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CHAPTER 6
Pressure (Welded) Vessel Design
Pressure Vessel is a closed vessel having an internal pressure between 15 psig to 3000 psig
(Perry and Green, 1997). Whereas, atmospheric and low pressure tanks are designed to operate at
pressures between atmospheric to 0.5 psig, and, 0.5 to 15 psig respectively (Kohan, 1987).
The
American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code contains rules for
the design, fabrication and inspection of boilers and pressure vessels. ASME Code is acceptable in
most of the States in the US and all Canadian provinces. Section VIII Division I of ASME Boiler and
Pressure Vessel Code deals specifically with pressure vessels. Most pressure vessels used in the
process industry in the US are designed in accordance with the specification of this section.
Pressure vessels may include reflux drum, storage tanks, heat exchangers, chemical reactors,
distillation columns, absorption tower, stripping columns and many more.
SHELL THICKNESS
In general, the minimum wall thickness of welded metal plates subject to pressure, excluding
corrosion allowances, should not be less than 2.4 mm (Peters et al., 2004).
To provide for the vessel sufficient rigidity especially at low pressures, the minimum wall
thickness at different cylindrical shell diameters should be (Seider, 2004).
Vessel inside diameter (ft)
Up to 4
4-6
6-8
8-10
10-12
Minimum wall thickness (inch)
¼
5/16
3/8
7/16
1/2
In practical designation, the shell is considered thin if the ratio of circumferential radius of
curvature to wall thickness is greater than 10. Many pressure vessels are relatively thin, having
radius of thickness ratio between 10 to 500 (Bhaduri, 1984).
Shell Thickness Working Equations
The needed Shell thickness of pressure vessels is a function of the ultimate tensile strength
of the metal at operating temperature, operating pressure, vessel diameter and welding joint
efficiency (Peters et al, 2004). In the recent American Society of Mechanical Engineers (ASME) Code
(VIII-I), the working equation for the determination of shell thickness of cylinder subjected to
internal pressure based on inside diameter is given as:
tp
PR
C
SE 0.6 P
eq 6-1
PRESSURE WELDED VESSEL DESIGN
2
where
tp = shell thickness required (inch) [m]
P = Internal gauge pressure (psig) [kN/m2]
R = Inside Radius (inch) [m]
S = Allowable stress (psi) [kN/m2]
E = Joint efficiency factor (Table 6-4)
C = Corrosion allowance (inch) [m]
Provided that
R
2
1.
tp less than or equal to
and
2.
Pressure is less than or equal to 0.385 SE (Jawad and Farr, 1988).
Alternative ASME equation based on outside diameter of a cylindrical shell is given as:
PR
C
SE 0.4 P
tp
eq 6-2
ASME Pressure Vessel Code formula excludes corrosion, wind and earthquake allowances
(Mulet, 1981) as cited by (Seider, 2004). The recommended wall thickness, tv, requirement of vertical
pressure vessel or tower incorporating wind load based on wind velocity of 140 miles/hr, which is
substantially sufficient to handle additional earthquake load is,
tv = tp [ 0.75 + 0.22 E ( L/Di)2/Pd }
eq 6-3
The above equation is applicable for 10 > ( L/Di)2/ Pd > 1.34
If the ratio is less than 1.34, then tv = tp
Table 6-1. Design equations and data for pressure vessels based on the ASME Boiler and Pressure
Vessel/Code. Adapted from ASME as cited by Peters et al., 2004.
Recommended design equations for vessels
Under internal pressure
Limiting conditions
For cylindrical shells
t
t
Pri
SE J - 0.6P
SE J
ri
SE J
P
P
Cc
t
1/2
ri
or P
Cc
ri
2
0.385SE J
For spherical shells
t
t
Pri
SE J - 0.2P
Cc
or P
1/3
t
ri
2SE J
2P
2SE J
P
ri
Cc
ri
2
0.385SE J
PRESSURE WELDED VESSEL DESIGN
t
For ellipsoidal head
or P
PD a
2SE J - 0.2P
t
3
0.356ri
0.665SE J
Cc
0.5 (minor axis) 0 = 0.25Da
For torispherical (spherically dished) head
0.885 PL a
SE J - 0.1P
t
Cc
r = knuckle radius = 6% of inside crown
radius and is not less than 3t
For hemispherical head
Same as for spherical shells with ri = La
***Nomenclature for Table 6-1
a = 2 for thickness <0.0254 m and 3 for thickness 0.0254 m
Cc = allowance for corrosion, m
Da = major axis of an ellipsoidal head, before corrosion allowance is added, m
EJ = efficiency of joints expressed as a fraction
IDD = inside depth of dish, m
La = inside radius of hemispherical head or inside crown radius of torispherical head, before corrosion allowance is added,
m
n = 1.2 for D 1.55m, 1.21 for D = 1.55-2.0 m, 1.22 for D = 2.0-2.7 m, and 1.23 for D > 2.7 m
OD = outside diameter, m
P = maximum allowable internal pressure, kPa (gauge)
r = knuckle radius, m
ri = inside radius of shell, before corrosion allowance is added, m
S = maximum allowable working stress, kPa
3
t = minimum wall thickness, m
= density of metal, kg/m
+
See the latest ASME Boiler and Pressure Vessel Code for further details.
