$(25$pts$)$ A beam's cross$-$section experiences a bending moment of $M=10$kip$*ft$ and a normal force $N=600lbf.$

a$.$ Show that the $2^{nd}$ moment of the area about the centroid$/$neutral axis is Ixc$=967\mathrm{.}5$in ${?}^4.$

b$.$ Show that the cross$-$sectional area is $30i{n}^2.$

c$.$ Find the normal stress due to the bending moment $M$ at the top, centroid, and bottom of the beam's cross section, indicating positive for tension, negative for compression.

d$.$ Find the average normal stress over the cross$-$section due to the normal force $N.$ e$.$ Find the net normal stress at the top, centroid, and bottom of the beam's crosssection.$(25$pts$)$ A beam's cross$-$section experiences a bending moment of M$=10$kip$*$ft and a normal force N$=600$lbf $.$ a$.$ Show that the $2^($nd $)$ moment of the area about the centroid$/$neutral axis is Ixc$=967\mathrm{.}5$in $(4).$ b$.$ Show that the cross$-$sectional area is $30$in$^(2).$ c$.$ Find the normal stress due to the bending moment M at the top, centroid, and bottom of the beam's cross section, indicating positive for tension, negative for compression. d$.$ Find the average normal stress over the cross$-$section due to the normal force N $.$ e$.$ Find the net normal stress at the top, centroid, and bottom of the beam's crosssection.