Kinematic and static analysis of plane reciprocal frames

Reciprocal frames and reciprocal structures have already been considered of great interest in the past, as witnessed by the work of Leonardo da Vinci and of other important scientists and architects. Recent researches show that both the shape and the mechanical behaviour of such structures are really complexes, due to the concept of reciprocity. The position of each structural element in the space, indeed, as well as the way they transfer loads, depends on the position and on the role of adjacent elements, so that the structure must be studied as a whole and it can hardly be decomposed in simpler substructures. In this paper we focus on the statical and mechanical determinacy of a specific subset of this kind of structures, i.e. the multiple plane reciprocal frames. In this structures the shape can be easily defined in plane coordinates, so that only the mechanical behaviour needs to be studied. The presence of mechanisms or the possibility of self-stress states is largely related to the kind of internal constraints joining each bar to the others. The study is developed starting from the basic works on pinned bars assemblies [5], [8], in which the statical and kinematical determinacy are discussed by means of a matrix formulation of the equilibrium and compatibility equations. The extension of such formulation from pinned bars assemblies to plane reciprocal frames is the main goal of the research.