A simply$-$supported beam with $6\mathrm{.}75m$ length is under vertical loads and has the cross$-$sectional dimensions as shown in figure. It is made of an elastic perfectly plastic material having tensile and compressive yield stress of $s_Y=250$MPa.

a$)$ Determine the elastic moment $M_Y$ of the beam

b$)$ Determine the plastic moment $M_p$ of the beam

$($C$)$ Determine the shape factor

$($d$)$ Determine the value of $W$ at collapse stage

solve and show all working and numbers