The beam cross$-$section shown on the right$-$hand side is subjected to design moment of $M_d=200kN.$m$.$

a$)$ Based on the given geometrical and material properties, determine moment capacity $M_r$ of the cross section.

b$)$ Can the given section safely carry the design moment?

If yes, stop the solution herein. If not,

c$)$ Design the section $($without changing the geometrical and material properties and amount of tension reinforcement$)$ such that a ductile behavior is obtained.

Materials: $C\frac{20}{25},S420,d^{\text{'}}=30mm.$ Tension reinforcement $A_s=518.(30$ points$)$