Two solid cylindrical rods are joined at $B$ and loaded as shown. Rod $AB$ is made of aluminum and rod $BC$ of brass. If the total deformation of the rod cannot exceed $0\mathrm{.}05$ in $.$ and the allowable stresses are $20$ ksi for aluminum and $30$ ksi for brass, determine the maximum allowable load P that can be applied as shown.

Gives:

$=0\mathrm{.}05ml$

${}_{AB}=20$kSI

${}_{BC}=30$kSI

$P_B=$

$P_{BC}=25k$