Question $1$: A T$-$beam with uneven overhangs is constructed monolithically with the two columns used to support the beam. The columns are $400mm400mm$ in cross section, and the beam resists a uniformly distributed factored load of $w_f=80k\frac{N}{m}.$ The corresponding factored shear force and bending moment diagram are given below.

Assume the beam is not exposed and use the beam cross$-$section given with an assumed effective depth $d=540mm.f_c^{\text{'}}=35$MPa and $f_y=400$MPa.

$[25$ marks$](1$a$)$ design the beam for flexure and show your required reinforcement using an appropriate sketch$($es$)$ of the cross$-$section. Remember to check cover and bar spacing requirements $($this includes checking the serviceability requirement for cracking$).$

$[2$ marks$](1$b$)$ Explain why the moment at the two support faces of each column are not equal $($ie$.129\mathrm{.}6221\mathrm{.}6$ and $366\mathrm{.}8313\mathrm{.}6).$