The beam, with symmetric cross$-$section about y $($all thicknesses of $20$ mm $)$ as shown, is subjected to an internal moment of $M=40kN.$m and a shear force of $V=120kN.$ For this system,

a$)$ determine the location of the neutral axis, $\frac{?}{\text{b}\text{a}\text{r}}(y)($measured from the bottom of cross$-$section as shown$)$ and the area moment of inertia, I about the neutral axis $($NA or z$-$axis$),$

b$)$ the maximum compressive, $({}_{\text{m}\text{a}\text{x}}{)}_c$ and tensile, $({}_{\text{m}\text{a}\text{x}}{)}_t$ normal stresses, and

c$)$ the maximum transver e shear stress, $({}_V{)}_{\text{m}\text{a}\text{x}}$

d$)($Bonus: $2\mathrm{.}5$pts$)$ determ ine the amount of internal moment resisted by the flange $($the bottom plate$).$