Simplified closed‐form expressions for horizontal reactions in linear elastic arches under self‐weight

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Finite and/or discrete element modeling are typical modern tools for determining reactions and internal forces in arches. However, while these tools are excellent in performing detailed analysis, they might be less suitable for conceptual design and “back-of-the-envelope calculation” due to their complexity of application. Simplified closed-form formulae for reactions and internal forces might be more appropriate as they enable fast solutions and easy development of parametric studies. Hence, the aim of this paper is to present novel simplified closed-form expressions for determination of horizontal reactions in segmental, catenary, and parabolic arches under self-weight. Three typical structural systems for symmetric linear-elastic arches with constant cross-section and various rise‐to‐span ratios were considered: three-hinged, two-hinged, and hingeless. It was found that the horizontal reactions, to large extent, do not depend on arch shape or number of hinges, but only on linear weight, span, and equivalent angle of embrace. Surprisingly, with few exceptions, single formula presented in this paper provides almost universal solution for all shapes of arches, rise-to-span ratios, and boundary conditions. In addition, linear relationship between horizontal reactions of the three structural systems (hingeless, three-hinged, and two-hinged) was discovered, which is valid for any shape (segmental, parabolic, and catenary) and any rise-to-span ratio.

Original languageEnglish (US)
Title of host publicationIASS Symposium 2019 - 60th Anniversary Symposium of the International Association for Shell and Spatial Structures; Structural Membranes 2019 - 9th International Conference on Textile Composites and Inflatable Structures, FORM and FORCE
EditorsCarlos Lazaro, Kai-Uwe Bletzinger, Eugenio Onate
PublisherInternational Center for Numerical Methods in Engineering
Pages282-289
Number of pages8
ISBN (Electronic)9788412110104
StatePublished - 2019
EventIASS Symposium 2019 - 60th Anniversary Symposium of the International Association for Shell and Spatial Structures; Structural Membranes 2019 - 9th International Conference on Textile Composites and Inflatable Structures, FORM and FORCE - Barcelona, Spain
Duration: Oct 7 2019Oct 10 2019

Publication series

NameIASS Symposium 2019 - 60th Anniversary Symposium of the International Association for Shell and Spatial Structures; Structural Membranes 2019 - 9th International Conference on Textile Composites and Inflatable Structures, FORM and FORCE

Conference

ConferenceIASS Symposium 2019 - 60th Anniversary Symposium of the International Association for Shell and Spatial Structures; Structural Membranes 2019 - 9th International Conference on Textile Composites and Inflatable Structures, FORM and FORCE
Country/TerritorySpain
CityBarcelona
Period10/7/1910/10/19

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Civil and Structural Engineering
  • Mechanical Engineering
  • Building and Construction

Keywords

  • Closed-form equations
  • Hingeless arch
  • Horizontal reaction
  • Parabolic and catenary shape
  • Segmental
  • Symmetric linear-elastic arch
  • Three-hinged
  • Two-hinged

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