Calculated the diameter of an aluninium shaft , Mechanical Engineering

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 = Es = 201 GN/m2 and Ealuminium = Ea = 67 GN/m2.

Solution

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

1256_Calculated the diameter of an aluninium shaft.png

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

Therefore,

2098_Calculated the diameter of an aluninium shaft1.png

i.e.

60_Calculated the diameter of an aluninium shaft2.png

or ∴

1531_Calculated the diameter of an aluninium shaft3.png

Da  = (3 × (50)4 )1/ 4  = 65.8 mm

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

Posted Date: 1/21/2013 6:17:02 AM | Location : United States







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