1. A crane hook is to be designed to carry a load F as shown in the Figure Q2.1 below B A To F I R- To B n T1 Cross section AB Figure Q2.1: Crane hook The hook can be modeled as a three-quarter circular ring with a rectangular cross section. The stresses induced at the inner and outer fibers at section AB should not exceed the yield strength of the material. Formulate the problem of minimum volume design of the hook using To, In. b. and has design variables. MC = and s Aero = MC Aer where M is the Note: The stresses induced at points A and B are given by: A bending moment due to the load (-FR). R the radius of the centroid, to the radius of the outer fiber, n, the radius of the inner fiber, C, the distance of the outer fiber from the neutral axis = Ro-. Ci the distance of inner fiber from neutral axis In-Ti. In the radius of neutral axis, given by r = h A the cross-sectional area of the hook-bh, and e the distance between the centroidal and neutral axes -= R-I-