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Article History

Received: 17 March 2026

Revised: 15 June 2026

Accepted: 18 June 2026

First Online: 22 July 2026

Declarations

Conflict of interest: The authors declare no competing interests.

Replication of results: The results presented in this paper can be replicated by applying the closed-form analytical expressions derived in Sect.  . The geometry of the arch and each voussoir is fully determined by Eqs. ( – ), which require only two input parameters: the span L and the height H of the arch. The catenary curve parameters a and c are obtained by solving the system formed by Eqs. ( ) and ( ) using the Newton–Raphson method. The eccentricity of each voussoir's centroid, the dimensions of the additional prisms and the minimum number of voussoirs are subsequently calculated through the explicit expressions provided in Eqs. ( – ), without the need for iterative numerical methods. No external code or dataset is required to reproduce the figures and results shown in this paper, as all numerical values can be derived directly from the equations presented herein.