Q$1.$ For the beam shown: $(35$ points$)$

A$.$ Draw its Free Body Diagram

B$.$ Using equilibrium equations, calculate support reactions at A and $B$

C$.$ Draw the beam's shear and moment diagrams. $($Note: you will need to cut the beam in $4$ sections.$)$

D$.$ Using the moment diagram find the maximum moment and its location along the beam.

E$.$ If the cross section of the beam is as shown below; calculate the maximum normal stress due to bending at:

a$.$ Neutral axis $($a$-$a$)$

b$.$ Top of the beam $(b-b)$

c$.$ Along the $c-c$ line

Use the attached table to find the beam's second moment of area.