### AAG2018 - Advances in architectural geometry

# Workshop 13: Design and fabrication of bending-active structures with controlled shapes: the arc lam

Website: http://www.architecturalgeometry.org/aag18/workshop-13-bending-active-structures/

This workshop will explore the design of bending-active structures with variable cross-sections to fit a target design shape. Over the two days, the participants will use computational form-finding tools for bending-active structures, and design and build an arc lamp. The participants will learn state-of-the-art methods for simulating bending-active behavior, and for the control and optimization of their equilibrium shapes. These methods can be applied to the design of large scale bending-active structures such as elastic gridshells. The workshop is appropriate for all levels of expertise with bending-active simulations; we will provide the participants with computational tools and workflows to successfully design their own sculptures.

Shell structures derive their structural efficiency from their geometry. While their form minimizes bending moments, they are complex to build. Bending-active is a construction method to create curved shell geometry by elastically bending initially straight rods. It allows the creation of shell-like shapes with a simpler construction process, leading to lightweight structures with possibly long spans and quickly erected. Examples of such constructions include the well-known elastic gridshell of the Mannheim Multihalle by Frei Otto, and many others since then with regular and irregular arrangements of the rods, different materials like GFRP for the rods and concrete for the cover, or plate-like base elements.

Automatically predicting the equilibrium shape of the bending-active structure at the end of this process is critical to enabling their design, as it is very difficult to intuit the shapes they can take. In addition, no good criterion exists for predicting if a surface can be approximated by a given arrangement of rods, or which arrangement would give the best result. As a result, all design workflows start by simulating the equilibrium shape of the structure considered, a process which can be time-consuming and error-prone, before analyzing the qualities of the resulting design.

By automating this process, carefully tuning it for speed and reliability, and integrating it in an optimization loop, the designer gains access to a design workflow where objectives can be specified for the design. The rods arrangement, lengths and properties needed to reach these objectives is the result of this workflow. Most importantly, this lets designers come as close as possible to a target shape that they define.

Computational form-finding methods usually output forms that minimize the stresses in a given structure, for example in the design of compression-only shells. In bending-active structures, the normal form-finding process finds the equilibrium shape by minimizing the bending energy in the structure. It is possible to further optimize the resulting structure to reduce stresses under live loads or buckling sensitivity for example. While this helps reduce the material quantities and increase the performance of the shell structure, the designer has limited control over the resulting shape. By defining a desired target shell shape, structural optimization tools can be successfully applied to find forms that both minimize structural material volumes and resemble the target shape. Modifying the equilibrium shape is most easily achieved by varying the cross-section of the rods. While this does not apply to all materials, timber lends itself quite well to varying cross-sections.

The change of cross-section of a rod changes the radius to which it will bend. Rods of variable cross-section in bending-active shell structures could possibly open up the variety of shapes that can be achieved, for example leading to elastic gridshells with increased usable space thanks to more vertical shapes near the ground. The ICD/ITKE bending-active structure is such an example. Using the concept of target shape, rods of variable cross-section and computation form finding and structural optimization tools, this workshop will explore new shapes of bending-active structures, both physically and computationally. Getting more control on the final geometry of such computationally form-found structures creates new opportunities for designers and structural engineers to build beautiful and efficient structures. The workflow will be tested with the construction of a wooden arc lamp, offering some hands-on experience with bending-active structure to the participants. The lamps will be on exhibition during the conference.