$3-53$ The part shown is loaded at point $C$ with $300$ N in the positive $x$ direction and at point $E$ with $200$ N in the positive $y$ direction. The diameter of the bar ABD is $12$ mm $.$ Evaluate the likelihood of failure in section $AB$ by providing the following information: $($a$)$ Determine the precise location of the critical stress element at the cross section at $A($i$.$e$.,$ specify the radial distance and the angle from the vertical $y$ axis$).$

$($b$)$ Sketch the critical stress element and determine magnitudes and directions for all stresses acting on it$.$

$($c$)$ Sketch the Mohr's circle for the critical stress element, approximately to scale. Label the locations of all three principal stresses and the maximum shear stress.

$($d$)$ For the critical stress element, determine the three principal stresses and the maximum shear stress.

Problem $3-53$

Dimensions in m