CYLINDRICAL SHELL UNDER UNIFORM INTERNAL PRESSURE
(SEE RD-1171.1)
The minimum thickness of cylinder shells under internal pressure shall be the greater of (a) or (b) below, but not less
than 1/4 in. (6 mm).
Internal pressure, P
5.0
72.5
bar Tensile modulus in the longitudinal
psi (axial) direction, E1
28137.3
28137300
ksi
psi
Inside diameter of shell, D
203.2
8.0
101.6
4.0
mm Tensile modulus in the
in circumference (hoop) direction, E2
mm Length of Shell, L
in
1004.5
1004502
1314
51.73
ksi
psi
mm
in
Inside radius of shell, R
Select the greater of (a) or (b) below :
a. Longitudinal Stress, t1
t1 =
PR
2 (0.001 E1)
=
0.005
=
0.13
b. Circumference Stress, t2
t2 =
in
mm
PR
0.001 E2
=
0.29
=
7.33
Therefore let t = t2 =
in
mm
8
mm
>
0.13
mm
=
0.31
in
CYLINDRICAL SHELL UNDER EXTERNAL PRESSURE
(SEE RD-1171.2)
The maximum allowable external pressure between stiffening elements is computed by following :
Outside diameter, Do
Do = 2 (R + t)
= 2 (19.1 +0.87)
Axial tensile modulus, Eat
8.6
in.
Design factor, F
5.0
219.2
mm
A knockdown factor using rigorous
equations, KD
0.84
Length of Shell, L
28137.3
ksi
28137300
psi
1004.5
ksi
1004502
1500
59.06
psi
mm
in.
Hoop flexural modulus, Ehf
Length of Shell, L
Ehf
3/2
Eat
Eaf
1/2
(1 -ʋx ʋy)
1/2
L
2
2
Flexural poisson's ratio in the hoop
diraction, ʋx
Reduction factor, Υ
(a) Υ = 1 - 0.001 Zp, if Zp ≤ 100,
(b) Υ = 0.9, if Zp > 100
0.39
0.00674532 0.920814857 2566.14964
(Do / 2) t
≤
15.94
100
Allowable external pressure, Pa
KD 0.8531 Υ Ehf
(1 - ʋx ʋy)
=
167.40
3/4
3/4
1/4
Eat
1/2
L (Do/2)
psi
t
F
5/2
in
0.39
=
Pa =
mm
Flexural poisson's ratio in the axial
diraction, ʋx
Coefficient, Zp
Zp =
1500
59.06
90724.7081 541.9689949
0.98
THICKNESS OF HEAD SHELL UNDER INTERNAL PRESSURE
(SEE RD-1173.1)
The required thickness of vessel heads under internal pressure shall be computed by the appropriate equation for
ellipsoidal head :
Internal pressure, P
5.0
72.5
203.2
8.0
Inside diameter of shell, D
bar Design modulus for the head, Ehd
psi
mm
in
1004.5
ksi
1004502
psi
Minimum thickness of head, t2
t2 =
PD
2 (0.001 Ehd)
=
=
0.29
7.33
in
mm
THICKNESS OF HEAD SHELL UNDER EXTERNAL PRESSURE
(SEE RD-1173.2)
The required thickness of an ellipsoidal head under external pressure shall be determined in the same manner as outlined in RD-1172.2 using the following equation :
Outside radius of crown portion of
head, D
Design modulus of head, E
4
101.6
in.
mm
Flexural poisson's ratio in the axial
diraction, ʋ1
0.39
1004.5
1004502
ksi
psi
Flexural poisson's ratio in the hoop
diraction, ʋ2
0.39
Factor depending on ellipsoidal head
proportions, Ko
0.90
Design factor, F
5.0
Height of head, H
101
4.0
mm
in.
Major - to - Minor axis ratio :
Do
h
Allowable external pressure, PA
PA =
=
0.41 (E/F) (t)
3 (1 - ʋ1 ʋ2)
1/2
191.76
psi
2
(Ko Do)
6865.29512 35.80128162
2
=
8.0
4.0
=
2.0