6.33550E-15
0.3 -3.62510E-07 9.01762E-09 -1.24960E-10 1.06743E-12 -5.33570E-15
0.4 -8.06470E-08 1.46557E-09 -1.09650E-11 2.84023E-14 1.52304E-17
0.5 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.6 4.87650E-09 -2.33200E-10 5.13313E-12 -5.70940E-14 3.17302E-16
0.7 -1.81480E-08 3.88068E-10 -5.54280E-12 4.99395E-14 -2.55870E-16
0.8 -2.62660E-08 6.99127E-10 -1.15610E-11 1.13080E-13 -5.99740E-16
0.9 -3.24290E-08 7.59367E-10 -1.16550E-11 1.09684E-13 -5.72670E-16
1 -1.46850E-08 2.79200E-10 -3.87640E-12 3.48700E-14 -1.78540E-16
*
μ
11
C
12
C
13
C
14
C
15
C
0.05 -1.81420E-15 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.1 -2.92160E-16 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.15 5.45478E-18 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.2 0.00000E+00 -3.78601E-02 1.24548E-03 -1.83300E-05 1.01840E-07
0.25 1.40788E-17 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.3 1.18572E-17 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.4 -3.38450E-20 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.5 0.00000E+00 -2.00096E-02 4.98896E-04 -6.14640E-06 3.41459E-08
0.6 -7.05110E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.7 5.68605E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.8 1.33276E-18 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.9 1.27259E-18 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
1 3.96745E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
2010 SECTION VIII, DIVISION 2
5-130
Table 5.E.17 – Stress Factor
x
y
K – Square Hole Pattern
Notes:
1.
2345678 9 10
1234567891011
234
12 13 14 15
1
xy
CCCCCCCCCC C
K
CC C C
θ
θθθθθθθ θ θ
θθ θ θ
+++++++++ +
=
++ + +
2. See Figure 5.E.4 for definition of
x
y
K and
θ
(
θ
is in Degrees, 090
θ
≤
≤ )
3.
Valid range is 0.1 1.0
μ
∗
≤≤, data for 0.05
μ
∗
= is provided for information only.
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2010 SECTION VIII, DIVISION 2
5-131
Table 5.E.18 – Stress Factor
x
z
K And
yz
K – Square Hole Pattern
*
μ
1
C
2
C
3
C
4
C
5
C
0.05 -8.65900E-05 0.00000E+00 3.39079E-06 0.00000E+00 -9.00340E-08
0.1 -9.16630E-06 1.70502E-04 -2.18240E-04 3.03915E-05 -2.60740E-06
0.15 -7.50710E-06 -1.70443E-03 6.97716E-06 -6.04360E-06 8.60699E-08
0.2 5.53257E-07 -3.89704E-03 -1.93130E-05 -2.30990E-06 -3.09000E-07
0.25 3.23710E-07 -6.44426E-03 -6.52400E-05 2.93245E-06 -5.32400E-07
0.3 -6.76800E-07 -9.59777E-03 3.72356E-05 -8.93710E-06 3.33448E-07
0.4 2.53798E-06 -1.47723E-02 -2.99370E-05 2.92311E-06 -3.37840E-07
0.5 8.12376E-06 -1.93888E-02 2.78977E-05 -3.32890E-06 2.15640E-07
0.6 3.52335E-06 -2.25507E-02 -1.01380E-04 1.34464E-05 -8.10840E-07
0.7 7.44733E-06 -2.58912E-02 -2.05060E-05 4.19794E-06 -2.12710E-07
0.8 1.25243E-05 -2.86525E-02 4.06228E-06 -3.16500E-06 5.12292E-07
0.9 -9.44320E-06 -3.16364E-02 -3.74000E-05 8.62779E-06 -5.59110E-07
1 -1.97550E-05 -3.43965E-02 -1.45890E-04 1.85432E-05 -1.03270E-06
*
μ
6
C
7
C
8
C
9
C
10
C
0.05 0.00000E+00 1.39181E-11 0.00000E+00 -2.65320E-15 0.00000E+00
0.1 1.08751E-07 -2.67100E-09 4.13442E-11 -4.00270E-13 2.20859E-15
0.15 -5.10320E-10 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.2 1.60946E-08 -3.29790E-10 3.54744E-12 -2.20680E-14 8.74181E-17
0.25 2.31330E-08 -4.96950E-10 6.17680E-12 -4.62380E-14 2.01806E-16
0.3 -1.09310E-08 3.01384E-10 -5.42280E-12 5.71883E-14 -3.19690E-16
