Determine the maximum stress - thick cylinder:

A thick cylinder of steel with an internal diameter of 100 mm & external diameter of 200 mm is subjected to an internal pressure of 80 N/mm². Determine the maximum stress induced in the material and the alteration in the external diameter.

Take Young's Modulus = 2 × 10⁵ N/mm² and Poisson's ratio = 0.3.

Solution

By using Lame's expressions for the inside and outside pressure, we get

                  80 = b/50² - a

and

0 = (b/100²) - a

On solving out, we obtain, b = 266666.67 and a = 26.667.

Therefore, the maximum stress (Hoop stress at the inner surface of the cylinder)

=   (b/50²) + a = (266666.67/50² ) + 26.667

= 133.33 N/mm²

To discover the strain at the outer surface.

Hoop stress at surface = (266666.67 /100^{2) +} 26.667 = 53.33 N/mm²

As, pressure outside is zero.

 Hoop strain = 53.33 / E = 53.33 / (2 × 10⁵)

= 2.666 × 10^{- 4}

Therefore, increase in external diameter = 2.666 × 10^{- 4} × 200 = 0.053 mm .