$(25\%)$

The composite aluminum post shown is reinforced with a titanium core. The post was installed when $T_0=70F$ and $P=0.$

When $P=100,000lbs.$ and $T=200F,$ determine ${}_{AL}=12\mathrm{.}8{10}^{-6}i\frac{n}{i}\frac{n}{{?}^{\frac{?}{F}}},E_{AL}=10{10}^3$ksi ${}_{Tl}=5\mathrm{.}2{10}^{-6}i\frac{n}{i}\frac{n}{}F{E}_{TI}=18{10}^3$ksi

a$)$ The force in the aluminum. $F_{AL}=$

b$)$ The force in the titanium core. $F_{TI}=q,$

c$)$ The deflection of the top of the post. ${}_P=$

$(1)$ Equilibriom

$(7)$

$(2)$ Com patibility

$(1){}_{AL}={}_{TI}q,$

$(3)$ Rewrite compatibilis

$(4)q,$ Please solve thoroughly, studying for a final!