Topic: Strength of Materials
Two steel rails each of 12 m length are laid with a gap of 1.5 mm at ends at a temperature of 24°C. The thermal stress produced at a temperature of 40°C is (take E = 2 × 10^5 N/mm², coefficient of thermal expansion = 12 × 10^-6 /°C)
- A. 10.5 N/mm²
- B. 12.5 N/mm²
- C. 13.4 N/mm²
- D. 15.5 N/mm²
Answer: C. 13.4 N/mm²
Explanation: Free expansion of the rail is alpha * L * delta_T = 12e-6 * 12000 * (40 - 24) = 2.304 mm. The allowed expansion gap is 1.5 mm. The restricted expansion that causes stress is 2.304 - 1.5 = 0.804 mm. Thermal stress = Strain * E = (Restricted Expansion / L) * E = (0.804 / 12000) * 200000 = 13.4 N/mm².