Knowledge of Lame’s equation for thick cylinder. And therefore variation of radial and hoop stress across the wall thickness.

NUMERICAL PROBLEM

In a hydraulic press, the cylinder has an internal diameter of 30cm. The cylinder has to withstand an internal pressure of 10 MPa without the material being stressed beyond 20 MPa. Determine the thickness of the metal.

LOGICAL APPROACH

- We have the internal radius, ri and we are provided with value of inside pressure, which is nothing but radial stress, σr at the inner surface of cylinder.
- We also have a maximum limiting pressure to which the cylinder material can be subjected, that is value of hoop stress, σθ at the inner surface.
- Substituting value of σθ and σr in Lame’s equation: σθ = A + B/ r2; σr = A – B/ r2, we can get value of the constant A and B.
- Using value of A and B, and solving for value of radial stress, σr at the outer surface of cylinder (which is equal to zero), we can calculate the outer radius, ro
- And therefore the metal thickness, t = ro - ri.

ANSWER

Thickness = 10.981 cm