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dc.contributor.authorMcRobie, Aen
dc.contributor.authorBaker, Wen
dc.contributor.authorMitchell, Ten
dc.contributor.authorKonstantatou, Marinaen
dc.date.accessioned2017-01-26T14:18:52Z
dc.date.available2017-01-26T14:18:52Z
dc.date.issued2016-06-01en
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/262064
dc.description.abstractThis 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.
dc.publisherSage
dc.titleMechanisms and states of self-stress of planar trusses using graphic statics, Part III: Applications and extensionsen
dc.typeConference Object
prism.endingPage111
prism.issueIdentifier2-4en
prism.publicationDate2016en
prism.publicationNameProceedings of the International Association for Shell and Spatial Structures (IASS)en
prism.startingPage102
prism.volume31en
dc.identifier.doi10.17863/CAM.7309
rioxxterms.versionofrecord10.1177/0266351116660791en
rioxxterms.versionVoRen
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2016-06-01en
dc.contributor.orcidKonstantatou, Marina [0000-0003-0593-9407]
rioxxterms.typeConference Paper/Proceeding/Abstracten
cam.issuedOnline2016-08-03en
dc.identifier.urlhttps://journals.sagepub.com/doi/10.1177/0266351116660791en
pubs.conference-nameInternational Association for Shell and Spatial Structuresen
pubs.conference-start-date2015-08-17en
cam.orpheus.successThu Nov 05 11:56:36 GMT 2020 - Embargo updated*
rioxxterms.freetoread.startdate2017-06-01


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