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.
FOR SOLID SHAFT
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)