The thin walled cylindrical pressure vessel of inner diameter (d) and thickness (t) is subjected to an internal fluid pressure (p). If E=Young’s Modulus and μ=Poisson’s ratio, find the strains in the circumferential and longitudinal directions. Using these results compute the increase in diameter and length of a steel pressure vessel filled with air and having an internal pressure of 16 MPa. The vessel is 3m long and has an inner radius of .5m and thickness of 9mm as show in fig. Est=200GPa and μ=0.3

A thin cylindrical shell:

l = 3000 mm

(radius) r = 0.5 m

d = 2r = 1m = 1000 mm

t = 9 mm

E = 200 $Gpa = 200 \times 10^5 \ N/mm^2$

$\mu = 0.3$

P = 16 Mpa = 16 $N/mm^2$

To Find:

a] En

b] El

A] Circumferential strain (En)/ Hoop strain:

$En = \frac{\sigma n - \mu \sigma l}{E}$

But,

$ \sigma n = \frac{pd}{2 t}$ and $\sigma l = \frac{\sigma n}{2}$

$\therefore \ \sigma n = \frac{16 \times 1000}{2 \times 9}$

$\sigma n = 888.89 \ N/mm^2$ and $\sigma l = \frac{888.89}{2} = 444.44 \ N/mm^2$

$\therefore \ En = \frac{888.89 – 0.3 \times 444.44}{2 \times 10^5}$

$En = 3.77 \times 10^{-3}$

B] Longitudinal strain (El):

$El = \frac{\sigma l - \mu \ \sigma n}{E}$

$= \frac{444.44 – 0.3 \times 888.89}{2 \times 10^5}$

$El = 88.8 \times 10^{-4}$