Two-way reciprocal frame

The paper reports on research aimed at developing a new design method for constructing double-curved structures, integrating two well-established and widely studied systems: the reciprocal system and the two-way joist (waffle) system. This leads to the creation of the Two-Way Reciprocal Frame, which enhances the remarkable structural intelligence of reciprocal frames while incorporating the geometric rigor of waffle structures. Within the relative freedom of form, the small structural elements remain orthogonal to each other, resulting in a highly regular grid when projected onto the horizontal plane. The elements consist of vertical lamellae joined together using custom-shaped half-lap joints, allowing for reciprocal arrangement. This apparent complexity is managed through a computational design algorithm that directly generates file-to-factory outputs for numerical control cutting (CNC) and digital fabrication. In particular, the orthogonality of the elements and the shaped half-lap joint enable the use of simple and cost-effective machines, such as laser cutters and three-axis CNC routers, as the shaping process requires only orthogonal cuts to the plane of the base panels. The study emerges from the integration of technological, structural, and geometrical disciplines.