Topological classes of statically determinate beams with arbitrary number of supports

The paper presents all topologies of statically determinate beams with arbitrary number of pin supports. The geometry of each beam with a fixed topology is optimized by a genetic algorithm, with absolute maximum moment as the objective function. An equality relation between minimum values of this function is defined on the set of all topologies as an equivalence relation. This relation partitions the set of topologies into equivalence classes, called topological classes, for uniform, linear and parabolic gravity loads. An in-depth description of these classes is provided. Exact formulas for optimal locations of supports and hinges are found for the uniform load.