Optimum Frameworks under Single Load System

For a single load system, Michell has proposed a deformation criterion which a framework must satisfy if it is to be of minimum volume. The criterion is that the members of the optimum framework to equilibrate a given force system must all be strained by the same amount, the sign depending on the sign of the axial stress carried by the member. A general class of frames, satisfying the Michell condition of strain, consists of those whose bars, before and after deformation, form curves of orthogonal systems. The two basic orthogonal curvilinear systems used in the development of the Michell optimum structures are the polar coordinate system and the equiangular spiral system. Optimum structures are developed for six different force systems. These consist of (1) self-equilibrating systems of concentrated forces that can be supported by a truss or a simple beam, and (2) self-equilibrating system of forces and couples that can be supported by a cantilever beam or a prismatic beam with fixed ends.