design of heads
DESCRIPTION
haesdTRANSCRIPT
![Page 1: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/1.jpg)
4.3 Designing Heads subject
to Internal Pressure
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Stresses in Heads
Heads are one of the important parts in pressure vessels
and refer to the parts of the vessel that confine the shell
from below, above, and the sides.
The ends of the vessels are closed by means of heads
before putting them into operation
The heads are normally made from the same material as
the shell and may be welded to the shell itself. They also
may be integral with the shell in forged or cast
construction.
The head geometrical design is dependent on the geometry
of the shell as well as other design parameters such as
operating temperature and pressure
![Page 3: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/3.jpg)
Types of Head
•Flanged
•Ellipsoidal
•Tori - spherical
•Hemispherical
•Conical
•Tori -conical
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Classification according to the shape: i. Convex heads
Semi-spherical head
Elliptical head
Dished head (spherical head with hem)
Spherical head without hem
![Page 9: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/9.jpg)
ii. Conical heads
Conical head without hem
Conical head with hem
iii. Flat heads
![Page 10: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/10.jpg)
1.Semi-spherical head
i. Molding of heads
Small diameter and thin wall
——
Integrally heat-pressing
molding
Large diameter
—— Spherical petal welding
球瓣式组焊
Di
![Page 11: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/11.jpg)
ii. Calculating equation for thickness
][ 4 c
t
ic
p
DpS
][ 4
2Cp
DpS
c
t
icd
valueofround][4
S 12
CCp
Dp
c
t
icn
![Page 12: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/12.jpg)
2.Thickness calculating equation
of elliptical head
b
a
S
pam
2max
hi (
b)
ho
Di S
Ri (a)
i. Calculating equation
for thickness:
For the elliptical heat
whose m = a / b ≤ 2
![Page 13: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/13.jpg)
2. The maximum stress should be at the top point:
Putting m = a / b, a = D / 2 into the equation,
getting:
S
mpD
4max
t
S
mpD][
4max
t
mpDS
][ 4
Then:
Under the condition about strength:
![Page 14: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/14.jpg)
(1)Replacing P with Pc
(2)Multiplying []t with welded joint efficiency
(3)Substituting D with Di, D = Di + S
(4) m = a / b = Di / 2 hi
Putting these conditions into the equation:
getting:
i
i
c
t
ic
ct
ic
h
D
p
Dpm
mp
DpS
45.0 ][2
2
2 ][2
m = a / b = Di / 2 hi
![Page 15: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/15.jpg)
For the standard elliptical head whose m=2:
c
t
ic
p
DpS
5.0 ][2
For the elliptical head whose m>2:
at boundary » and m at the top point
Then introducing the stress strengthening
coefficient K to replace (Di / 4hi)
![Page 16: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/16.jpg)
In this equation:
2
22
6
1
i
i
h
DK
c
t
ic
p
DpKS
5.0 ][ 2
For standard elliptical head: K=1
This is the common equation for calculating
the wall thickness of elliptical heads.
![Page 17: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/17.jpg)
Beside these conditions:
for standard elliptical heads Se ≮ 0.15% Di
for common elliptical heads Se ≮ 0.30% Di
The straight side length of standard
elliptical heads should be determined
according to P103, Figure 4-11
![Page 18: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/18.jpg)
iii. Working stress and the maximum
allowable working pressure
e
eict
S
SKDp
2
5.0
ei
e
t
SKD
Sp
5.0
][2][
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3.Dished head
i. Structure
Containing three parts:
Sphere: Ri
Transition arc (hem): r
Straightedge: ho (height)
Di
r
ho
c
t
ic
p
RpMS
5.0 ][2
r
RM i3
4
1
M —— Shape factor of dished head
and
ii. Calculating equation for thickness
![Page 20: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/20.jpg)
iii. Working stress and the maximum
allowable working pressure
e
eict
S
SMRp
2
5.0
ei
e
t
SMR
Sp
5.0
][2][
![Page 21: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/21.jpg)
iv. Dished head
When Ri = 0.9 Di & r = 0.17 Di
the dished head is standard dished head
and M = 1.325
So the equation is:
c
t
ic
p
DpS
5.0 ][2
2.1
![Page 22: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/22.jpg)
4.Conical head
i. Structure
*without hem (suitable for ≤ 30 o )
without local strength
with local strength
*with hem (suitable for > 30 o )
—— Adding a transition arc and a
straightedge between the joint
of head and cylinder
![Page 23: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/23.jpg)
ii. Calculating equation for thickness
The maximum stress is in the main aspect
of conical head.
cos
1
2 maxmax
S
pD
m
t
maxmax ][ cos
1
2
S
pD
According to the strength condition:
![Page 24: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/24.jpg)
Then
cos
1
][2
t
pDS
cos
1
][2
c
t
cc
p
DpS
Replacing P with Pc, considering , and
changing D into Dc ,D=Dc+S
![Page 25: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/25.jpg)
This equation only contains the membrane
stress but neglects the boundary stress at the
joint of cylinder and head. Therefore the
complementary design equation should be
established:
(1)Discriminating whether the joint of
cylinder and head should be reinforced
or not.
(2)Calculation for the local reinforcement.
