Prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach

This paper presents an algebraic approach that unifies both the elastic and limit theories of static structural analysis. This approach reveals several previously unpublished improvements, which are based on several dualities in the mathematical description. Firstly, we show a novel duality between...

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Autores principales:	Jaime Cervera Bravo, Laura Navas-Sánchez
Formato:	article
Lenguaje:	EN
Publicado:	The Royal Society 2021
Materias:	structural analysis prestress theory structural dualities plasticity limit states ductility Science Q
Acceso en línea:	https://doaj.org/article/11f91ab4063f4b788ac98178f2006984
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spelling	oai:doaj.org-article:11f91ab4063f4b788ac98178f20069842021-12-01T08:05:33ZPrestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach10.1098/rsos.2104592054-5703https://doaj.org/article/11f91ab4063f4b788ac98178f20069842021-12-01T00:00:00Zhttps://royalsocietypublishing.org/doi/10.1098/rsos.210459https://doaj.org/toc/2054-5703This paper presents an algebraic approach that unifies both the elastic and limit theories of static structural analysis. This approach reveals several previously unpublished improvements, which are based on several dualities in the mathematical description. Firstly, we show a novel duality between the solutions to two different problems: the elastic solution to the internal forces of an externally loaded structure, and the nodal displacements induced by prestressing in one or several elements of the same structure. This duality is proven and discussed. The application of this solution to the limit state analysis is very productive, and includes the determination of the ductility requirements necessary to achieve full plastic behaviour, and the assessment of the prestress needed to limit or eliminate such requirements. The unified framework also allows to obtain the elasto-plastic deformed state at the beginning of the plastic structural collapse. We have also detailed the theoretical duality between two classes of structures—hyperstatic and hypostatic—which was derived from the linear algebra principles that define these solutions. Finally, we studied and exposed the dimensionality reduction of structural problems given by the singular value decomposition and the eigenvalues problem. An illustrative example that clearly illustrates all these points is provided.Jaime Cervera BravoLaura Navas-SánchezThe Royal Societyarticlestructural analysisprestress theorystructural dualitiesplasticitylimit statesductilityScienceQENRoyal Society Open Science, Vol 8, Iss 12 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	structural analysis prestress theory structural dualities plasticity limit states ductility Science Q
spellingShingle	structural analysis prestress theory structural dualities plasticity limit states ductility Science Q Jaime Cervera Bravo Laura Navas-Sánchez Prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach
description	This paper presents an algebraic approach that unifies both the elastic and limit theories of static structural analysis. This approach reveals several previously unpublished improvements, which are based on several dualities in the mathematical description. Firstly, we show a novel duality between the solutions to two different problems: the elastic solution to the internal forces of an externally loaded structure, and the nodal displacements induced by prestressing in one or several elements of the same structure. This duality is proven and discussed. The application of this solution to the limit state analysis is very productive, and includes the determination of the ductility requirements necessary to achieve full plastic behaviour, and the assessment of the prestress needed to limit or eliminate such requirements. The unified framework also allows to obtain the elasto-plastic deformed state at the beginning of the plastic structural collapse. We have also detailed the theoretical duality between two classes of structures—hyperstatic and hypostatic—which was derived from the linear algebra principles that define these solutions. Finally, we studied and exposed the dimensionality reduction of structural problems given by the singular value decomposition and the eigenvalues problem. An illustrative example that clearly illustrates all these points is provided.
format	article
author	Jaime Cervera Bravo Laura Navas-Sánchez
author_facet	Jaime Cervera Bravo Laura Navas-Sánchez
author_sort	Jaime Cervera Bravo
title	Prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach
title_short	Prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach
title_full	Prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach
title_fullStr	Prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach
title_full_unstemmed	Prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach
title_sort	prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach
publisher	The Royal Society
publishDate	2021
url	https://doaj.org/article/11f91ab4063f4b788ac98178f2006984
work_keys_str_mv	AT jaimecerverabravo prestressbehaviourandductilityrequirementsinstructuressolutionsfromaunifiedalgebraicapproach AT lauranavassanchez prestressbehaviourandductilityrequirementsinstructuressolutionsfromaunifiedalgebraicapproach
_version_	1718405397293826048

Prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach

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