Christoph Gengnagel

Active Bending, a Review on Structures where Bending is Used as a Self-Formation Process:

In this paper structures that actively use bending as a self-forming process are reviewed. By bringing together important material developments and various historical as well as recently built samples of such structures, the aim is to show coherences in their design approach, structural systems and behaviour. Different approaches to bending-active structures are defined and described. By making this work accessible and categorising it, this paper aims to contribute to an emerging development. A differentiation of such structures is suggested based on their design approaches. Three such approaches are differentiated: the behaviour based approach, the geometry based approach and current research that seeks to integrate the two. In this paper the nature of these approaches and some important project samples are discussed.

Materials for Actively-Bent Structures

Active bending structures need materials with specific mechanical properties such as large admissible strain and sufficiently high stiffness to prevent buckling. This paper proposes to investigate the materials that could be used following Ashbys selection method. Then it focuses on the most affordable materials which are glass fibre reinforced polymers (GFRP) and natural fibre reinforced polymers (NFRP). As the initial selection is based on short term characteristics, the long term behaviour of fibre reinforced polymers is then addressed based on recent durability studies which are needed to ensure the performance, reliability and safety of a structure. It is shown that, depending on the loading type (tension, bending, torsion, alone or in combination…) and on the nature of the components (fibres, matrix and interfaces), the material undergoes several phenomena reducing its mechanical performances and potentially leading to its failure. Finally, this knowledge of the materials, which allows for a better understanding of the specific relation between the material and the active bending structures, is used to give a framework for stress limitations and recommendations for further optimisation of reliable structures.

On the Materiality and Structural Behaviour of Highly-Elastic Gridshell Structures

Gridshell structures made of highly elastic materials provide significant advantages thanks to their cost-effective and rapid erection process, whereby the initially in-plane grid members are progressively bent elastically until the desired structural geometry is achieved. Despite the strong growing interest that architects and engineers have in such structures, the complexity of generating grid configurations that are developable into free-form surfaces and the limitation of suitable materials restrict the execution of elastically bent gridshells.

Topology Optimisation of Regular and Irregular Elastic Gridshells by Means of a Non-linear Variational Method

Gridshells composed of elastically-bent profiles offer significant cost and time advantages during the production, transport and construction processes. Nevertheless, the shaping of the initially flat grid also generates important bending stresses on the structures, reducing therewith their bearing capacity against external loads. An optimisation of the grid topology in order to minimise the profiles curvature and, with it, the initial stresses is therefore crucial. In this paper a non-linear variational method for optimising topologies of elastic gridshells with regular and irregular meshes is presented. Different case studies of double-curved gridshells show the advantages and capacity of this method.

Hybrid Tower, Designing Soft Structures

This paper presents the research project Hybrid Tower, an interdisciplinary collaboration between CITA—Centre for IT and Architecture, KET—Department for Structural Design and Technology, Fibrenamics, Universidade do Minho Guimaraes, AFF a. ferreira & filhos, sa, Caldas de Vizela, Portugal and Essener Labor fur Leichte Flachentragwerke, Universitat Duisburg-Essen. Hybrid Tower is a hybrid structural system combining bending active compression members and tensile members for architectural design. The paper presents two central investigations: (1) the creation of new design methods that embed predictions about the inherent interdependency and material dependent performance of the hybrid structure and (2) the inter-scalar design strategies for specification and fabrication. The first investigation focuses on the design pipelines developed between the implementation of realtime physics and constraint solvers and more rigorous Finite Element methods supporting respectively design analysis and form finding and performance evaluation and verification. The second investigation describes the inter-scalar feedback loops between design at the macro scale (overall structural behaviour), meso scale (membrane reinforcement strategy) and micro scale (design of bespoke textile membrane). The paper concludes with a post construction analysis. Comparing structural and environmental data, the predicted and the actual performance of tower are evaluated and discussed.

