Problem $1$: $100$ points

For the beam section given: Concrete is $C30$ and longitudinal reinforcement is $S420$ steel and Es $=2{10}^5$MPa. If $A_{s1}=3619m{m}^2,A_{s2}=509m{m}^2,$ and $A_{s3}=1018m{m}^2$ then for design ultimate moment capacity of the section, find force in all three steels, and moment capacity of the section using trial and error.

For initial value for concrete compression depth $"$c$"$ use $=250mm$

Note: fcd $=20$Mpa, fyd: $365$MPa and ${}_{sy}=0\mathrm{.}001825$