Question

(a) A simply supported beam of hollow rectangular section is to be designed for min mum weight to carry a vertical load Fy and an axial load P as shown in Fig. 2. The deflection of the beam in the y direction under the self-weight and Fy should not exceed 0.5 in. The beam should not buckle either in the yz or the xz plane under the axial load. Assuming the ends of the beam to be pin ended, formulate the opti- mization problem using xi, i - 1,2, 3, 4 as design variables for the following data: Fy 300 lb, P40,000 b,120 in., E30 x 106psi, 0.284 lb/in'3, lower bound on Xi and X2 = 0.125 in, upper bound on xi, and X2-4 in (b) Formulate the problem stated in part (a) using x1 and x2 as design variables, assuming the beam to have a solid rectangular cross section. Also find the solution of the problem using a graphical technique. Jy jy Cross section of beam Figure 2 Simply supported beam under loads.

Answer 1