Compare solid shaft with the hollow, Mechanical Engineering

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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,

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

T  = 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

 

 


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