A FORM FINDING METHOD FOR POST FORMED TIMBER GRID SHELL STRUCTURES Bernardino D’Amico 1 , Abdy Kermani 2 , Hexin Zhang 3 ABSTRACT: Timber grid shells provide efficient ways of covering large openings with relatively small amount of materials. With three-dimensional CAD software, it is now possible to model a free-form surface and discretize it in smaller straight elements, thus postponing the design of the node-connections geometry to the manufacturing process (i.e. by Computer-Aided-Manufacturing). A “low-tech” method for building free-form timber grid shell structures with standardized connections is that of assembling an initially flat grid of continuous rods and then, post-forming (bending) it in a double curved shape. Accordingly, the latter method doesn’t require high-tech manufacturing processes. However, being the final shape influenced by equilibrium of the internal forces, a form-finding procedure is required. A novel “facilitating” numerical framework is introduced in this paper: For a given continuous reference shape, a geometrically similar discrete model is found by implementation of a six degree of freedom formulation of the Dynamic Relaxation method. Numerical methods to the finding of grid cutting pattern, as well as, a Newton-Raphson method to assess the allowable timber cross- section, are illustrated. The theory is validated by numerical examples of a single-rod case and a corrugated barrel vault. KEYWORDS: Free-form structures, Grid shell, Solid wood, Form-finding, Parametric design, Dynamic Relaxation, Newton-Raphson. 1 INTRODUCTION 123 A grid shell is a structure that gains its strength and stiffness through its double curvature configuration. Its advantages are a minimum use of materials, structural efficiency and the creation of a large volume, as well as the potential for quick and cost-effective construction, (Harris et al. [1]). Form-resistant grid shell shapes can be realized by connecting short straight beam elements together into nodes so discretizing the curved surface to a facetted shell or bending initially flat elastic rods such as solid timber planks/laths obtaining thus real continuous curves. For this second case, two sub-categories can be defined [1] differentiating on the geometric parameters assigned to generate a grid onto a continuous surface: If screwed laminated timber ribs are arranged following geodesic patterns (shortest curve onto a surface for two given points) the planks composing the rods will only be 1 Bernardino D’Amico, Centre for Timber Engineering (CTE), Edinburgh Napier University, 10 Colinton Road, Edinburgh, UK. Email: b.d’amico@napier.ac.uk Canada. 2 Prof. Abdy Kermani, director of CTE, Edinburgh Napier University, 10 Colinton Road, Edinburgh, UK. Email: a.kermani@napier.ac.uk 3 Dr. Hexin Zhang, School of Engineering & the Built Environment, Edinburgh Napier University, 10 Colinton Road, Edinburgh, UK. Email: j.zhang@napier.ac.uk subjected to torsion and bending around the weak axis [2] (e.g. Hanover Expo Canopy, 2000 by Julius Natterer) enhancing the allowable width of the cross-section of the planks. A different approach was adopted in the design of the Mannheim timber grid shell for the Garden Festival [3]. In this case, it was assumed a constant distance between consecutive nodes of the same rib (composed by two overlapping timber laths). According to Pirrazzi et al. [2] the resulting (Chebyshev net) geometry of the grid shell did not follow the geodesic paths. However, this second design approach allowed the possibility of assembling the grid shell laid out flat and eventually “post - forming” it in a double curved geometry by imposing external displacements under the form of temporary crane/cable systems or adjustable scaffolding [4-6]. Since the construction of the Mannheim grid shell, this technique only rarely has been used. According to Kelly et al: “The reason for the apparent lack of enthusiasm may stem from the unique challenges associated with the design and formation process” [7]. In fact, in order to draw out the post-formed grid shape (and gain information on internal stress field) a form finding analysis with large displacements formulation is required to simulate the curvature formation process. Regardless of the adopted numerical method, the form finding will requires the definition of initial parameters to be performed, such as the cutting pattern geometry of the flat grid and external imposed displacements magnitude and direction. To