![Page 26: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/26.jpg)
Conical head without hem ( ≤ 30 o )
(1)Not require reinforcing
(consistent thickness for the whole head)
main aspect:
cos
1
][2
c
t
cc
p
DpS
cos
1
][2
c
t
sic
p
DpS
small aspect:
![Page 27: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/27.jpg)
(2)Require reinforcing
(for the thickness of joint,
the reinforcement region)
Main aspect:
c
t
icr
p
DpQS
][2
c
t
sicr
p
DpQS
][2
Small aspect:
![Page 28: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/28.jpg)
Interpretation:
Dc —— inside diameter of main aspect
Di.s —— inside diameter of small aspect
Di —— inside diameter of cylinder
Q —— coefficient (Consulting the Figure
4-16 or 4-18 in book)
![Page 29: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/29.jpg)
Conical head with hem ( > 30 o )
(1)Thickness of hem at the transition section
c
t
sic
p
DpKS
5.0 ][2
c
t
sic
p
DpfS
5.0 ][
K —— coefficient (Consulting Figure4-13)
f —— coefficient (Consulting Figure4-14)
(2)Thickness of conical shell at the joint with
transition section
![Page 30: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/30.jpg)
4.Flat head
i. Structure
The geometric form of flat heads:
rotundity, ellipse, long roundness,
rectangle, square, etc.
ii. Characteristics of load
Round flat with shaft symmetry which is
subjected to uniform gas pressure
![Page 31: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/31.jpg)
(1)There are two kinds of bending stress states,
distributing linearly along the wall.
(2)Radial bending stress r and hoop bending
stress t distributing along the radius.
![Page 32: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/32.jpg)
▲Fastening the periphery
max = r.max
The maximum stress is
at the edge of disk.
S
R
p
0
t
r.
ma
x
r
2
max. 188.0
S
DPr
S
PD
S
R
275.0
![Page 33: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/33.jpg)
▲ Periphery with simply supported ends
max = r.max = t.max
The maximum stress is
in the center of disk.
S
R
P
t
r.
ma
x
0
r
2
max. 31.0
S
DPr
S
PD
S
R
2 24.1
![Page 34: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/34.jpg)
iii. Calculation equation for thickness
From the condition of strength max ≤ []t ,
getting:
Fastening the periphery
t
PDS
][
188.0
t
PDS
][
31.0
Periphery with simply supported ends
![Page 35: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/35.jpg)
In fact, the supporting condition at boundary
of flat head is between the previous two.
After introducing the coefficient K which is
called structure characteristics coefficient and
considering the welded joint efficient , getting
the calculating equation for thickness of round disk:
t
ccp
PKDS
][
valueofroundS 12 CCSpn
![Page 36: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/36.jpg)
5.Examples
Design the thicknesses of cylinder and heads
of a storage tank. Calculating respectively the
thickness of each heads if it’s semi-spherical,
elliptical, dished and flat head as well as
comparing and discussing the results.
Known: Di = 1200 mm Pc = 1.6Mpa
material: 20R []t = 133Mpa C2 = 1 mm
The heads can be punch formed by a complete
steel plate.
![Page 37: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/37.jpg)
Solution:
(1)Determining the thickness of cylinder
][ 2 c
t
ic
p
DpS
mm 26.7
6.10.11332
12006.1
mmCSSd 26.80.126.72
C1 = 0.8 mm (Checking Figure 4-7)
Sd + C1 = 8.26 + 0.8 = 9.06 mm
Round it of, getting: Sn = 10 mm
= 1.0 (Double welded butt, 100% NDE)
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(2)Semi-spherical head
][ 4 c
t
ic
p
DpS
mm 62.3
6.10.11334
12006.1
mmCSSd 62.40.162.32
C1 = 0.5 mm (Checking Figure 4-7)
Sd + C1 = 4.62 + 0.5 = 5.12 mm
Round it of, getting: Sn = 6 mm
= 1.0 (wholly punch forming)
![Page 39: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/39.jpg)
(3)Standard elliptical head
c
t
ic
p
DpS
5.0 ][2
mm 24.7
165.00.11332
12006.1
mmCSSd 24.80.124.72
C1 = 0.8 mm (Checking Figure 4-7)
Sd + C1 = 8.24 + 0.8 = 9.04 mm
Round it of, getting: Sn = 10 mm
= 1.0 (wholly punch forming)
![Page 40: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/40.jpg)
(4)Standard dished head
c
t
ic
p
DpS
5.0 ][2
2.1
mm 69.8
6.15.00.11332
12006.12.1
mmCSSd 69.90.169.82
C1 = 0.8 mm (Checking Figure 4-7)
Sd + C1 = 9.69 + 0.8 = 10.49 mm
Round it of, getting: Sn = 12 mm
= 1.0 (wholly punch forming)
![Page 41: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/41.jpg)
(5)Flat head
K = 0.25; Dc = Di = 1200 mm; []t = 110 Mpa
t
ccp
PKDS
][
mm 36.72
0.1110
6.125.01200
mmCSSd 36.730.136.722
C1 = 1.8 mm (Checking Figure 4-7)
Sd + C1 =73.36 + 1.8 = 75.16 mm
Round it of, getting: Sn = 80 mm
= 1.0 (wholly punch forming)
![Page 42: Design of Heads](https://reader034.vdocument.in/reader034/viewer/2022052217/55cf9441550346f57ba0ac15/html5/thumbnails/42.jpg)
Comparison:
Head-form
Sn mm
kg
Semi-sphe. Elliptical Dished Flat
6
106
10 12 80
137 163 662
Selection:
It’s better to use the standard elliptical
head whose thickness is the same to that of
cylinder.