A $2D$ stress element has tractions acting on surfaces normal to the $x-$axis and $y-$axis. $$

a$)$ Using a force balance, calculate the normal and shear stress components of this $2$D element on a surface that is $45$ degrees CCW from the x $-$axis $($shown above$).$ Show your work. $[12$ pts$]$

b$)$ Draw the $2$D Mohr's circle for this stress element and clearly label the points on Mohr's circle that represent $[5$ pts$]$:

The $45$ degree surface computed in part $($a$).$ Label $"45$ deg".

The surface normal to the x$-$axis. Label $"$x$-$axis".

The surface normal to the y$-$axis. Label $"y-$axis".