Question $1(1$ point$)$

A rod subjected to the axial loads shown consists of titanium in rod BC $($diameter $4$ inches$)$ and aluminum rods $AB$ and $CD,$ each having a diameter of $2$ inches. There is a screw hole near $D,$ creating a stress concentration factor of $K=2\mathrm{.}4$ at that location. Assume elastic behavior.

Material properties:

Titanium: $E_1=17,400$ksi,$a_1=8\mathrm{.}6{10}^{-6}{C}^{-1}$

Aluminum $E=10,600$ksi,$a_1=23{10}^{-6}C{C}^{-1}$

Determine the displacement of $D$ with respect to $B$ due to mechanical stress. $($This means you don't need to calculate anything for section $AB).$

The force in CD is $-6$ kip $($compression$),$ and the force is BC is $4$ kip $($tension$).$ Assume the average stress can be assumed at a distance greater than $2$ d from the screw hole.

Give your answers to $3$ significant figures. Be sure to include units.

A Determine the TOTAL displacement of $D$ if