M H B Figure 1: Crane AB holding a mass M The crane shown in figure 1 is made of an Aluminum Alloy 2014-T6 beam AB of square cross section having a side length equal to a and length L-4 m. AC is a rigid support and beam AB is pinned at A. CB is an A-36 steel rope of diameter D=5 mm pinned at C to the rigid support. At an angle 60°, the crane is supposed to carry a load M-150 kg. Using H=0.5 m: a) Find the minimum dimension of the square cross section a to avoid failure by buckling or yielding in the beam. Use the AISC recommendations. b) Use the second Castigliano theorem to compute the vertical and horizontal displacements of point B using a = 200 mm. Neglect the contribution of the shear force in the strain energy.