Draw a small element with ${}_{}=+20$MPa,${}_{yy}=+10$MPa, and ${}_{xy}=-8$MPa. $($Note: this is still

mechanics convention, so you should draw the shear going DOWN on the right face and TO THE

LEFT on the upper face$).$ Do the following: a$)$ Draw Mohr's circle. b$)$ Find the radius, which is also

${}_{xy}^{\text{M}\text{a}\text{x}},$ or the maximum in$-$plane shear stress. c$)$ Find the principal stresses and show them on a

properly oriented element.

Answers: Principal stresses are $+24\mathrm{.}4$ and $+5\mathrm{.}57$ MPa $,$ max in$-$plane shear is $9\mathrm{.}43$ MPa $,$ your

element should have a face $29$ degrees cw from the vertical with the principal stress of $24\mathrm{.}4$

MPa $($the other is on the face perpendicular to that$).$