Geometric Stability of Reciprocal Structures

Reciprocal structures exhibit complex geometries with an architectural and structural appearance that lacks a clear hierarchy. This absence of hierarchy makes the design of their connections particularly challenging, especially when aiming to prevent local and global geometric instabilities, such as rigid beam rotations around their longitudinal axes, among other issues. As a result, there is significant uncertainty and a general lack of confidence among designers toward reciprocal structures. This is further exacerbated by the absence of well-defined design guidelines for connections and a universal method for assessing their geometric stability. Consequently, most reciprocal structures built worldwide are limited to either elementary modules or simplified geometries, or rely on completely fixed or welded connections, compromising the essence of reciprocity and aligning them more closely with the principles of gridshells. This paper sheds light on how reciprocal structures should be designed in terms of global geometry, connections, and supports, and it compares the effectiveness of five methods for evaluating their geometric stability.