3. A cantilever beam-column of rectangular cross section and length (1) of 1.27m is required to carry an axial load (P) of 12.5 Kg and a transverse load (P) of 5 Kg. It is to be designed to avoid the possibility of yielding and buckling and for minimum weight. Formulate the optimization problem by assuming that the beam-column can bend only in the vertical (xy) plane. Assume the material to be steel with a specific weight of 82 kN/m, Young's modulus of 207 GPa, and a yield stress of 207 MPa. The width of the beam is required to be at least 12.5 mm and not greater than twice the depth. Outline the options available for solving this problem. [Hint: The compressive stress in the beam due to P, is and that 6P bd2 due to Py is The critical buckling load is given by 2 Ebd3 4812