Problem # $8(20$ points$)$

The state of a plane stress ata point $P$ within a loaded body is shownbelow. Using Mohr's Circle:

a$)$ Determine the principal stresses and its corresponding shear stress. $[8$ points$]$

b$)$ Determine the maximum in$-$plane shear stress and its associated normal stress. $[4$ points$]$

c$)$ Draw a properly oriented element and clearly represent the principal $($normal$)$ stresses on it$.[8$ points$]$