Stepped bar ABC is fabricated out of aluminum and supported by a fixed support at C as shown. The cross-sectional area of step AB is $A_{AB} = 2.5 \, in^2$ and the cross-sectional area of step BC is $A_{BC} = 3.5 \, in^2$. Determine the normal stress in steps AB and BC and the total deformation of the stepped bar under the applied forces.
Take $F_A = 7.5 \, kips$, $F_B = 4 \, kips$, $L_{AB} = 12 \, in$, and $L_{BC} = 16 \, in$.
$\sigma_{AB} = 3$ ksi
$\sigma_{BC} = 1.167$ ksi
$\delta_{ABC} = 0.0052$ in