Question

Compare a solid shaft with a hollow shaft, by strength and by their weight.

Answer 1

(a) Comparison by strength: Assume that both the shaft have same length, material, same weight and hence the same maximum shear stress. Let, 

D_S = Diameter of the solid shaft. 

D_H = External Diameter of the Hollow shaft 

d_H = Internal diameter of the hollow shaft 

A_S = Cross sectional Area of solid shaft 

A_H = Cross-sectional area of hollow shaft 

T_S = Torque transmitted by the solid shaft 

T_H = Torque transmitted by the hollow shaft

T_H /T_S = 1.44 

This show that the torque transmitted by the hollow shaft is greater than the solid shaft, thereby proving that the hollow shaft is stronger than the solid shaft. 

(b) Comparison by weight: Assume that both the shaft have same length, material, Now if the torque applied to both shafts is same, then the maximum shear stress will also be same in both the cases.

Let W_H = Weight of hollow shaft 

 W_S = Weight of Solid shaft 

Then, W_H/W_S = A_H/A_S 

W_H/W_S = 0.7829