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/mm^{2}. 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/mm^{2}. Therefore, the stresses shall be compressive in nature.
Diameter, d = 400 mm.
Thickness, t = 5 mm.
External pressure, p = 2 N/mm^{2}.
∴ Hoop stress, σ_{h} = pd/4t = 2 × 400 / (4 × 5)
σ_{h} = 40 N/mm^{2} (compressive)