## 1 Introduction  
Elastic timber gridshells, also known as strained timber gridshells [1, 2] or active bending gridshells [3], are a highly efficient and architecturally expressive structural solution of great interest for application in lightweight roofs of medium and large spans. They are built from initially straight timber laths, of small cross-section and great length, which are elastically deformed until they reach the final shape, giving rise to a structural grid of continuous elements. Traditional elastic gridshells can be classified into two groups according to the curving process of the laths and the multilayer system used. The first, developed by Prof. [PERSON] and colleagues at the Institut fur leichte Flachentragwerke (Institute for Lightweight Structures) in Stuttgart, Germany, is based on the premise that a flat quadrangular grid of continuous timber laths connected by hinged joints that allow rotation around an axis perpendicular to the plane of the grid, can be transformed into a doubly curved surface. The transformation is possible owing to the elastic deformation of the laths and the lack of in-plane shear stiffness of the grid during the curving process [4]. Spectacular structures have been realised following this procedure, such as antifunicular surfaces as the Mannheim Multihalle gridshell (1975), with a maximum span of 60 m [5], or undulating forms as the Weald & Downland Living Museum gridshell (2002) [6] and the Savill Garden gridshell (2006) [7], with 15 and 25 m span, respectively. In all these structures, two layers of laths have been necessary to provide the grid with the required out-of-plane bending stiffness. The connection between the different layers is always made after the curving process. This results in a composite profile with high inertia, while maintaining the minimum radius of curvature of each lath. The connection system between the different timber layers is solved by means of mechanical fasteners that produce semi-rigid joints. This connection can be made in different ways: at the nodes using bolts, as in the Mannheim Multihalle [5] (Figure 1a); at the nodes and members, as in the Weald & Downland Living Museum gridshell [6] (Figure 1b), where shear blocks were used at the members and a patented steel connection at the nodes; or exclusively at the members by means of timber shear blocks fastened with screws to the laths, as in the Savill Garden gridshell [7] (Figure 1c). The second group of gridshells, developed at Ecole Polytechnique Federale de Lausanne (EPFL) in Switzerland by the engineer [PERSON], is based on the idea of constructing grids formed by two directions of curved elements generated by mechanical lamination. This is done by nailing and/or screwing multiple layers of overlapping laths together, creating a solid cross-section of ribs with high inertia (Figure 1d), so structures built with this technique are called ribbed shells [8]. Unlike [PERSON]'s concept, initially the laths do not have to be part of a grid and can therefore be individually curved [9]. This allows greater freedom in both surface geometry and mesh geometry, the latter being able to be irregular. Although the system allows any surface to be constructed and any grid layout to be adopted, [PERSON] used preferably canonical surfaces and geodesic paths for the laths, as these do not involve strong axis bending during the curving process. Impressive structures have been built following this technique, such as the cylindrical 22 m spanning Kleinmachnow Sporthalle in Berlin (1997); several spherical shells, such as the 25 m side Polydome EPFL (1991); or the Expodach in Hannover (1999) [10]. Recent research carried out by the authors has combined features of both procedures to develop an innovative concept of long gridshells supported only on their short sides that offers new and interesting architectural applications. The grid layout consists of three directions of bent laths to provide out-of-plane bending stiffness (Figure 2 left).