Question $2(7$ points$)$

At an interview for Company XYZ$,$ your future co$-$workers want to see if you can determine the state of stress in a structure and use Mohr's Circle.

a$)(2$ pt$.)$ Please write an expression for the state of stress at point $Q$ using the given parameters and proper subscripts based on the given xyz$-$coordinate system. Note: Point $Q$ is at the most negative$--$ direction on the cylindrical portion with the x $-$axis going through its center line. Force $P$ is in the $y$ direction acting a distance $b$ from the $x-$axis. The cross$-$section of the structure has a constant radius $c.$

b$)(1$ pt$.)$ If $P=500N,b=2cm,$ and $c=1cm,$ please describe the state of stress numerically with appropriate units.

c$)(2$ pt$.)$ Draw Mohr's circle to describe the state of in$-$plane stress.

d$)(2$ pL$)$ Use Mohr's circle to determine the angle of rotation about the normal axis for the material clement to be in a state of in$-$plane principal stresses. Please remember that counterclockwise rotation about the normal axis has a positive value. What are the numerical values with appropriate units for the in$-$plane principal stresses?