The following beam has a variable cross section, i.e., the initial height of 3 m and a final height of 1 m, with a constant thickness of 2 m. The beam has a length of 6 m, with a Young's Modulus of 120 GPa, and a force is applied with magnitude P=10 kN. Using Castigliano's theorem, answer the following questions: a) Find the deflection at free end? (20%) b) Find the deflection at the middle of the beam? (20%) |h=3m L=6m P h=1m