CUED Publications database

The geometry of structural equilibrium.

McRobie, A (2017) The geometry of structural equilibrium. R Soc Open Sci, 4. 160759-. ISSN 2054-5703

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Abstract

Building on a long tradition from Maxwell, Rankine, Klein and others, this paper puts forward a geometrical description of structural equilibrium which contains a procedure for the graphic analysis of stress resultants within general three-dimensional frames. The method is a natural generalization of Rankine's reciprocal diagrams for three-dimensional trusses. The vertices and edges of dual abstract 4-polytopes are embedded within dual four-dimensional vector spaces, wherein the oriented area of generalized polygons give all six components (axial and shear forces with torsion and bending moments) of the stress resultants. The relevant quantities may be readily calculated using four-dimensional Clifford algebra. As well as giving access to frame analysis and design, the description resolves a number of long-standing problems with the incompleteness of Rankine's description of three-dimensional trusses. Examples are given of how the procedure may be applied to structures of engineering interest, including an outline of a two-stage procedure for addressing the equilibrium of loaded gridshell rooves.

Item Type: Article
Uncontrolled Keywords: Clifford algebra Maxwell reciprocal diagrams Rankine reciprocal diagrams graphic statics three-dimensional frames
Subjects: UNSPECIFIED
Divisions: Div D > Structures
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:26
Last Modified: 24 Aug 2017 01:30
DOI: