Question

A horizontal steel railroad track has a length of $100\, m$, when the temperature is $25^{\circ} \,C.$ The track is constrained from expanding or bending. The stress on the track on a hot summer day, when the temperature is $40^{\circ} \,C$ is (Note : The linear coefficient of thermal expansion for steel is $1.1 \times 10^{-5}/^{\circ} C$ and the Young’s modulus of steel is $2 \times 10^{11}$ Pa)

• A. $6.6\times 10^{7}$ Pa
• B. $8.8 \times 10^{7}$ Pa
• C. $3.3\times 10^{7}$ Pa
• D. $5.5\times10^{7}$ Pa

Answer 1

Answer: (C)

As the steel rail is contrained from expansion, the expansion pressure causes stress in the steel rail.
Thermal stress depends upon coefficient of expansion a and rise of temperature $\Delta T$
$\therefore $ Thermal stress $\sigma \propto \alpha\Delta T$
$\Rightarrow \sigma=Y \cdot \alpha \cdot \Delta T$ (where, $Y=$ Young's modulus)
$\therefore \sigma =2 \times 10^{11} \times 11 \times 10^{-5} \times(40-25)$
$=3.3 \times 10^{7} Pa$