A built$-$up section made up by rigidly joining equal$-$leg angles to steel plates $($Figure $1)$ is used as a horizontal cantilever beam. The beam is as shown in Figure $2($All dimensions are in mm$).$ Figure $1$

$1.$ Design your sections $($each group should pick their individual sections $(5$ Marks$)$

$2.$ Determine the shear stress distribution at section C of the cantilever beam and plot the shear stress distribution diagram for section C $(25$ Marks$)$

$3.$ Use the conjugate beam method to calculate the slope and deflection at the free end of the beam $($E $=200$ GPa$)(15$Marks$)$