$4.)$ A large structural beam has a cross$-$section that is composed of

carbon$/$epoxy $(E=20{10}^6)$ and steel $(E=30{10}^6).$

Calculate the modulus$-$weighted section properties $(EA,E{I}_{yy},E{I}_{zz},$

$\{$:$E{I}_{yz})$ about the coordinate axes $(y,z).$ Are the $(y,z)$ axes the

modulus$-$weighted principal axes of the cross section? If not

calculate the orientation angle to the modulus$-$weighted principal

axes that make $(E{I}_{yz}=0),$ then calculate the modulus weighted

section properties about these new axes. INCLUDE PROPER

UNITS.