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GATE 2017 ME (ME1) – Question 25

Mechanics of Materials · Deflection of beams · 1 mark · Numerical answer

A solid circular steel shaft transmits 40 kW at 500 rpm. Its diameter is 40 mm. Find the maximum shear stress in MPa.

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Correct answer: 60 to 61

Explanation

Angular speed is $\omega=2\pi(500)/60=52.3599$ rad/s, giving torque $T=P/\omega=40000/52.3599=763.944$ N m. For a solid circular shaft, $\tau_{max}=16T/(\pi d^3)$. With $d=0.04$ m, $\tau_{max}=60.7927\times10^6$ Pa = 60.79 MPa.

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