please answer with equations from As$3600-2018$

Problem:

The figure illustrates the cross$-$section of a reinforced concrete column with a hexagonal shape $($equal sides$),$ primarily for architectural purposes, and is reinforced with $4N32$ and $4N24$ steel bars. The material properties are specified as $f_c=40$MPa for concrete compressive strength and $f_{sy}=500$MPa for the yield strength of steel reinforcement. This column section experiences combined axial compression and bending about a horizontal axis $(x-x$ axis$).$

$($a$)$ Calculate the pure axial compression capacity of the section, Nuo. $(1$ mark$)$

$($b$)$ Determine the depth of the plastic centroid, $d_{pc},$ for the section about a horizontal axis. $(2$ marks$)$

$($c$)$ Determine $N_u$ and $M_u$ at the balanced condition. $(5$ marks$)$

$($d$)$ Calculate design bending capacity $M_u$ at the pure bending condition. $(5$ marks$)$