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.
DS = Diameter of solid shaft.
DH = External Diameter of Hollow shaft
dH = Internal diameter of hollow shaft
AS = Cross sectional Area of solid shaft
AH = Cross-sectional area of hollow shaft
TS = Torque transmitted by solid shaft
TH = Torque transmitted by hollow shaft
TH /TS = 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, WH/WS = AH/AS
WH/WS = 0.7829