Question

1.) A steel railroad track has a length of 23 m when the temperature is 6◦C. What is the increase in the length of the rail on a hot day when the temperature is 40 ◦C? The linear expansion coefficient of steel is 11 × 10−6 (◦C)−1.Answer in units of m.

2.)Suppose the ends of the rail are rigidly
clamped at 6◦C to prevent expansion.
Calculate the thermal stress in the rail if
its temperature is raised to 40 ◦C. Young’s
modulus for steel is 20 × 1010 N/m2.Answer in units of N/m2.

Answer 1

1)

$$\Delta L=\alpha L\Delta T$$

$$\Delta L=(11\cdot 10^{−6})(23)(40-6)=0.0086\ m$$

2)

$$\sigma=Y\frac{\Delta L}{L}=Y\alpha \Delta T$$

$$\sigma=(11\cdot 10^{−6})(20\cdot 10^{10})(40-6)=7.5\cdot 10^{7}\frac{N}{m^2}$$