On Deployable Reciprocal Frames: from the mathematical description to the architectural applications

Reciprocal Frames are an interesting but almost unknown class of structures, based on the assemblage of straight one dimensional elements into spatial structures. They differ from truss structures because elements are joined by contact at intermediate and end points, and they can reach stability without the need of pins. RF aroused lively interest in scientists since antiquity, as the studies of Leonardo da Vinci, Villers de Honnecourt and Sebastiano Serlio confirm, and the interest has increased recently as an effect of the realizations of many timber reciprocal structures all around the world. The research illustrated in the paper concerns the study of the mechanical behavior of such structures, starting from the kinematic and static determinacy of plane configurations, with the aim to understand the basic properties of these structures. In spite of their apparent simplicity, the mechanics of RF is very complex, involving contact and friction problems, and frequently the geometry itself of two dimensional RF leads to complex analyses. The concept of reciprocity, in fact, make the position of each element determinate by the position of all the other ones, so that large configurations cannot be obtained simply adding new elements to smaller configurations. While recent applications in architecture seem to emphasize the simplicity and the naiveness of this kind of construction, trough timber construction, for instance, or for buildings with a specific social role, as museums or small theaters, we are firmly convinced that RF can be of interest when approached in more technological way. Our research is then specifically oriented to Deployable RE, in which a high tech construction can improve consistently the performances, allowing the design of innovative structures. An promising application of DRF are historical buildings and archeological sites, when the level of damage makes hard to recover the original functionality, so that reversible and non-invasive intervention are required.