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A steel rod is clamped rigidly at both ends and then heated through a temperature rise $\Delta T$. If $\alpha$ is the coefficient of linear expansion and $Y$ the Young's modulus, the thermal stress developed in the rod is

A$Y\alpha\Delta T$
B$\alpha\Delta T / Y$
C$Y / (\alpha\Delta T)$
D$\alpha\Delta T$
Answer & Solution
Correct answer: A. $Y\alpha\Delta T$
Without constraint, the rod would expand by $\Delta L = L\alpha\Delta T$, giving strain $\varepsilon = \alpha\Delta T$. Because both ends are clamped, this strain is suppressed — the rod develops a compressive stress $\sigma = Y\varepsilon = Y\alpha\Delta T$. This is the classic thermal-stress 'trap' on the cheat sheet.
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