GATE 2017 CE (CE1) – Question 14
An elastic bar of length $L$, uniform area $A$, thermal-expansion coefficient $\alpha$ and Young’s modulus $E$ is fixed at both ends. A temperature increase $T$ causes axial stress $\sigma$. With all other parameters unchanged, if the length is doubled, the stress becomes
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Correct answer: (A) $\sigma$
Explanation
Fixed ends prevent net thermal strain. The mechanical strain is therefore $-\alpha T$, and the induced compressive stress is $-E\alpha T$. Length cancels when compatibility is written as $\alpha TL-\sigma L/E=0$ in magnitudes. Doubling $L$ changes both free expansion and elastic compliance proportionally, leaving stress unchanged: A.