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Mechanisms and states of self-stress of planar trusses using graphic statics, part II: Applications and extensions

McRobie, A and Baker, W and Mitchell, T and Konstantatou, M (2016) Mechanisms and states of self-stress of planar trusses using graphic statics, part II: Applications and extensions. International Journal of Space Structures, 31. pp. 102-111. ISSN 0266-3511

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Abstract

© The Author(s) 2016. This article extends the overview relating graphic statics and reciprocal diagrams to linear algebra-based matrix structural analysis. Focus is placed on infinitesimal mechanisms, both in-plane (linkage) and out-of-plane (polyhedral Airy stress functions). Each self-stress in the original diagram corresponds to an out-of-plane polyhedral mechanism. Decomposition into sub-polyhedra leads to a basis set of reciprocal figures which may then be linearly combined. This leads to an intuitively appealing approach to the identification of states of self-stress for use in structural design and to a natural ‘structural algebra’ for use in structural optimisation. A 90° rotation of the sub-reciprocal generated by any sub-polyhedron leads to the displacement diagram of an in-plane mechanism. Any self-stress in the original thus corresponds to an in-plane mechanism of the reciprocal, summarised by the equation s = M* (where s is the number of states of self-stress in one figure, and M* is the number of in-plane mechanisms, including rigid body rotation, in the other). Since states of self-stress correspond to out-of-plane polyhedral mechanisms, this leads to a form of ‘conservation of mechanisms’ under reciprocity. It is also shown how external forces may be treated via a triple-layer Airy stress function, consisting of a structural layer, a load layer and a layer formed by coordinate vectors of the structural perimeter.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div D > Structures
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 20:03
Last Modified: 11 Jan 2018 02:56
DOI: