Determine the change in diameter, Mechanical Engineering

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, σh  = pd /4t = 1 × 1800/4 × 10 = 45 N/mm2

∴ Hoop strain, ε h = (σh /E )(1 - v) = (45/2 × 105) (1 - 0.3) = 1.575 × 10- 4

∴ Increase in diameter = εh × d

= 1.575 × 10- 4 × 1800 = 0.2835 mm

Posted Date: 1/21/2013 2:06:45 AM | Location : United States







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