Given the beam and cross$-$section, draw the shear and moment diagram of the beam. Determine the location $\frac{?}{\text{b}\text{a}\text{r}}(y)$ of the centroid C and the Moment of Inertia about the centroidal x axis $(I_{\stackrel{}{x}})$ of the beam having the cross$-$sectional area shown $(35$ pts $)$

Bonus $(5$ pt$)$:

Draw the FBD of the section between $2$ ft and $4$ ft $($i$.$e$.2x4)$

What is the equation for shear between $x=2$ and $x=4$ feet $($i$.$e$.2x4)?$

What is the equation for moment between $x=2$ and $x=4$ feet $($i$.$e$.2x4)?$