Design rules for timber log reciprocal floors, based on mass optimization under stiffness constraint

Abstract

Building with raw timber allows to reduce the price of construction and to make it more competitive with respect to concrete or steel construction. For a few years now, the combination of parametric design and robotic tools make possible the fast and precise milling of timber logs for their accurate connection. However, the spans are quickly limited by the logs length. In this context, reciprocal structures are relevant, since they allow to build large spans structures with short beams. Finally, the architectural interest of reciprocal structures is not to prove. However, the choice of the most efficient reciprocal frame, as well as its structural relevance in terms of mass and stiffness is, most of the time, ruled by subjective considerations. This paper focuses on rectangular floors composed of reciprocal moduli and has three objectives: (1) to develop a general mass and stiffness optimization method for reciprocal floors, which is not only necessary to limit the price, but also to reduce their thickness, (2) to define design rules for reciprocal floors, in particular for the choice of the best engagement ratio, and (3) to compare the structural efficiency of reciprocal floors with the one of “traditional” floors with parallel logs. Coming from a dimensionless transformation of the equilibrium equations, the results of this article will thus give the designers keys to better design reciprocal structures, evaluate their structural performances and relevance, and justify their choices.