$(2)$ The cantilevered bar shown below is made from a ductile material and is statically loaded with Fx $=75lbfFy=-200lbf,$ and $Fz=100lbf.$ Analyze the stress situation in rod AB by obtaining the following information. $(5$ points$).$

$($a$)$ Determine the precise location of the critical stress element. $($b$)$ Sketch the critical stress element and determine magnitudes and directions for all stresses acting on it$.($c$)$ For the critical stress element, determine the principal stresses and the maximum shear stress.

$(3)$ For problem $(2),$ if the rod AB is made of $4130$ Annealed Steel, what is the safety factor of the design? $(2$ points$)$

$(4)$ Repeat the analysis of problem $(2)$ if rod $AB$ is made of brittle material with yield strength in tension of $47$ kpsi and in compression of $60$ kpsi $.$ What is the safety factor of the design? $(3$ points$)$