GATE 2026 AG – Question 39
A 540 rpm tractor PTO drives a tiller through a flange coupling with a shear pin parallel to the shaft,60 mm from its axis. The tiller normally needs 40 kW. Allowable pin shear stress is 200 MPa, and the pin must fail at 150% rated torque. Neglect bending, stress concentrations and losses. Use π=3.14;find the nearest pin diameter in mm.
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Correct answer: (B) 10.6
Explanation
Rated torque is $T=P/\omega=40000/[2(3.14)(540)/60]=707.71$ N·m. Failure torque is $1.5T=1061.57$ N·m. The single-shear force is $F=T_f/r=1061.57/0.060=17692.85$ N. Set $F=\tau\pi d^2/4$ with $\tau=200$ N/mm²,giving $d=\sqrt{4F/(3.14\cdot200)}\approx10.62$ mm. **B**.