compare solid shaft with the hollowcompare solid

Question

Compare solid shaft with the hollow:

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

Sol.: (a) Comparison by strength: Assume that both the shaft has same length, material, and same weight and hence the same maximums shear stress.

Let,

D_S   = Diameter of solid shaft.

D_H  = External Diameter of Hollow shaft

d_H   = Internal diameter of hollow shaft

A_S    = Cross sectional Area of solid shaft

A_H   = Cross-sectional area of hollow shaft

T_S    = Torque transmitted by solid shaft

T_H   = Torque transmitted by hollow shaft

T_H  /T_S = 1.44

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

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

Let WH  = Weight of the hollow shaft

WS = Weight of the Solid shaft

Then,                               W_H/W_S = A_H/A_S

W_H/W_S = 0.7829