# Analysis of Planar Double-Layer Timber Spatial Frames by Using Parametric Tools
## 1 Introduction  
### Space Frames  
A space frame is often defined as a structural system designed from linear elements arranged in such a way that the transmission of forces is three-dimensional. This leads to an idea of opposition between spatial structures and so-called \"flat\" ones. However, the division between \"flat\" and \"spatial\" structures refers not to the structure itself, which is always spatial, but to the methods of analysis [1]. In planar systems, stresses are transmitted from the less rigid elements to the more rigid ones up to the foundations. On the way to the foundation, the forces become, as well as the section, larger and larger. On the contrary, in a space frame structure, all the elements contribute according to the three-dimensional geometry given to them, with no obvious force transfer sequence. In other words, the transmission of forces to the support is bifurcated in several elements so as not to have a concentration of forces in just a few elements. The objective of this type of construction is to use the minimum amount of material to obtain lightweight structures without losing stiffness, stability and resistance. These are appealing structures not only from the engineering point of view, but also from the architectural one. These systems have led to the understanding of the building as a living being, as an organic structure, capable of adapting to the uncertainty of the future. There are approaches such as those of [PERSON], who plays with the natural growth of thespatial frames from the multiplication of the base spatial module. Another well-known project is the Fun Palace by [PERSON] and [PERSON] (Figure 1), a dismountable and reconfigurable artefact capable of housing any program that could respond to social needs. This logic is even extrapolated to the city and territory, giving rise to projects such as, among others, the megastructures of [PERSON] (Figure 1) or the three-dimensional urbanism of [PERSON]. In recent years, research has been carried out in several related areas. On the one hand, calculation methods have been proposed to measure the carbon emissions for the lifetime of the frames [2]. On the other hand, robotization processes are being developed for assembly and disassembly [3,4]. In this regard, a very promising line of research has been opened with respect to the possibilities of disassembly and reuse of the frames [5, 6, 7, 8]. Given the current emerging context, this is a path that undoubtedly deserves to be investigated. Back to the strictly structural-engineering aspect, spatial structures can be grouped into three main categories [9,10] (Figure 2):  
1. lattice discrete structures: they are based on discretization to create a more or less regular frame (grid, barrel vaults, domes, towers and free forms). 2. continuous structures: a single surface acting as a membrane (slabs, shell, fabric). 3. biform structures: combination of both discrete and continuous parts. This paper will be centered on the first group for two main reasons:  
* Both planar and curved surfaces can be used. This research is focused on flat frames with the awareness that processes designed for a simple shape can be extrapolated to more complex ones. Parametrically, it is possible to apply any algorithmically designed process to any type of geometry. That said, in shell structures, stiffness is achieved through shape. Their geometry directly derives from their flow of forces and defines their load-bearing behavior and lightness [11]. On the other hand, lattice spatial structures achieve resistance through cross-section. Being multiple-layer structures, the very composition of the sheet has a lever arm that stiffens them. By not being so form-dependent, the range of application of lattices is considerably wider, and that makes them appealing as the scope of this work. Figure 1: (**a**) [PERSON], Fun Palace. (Source: toran, iv.