Two steel bars $(E_s=200$GPa and ${}_S=11\mathrm{.}7\frac{{10}^{-6}}{C})$ are used to reinforce a brass bar $(E_b=105$GPa and ${}_b=20\mathrm{.}9\frac{{10}^{-6}}{C}).$ When

the steel bars were fabricated, the distance between the centers of the holes that were to fit on the pins was made $0\mathrm{.}5mm$ smaller

than the $2m$ needed. The steel bars were then placed in an oven to increase their length so that they would just fit on the pins.

Following fabrication, the temperature in the steel bars dropped back to room temperature. Determine the maximum load $P$ that may

be applied to the brass bar if the allowable stress in the steel bars is $31\mathrm{.}5$MPa and the allowable stress in the brass bar is $25$MPa.