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Minimum thickness of the gothic arch

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Abstract

The paper investigates how the shape affects the Couplet–Heyman minimum thickness of the masonry pointed arch. The minimum thickness is such a structural thickness, at which a vault made of rigid voussoirs is stable for self-weight. It is expressed as a function of the pointed generator curve’s deviation from the semicircle. The arch is analysed in its undisplaced, geometrically perfect state. In the present study, perfect symmetry is assumed, and any disturbance in the symmetry is not considered. The joints between the voussoirs are placed in the radial direction. Two approaches are applied to derive the minimum thickness of the pointed arch, like Limit State Analysis (henceforth LSA) and Discrete Element Modelling (henceforth DEM). The application of the LSA leads to a nonlinear optimisation problem, which is solved by the so-called active set method. DEM technique is also applied, in which the model consists of discrete blocks each of which can move independently from each other. In DEM, sliding failure can freely develop during the loading process, which is neglected in the LSA. The results of the analyses show great correspondence, if sliding failure does not appear.

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Acknowledgements

The author would like to thank Dr. Fabian Dedecker of ITASCA Consulting Inc. for his mentorship as well as the ITASCA Education Partnership Program for providing a copy of 3DEC to assist in the research and Tamás Forgács for his very remarkable notes. Financial support from the NKFI 100770 project is also gratefully acknowledged.

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  1. Department of Structural Mechanics, Budapest University of Technology and Economics, Mûegyetem rkp. 3, Budapest, 1111, Hungary

    G. Lengyel

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  1. G. Lengyel
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Lengyel, G. Minimum thickness of the gothic arch. Arch Appl Mech 88, 769–788 (2018). https://doi.org/10.1007/s00419-018-1341-6

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  • DOI: https://doi.org/10.1007/s00419-018-1341-6

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