Question

A steel railroad track has a length of 40 m when the temperature is -3◦C. What is the increase in the length of the rail on a hot day when the temperature is 31◦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 -3◦C to prevent expansion. Calculate the thermal stress in the rail if its temperature is raised to 31◦C. Young’s modulus for steel is 20 × 1010 N/m2.Answer in units of N/m2.

Answer 1

1)

$$\Delta l=\alpha \Delta Tl$$

$$\Delta l=(11 \cdot 10^{−6})(31-(-3))(40)=0.015\ m$$

2)

$$σ=YαΔT$$

$$σ=(11⋅10 ^ {−6} )(20⋅10 ^ {10} )(34)=7.5⋅10^7\frac{N}{m^2}$$