find out the thickness of the metal and the hoop

Question

Find out the thickness of the metal and the hoop stress:

The cylinder of a hydraulic press has an internal diameter of 0.3 m & is to be designed to withstand a pressure of 10 MN/m2 without the material being stressed over 20 MN/m2. Find out the thickness of the metal and the hoop stress on the outer side of the cylinder.

Solution

Internal radius = 0.3 /2= 0.15 m

Let the external radius be R.

Hoop stress shall be maximum at the inner side.

Therefore,

20 = (b/0.15² ) + a

Radial pressure at the inner side = 10 MN/m².

Therefore,

10 = (b/0.15²) - a

On solving, we obtain b = 0.3357 and a = 5.

For external pressure = 0, we obtain

0 = 0.3375/ R²  - 5

R = 0.26 m

Therefore, metal thickness = 0.26 - 0.15 = 0.11 m = 110 mm. At last, hoop stress at the outside of the cylinder shall be,

= (0.3375/0.26²) + 5

= 10.00 MN/m ²