Question

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

• A. $\sigma$
• B. $2\sigma$
• C. $0.5\sigma$
• D. $0.25\alpha \sigma$

Answer 1

The correct option is A $\sigma$


From compatibility

${\delta }_r={\delta }_R=0$

$\Rightarrow L\alpha \Delta T=\frac{RL}{AE}$

$\Rightarrow \sigma =\frac{R}{A}=Stress$

Hence Stress is independent of length of bar.