4.2 Pressure Vessel Examples
        Ex. 4.2.1

Example 4.2.1

Given: A cylindrical steel tank (pressure vessel) has Length L = 3.5 ft, Radius R = 10 in. and Thickness t = 0.10 in. The maximum stress that the pressure vessel steel can withstand is sf = 50 ksi. Assume E = 30 Msi and n = 0.3

Req'd: The maximum allowable working pressure, Pw. (use a Factor of Safety of 2.0), and the change in radius at this pressure.

Sol'n: If the maximum stress of the steel is 50 ksi and the Factor of Safety is 2.0, the allowable (maximum working) stress in the pressure vessel is:

sw =
sf

F.S.
=
50 ksi

2
= 25 ksi

In a cylindrical pressure vessel, the hoop stress is always twice the longitudinal stress. Therefore in this problem we want to limit the hoop stress to 25 ksi

sH =
pR

t
pw =
swt

R
pw =
(25 ksi)(0.10 in.)

10 in.
= 0.25 ksi = 250 psi

The change in radius of the pressure vessel is given by:

DR =
pR2

Et
1 -
n

2
DR =
(250 psi)(10 in)2

(30 Msi)(0.10 in)
1 -
0.3

2
= 0.0071 in