0.4 1.47598E-08 -3.45240E-10 4.84820E-12 -4.08380E-14 1.90865E-16
0.5 -8.79080E-09 2.38954E-10 -4.04210E-12 4.10517E-14 -2.29180E-16
0.6 2.96526E-08 -6.57410E-10 9.03011E-12 -7.49820E-14 3.44094E-16
0.7 8.54418E-09 -2.09120E-10 3.16043E-12 -2.87240E-14 1.43406E-16
0.8 -2.58810E-08 7.24790E-10 -1.20140E-11 1.17377E-13 -6.25690E-16
0.9 2.39629E-08 -6.08270E-10 9.39984E-12 -8.70290E-14 4.43996E-16
1 3.80915E-08 -8.85470E-10 1.30648E-11 -1.18880E-13 6.08423E-16
*
μ
11
C
12
C
13
C
14
C
15
C
0.05 1.37550E-19 0.00000E+00 1.79422E-05 0.00000E+00 4.15212E-07
0.1 -5.25320E-18 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.15 0.00000E+00 2.23725E-03 -9.03060E-04 3.77631E-05 -5.40970E-07
0.2 -1.98940E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.25 -4.09670E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.3 7.31063E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.4 -3.82080E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.5 5.40118E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.6 -6.68450E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.7 -3.01410E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.8 1.40496E-18 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.9 -9.60370E-19 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
1 -1.33970E-18 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
2010 SECTION VIII, DIVISION 2
5-132
Table 5.E.18 – Stress Factor
x
z
K And
yz
K – Square Hole Pattern
*
μ
16
C
17
C
18
C
19
C
0.05 0.00000E+00 -9.82930E-11 7.22485E-15 -6.39790E-20
0.1 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.15 2.68316E-09 0.00000E+00 0.00000E+00 0.00000E+00
0.2 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.25 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.3 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.4 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.5 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.6 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.7 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.8 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
0.9 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
1 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00
Notes:
1.
2345678 9 10
1 2 3 4 5 6 7 8 9 10 11
,
23456810
12 13 14 15 16 17 18 19
1
xz yz
CCCCCCCCCC C
KK
CCCCCCCC
θ
θθθθθθθ θ θ
θθ θ θ θ θ θ θ
+++++++++ +
=
++ + + + + + +
2. See Figure 5.E.4 for definition of
x
z
K and
yz
K and
θ
(
θ
is in Degrees, 090
θ
≤
≤ )
3.
Valid range is 0.1 1.0
μ
∗
≤≤, data for 0.05
μ
∗
= is provided for information only.
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2010 SECTION VIII, DIVISION 2
5-133
Table 5.E.19 – Boundary Conditions for the Numerical Analysis (see Figure 5.E.3)
Pressure Region Applied Pressure
1
p
h
*
t
pp −
2
p
h
*
s
pp −
3
p
hs
pp −
4
p
h
p
−
5
p
ht
pp −
Definitions
Tube
Expansion Into
Tubesheet
Tube-To-
Tubesheet
Weld Location
*
t
p
*
s
p
h
p
unexpanded
Tubeside
⎟
⎠
⎞
⎜
⎝
⎛
−
A
A
qp
h
t
1
⎟
⎠
⎞
⎜
⎝
⎛
−
A
A
qp
ts
s
1
s
p
Shellside
⎟
⎠
⎞
⎜
⎝
⎛
−
A
A
p
h
t
1
()
11
ts h
s
t
AA
p
qqp
AA
⎛⎞
−−−
⎜⎟
⎝⎠
t
p
expanded Tubeside
⎟
⎠
⎞
⎜
⎝
⎛
−
A
A
qp
h
t
1
⎟
⎠
⎞
⎜
⎝
⎛
−
A
A
qp
ts
s
1
s
ts
t
ts
p
h
t
p
h
t
⎟
⎠
⎞
⎜
⎝
⎛
−+ 1
Shellside
⎟
⎠
⎞
⎜
⎝
⎛
−
A
A
p
h
t
1
()
11
ts h
s
t
AA
p
qqp
AA
⎛⎞
−−−
⎜⎟
⎝⎠
t
p
Notes:
1.
