$11\mathrm{.}2$ Materials commonly used in engineering tend to change their dimensions $($either expanding or contracting$)$ when subjected to temperature changes. The linear coefficient of thermal expansion $()$ is a measure of the change in length per unit of length per degree temperature change. For a body free to expand or contract, the magnitude of the dimensional change is

$=aL(T)$

If a body is restrained against dimensional change due to temperature change, an internal stress $($temperature stress$)$ will develop. This value is calculated from

$=E(T)$