Allied & ICAR Exam Bank • ALLIED_1081NAT • 2 Marks
Section 2: Farm Machinery
Machine Design
Subtopic: Keys and Couplings
Question Statement:
A rectangular sunk key of width $b = 10\text{ mm}$, height $h = 8\text{ mm}$, and length $L = 50\text{ mm}$ fits into a 40 mm diameter shaft. If the torque transmitted is 400 N$\cdot$m, the shear stress induced in the key in MPa is:
Answer Key:
40
Step-by-Step Solution & Explanation
Tangential force at shaft surface: $F = \frac{T}{r} = \frac{400}{0.02} = 20,000\text{ N}$. Shearing area $A_s = b \times L = 10\text{ mm} \times 50\text{ mm} = 500\text{ mm}^2$. Shear stress $\tau = \frac{F}{A_s} = \frac{20000}{500} = 40\text{ N/mm}^2 = 40\text{ MPa}$.