GATE Civil Engineering
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An elastic bar of length $L$, uniform cross sectional area $A$, coefficient of thermal expansion $\alpha$, and Young’s modulus $E$ is fixed at the two ends. The temperature of the bar is increased by $T$, resulting in an axial stress $\sigma$. Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be

  1. $\sigma$
  2. $2 \: \sigma$
  3. $0.5 \: \sigma$
  4. $0.25 \: \alpha \: \sigma$
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