Answer to Question #108790 in Physics for mathew hill

Question

Suppose the ends of the rail are rigidly
clamped at 7◦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

The thermal stress

$$\sigma=E\alpha\Delta T=\\ {=(20\times 10^{10}\:\rm N/m^2)\times (13\times 10^{-6}\:\rm \degree C^{-1})\times (24\degree C)=}\\ {=6.24\times 10^7\rm N/m^2.}$$