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On the Modelling of Vaulted Structures of Equal Strength

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Abstract

The optimization of vaulted structures has primarily concentrated on the determination of the structure midsurface, governing the direction of forces flow, and the thickness variation, affecting the corresponding stress developed in a structure. The problems related to such optimizations are the so-called catenary of equal strength and its later three-dimensional equivalent, the membrane of equal strength. The present paper elaborates on the equilibrium analysis and analytical expressions that describe the resulting shapes and provides the visualization of the corresponding solutions as particular forms of vaulted structures of great span. Based on the analysis of the geometrical properties of midline and intrados curve, the study shows that there is only one shape of such a structure’s midsurface, whereby material properties affect only its size, which has, however, a theoretical limit. In addition, using FEM, various arch and dome sizes and materials are considered, and the assumption about equal stress distribution within such structures is confirmed.

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Acknowledgements

This research is supported by the Ministry of Education, Science and Technological Development through the Project no. 451-03-68/2020-14/200156.

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Authors and Affiliations

  1. Department of Architecture, Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21101, Novi Sad, Serbia

    Dimitrije Nikolić

  2. Department of Civil Engineering and Geodesy, Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21101, Novi Sad, Serbia

    Vladimir Živaljević

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  2. Vladimir Živaljević
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Correspondence to Dimitrije Nikolić.

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Nikolić, D., Živaljević, V. On the Modelling of Vaulted Structures of Equal Strength. Nexus Netw J 22, 1219–1236 (2020). https://doi.org/10.1007/s00004-020-00507-y

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