The Application of 2D and 3D Graphic Statics in Design

Abstract

This paper focuses on the use of graphic statics in both the two and three-dimensional layout of structures, and in the purely geometric panelization of architectural surfaces. The paper will present an in-house computer program for graphic statics including an untangling algorithm, a topology optimizer based on the Newton method with constraints and discrete step as well as an optimization procedure based on virtual work. In the second section, we show how graphic statics can be generalized to 3D to enable form-finding of 3D funicular structures. In contrast to other form-finding techniques like the force density method, this method is straightforward to use in the design of structures that have both compression and tension forces. We demonstrate the utility of this approach via examples of form-finding of a bridge with a tensioned curved deck supported by a spatially curved compression arch. Finally, we will show how graphic statics can be used in a purely geometric context to lay out flat panels on architectural surfaces of arbitrary topological complexity. Since graphic statics relates the equilibrium of forces in a 2D truss structure to the orthogonal projection of a 3D plane-faced polyhedron (the discrete Airy function), it is possible to use 2D equilibrium to define and control 3D plane-faced architectural surfaces. This approach provides an intuitive method for engineers, normally more familiar with equilibrium than pure geometry, to understand and rationalize architectural surfaces. Using this approach, we show how graphic statics can be used to derive, explore, and reason about architectural planar panelizations. Unlike variational approaches to surface planarization, it is straightforward to handle a surface of any topology; pentagons, octagons etc. are treated just as easily as quads and triangles. We also believe this approach allows clearer reasoning about the limitations and design degrees-of-freedom of different panelization strategies.