Shell Wall thickness for vacuum vessels may be calculated (Kalis, 1986) with this equation
Pc
T
2.6 e
Do
Te
Do
2
Em
T
0.45 e
Do
0.5
eq 6-4
where
Pc
Te
Do
Em
= Collapsing pressure (psi)
= Thickness to withstand external pressure (inch)
= Outside diameter (inch)
= Material’s modulus of elasticity
Te must be high enough so that Pc is five times greater than the difference between
atmospheric pressure and design vacuum pressure
PRESSURE WELDED VESSEL DESIGN
4
Mulet et al , 1981, as cited by Seider, 2004, presented an alternative equation for the
calculation of cylindrical wall thickness at vacuum, tE,
tE = 1.3 ( PdL/EMDo ) 4
eq 6-5
a correction factor is added ,tEC
tEC = L ( 0.18Di-2.2 ) x 10 -5- 0.19
eq 6-6
Thus, the wall thickness of vessels at vacuum incorporating wind and earthquake loads is,
tV = tE + tEC
eq 6-7
tp = wall thickness (for internal pressure)
Di = inside diameter
L = cylindrical shell length
Pd = internal design gauge pressure
S = maximum allowable stress
lb
in 2
E = fractional weld efficiency
Po = operating gauge pressure
tv = wall thickness of vessels or tower incorporating wind and earthquake loads
tE = wall thickness of vessel or tower @ vacuum
tEC = correction added to tE, , (tV = tE + tEC)
To include corrosion allowance, tc, Seider (2004) recommended 1/8 inch for noncorrosive
conditions. Backhurst and Harker (1973) recommended 1/8 up to 3/16 corrosion allowance for
noncorrosive and ¼ for corrosive environments.
ts = tV + tc
eq 6-8
where
ts = cylindrical wall thickness incorporating wind, earthquake and corrosion allowances.
For Spherical Shell, ASME code as cited by Kohan (1987) provide for equation to calculate the
maximum allowable internal working pressure.
P
SEt p
R
0.2t p
where
P
R
tp
E
S
=
=
=
=
=
internal working gauge pressure (psig)
Inside Radius (inch)
Minimum required thickness (inch)
Lowest joint efficiency
Max allowable stress (psi)
eq 6-9
PRESSURE WELDED VESSEL DESIGN
5
Material of Construction
In a noncorrosive environment, carbon steel and low alloy steel are commonly used
material of construction for pressure vessel at low temperature (-20 to 650oF) and high temperature
(650 – 900oF) respectively. Carbon steel, SA 285 grade C has a maximum allowable stress of 13,750
psi, while a low alloy steel, SA 387B has a maximum allowable stress of 15, 00 psi (Seider, 2004).
Stainless steel 304 and 316 also known materials for pressure vessel (Peters et al., 2004). Stainless
steel 300 series could even be used up to 1,500oF (Perry and Green, 1997). Maximum allowable
stress varies from material to material and design temperatures. Tables 6-2 and 6-3 show
maximum allowable stress of different pressure vessel materials. Table 6-4 shows modulus of
elasticity for carbon steel and low allow steel at different temperature (Seider, 2004).
Table 6-2. Recommended stress values. Adapted from ASME as cited by Peters et. al., 2004.
Recommended stress values
Metal
Temp., ºC
S, kPa
Joint efficiencies
For double-welded butt joints
If fully radiographed = 1.0
If spot-examined = 0.85
If not radiographed = 0.70
Carbon steel
(SA-285, Gr. C)
-29 to 343
399
454
94,500
82,700
57,200
In general, for spot examined
If electric resistance weld = 0.85
If lap-welded = 0.80
If single-butt-welded = 0.60
Low-alloy steel
for resistance to
H2 and H2S
(SA-387, Gr. 12C1.1)
-29 to 427
510
565
649
94,500
75,800
34,500
6,900
High-tensile steel
for heavy-wall
vessels
(SA-302, Gr.B)
-29 to 399
454
510
538
137,900
115,800
69,000
42,750
-29
343
427
538
128,900
77,200
72,400
66,900
-29
345
427
538
128,900
79,300
75,800
73,100
38
204
38
204
46,200
20,700
15,900
6,900
High-alloy steel
for cladding and
corrosion resistance
Stainless 304
(SA-240)
Stainless 316
(SA-240)
Nonferrous metals
Copper
(SB-11)
Aluminum
(SB-209, 1100-0)
PRESSURE WELDED VESSEL DESIGN
6
Table 6-4. Modulus of elasticity values, EM for carbon steel and low-alloy steel as a
function of temperature (Seider, 2004).
