Problem $3\mathrm{.}5(20$ points$)$

Two rods $AB$ and $BC,$ made of two different materials, are joined at the collar $B$ and fixed at the ends $A$

and C$.$ Initially, the temperature $(T_0)$ equals $50F$ and there is no stress in the members. After some time,

the temperature increases of $xF,$ and the normal $($compressive$)$ stress in each member equals $4186$

psi. What is the final temperature? Additional data is given in Figure $3\mathrm{.}5.$

Additional question $($optional$,$ ungraded$)$: Determine the displacement of point B$.$

For MEMBER AB :

$A=1\mathrm{.}5i{n}^2$

$E_1=14\mathrm{.}6{10}^6$

${}_1=9\mathrm{.}8{10}^{-6}F$

for MEMBER BC:

$A=1.si{n}^2$

$E_2=10\mathrm{.}6{10}^6$

${}_2=12\mathrm{.}8{10}^{-6}(F{)}^{-1}$

Figure $3\mathrm{.}5$