$6\mathrm{.}4-8$ An element in pure shear is subjected to stresses ${}_{xy}=-14\mathrm{.}5$MPa, as shown in the figure. Using Mohr's circle, determine:

$($a$)$ The stresses acting on an element oriented at a counterclockwise angle $=22\mathrm{.}5$ from the x axis.

$($b$)$ The principal stresses.

Show all results on sketches of properly oriented elements.

PROB. $6\mathrm{.}4-8$