A pipe$-$rod system with flanges at ends A and C was supposed to exactly fit

between two rigid walls, as shown in Figure $2.$ Bolts are installed in the flange at C and are

tightened until the gap of $=0\mathrm{.}1$ in$.$ is closed. After the flange has been tightened against the

walls at C$,$ the temperature of the pipe$-$rod system ABC is increased uniformly by $50\backslash$deg F$.$

$$ Element $(1)$ is a steel pipe with outer diameter do $=2$ in$.$ and inner diameter di $=1\mathrm{.}5$ in$.$

E$1=30$ x $103$ ksi, $\backslash$alpha $1=6\mathrm{.}5$ x $10-6/\backslash$deg F$.$

$$ Element $(2)$ is a solid aluminum pipe with diameter d $=0\mathrm{.}75$ in$.$ E$2=10$ x $103$ ksi, $\backslash$alpha $2=13$

x $10-6/\backslash$deg F$.$

Determine the stress induced in each element and the total displacement $$B of joint B as a

result of closing the gap $$ and temperature increase