Engineering Material Series - Solid Shaft Or Hollow Shafts - Which Is Stronger?

What seem better by sight may not really be better in the real sense. Many people may say that solid shaft are better than their hollow counterpart. However, we can not just judge by sight. It is technically proven that hollow shaft are better. Better? you may ask. Yes better. How?

To prove this we have to compare the shaft bending stress developed for the same applied bending moment to the hollow shaft and solid shaft of the same weight.


We will use the beam bending equation here for the calculation of bending moment stress:

The bending stress (F_s) developed in a solid shaft is given by:

                                

                                F_s  = (32 X M)/(∏ X D³).........…..  Eq.1

And the bending stress (F_h) developed by the same amount of bending moment (M) in a hollow shaft is given by:

                         F_h  = (32 X M X D₀)/(∏ X (D₀⁴- D_i⁴)) ……..Eq.2

Where,

M  – The applied bending moment for both the shafts

D  – The diameter of the solid shaft

D₀  – Outer diameter of the hollow shaft

D_i  – The inner diameter of the hollow shaft


Now, the ratio of F_h/F_s can be arrived by dividing the Eq.2 to the Eq.1 as:

                   F_h/F_s  = (D₀ X D³)/(D₀⁴-D_i⁴) = (D/D₀)³/(1-(D_i/D₀)⁴) ……Eq.3

You can observe from the Eq.3 that:

    as,    D₀ > or = D and D₀ > D_i

so the numerator of the Eq.3 is much smaller than the denominator.

So, it can be said that the bending stress developed in a hollow shaft is lesser than that at a solid shaft of same weight or in other word, hollow shaft is stronger in bending than a same weight solid shaft.

Conclusively we can agree that in engineering, thing should not be judged by common sight. It could be very deceptive.

mechguru 

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