A $2$ m long beam $($Fig$.1$ a$)$ with a T$-$shaped cross$-$section $($Fig$.1$ b$)$ is rigidly built in at the left end and simply supported at the midspan and right end. The beam is made of the elastic $-$ ideal plastic material with yield strength ${}_y=450$MPa, Young's modulus $E=207$ GPa and Poisson's ratio $v=0\mathrm{.}31.$ The beam is loaded by a concentrated load, $F,$ applied $0\mathrm{.}4$ m from the left end and a uniformly distributed load with the intensity equal to $w=2*\frac{F}{1}m$ as shown in Fig. $1$ a$.$ Find the value of $F$ corresponding to the onset of the plastic collapse.