A simple steel beam with section IPE $180,$ span of $6$ m and loaded with a concentrated load of $50$

kN in the middle of the beam. The steel grade is st$37($fy$=2\mathrm{.}4$ t$/$cm$2,$Fu$=3\mathrm{.}6$ t$/$cm$2)$ It is re quired to

answer the following:

$1.$ Calculate the elastic moment of the beam.

$2.$ Calculate the plastic moment of the beam.

$3.$ Calculate the shape factor.