Determine the magnitude and nature of the stresses:

A thin spherical hollow steel shell of 400 mm diameter & 5 mm thickness is immersed into a liquid container pressurized to 2 N/mm². Determine the magnitude and nature of the stresses induced in the material of the shell.

Solution

In this case, the shell is subjected into an external pressure of 2 N/mm². Therefore, the stresses shall be compressive in nature.

Diameter, d = 400 mm.

Thickness, t = 5 mm.

External pressure, p = 2 N/mm².

∴ Hoop stress, σ_h  = pd/4t  = 2 × 400 / (4 × 5)

                      σ_h  = 40 N/mm² (compressive)