Psi x 106
Temperature (ºF)
-20
200
400
650
700
800
900
Carbon Steel
30.2
29.5
28.3
26.0
-
Low-alloy Steel
30.2
29.5
28.6
27.0
26.6
25.7
24.5
Recommended Design Pressure and Temperature
Design pressure used in the calculation of wall thickness should always be greater than the
operating pressure. Similarly, design temperature may be equal to operating temperatue plus 50oF.
The following are recommended design pressures at different operating pressure (Seider, 2004);
Operating Pressure ,Po (psig)
0 -5
10 – 1,000
1,000 +
Design Pressure ,Pd (psig)
10
P= exp{0.60608+0.91615[ln Po] + 0.0015655 [ ln Po ]2 }
1.1Po
Welding
Welding will heat the metal surrounding the welding area which could result in warping,
shrinking of the welded area (Kennedy, 1982). It is for this reason that at times, stress relieving is
required to release locked-up localized stresses. Stress relieving may be accomplished either by
annealing or hammering. After welding, test are often employed to locate weld defects and other
structural trouble inside the weld. Radiographing is often used to find these weld defects.
Radiography is an inspection test where welded joints are exposed to x-ray to detect excessive
porosity, defective fusion and other defects in the welding process (Kennedy, 1982).
Weld efficiency, E, reflects the integrity of the welding. Carbon steel having thickness up to
1.25 inch requires only a 10% spot X-ray check where the weld efficiency is 85 %. However, for
thicker walls, a 100% X-ray check is required, allowing a value of 100% efficiency (Seider, 2004).
Longitudinal joints are more highly stressed than circumferential joints requires a minimum butt
welding. Similarly, all vessels in lethal application shall have an all butt weld connection and fully
radiographed. Also all vessels fabricated on carbon or low alloy steel requires post-heat treatment
(Perry and Green, 1997). All welded joints of cryogenic tanks must be butt welded, postweld heat
treated and X- ray examined (Kohan, 1987). Depending on the degree of radiograph examination
used to check the integrity of the welded joint, and the type of welded joint, computation of wall
PRESSURE WELDED VESSEL DESIGN
7
thickness of pressure vessel will have different joint efficiencies. ASME section VIII classifies
radiographic examination as full radiography, spot radiography and no spot radiography.
For double butt joint, the following are the corresponding efficiencies
Full radiography
Spot radiography
No radiography
100%
85%
70 %
This decrease in joint efficiency from full to no spot radiography would result to a more shell
wall thickness. Hence , as a rule, when welded joint efficiency is not known, assume a no spot
radiography and use 70% joint efficiency if double butt joint is to be used (Kohan, 1987). This will
provide for an allowance on wall thickness, but should later be check for the appropriate type of
welded joint. Table 6-5 shows different type of welded joints and corresponding efficiencies and
limitations (Jawad and Farr, 1988).
Figure 5-1. Welded Joint Categories.
PRESSURE WELDED VESSEL DESIGN
8
Table 6-5. Maximum Allowable Joint Efficiencies1 for Arc and Gas Welded Joints. Adapted from
Jawad, M. H., and J. R. Farr, 1988.
Typ
e
No.
(1)
(2)
(3)
4)
Joint Description
Butt joints as attained by
double-welding or by other
means which will obtain the
same quality of deposited
weld metal on the inside and
outside weld surfaces to agree
with the requirements of UW35; welds using metal backing
strips which remain in place
are excluded.
Single welded butt joint with
backing strip other than those
included in (1)
Single-welded
butt
joint
without use of backing strip
Double full fillet lap joint
Double full fillet lap joint
Single full fillet lap joints with
plug welds confirming to UW17
(5)
Single full fillet lap joints with
plug welds confirming to UW17
(6)
Single full fillet lap joints
without plug welds
Degree of Radiographic
Examination
a
b
c
Full
Spot
None
Limitations
Joint
Category
None
A, B, C & D
1.0
0.85
0.70
(a) None except as shown in (b)
below
(b) Circumferential butt joints
with one plate offset, see UW13(c) and Fig. UW-13.1 (k).
