A solid steel shaft 10 m long and 70mm diameter issubjected to a torque of 4.5 k

Question

A solid steel shaft 10 m long and 70mm diameter issubjected to a torque of 4.5 kNm. In order to save the weight the solid shaft is to bereplaced be a thin walled hollow shaft of wall thickness10mm. What diameter of hollow shaft is required to carry the sametorque if the maximum allowable stress is the same as thatexperienced by the solid shaft? If the modulus of rigdity of the steel is 80 x 109N/m2 calculate the angle of twist for the thinwalled shaft. Considering materials/ manufacturing costs and applicationconstraints such as weight, inertia, balance, size and reliability,describe a suitable application for each type of shaft stating whythat type is more suitable than the alternative.

Explanation / Answer

GIVEN THAT

L=10m ; d=70*10^-3 ; T = 4.5*10^3 N.m ; C= 80*10^9 N/m^2

We know that

T/J = /(d/2)   -------------- (1)

Or = T/J*d/2

Where for solid shaft J= (/32)*d^4

Substituting in (1) we get

= [4.5*10^3*70*10^-3]/[2.357*10^-6*2]

= 66.822*10^6 n/m^2

FOR HOLLOW SHAFT

J= (/32)*(do^4 - di^4)

where do = outer diameter

           di = inner diameter

Thickness of shaft t= 10mm =0.01m

    di = do -2t

   di = do -0.02

so     J= (/32)*[do^4- (do -0.02)^4]

substitute the expression of J in (1) to getdo

NOTE:- Volume of material required is for hollow shaft shaft isless than that of solid shaft. for the same stress requirements.Hence weight reduces when hollow shafts areused

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