$5\mathrm{.}14$ For the beam cross section shown, bending is about the z axis. All dimensions are in inches and, where appropriate, are between the centers of the $0\mathrm{.}25-$in walls. Determine

$($a$)$ the second$-$area moments I, I, and lyr

$($b$)$ the orientation of the principal axes of the second$-$area moments.

$($c$)$ the values of the principal second$-$area moments I and In$.$

$($d$)$ the location and magnitudes of the maximum tensile and compressive bending stresses if M$=20$ kip$-$in$.$