Calculated the diameter of an aluninium shaft:

Calculated the diameter of an aluninium shaft that is designed to store the similar amount of strain energy per unit volume as a 50 mm diameter steel shaft of the similar length. Both shafts are subjected to equivalent compressive axial loads. What shall be the ratio of the stresses set up in the two shafts?

Take Esteel = E_s = 201 GN/m² and E_aluminium = E_a = 67 GN/m².

Solution

As the strain energy per unit volume of the two shafts is equivalent, we get

But we know stress,  σ=  load / area of cross-section

Therefore,

i.e.

or ∴

D_a  = (3 × (50)⁴ )^{1/ 4}  = 65.8 mm

The needed diameter of the aluminium shaft is equal to 65.8 mm.