$(10$ Marks$)$ Beam $AE,$ with cross$-$section as shown in Figure $($a$),$ is subjected to a distributed load

over $AD$ and a concentrated load at $A$ as shown in Figure $($b$).$ Neglect the self$-$weight of the beam.

$(1)$ Locate the neutral axis by determining coordinate $\frac{?}{\text{b}\text{a}\text{r}}(y).$

$(2)$ Determine the second moment of area I about the neutral axis.

$(3)$ Determine the bending moment at section $C$ of the beam.

$(4)$ Determine the maximum tensile and compressive stresses at section $C.$

$($a$)$

$($b$)$