Structural and Multidisciplinary Optimization

, Volume 60, Issue 5, pp 1957–1966 | Cite as

Catenary arch of finite thickness as the optimal arch shape

  • Dimitrije NikolićEmail author
Research Paper


Based on the analogy with the load path of a homogeneous hanging chain, catenary has been for over three centuries considered to be an ideal masonry arch’s shape. In the present research, after the thrust line theory, complete insight into the equilibrium analysis of catenary arch of finite thickness under its own weight is provided. It is concluded that, in accordance with the common criterion—the existence of only normal (axial) forces—the ideality has previously been unjustifiably attached to such an arch, since there are shear forces present as well. However, with respect to so-called Couplet-Heyman’s assumptions (unilateral rigid no-tension material), it is shown that any catenary arch is stable under its own weight.


Catenary arch Thrust line analysis Masonry arch Minimum thickness Optimal shape 



I would like to thank Professor Ivica Bošnjak for providing valuable remarks and help regarding thrust line analysis carried out in this research. The paper was done within the Project No. TR36042 supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia.

Compliance with Ethical Standards

Conflict of interest

The author declare that there is no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Technical Sciences, Department of ArchitectureUniversity of Novi SadNovi SadSerbia

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