Locally Varied Auxetic Structures for Doubly-Curved Shapes

In this paper we present a computerized design method which could ultimately serve to greatly simplify the production of free form reinforced concrete components. Using any desired doubly-curved shape as a starting point, we developed a digital workflow in which the spatial information of the shape is processed in such a way that it can be represented in a two-dimensional pattern. This pattern is materialized as an auxetic structure, i.e. a structure with negative transverse stretching or negative Poisson’s ratio (Evans and Alderson in Adv Mater 12(9):617–628, 2000). On a macroscopic scale, auxetic behaviour is obtained by making cuts in sheet materials according to a specific regular pattern. These cuts allow the material to act as a kinematic linkage so that it can be stretched up to a certain point according to the incision pattern (Grima in J Mater Sci 41:3193–3196, 2006, J Mater Sci 43(17):5962–5971, 2008). Our innovative approach is based on the creation of auxetic structures with locally varying maximum extensibilities. By varying the form of the incisions, we introduce local variations in the stretching potential of the structure. Our focus resides on the fully-stretched structure: when all individual facets are maximally stretched, the auxetic structure results in one specific spatial shape. Based on this approach, we have created an iterative simulation process that allows us to easily identify the auxetic structure best approximating an arbitrary given surface (i.e. the target shape). Our algorithm makes it possible to transfer topological and topographical information of a given shape directly onto a specific two dimensional pattern. The expanded auxetic structure forms a matrix resembling the desired shape as closely as possible. Material specific information of the shape is further embedded in the auxetic structure by implementing an FE-analysis into the algorithm. We have thus laid the digital groundwork to produce out of this matrix, in combination with shotcrete, the desired building components as a next step.

Structural Assessment of Rapid Deployment Canopy Structure

A lightweight, deployable canopy system has been designed to provide weather protection for events seating. Built as a cantilever truss fixed to the back of seating systems, the canopy avoids the use of columns within the viewing area and is deployed from the ground level. A full-scale prototype has been tested to demonstrate its fulfilment of its functional requirements. Current research looks at methods to optimise the structural performance of the system to make it more reliable and efficient. The points considered include the use of curved and continuous members in the compression chord, the making of tension chord and diagonal bracing members from cables and the optimisation of the cantilever geometry. The potential use of straight and non-continuous compression chord members is discussed. The importance of controlling the geometry of the structure and how it can lead to more desirable internal force distributions is also studied. This work will help guide the ongoing development of the new system to make it both more reliable and more cost effective.

Shaping hybrids – Form finding of new material systems

Form-finding processes are an integral part of structural design. Because of their limitations, the classic approaches to finding a form – such as hanging models and the soap-film analogy – play only a minor role. The various possibilities of digital experimentation in the context of structural optimisation create new options for the designer generating forms, while enabling control over a wide variety of parameters. A complete mapping of the mechanical properties of a structure in a continuum mechanics model is possible but so are simplified modelling strategies which take into account only the most important properties of the structure, such as iteratively approximating to a solution via representations of kinematic states. Form finding is thus an extremely complex process, determined both by the freely selected parameters and by design decisions.

Simulation Methods for the Erection of Strained Grid Shells Via Pneumatic Falsework

The practical benefits of strained (a.k.a. ‘elastic’) grid shells, such as low material usage and fabrication simplicity, are undermined by the methods typically used for their erection. Established erection methods for strained grid shells (‘lift up’, ‘push up’ and ‘ease down’) can be time-consuming, costly and can overstress the system locally (Harris et al. in Build Res Inf 31:427–454, 2003; Quinn and Gengnagel in Mob Rapidly Assem Struct IV 136:129, 2014). The feasibility of and methodology for using inflated pneumatic cushions for the erection of strained grid shells (Otto et al. 1987) is investigated based on geometrically non-linear FE simulations and a scaled physical model for a case study of a dome with a 30 m span, 10 m pitch and constant double curvature. This paper provides a detailed write-up of the scaled physical experiment as well as the developed FE method. A detailed comparison is carried out between different erection methods for strained grid shells in order to evaluate key performance criteria such as bending stresses during erection and the distance between shell nodes and their spatial target geometry. The risk of beam-overstressing for existing erection methods along with challenges caused by modern safety restrictions, scaffolding costs and build duration can be drastically reduced or even eliminated by making use of inflated pneumatic falsework for the erection of strained grid shells. Finally it is argued that the use of pneumatic falsework has the potential to once again facilitate large-span \( \left( {L \ge 30\,{\text{m}}} \right) \) strained grid shell structures such as have not been realised since the likes of the extraordinary “Multihalle Mannheim” (Happold and Liddell in Struct Eng 53:99–135, 1975).