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Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Young's modulus and coefficient of thermal expansion of Q are twice the corresponding values of P. Assume the bars to be perfectly bonded at the interface, and their weights to be negligible. The bars are held between rigid supports as shown in the figure and the temperature is raised by ΔT. Assume that the stress in each bar is homogeneous and uniaxial. Denote the magnitudes of stress in P and Q by σ1 and σ2, respectively. Which of the statement(s) given is/are CORRECT?

1. The interface between P and Q moves to the left after heating
2. The interface between P and Q moves to the right after heating
3. σ1 < σ2
4. σ1 = σ2

Correct answer: σ1 = σ2

Solution

The correct option is that the stresses in both bars are equal (σ1 = σ2) because they are perfectly bonded and experience the same temperature change, leading to equal stress distribution despite differing material properties.

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