A rectangular beam has a width of $200$ mm and an effective depth to the centroid of the tension reinforcement of $400$ mm $.$ The tension reinforcement consists of $6-25mm$ diameter bars placed in two rows. Compression reinforcement consisting of $2-25mm$ diameter bars is placed $62\mathrm{.}5$ mm from the compression face of the beam. $fc=34\mathrm{.}6$MPa, $fy=414\mathrm{.}7$MPa.

a$.$ Determine the depth of compression block $($a$).$

b$.$ Determine the maximum steel ratio $({}_{\text{m}\text{a}\text{x}}).$

c$.$ Determine the design moment capacity of the beam $(M_u).$