Question $1$: $(20$ points$)$

an allowable tensile stress of $130$ MPa and an allowable compressive stress Figure $1$ shows the cross$-$section of a beam made from a material having $160$ MPa. The bending moment M is applied to the beam in the y$-$z plane and forms an angle

of $30$ with the horizontal direction.

b$)$ Calculate the moments of inertia ly and lz about the principal axes $(5$ points$).$ a$)$ Determine the location of the centroid C of the cross$-$section of the beam $(5$ points$).$

c$)$ Determine the maximum allowable moment M that can be applied to the beam $(10$ points$).$