determine the change in diametera thin spherical

Question

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/mm². Determine the change in diameter if the Young's

Modulus of the material is 2 × 10⁵ N/mm² 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/mm².

∴ Hoop stress, σ_h  = pd /4t = 1 × 1800/4 × 10 = 45 N/mm²

∴ Hoop strain, ε _h = (σ_h /E )(1 - v) = (45/2 × 10⁵) (1 - 0.3) = 1.575 × 10^{- 4}

∴ Increase in diameter = ε_h × d

= 1.575 × 10^{- 4} × 1800 = 0.2835 mm