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/0.15^{2} ) + a
Radial pressure at the inner side = 10 MN/m^{2}.
10 = (b/0.15^{2}) - a
On solving, we obtain b = 0.3357 and a = 5.
For external pressure = 0, we obtain
0 = 0.3375/ R^{2} - 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,
= (0.3375/0.26^{2}) + 5
= 10.00 MN/m^{ 2}