McRobie, A and Baker, W and Mitchell, T and Konstantatou, M (2015) *Mechanisms and states of self-stress of planar trusses using graphic statics, Part III: Applications and extensions.* In: International Association for Shell and Spatial Structures, 2015-8-17 to 2015-8-20, Amsterdam, The Netherlands.

## 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.

Item Type: | Conference or Workshop Item (UNSPECIFIED) |
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Subjects: | UNSPECIFIED |

Divisions: | Div D > Structures |

Depositing User: | Cron Job |

Date Deposited: | 17 Jul 2017 20:03 |

Last Modified: | 27 Feb 2018 02:04 |

DOI: |