
The Airshell Prototype
This paper by Alessandro Liuti, Sofia Colabella, and Alberto Pugnale, presents the construction of Airshell, a small timber gridshell prototype erected by employing a pneumatic formwork.
Form finding and structural analysis of actively bent timber grid shells
Grid shells are efficient structural systems covering large open spaces with relatively small amount of materials. Also, post forming techniques allow realization of geometrically complex (free-form) shapes by means of standard connection systems.
However, due to complexity of the analysis-design process, they are rarely utilized in construction design. In this paper, a ‘facilitating’ numerical framework is introduced in which, 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, to handle members bending and torsional stiffness.
A grid cutting pattern algorithm is introduced, as well as methods to numerically simulate the double-layer construction technique and a novel (singlenode) cylindrical joint model.
The methods are extensively tested and validated on a range of structures, from ‘simple’ single-rod cases to more complex, actively bent, grid shell frameworks.
Free-form grid-shell structures can be formed by connecting short straight beam elements together into nodes thus converting a curved continuous surface in a faceted shell.
From a geometrical point of view, the described process deals with complex connection systems: Each element converges to the node of the grid at a different angle, thus non-standard connections (and Computer-Aided Manufacturing process) become inevitable.
A ‘low-tech’ method for building free-form structures using standard (bolted/screwed) connection systems is by bending initially flat elastic rods, such as solid timber planks/laths, to form actual continuous curves.
For timber grid shells made of continuous bending members, two subcategories can be defined differentiating on the geometric parameters assigned to generate a grid on a surface: If screwed laminated timber ribs are arranged following geodesic patterns (shortest curve on a surface for two given points) the planks composing the rib will only be subjected to torsion and bending around the weak axis enhancing the ‘allowable’ width of the the plank’s cross section.
This technique was used for the construction of the Hannover Expo pavilion. A different approach was adopted in the design of the Mannheim timber grid shell for the Garden Festival.
In this case, it was assumed a constant distance (50mm) between the consecutive nodes belonging to the same rib, which was built-up with two overlapping laths (double layer technique).
Accordingly, the resulting mesh geometry of the grid shell did not follow the geodesic paths (thus, lateral bending occurs as well).
However, this second design approach allowed the possibility of assembling the grid shell laid out flat (as a two-way mat of straight continuous rods) 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.
With the main grid eventually formed, additional bracing elements can be added to the system enhancing the in-plane shear stiffness of the equivalent shell. The terms post formed, actively or elastically bent are usually used to describe such kind of grid shell structures.
The work presented in this paper has aimed to facilitate the design of actively bent grid shells, with particular attention on the use of timber.
A numerical framework is developed to address a range of issues at various design stages, including, a viable form finding procedure, structural analysis and assembly definitions (flat mat geometry) by combining finite element procedures (Dynamic Relaxation) with numerical methods typical of the computational geometry (mesh manipulation and geometry intersection).
Further investigations, concerning the coupling of rotational degree of freedom, resulted in the development of a novel single-node numerical model for large rotation simulation of cylindrical joint systems.
In addition, a procedure is illustrated to allow changing the element’s crosssectional properties during the completion of the form finding stage by maintaining the corresponding ends reactions values.
Such procedure permits load analyses in which the increase in stiffness of the built-up timber ribs (for effect of shear blocks insertion) is taken into account, and at the same time maintains the equilibrium configuration (previously) obtained without shear blocks.
In order to allow the implementation of the described procedures, a detailed description of the equations involved is given.
After preliminary validation tests on ‘simple’ structural systems, the procedures are applied to the form finding, structural analysis and mat cutting patterns search of a grid shell dome, as well as the form finding analysis of a corrugated barrel vault.
The accompanying numerical tests demonstrated the reliability of the proposed method. The preliminary tests showed a good level of accuracy for the six DoF DR formulation in the estimation of the load-displacements functions.
Accordingly, the six DoF DR can be used for non-linear buckling analyses at the completion of the form finding routine, thus allowing to take into account the effect of pre-stress (and material relaxation) on the final load bearing capacity.
This paper by Alessandro Liuti, Sofia Colabella, and Alberto Pugnale, presents the construction of Airshell, a small timber gridshell prototype erected by employing a pneumatic formwork.
In this paper by Gregory Charles Quinn, Chris J K Williams, and Christoph Gengnagel, a detailed comparison is carried out between established as well as novel erection methods for strained grid shells by means of FE simulations and a 3D-scanned scaled physical model in order to evaluate key performance criteria such as bending stresses during erection and the distance between shell nodes and their spatial target geometry.
In this paper by Frederic Tayeb, Olivier Baverel, Jean-François Caron, Lionel du Peloux, ductility aspects of a light-weight composite gridshell are developed.
In this paper by Julian Lienhard, Holger Alpermann, Christoph Gengnagel and Jan Knippers structures that actively use bending as a self forming process are reviewed.
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