Problem $3(35$ points$)$

A loaded machine component undergoes the following strains at a given point:

a$.$ Draw Mohr's circle to scale and from this, find:

${}_{P_1},{}_{P_2},{}_P,{}_{\text{m}\text{a}\text{x}},$ and $2,$ the angle from the $x$ axis to the $-$axis

Assume that this is a plane strain problem, with ${}_z=0.$ Also determine the radius and distance

to the center of the circle from the origin.

b$.$ Confirm your Mohr's circle results by using the angle $$ that you found $($from your sketch$)$ along

with ${}_x,{}_y,{}_{xy}($initially given$),$ to confirm your value for ${}_{P_1}.$ Please show your calculation that

you used to verify this.