ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules
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2010 SECTION VIII, DIVISION 2
4-295
4.15.7 Tables
Table 4.15.1 – Stress Coefficients For Horizontal Vessels on Saddle Supports
Stress Coefficient
2
1
2sin
sin cos
sin
cos
K
π
Δ
Δ+ Δ⋅ Δ−
Δ
=
Δ
⎛⎞
−Δ
⎜⎟
Δ
⎝⎠
2
*
1
2sin
sin cos
sin
1
K
π
Δ
Δ+ Δ⋅ Δ−
Δ
=
Δ
⎛⎞
−
⎜⎟
Δ
⎝⎠
2
sin
sin cos
K
α
π
ααα
=
−+ ⋅
3
sin sin cos
sin cos
K
αα αα
π
πα α α
−⋅
⎛⎞⎛ ⎞
=
⎜⎟⎜ ⎟
−+ ⋅
⎝⎠⎝ ⎠
2
4
3sin
8sincos
α
π
ααα
⎛⎞
=
⎜⎟
−+ ⋅
⎝⎠
K
5
1cos
sin cos
K
α
π
ααα
+
=
−+ ⋅
2 2
23
6
2
3cos sin 5sin cos cos sin cos sin 1 sin 2
sin
44244 24
sin 1 sin 2
2
24
β
ββββββ β β
ββ
ββ β β β
ββ
π
ββ
⎡⎤
⎛⎞ ⎛⎞
−+−+− −−
⎢⎥
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
⎢⎥
⎣⎦
=
⎡⎤
⎛⎞
−−
⎢⎥
⎜⎟
⎝⎠
⎢⎥
⎣⎦
K
6
7
0.5
4
m
K
a
Kwhen
R
=≤
76 6
31
0.5 1
22
⎛⎞
=− <<
⎜⎟
⎝⎠
mm
aa
KK K when
RR
76
1
m
a
KK when
R
=≥
2010 SECTION VIII, DIVISION 2
4-296
Table 4.15.1 – Stress Coefficients For Horizontal Vessels on Saddle Supports
Stress Coefficient
2
8
2
cos 2 9sin cos sin
cos 1 3
44
sin
2
sin 1 sin 2
2
24
K
βββ β
β
ββ
β
β
π
ββ
π
ββ
⎡⎤
⎛⎞
−+ −
⎢⎥
⎜⎟
⎝⎠
⎢⎥
⎣⎦
=+
⎡⎤
⎛⎞
−−
⎢⎥
⎜⎟
⎝⎠
⎢⎥
⎣⎦
()
9
11
cot cos sin
22
K
π
ββ ρρρ
π
⎧⎫
⎡⎤
=−+− +
⎨⎬
⎢⎥
⎣⎦
⎩⎭
()
(
)
10
13
sin cos cot
22 sin
K
π
β
ρρ ρ πβ β
π
β
−
⎧⎫
⎡⎤
=++−−
⎨⎬
⎢⎥
⎣⎦
⎩⎭
Notes:
1.
5
612
π
θ
Δ= +
2.
0.95
2
θ
απ
⎛⎞
=−
⎜⎟
⎝⎠
3.
2
θ
βπ
=−
4. The relationship between
ρ
and
θ
is given by
(
)
tan 0.5 cot
ρ
ρπββ
=+−
⎡
⎤
⎣
⎦
. Values for
ρ
for a specified
θ
are shown in the table below.
Relationship Between
ρ
and
θ
θ
120° 130° 140° 150° 160° 170° 180°
ρ
93.667° 91.133° 87.833° 84.167° 79.667° 74° 66.933°
Note:
() () ()
247
234
158.58 7.8668 8.8037 10 4.3011 10 8.0644 10
ρ
θθ θ θ
−−−
=− + − + −
for all values of
θ
that satisfy 120 180
θ
°°
≤≤ . This curve fit provides
ρ
in degrees.
5. The angles ,, ,and
θ
βρ
Δ are in radians in the calculations.
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2010 SECTION VIII, DIVISION 2
4-297
4.15.8 Figures
L
=
=
=
=
a
=
=
b
h
2
Figure 4.15.1 – Horizontal Vessel on Saddle Supports
2010 SECTION VIII, DIVISION 2
4-298
< a
b
x
1
x
2
(a)
a
< a
b
x
1
x
2
(b)
a
=
=
b
1
e
r
θ
1
/2
θ/2
<6°
G
1
,H
1
Figure 4.15.2 – Cylindrical Shell Without Stiffening Rings
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2010 SECTION VIII, DIVISION 2
4-299
< a
a
x
1
x
2
Y
Y
C
1
C
2
e
< a
a
x
1
x
2
Y
Y
C
1
C
2
e
< a
a
x
1
Y Y
C
1
C
2
e
x
2
(a)
< a
a
Y Y
C
1
C
2
e
x
2
(b)
x
1
a
Y
C
2
C
1
e
< a
a
x
1
Y
t
x
2
h < 1.56 R
m
t
==
(c)
Figure 4.15.3 – Cylindrical Shell With Stiffening Rings in the Plane of the Saddle
2010 SECTION VIII, DIVISION 2
4-300
< a
a
x
1
x
2
Y
Y
C
1
C
2
t
< a
a
x
1
x
2
Y Y
C
1
C
2
t
x
2
x
2
==
1.56 R
m
t < h < R
m
x
2
x
2
==
1.56 R
m
t < h < R
m
< a
a
x
1
Y Y
C
1
C
2
t
x
2
(a)
x
1
x
2
1.56 R
m
t < h < R
m
< a
a
Y Y
C
1
C
2
t
x
2
(b)
x
1
x
2
x
2
==
==
1.56 R
m
t < h < R
m
Figure 4.15.4 – Cylindrical Shell With Stiffening Rings on Both Sides of the Saddle
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2010 SECTION VIII, DIVISION 2
4-301
β/6
θ
Δ
AB
β
Δ = +
β θ
62
(a)
C
D
β/20
θ
EF
β
α
α = 0,95β
(b)
(c)
Figure 4.15.5 – Locations of Maximum Longitudinal Normal Stress and Shear Stress in the Cylinder
2010 SECTION VIII, DIVISION 2
4-302
θ
GH
β
Maximum Bending Moment:
Shell without stiffeners or shell
stiffeners in the plane of the saddle
(a)
θ
IJ
β
Maximum Bending Moment:
Shell stiffeners on both sides
of the saddle
ρ
(b)
Figure 4.15.6 – Locations of Maximum Circumferential Normal Stresses in the Cylinder
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2010 SECTION VIII, DIVISION 2
4-303
Minimize This Offset
Vessel Head
Vessel Skirt
Figure 4.15.7 – Skirt Attachment Location on Vertical Vessels
2010 SECTION VIII, DIVISION 2
4-304
Hot-Box Cavity - This Space To Be
Left Free Of Insulation And Vents
Typical Segmented Ring
Insulation
Typical Vent
Optional Fireproofing
Dimension established based
on thermal stress analysis
Dimension established based
on thermal stress analysis
Figure 4.15.8 – A Typical Hot-Box Arrangement for Skirt Supported Vertical Vessels
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