$.$ The compound beam at left has segments $AB$ and $BCD{?}^{+-}$joined by a pin connection $($i$.$e$.$ no internal moment$)$ just right of $B($see figure part $($a$)).$ The beam cross section is a double$-$Tee made up from three $50$ mm X $150$ mm wood members $($see figure part $($b$)).$

a$)$ Draw the shear and moment diagrams of the beam.

b$)$ Find the centroid $C$ of the double$-$T cross section $(c_1,c_2),$ then compute the moment of inertia $I_z(m{m}^4).$

c$)$ Find the maximum tensile normal stress ${}_t$ and maximum compressive normal stress ${}_c$ for

the loading shown.

PLEASE BREAK DOWN