For a plane stress element with:

${}_x=-6$MPa,${}_y=4$MPa, and ${}_{xy}=10$MPaccw

$($a$)$ Draw a Mohr's circle diagram for the element with labels indicated for the

axes, component stresses, principal stresses, and relevant angles.

$($b$)$ Find the principal normal stresses, ${}_1$ and ${}_2,$ and extreme value sheer

stresses, ${}_1$ and ${}_2,$ using the geometry of the circle.

$($c$)$ Draw the stress element with ${}_1$ and ${}_2$ properly aligned with respect to

the xy coordinates. Calculate the angle from the x $-$axis using the geometry

of the circle and indicate this on your figure. Include any other stresses that

are present on the element.

$($d$)$ Draw the stress element with ${}_1$ and ${}_2$ properly aligned with respect to

the $xy$ coordinates. Calculate the angle from the x $-$axis using the geometry

of the circle and indicate this on your figure. Include any other stresses that

are present on the element.