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IASS 2016 Tokyo Symposium: Spatial Structures in the 21st Century


IASS Symposium 2016

SESSION: Graphic Statics

Reciprocal constructions using conic sections & Poncelet duality

< Table of Contents for Graphic Statics
  • Proceedings Name: IASS 2016 Tokyo Symposium: Spatial Structures in the 21st Century
  • ISSN: (Electronic Version) 2518-6582
  • Session: Graphic Statics
  • Pages: 10
  • Title: Reciprocal constructions using conic sections & Poncelet duality
  • Author(s): Marina Konstantatou, Allan McRobie
  • Keywords: structural design, graphic statics, reciprocal diagrams, projective geometry. Airy stress function, static equilibrium, Maxwell, Rankine, Poncelet duality, truss
Abstract
Graphic Statics offer a geometrical framework for the design & analysis of structural systems with reciprocity between the 'form' and 'force' diagrams being a fundamental notion. In this paper we provide a detailed illustration and explanation of Maxwell's reciprocal construction for 2-dimensional trusses through a 3-dimensional paraboloid of revolution. Even though Maxwell briefly mentions this method there is no record of the detailed construction. The main focus of this research is placed on the synthesis of Poncelet duality in projective geometry and of reciprocity in graphic statics resulting in the definition of a generalised dual statement for the construction of reciprocal diagrams (Maxwell 2D & Rankine 3D). This is based on the construction of their higher dimensional discrete Airy stress functions, using conic sections. We generalise the construction for other conics, such as the sphere and ellipsoid, and we extend the definition for 3-dimensional trusses and corresponding higher-dimensional conic sections.

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