Circumferential butt joints
only. Not over 5/8in. thick and
not over 24in outside diameter
longitudinal joints not over
3/8in. thick
circumferential joints not over
5/8in. thick
2
(a) Circumferential joints for
attachment of heads not over
24in. outside diameter to shells
not over 1/2in. thick.
(b) Circumferential joint for the
attachment to shells of jackets
not over 5/8in. in nominal
thickness where the distance
from the center of the plug
weld to the edge of the plate is
not less than 1-1/2 times the
diameter of the hole for the
plug.
(a) For the attachment of
heads convex to pressure to
shells not over 5/8in. required
thickness. only with use of fillet
weld on
inside of shells, or
(b) For attachment of heads
having pressure on either side.
To shells not over 24in. inside
diameter and not over 1/4in.
required thickness with fillet
weld on outside of head flange
only.
A, B, C & D
0,90
0.80
0.65
A, B & C
0.90
0.80
0.65
A, B & C
NA
NA
0.60
A
NA
NA
0.55
B&C
NA
NA
0.55
B
NA
NA
0.50
C
NA
NA
0.50
A&B
NA
NA
0.50
1 E = 1.0 for butt joints in compression.
2 joints attaching hemispherical heads to shells are excluded .
PRESSURE WELDED VESSEL DESIGN
9
Plate thickness increments
It is noteworthy to emphasize that vessels fabricated from metal plates may be assumed to
come in the following increments (Seider, 2004). Final vessel wall thickness is established by
rounding off to the next increment.
Metal plate thickness, inch
Increments, inch
3/16 to 1/2
1/16
5/8 to 2
/8
2 ½ to 3
¼
HESSE AND RUSHTON METHOD
In chemical engineering pressure vessel course, the classical book on Process Equipment
Design authored by Hesse and Rushton (1975) has been in used as the course textbook. In the
succeeding paragraphs, calculation methods, conditions and data were reproduced in toto from the
said textbook.
Shell Thickness
Shell thickness of welded pressured vessel may be calculated using the given equation
(Hesse and Rushton, 1975):
tp
PD
2Se P
C
eq 6-10
where
tp
P
D
S
e
C
= shell thickness (inch)
= Max allowable working pressure (psi)
= Inside diameter (inch)
= Max allowable tensile stress (psi) (Table 6-6)
= Efficiency of welded joint (Table 6-7)
= Corrosion allowance
The above equation is applicable as long as the following conditions are met:
1. tp < 0.10D
2. tp > tmin
where
tmin
D 100
1000
eq 6-11
PRESSURE WELDED VESSEL DESIGN
10
Table 6-6. Materials and Allowable Working Stresses for Unfired Pressure Vessels, Adapted from
ASME-UPV Code by cited by Hesse, H.E. and J.H. Rushton, (1975) Process Equipment
Design.
ASME
Code
Spec.
No.
S-2
S-1
S-42
S-44
S-43
S-55
S-44
S-43
S-55
S-44
S-43
S-28
Material Data
and Description
Steel plates - flange and
firebox quality
Carbon steel for boilers
Carbon-silicon steel,
ordinary strength range
Molybdenum steel
Low-carbon nickel steel
Carbon-silicon steel, high
strength range, 4-1/2”
plates and under
Chrome-manganesesilicon
alloy steel
Grad
e
Specified
Minimum
Tensile
Strength
1000 psi
A
B
45
50
A
B
A
A
55
60
Allowable Unit Tensile Stress, Thousands psi
at Various Temperatures, °F
- 20
to
650
700
750
800
850
900
950
1000
9.0
10.0
11.0
11.0
12.0
13.0
8.8
9.6
10.4
10.4
11.4
13.0
8.4
9.0
9.5
9.5
10.4
13.0
6.9
7.5
8.0
8.5
9.1
12.5
5.7
6.0
6.3
7.2
7.4
11.5
4.4
4.4
4.4
5.6
5.6
10.0
2.6
2.6
2.5
3.8
3.8
8.0
2.0
2.0
5.0
13.0
12.3
11.1
9.4
7.6
5.6
3.8
2.0
14.0
14.0
14.0
15.0
14.0
13.3
13.3
15.0
14.0
11.9
11.9
15.0
13.5
10.0
10.0
14.4
12.0
7.8
7.8
12.7
10.2
5.6
5.6
10.4
8.0
3.8
3.8
8.0
5.0
2.0
2.0
5.0
15.0
14.1
12.4
10.1
7.8
5.6
3.8
2.0
65
A
B
B
B
C
C
A
B
70
75
85
Design Stress
Design stress, S maybe estimated using the given equation:
S = Su x F m x F s x F r x F a
eq 6-12
Where
Su
Fm
Fs
Fr
Fa =
= Minimum Specified Tensile Strength
= Material Factor
Fm = 1 for Grade A material
Fm = 0.97 for Grade B material
Fm = 0.92 for Grade C material
= Temperature Factor (Use Table 6-8)
= Stress Relief (SR) Factor
Fr = 1.06 When SR is applied
Radiographing Factor
Fa = 1.12 when Radiographing is applied and subsequent repair of defects
Note: Both Stress Relief and Radiographing factors are equal to unity when not applied on welded
joints.
