A solid circular ductile shaft with yield stress 280 MPa carries torque 10 kN m. Using Tresca theory, find minimum radius avoiding yield, in cm to 2 decimals.
Pure torsion has maximum shear $\tau=2T/(\pi r^3)$. Tresca permits τ = σy/2 = 140 MPa at yield. Thus $r=[2(10000)/(\pi\,140\times10^6)]^{1/3}=0.03569$ m, or 3.57 cm.
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