$(25$pts$)$ A beam with the cross$-$section shown is loaded with a $15$kip$*ft$ moment. Assume that the

flanges are both centered on the web.

a$.$ Show that the centroid$/$neutral axis of the beam is $5\mathrm{.}5625in$ up from the bottom and

centered.

b$.$ Show that the $2^{nd}$ moment of the area Ixx about the centroid is approximately $200i{n}^4.$

Give answer to $4$ significant figures.

c$.$ What is the normal stress in ksi at the top and is it in compression or tension?

d$.$ What is the normal stress in ksi at the bottom and is it in compression or tension?

e$.$ What is the normal stress in ksi at the neutral axis and is it in compression or tension?