$2$ Consider the beam shown in Figure $2,$ supported by web cleats and loaded by two concentrated loads, $P=70\mathrm{.}0kN($design loads$).$ Design the beam using a HEA profile, in S $235$ steel and $G=81$GPa, according to $EC3-1-1.$ Consider free rotation at the supports with respect to the y $-$axis and the z $-$axis. Also assume free warping at the supports but consider that the web cleats do not allow rotation around the axis of the beam $($x axis$).$

Assume:

a$)$ unbraced beam;

b$)$ beam braced at the points of application of the concentrated loads.

$(20$ Marks$)$

trated loads