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

Accepted version
Peer-reviewed

Type

Conference Object

Change log

Authors

Baker, W 
Mitchell, T 
Konstantatou, Marina  ORCID logo  https://orcid.org/0000-0003-0593-9407

Abstract

This paper extends the overview (Baker et al. [2], Mitchell et al. [10]) 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 selfstress 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.

Description

Keywords

Journal Title

Proceedings of the International Association for Shell and Spatial Structures (IASS)

Conference Name

International Association for Shell and Spatial Structures

Journal ISSN

Volume Title

31

Publisher

Sage