A brass rod 3 m long is fixed at both its ends. If the thermal stress is not to exceed 76.5 MPa, what will be the temperature through which the rod should be heated? (Consider α = 17 × 10^-6/°C and E = 90 GPa)

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BHEL Engineer Trainee Mechanical 24 Aug 2023 Official Paper

Answer 1

Concept:

When a rod is fixed at both ends and heated, thermal stress is developed. The thermal stress is given by:

\( \sigma = E \cdot \alpha \cdot \Delta T \)

Where, \( \Delta T \) is the rise in temperature, \( E \) is the modulus of elasticity, and \( \alpha \) is the coefficient of thermal expansion.

Given:

Thermal stress, \(\sigma = 76.5 \times 10^6 \, \text{Pa}\)

Modulus of elasticity, \(E = 90 \times 10^9 \, \text{Pa}\)

Coefficient of thermal expansion, \(\alpha = 17 \times 10^{-6}/^\circ C\)

Temperature rise, \( \Delta T = \frac{\sigma}{E \cdot \alpha} = \frac{76.5 \times 10^6}{90 \times 10^9 \cdot 17 \times 10^{-6}} = 50^\circ C \)