TY - GEN
T1 - Simplified closed‐form expressions for horizontal reactions in linear elastic arches under self‐weight
AU - Glisic, Branko
N1 - Publisher Copyright:
Copyright © 2019 by Branko Glisic Published by the International Association for Shell and Spatial Structures (IASS) with permission.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Closed-form equations
KW - Hingeless arch
KW - Horizontal reaction
KW - Parabolic and catenary shape
KW - Segmental
KW - Symmetric linear-elastic arch
KW - Three-hinged
KW - Two-hinged
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M3 - Conference contribution
AN - SCOPUS:85102397499
T3 - IASS 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
SP - 282
EP - 289
BT - IASS 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
A2 - Lazaro, Carlos
A2 - Bletzinger, Kai-Uwe
A2 - Onate, Eugenio
PB - International Center for Numerical Methods in Engineering
T2 - IASS 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
Y2 - 7 October 2019 through 10 October 2019
ER -