Problem $2-$ RC beam design

Figure $1$ shows a beam with a cross$-$section of $300$mmxx$600$mm $($width x depth$).$ characteristic concrete strength is $30$ MPa and characteristic steel yield strength is $500$MPa. The sections at mid$-$span A$-$A and end$-$span B$-$B are shown together with the rebar design

$($a$)$ Start from the first principle of strain profile and stress block, derive the equation as per design code AS$3600$ for singly reinforced bending design.

$($b$)$ Determine the bending moment that can be taken by the beam at mid$-$span.