A steel plate with a rectangular cross section $(10mm50mm)$ is resting on a frictionless surface under the sun. The plate temperature is measured to be at $80C$ and a length of $4m.$ The plate is then moved into a cold room and is left to rest on a frictionless surface. After several hours, the plate temperature is measured to be at $5C$ The steel has a yield and tensile strength of $250$ and $400$ MPa respectively, a modulus of elasticity equal to $200$GPa and a coefficient of thermal expansion equal to $1\mathrm{.}1{10}^{-5}\frac{m}{m}\frac{?}{?}C.$