$1.$ Consider a homogeneous isotropic prismatic beam which is fixed at one end and free at the opposite end as shown in the figure below. The beam is subjected to surface tractions and an end load as shown in the figure. If the material of the beam is Aluminum $2024-$T$4,$

a$)$ What are the centroidal displacements at the free end $?$

b$)$ Compute the bending stress at point A located on the section at $\backslash (\backslash$mathrm$\{$x$\}=50\backslash )$ inches.

c$)$ Where does the absolute maximum bending stress occur and what is its magnitude $?$

d$)$ What is the factor of safety relative to the yield strength of the material?