Funicular structures are structures whose geometry is based on the funicular polygon, a term from graphic statics. Such structures work mainly with axial forces, almost without bending. Typical examples are arches and cables.
At the IABSE-IASS Symposium 2011 in London, I presented novel parametric tools for structural design in early stages. These have been developed at the Chair for Structural Design, ETH Zurich. Download the paper here.
Based on concepts of graphic statics, custom Grasshopper components have been implemented that allow for the interactive modelling of a planar funicular polygon in Rhino. Straight lines are interpreted as external forces, axial forces in the funicular are represented by tubes, red tubes are in tension, blue tubes are in compression. The tube section is proportional to the magnitude of the axial force.
These tools facilitate intuitive modelling of funicular, hence efficient, structural systems.
I am glad to announce that the paper "Geometry of Structural Form" for the conference Advances in Architectural Geometry 2010 has been accepted. My recent research,done at the the ETH Chair of Structural Design, will be presented. Techniques for parametric structural design,based on graphic statics, are described in this paper.
This grasshopper definition has been inspired by Nicholas Grimshaw's Waterloo Station, London.
Based on TNA, I implemented together with Philippe Block a grasshopper definition for the generation of structural freeform vaults. The image shows a structural surface with an non-uniform force distribution. This work is part of a resarch project done at the ETH Zurich.
This model of a compression-only vault has been build using rapid prototyping. It stands just by gravity and friction.
Implementation-wise the matrix computation routines from rhino SDK have been used inside grasshopper vb.net nodes. Download the grasshopper definition here. A tutorial video shows the use of the definition.
Thrust Network Analysis, a new method for generating compression-only vaulted surfaces and networks was developed by Philippe Block as part of his PhD.Using projective geometry, duality theory and linear optimization, it provides a graphical and intuitive method, adopting the same advantages of techniques such as graphic statics, but offering a viable extension to fully three-dimensional problems.
Form and force diagram, and the resulting compression only network.
Parametric explorations of the indeterminacy of compression-only networks by the modification of the force diagram.
The french mathematician Pierre Varignon (1654-1722) introduced the funicular polygon and the polygon of forces in his work Nouvelle Mecanique ou Statique. He describes a way to construct the form of a hanging rope with attached weights graphicaly. Based on this principle, a technique called graphic statics has been developed in the 19th century. The basic principle of graphic statics is the reciprocal relation between force polygon and funicular polygon. Recomended books: Luigi Cremona: Graphical Calculus (1890) and Edward Allen,Waclaw Zalewski: Form and Forces (2009) This grasshopper definition generates a funicular polygon for uniform loading. Download here.
In the 19th century, graphic statics, a geometric method for the analysis of the force distribution in structures, has been developed. This scientific, precise method has an intuitive and descriptive character based on reciprocal force diagrams. The recent emergence of parametric design techniques in architecture enables the construction of associative geometry in CAD systems. In this lecture, a novel approach will be presented, combining parametric tools with historic techniques of graphic statics. This highly interactive three-dimensional procedure provides direct control of form and forces at the same time. The aim of this approach is the integration of the flow of forces into the computer aided design process.
On this blog I documented some of my findings, ideas, and projects from the years 2009-2013. Its a private and non-commercial website, and the content isn´t updated any more, so please forgive broken links and outdated information. I keep it as a personal archive.
At the IABSE-IASS Symposium 2011 in London, I presented novel parametric tools for structural design in early stages. These have been developed at the Chair for Structural Design, ETH Zurich. Download the paper here.