0( )q for the U tube design=−
2.
1( )q for the Fixed Tubesheet design=
3.
2
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
p
d
f
A
A
p
ts
4.
2
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
p
td
f
A
A
t
p
h
5.
()
23
p
f
for the triangular pattern
π
=
6.
()
4
p
f
for the square pattern
π
=
2010 SECTION VIII, DIVISION 2
5-134
5.E.10 Figures
D
o
r
o
p
d
t
U
L
Solid Rim
Figure 5.E.1
Perforated Plate Geometry Details
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2010 SECTION VIII, DIVISION 2
5-135
P
t
P
s
P
s
P
t
-P
s
-P
s
P
s
P
t
P
s
P
s
(A) Hydrostatic Compression
(C) Desired Loading Condition w/ Holes Under Shell Pressure
(B) Finite Element Analysis Boundary Condition
Figure 5.E.2
Perforated Plate Geometry Details
2010 SECTION VIII, DIVISION 2
5-136
p
1
p
4
p
5
p
3
p
2
Solid Rim
Shell
Head or Channel
Equivalent Solid Perforated Plate
Outermost Tube
Shellside
Tubeside
Note: See Table 5.19 for definition of boundary conditions.
Figure 5.E.3
Boundary Conditions for Numerical Analysis
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2010 SECTION VIII, DIVISION 2
5-137
y
x
θ
σ
x
*
y
x
θ
σ
θ
= K
x
σ
x
∗
/μ∗
(a) Uniaxial Loading along X-direction (b) Uniaxial Loading along Y-direction
σ
θ
= K
y
σ
y
∗
/μ∗
σ
y
*
σ
y
*
σ
x
*
τ
xz
*
y
x
θ
τ
xz
*
z
x
(d) Transverse Shear Loading
τ
θz
= K
xz
τ
xz
*
/μ*
τ
xz
*
τ
xz
*
y
x
θ
σ
θ
= Κ
xy
τ
xy
∗
/μ∗
τ
xy
*
τ
xy
*
τ
xy
*
y
x
θ
τ
yz
*
z
τ
θz
= K
yz
τ
yz
*
/μ*
τ
yz
*
τ
yz
*
τ
yz
*
θ
σ
θ
σ
θ
σ
θ
τ
xy
*
(c) Pure Shear Loading
(e) Transverse Shear Loading
Figure 5.E.4
Stress Orientations For Perforated Plate With Triangular Pattern Holes
2010 SECTION VIII, DIVISION 2
5-138
y
x
θ
y
x
y
x
z
x
θ
z
y
K
yz
at θ = K
xz
at (90 - θ)
σ
x
*
σ
x
*
σ
y
*
σ
y
*
σ
θ
σ
θ
= (K
x
σ
x
∗+Κ
y
σ
y
∗)/μ∗
σ
θ
τ
xy
*
τ
xy
*
τ
xy
*
τ
xy
*
σ
θ
= Κ
xy
τ
xy
∗
/μ∗
τ
xz
*
τ
xz
*
τ
xz
*
τ
xz
*
τ
yz
*
τ
yz
*
τ
yz
*
τ
yz
*
τ
θz
= K
xz
τ
xz
*
/μ*
τ
θz
= K
yz
τ
yz
*
/μ*
(a) Uniaxial Loading in Pitch Direction
(b) Pure Shear Loading
(c) Transverse Shear Loading
Figure 5.E.5
Stress Orientations For Perforated Plate With Square Pattern Holes
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