Problem $1$

The rod shown in the figure has two cross$-$sectional areas, where the area of the larger cross$-$section is $6$ times larger than the smaller. The rod is subjected to three point loads, $P_1,P_2,$ and $P_3$ at points B$,$ C$,$ and D$,$ respectively. You may assume that the bar deforms in a linear$-$elastic manner. The cross section of the small rod is equal to $A=2i{n}^2$ and the modulus of elasticity is equal to $E=20,000$ksi.

a$)$ Find the support reactions at A and $E,$ if $P_1=10$ kips, $P_2=20$ kips and $P_3=40$ kips.

b$)$ Draw the axial force diagram.

c$)$ Identify how the position of point $C$ changes due to the applied loadings.

Figure $1\mathrm{.}1.$ Rod with point loads