On the Leonardo’s project for the tiburio of Milano cathedral: some consideration on static behaviour


Among the numerous intuitions and projects that have characterized Leonardo da Vinci's art and technique, the conception of architectural structures has an important role, including studies and the proposal for the project of the tiburio of the Milan Cathedral. Based on some hypotheses of reconstruction of geometries and structural systems developed in the architectural field, and formulated as an interpretation of original drawings, it was intended to test whether the solutions proposed by Leonado were also actually feasible, examining them with current structural modeling techniques, of evaluation of static functioning and definition of structural safety. Using the finite element method (FEM), two different proposals were investigated for the vaults and supporting arches of the tiburio, finding its substantial reliability even though this was hypothesized in the absence of technical verification tools that did not exist at the time.


Leonardo da Vinci, Architecture, Vault, Arch, Static, Reliability, FEM

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Apollonio, F., Gaiani, M., Bertacchi, G., & Frommel S. (2018, Nov. 7-8). Reconstruction and structural reenacting of Leonardo’s project for the tiburium of Milan cathedral. Virtual Models and Scientific Value. Historic Studies and Virtual Models in the Age of Digital Humanities. Talk conducted at Conference at Technische Universität, Berlin, Germany.

Benvenuto, E. (1991). An Introduction to the History of Structural Mechanics - Part II: Vaulted Structures and Elastic Systems. Berlin, Germany: Springer.

Bertolesi, E., Adam, J. M., Rinaudo, P., & Calderón, P. A. (2019). Research and practice on masonry cross vaults – A review. Engineering Structures, 180, 67-88.

Como, M. (2013). Statics of Historic Masonry Constructions. Berlin, Germany: Springer.

Di Pasquale, S. (1996). L’arte del costruire. Tra conoscenza e scienza. Venezia, Italy: Marsilio.

Giaccone, D. (2020). The peristyle of the Temple of Apollo at Syracuse: Historical hypotheses of reconstruction revisited through a finite element analysis. Digital Applications in Archaeology and Cultural Heritage, 16(e00138).

Giaccone, D., Fanelli, P., & Santamaria, U. (In press). Influence of the geometric model on the structural analysis of architectural heritage. Journal of Cultural Heritage.

Girardi, M., Padovani, C., Pellegrini, D., Porcelli, M., & Robol, L. (2020). Finite element model updating for structural applications. Journal of Computational and Applied Mathematics, 370(112675).

Gaetani, A., Monti, G., Lourenço, P.B., & Marcari, G. (2016). Design and Analysis of Cross Vaults Along History. International Journal of Architectural Heritage, 10(7), 841-856.

Guillaume, J. (1987). Le tiburio de la cathédrale de Milan. In P. Galluzzi (Ed.). Léonard de Vinci ingénieur et architecte (pp. 209-223). Montréal, Canada: Musée des beaux-arts de Montréal.

Heyman, J. (1966). The stone skeleton. International Journal of Solids and Structures, 2(2), 249-279.

Kurrer, K. E. (2008). The history of the theory of structures: from arch analysis to computational mechanics. Berlin, Germany: Ernst & Sohn.

Leonardo da Vinci, (1487ca). Codex Atlanticus. Biblioteca Ambrosiana, Milano, Italy.

Leonardo da Vinci, (1478-93). Codex Trivulzianus - 2162. Biblioteca Trivulziana, Milano, Italy.

Leonardo da Vinci, (1488-90 ca). Manuscript B – 2173. Bibliothèque de l’Institut de France, Paris, France.

Leonardo da Vinci, (1488-90 ca). Manuscript A – 2172, Bibliothèque de l’Institut de France, Paris, France.

Lignola, G. P., Giamundo, V., & Cosenza, E. (2014). Finite Element Modelling of the Archaeological Colonnade in Pompeii. In B.H.V. Topping, P. Iványi, (Eds.) Proceedings of the Twelfth International Conference on Computational Structures Technology, (paper 77). Stirling, United Kingdom: Civil-Comp Press. doi:10.4203/ccp.106.77

Milani. G., & Lourenço, P. B. (2007). Modelling masonry with limit analysis finite elements: Review applications and new directions. In B. H. V. Topping (Ed.), Civil Engineering Computations: Tools and Techniques (pp. 217-242). Stirling, United Kingdom: Saxe-Coburg Publications.

Modena, C. (2005). Design approaches of interventions for the safety and conservation of historic buildings, In C. Modena, P. B. Lourenço, P. Roca (Eds.), Structural Analysis of Historical Constructions (pp. 75-83). London, Great Britain: Taylor and Francis group.

Roca, P., Cervera, M., Pelà, L., Clemente, R., & Chiumenti, M. (2013). Continuum FE models for the analysis of Mallorca Cathedral. Engineering Structures, 46, 653-670.

Suárez, J., Boothby, T. E., & González, J. A. (In press). Constructive and structural analysis of a Baroque dome in Spain. The encamonada dome. Journal of Cultural Heritage.

Theodossopoulos, D., Sinha, B. P., Usmani, A. S., & Macdonald, A. J. (2002). Assessment of the structural response of masonry cross vaults. Strain, 38(2), 119-137.

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