**Type**: Poster & Model

**Year**: 2016

**Team**: Denis Hitrec, Eike Schling

**Office**: Technische Universität München, Chair of Structural Design, Prof. Dr.-Ing. Rainer Barthel

**Exhibition**: Advances in Architectural Geometry 2016, ETH Zurich

ASYMPTOTIC GRIDSHELL

Using asymptotic lines to design curved support structures

Design proposal of a pavilion for the Structural Membranes Conference 2017 in Munich

**Experimental Structures** is a research studio held annually at the Chair of Structural Design, Technische Universität München. We are searching for methods to simplify the construction of double curved surfaces. Through physical and computational experiments we demonstrate new possibilities for an intelligent symbiosis of form, structure and fabrication.

**Curvature of Lines on Surfaces
**A line on a surface can have three types of curvature:

**normal curvature**,

**geodesic curvature**and

**geodesic torsion**

Imagine an ant walking along a surface. To follow the implied line, the ant must either walk up or downhill to follow the

**normal curvature**; it could turn left or right to follow the

**geodesic curvature**; or it must turn around the axis of the line to be able to stand with its legs straight on the surface – this is called the

**geodesic torsion**. (Tang, Kilian, Bo, Wallner, Pottmann, AAG 2016)

By omitting one of the three curvature types we can create specific line networks, which have decisive advantages for the construction of curved support structures. Figure 1 shows the different types of curvature (

*left*) and their related curve networks. Indicated in the boxes are the bending or twisting of profiles, necessary to construct such networks.

**Asymptotic Lines
**At any point on an anticlastic surface there are two asymptotic directions. They are the direction of zero normal curvature. If we follow these directions, step by step, we can generate an asymptotic curve. This curve will only turn sideways (geodesic curvature), but never up or down (normal curvature).

Structural elements that run along asymptotic lines and are oriented orthogonally to the surface can be unrolled to become straight strips. This is a decisive advantage for fabrication and material efficiency. Furthermore, on a minimal surface, these „asymptotic strips“ always intersect at 90 degrees. This allows for a simplified construction with rectangular joints.

**Asymptotic Gridshell
**Design proposal of a pavilion for the Structural Membranes Conference 2017 in Munich.The design takes a clipping of a repetitive, cubic Schwarz D minimal surface, to generate an expressive sculptural space. The support structure follows a curve network of asymptotic lines. All elements can be constructed out of straight strips with orthogonal nodes. Future research will investigate material use, structural performance and assembly methods for this new type of gridshell.

Amazing work. Are the boundaries also made from flat strips?

In Asymptotic GRidshell (Inside/Out) the boundaries are curved and had to be cut individually. In our latest Pavillion, the Timber Vault, we managed to design only geodesic boundaries, so all elements are built from the same timber lamellas.