Determine the change in diameter:
A thin spherical shell of 1.8 m diameter is 10 mm thick. This is filled with a liquid so that the internal pressure is 1 N/mm^{2}. Determine the change in diameter if the Young's
Modulus of the material is 2 × 10^{5} N/mm^{2} and Poisson's ratio is 0.3.
Solution
Diameter of the shell, d = 1.8 m = 1800 mm.
Thickness, t = 10 mm.
Internal pressure, p = 1 N/mm^{2}.
∴ Hoop stress, σ_{h} = pd /4t = 1 × 1800/4 × 10 = 45 N/mm^{2}
∴ Hoop strain, ε_{ h} = (σ_{h} /E )(1 - v) = (45/2 × 10^{5}) (1 - 0.3) = 1.575 × 10^{- 4}
∴ Increase in diameter = ε_{h }× d
= 1.575 × 10^{- 4} × 1800 = 0.2835 mm