$4\mathrm{.}201$ Three $12010-mm$ steel plates have been welded together to form the beam shown. Assuming that the steel is elastoplastic with $E=200$GPa and ${}_Y=300$MPa, determine $($a$)$ the bending moment for which the plastic zones at the top and bottom of the beam are $40$ mm thick, $(b)$ the corresponding radius of curvature

Fig. P$4\mathrm{.}201$ of the beam. SOLVE WITH THE INERTIA CALCULATIONS DO NOT USE FORCE DIAGRAM