The paper deals with topological classes of statically determinate beams with an arbitrary number of pin supports. The beams carry piece-wisely distributed loads which are placed in such a way that bending moment values are extreme at any section. For such loads, it is sufficient to consider only two load cases with alternate spans uniformly loaded. Each beam with a fixed topology is subjected to geometrical optimization with the absolute maximum moment as the objective function. Exact formulas for optimal values of geometrical parameters are found for all topologies. An equality criterion between minimum values of the objective function is used as an equivalence relation. On the basis of this relation; the set of all topologies is divided into equivalence topological classes. Typical features of these classes are found and discussed.