PRESSURE WELDED VESSEL DESIGN
11
Welding may induce internal strain and stress on welded joints. In this case, stress relieving
such as by annealing or hammering may be employed to release localized stresses. A 6% increase in
the allowable design stress is allowed in some cases.
Radiographing, on the other hand, is an application of X-ray on welded joints to examine
defective fusion and other defects that may affect the integrity of the pressure vessel. If subsequent
repair of a detected defect is done, a 12% increase in the allowable design stress may also be
allowed.
Stress relieving is mandatory for:
1. tp > 1¼”
2. t p
D 50
(For thinner plates)
120
where D has a minimum value of 20 inches
3. ASTM A – 150
4. ASTM A – 149 (under certain conditions)
Whereas, Radiographing is mandatory for
1. ASTM A – 150
2. ASTM A – 149 (under certain conditions)
3. Lethal gases application
4. Nuclear Reactor applications
Table 6-7. Types of Welded Joint and Corresponding Efficiencies.
EFFICIENCY
CRITERIA
55%
65%
65%
tp < ⅝”
tp < ⅝”
tp > ⅝”
70%
80%
80%
90%
tp < ⅝”
tp < 1¼”
tp > 1¼”
tp > 1¼”
LAP WELD (For circumferential Joint)
Single Lap
Single Lap with plug weld
Double Lap
BUTT WELD (For circumferential and
longitudinal joints)
Single Butt
Single Butt with Back-up Strip
Double Butt
Double Butt with reinforce at center
PRESSURE WELDED VESSEL DESIGN
12
Table 6-7. Temperature Factor.
Metal Temperature,
°F
Plate and Forged
Steel, %
Cast Steel, %
Up to 650
700
750
800
850
900
950
1000
25.0
23.7
21.0
18.0
15.0
12.0
9.0
6.2
16.7
16.4
14.7
12.9
11.1
9.3
7.5
5.7
Adapted from Hesse, H.E. and J.H. Rushton, Process Equipment Design (1975)
Head Thickness
To estimate head thickness requirement for pressure vessel with internal pressure load
(concave), the following are the working equations for different head configurations. For external
pressure load, thickness computed from internal pressure load is multiplied by 5/3.
Standard Ellipsoidal
t
PD
2SE
Hemispherical
t
PD
4SE
Standard Dished
t
PLW
2SE
where
L = crown radius in inches = Do – 6
Kr = knuckle radius
= 0.06 Do
PRESSURE WELDED VESSEL DESIGN
13
Values for W or dished heads
Kr/L
W
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.25
0.50
1.0
1.8
1.7
1.65
1.6
1.55
1.50
1.47
1.44
1.41
1.40
1.38
1.37
1.35
1.32
1.30
1.25
1.12
1.0
For flat heads designed to permit fastening by means of lap joints with or without plug welds; the
required head thickness is given by
t
d
0.3 P
S
where t = is the head thickness
d = is the inner diameter of the flanged head
For flat heads which may be attached by single or double vee or V butt welds; the required
head thickness is given by
t
d
0.25 P
S
And for flat heads cut from a solid plate, the required head thickness is given by
t
d
0.5 P
S
PRESSURE WELDED VESSEL DESIGN
14
Problem 1. Determine the thickness of a 10 meter diameter spherical tank at 300KPa and 27F. The
material of construction is made of carbon steel. Use minimum corrosion
allowance.
Problem 2. A 12 in diameter S-2 Grade A steel has a working pressure and temperature of 500 psi
and 300F respectively. Determine the type of weld to be used and plate
thickness using Hesse and Rushton method.
Problem 3. Grade A S2 steel, butt welded pressured vessel for lethal gas application has an inside
diameter of 20 inches. If the working pressure is 900 psi and the working
temperature is 250ºF, what is the shell thickness of the vessel? (Use minimum
corrosion allowance and Hesse and Rushton method).