$(20\text{'})$ An eccentrically compressed column is a rectangular section. The dimensions of the section are $bh-500mm500mm,a_5=a_s^{\text{'}}=40mm,$ and $I_0=12\mathrm{.}5m.$ The strength of the concrete is $f_c=14\mathrm{.}3\frac{N}{m}{m}^2.$ The properties of the reinforcement are $f^{\text{'}}y=f_y-300\frac{N}{m}{m}^2,E_0-2{10}^5\frac{N}{m}{m}^2.$ If the axial compressive lorec $N_c-1600kN$ and the moment $M-1080kN.$ m are applied on the column and the section is symmetrically reinforeed, and hat$({)}_3=0\mathrm{.}55,$ determine $A_a-A_n^{\text{'}},$

$($It doesn't need to take P $-\frac{?}{{?}_{\frac{?}{?}}}$ effect into account.$)$

Reference formulas: $N_c={}_1{f}_{c}b{h}_0$;$,N_{c}e={}_1{f}_{c}b{h}_0^2(1-0\mathrm{.}5)+f_y^{\text{'}}{A}_s^{\text{'}}(h_0-a_s^{\text{'}})$;$e=e_i+\frac{h}{2}-a_s$;$e_i=e_0+e_a$