Question Bank • QB_FM_119 NAT • 2 Marks

Section 2: Farm Machinery

Machine Design

Subtopic: Measurement of force, stress, torque, speed, displacement and acceleration on machine elements – shafts, couplings, keys, bearings and knuckle joints

Question Statement:

A solid circular PTO drive shaft of diameter $d = 35\text{ mm}$ transmits a torque of $T = 400\text{ N}\cdot\text{m}$. Calculate the maximum torsional shear stress induced in the shaft in $\text{MPa}$. (Take $\pi = 3.1416$)

Answer Key:

47.53

Step-by-Step Solution & Explanation

Torsional shear stress formula: $\tau = \frac{16 T}{\pi d^3}$ Where $T = 400\text{ N}\cdot\text{m} = 400000\text{ N}\cdot\text{mm}$ and $d = 35\text{ mm}$: $d^3 = 42875\text{ mm}^3$ $\tau = \frac{16 \times 400000}{\pi \times 42875} = \frac{6400000}{134696} \approx 47.514\text{ N/mm}^2 = 47.51\text{ MPa}$
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