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How you evaluate the strength of solid and hollow circular shaft (Tmax)?

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Strength of a shaft may be defined as the maximum torque which can be applied to the shaft without exceeding allowable shear stress and angle of twist. 


From the torsion equation : T/J = τ/R = G.θ/L

Since T = τ.J/R 

= τ.[(πD4/32)/(D/2)] 

= τ.(π/16)D3 

Tmax = (π/16) τmax.D3 ...(i) 

Again since T/J = G.θ/L; T = J.G.θ/L 

= (ÀD4/32).G.θ/L 

Or ; Tmax = (πD4/32).G.θmax/L ...(ii)

Where ; 

Tmax = Maximum torque 

θmax = Maximum angle of twist 

τmax = Maximum shear stress 

Note: The strength of the shaft is the minimum value of Tmax from equation (i) and (ii). And for finding out diameter of shaft we take maximum value of dia obtained from equation (i) and (ii) 

As the same for hollow shaft 

Tmax = (π/16) τmax.(D4 – d4)/D ...(iii) 

= (π/32)(D4 – d4).G.θmax/L ...(iv)

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