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.[(πD^{4}/32)/(D/2)]

= τ.(π/16)D^{3}

T_{max} = (π/16) τ_{max}.D^{3 }...(i)

Again since T/J = G.θ/L; T = J.G.θ/L

= (ÀD^{4}/32).G.θ/L

Or ; T_{max} = (πD^{4}/32).G.θ_{max}/L ...(ii)

Where ;

T_{max} = Maximum torque

θ_{max} = Maximum angle of twist

τ_{max }= Maximum shear stress

Note: The strength of the shaft is the minimum value of T_{max} 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

T_{max} = (π/16) τ_{max}.(D^{4} – d^{4})/D ...(iii)

= (π/32)(D^{4} – d^{4}).G.θ_{max}/L ...(iv)