Search

In this work, a simplified structural analysis of the main dome of San Francesco di Paola in Naples is performed by adopting both analytical and graphical approaches. The analytical process is based on the simplified membrane theory and the graphical methodology on the slicing technique. Both methods are used to determine the safety of the dome design under vertical and horizontal loads. We explore the effects of earthquakes by introducing horizontal forces proportional to the weight. Since the slicing technique does not consider the hoop compressive stresses building up in the upper part of the cap, the geometrical safety factor obtained by combining the analytical with the graphical method for the sole dome is lower than the one obtained with the analytical method. The estimate of the a∕g factor for the dome-buttress structural system obtained with the graphical method is greater than the level accepted for the seismic area of Naples.

We take under consideration two masonry domes built during Italian Renaissance: the Santa Maria del Fiore dome in Florence by F. Brunelleschi and St. Peter's dome in Rome by Michelangelo. No original computation is known currently in reference to neither one nor the other. However present mathematical computations show that, even though probably unconsciously, the designs of both the domes were inspired by the use of catenary, a trascendent mathematical curve with excellent stability properties. It was defined and studied in details by Leibniz and Bernoulli brothers at the end of the 17th century (within the context of rising differential geometry) a long time later than both the domes were completely built. Therefore the two considered domes suggest that some practical applications of differential geometry in architecture design can be considered foregoing its theoretical formalization. Here we show some numerical computation which support this hypothesis. The aim of this work is to show that knowledge quite often is created in processes and not invented in a moment; in particular here we focus on the development of differential calculus related to its applications to equilibrium of masonry domes.

We aim at introducing comments and details on the role of Mathematics in the development of well-known challenging structures. In particular, we focus on masonry domes (and arches), since they can be considered landmarks in the history of Architecture.

This study presents the results of the static and dynamic assessment of the dome of the Basilica of Santa Maria degli Angeli in Assisi, designed by Galeazzo Alessi. The first section is devoted to an overview of the masonry domes designed by the Italian architect and focuses on the structural solutions adopted in the several cases described to better understand Alessi’s designing skills. In the second part, the drum-dome system is analyzed in order to attain a structural assessment. The static assessment is performed by means of limit analysis and finite element model approaches with non-linear mechanical behavior. The obtained results are consistent with the detected crack pattern and confirm the suitability of the reinforcement steel rings applied to the drum. The seismic assessment has been performed by response spectrum analysis. Due to the lack of specific information, a probabilistic approach for the material mechanical properties was used. The results obtained highlight an adequate seismic response...

In April of 2011, one of the masonry domes of the cathedral of Tortosa enclosure (Tarragona), built at late XVIII century, suddenly broke. The paper presents the evolution of the rupture and its causes, analyzing the cracking process initiated with the runout of the lantern. It is analyzed the equilibrium conditions starting from the initial constructive assessment in order to know the behavior of the dome and its bearing capacity. There are used complementary traditional graphical methods and tridimensional models by finite elements (FEM) by means of the free software Salome-Meca 6.3. Through the interpretation of the results, the assessment concludes that the dome by itself can hold the weight of the lantern. Thus, the cracking of one of the roof beams causes the bending of the lantern, and therefore the formation of collapse joints from the asymmetrical distribution of loads. En abril del 2011, una de las cúpulas tabicadas del recinto de la catedral de Tortosa (Tarragona), construida a finales del siglo XVIII, rompió repentinamente. El artículo presenta la evolución de la rotura y sus causas, analizando el progresivo proceso de fisuración iniciado con el descentramiento de la linterna. Con el objetivo de conocer el comportamiento de la cúpula y su capacidad portante, se analizan las condiciones de equilibrio a partir del estudio constructivo inicial. Se utilizan de manera complementaria métodos gráficos tradicionales y modelos tridimensionales por elementos finitos (MEF) con el programa libre Salome-Meca 6.3. A partir de la interpretación de los resultados, el estudio concluye que la cúpula por sí sola no tiene capacidad para mantenerse en equilibrio bajo el peso de la linterna. Así el efecto de las termitas sobre la sección de una de las vigas de cubierta provocará el asiento de la linterna y, en consecuencia, la formación de rótulas de colapso a partir de la distribución asimétrica de las cargas.

The present paper deals with the collapse behavior of an historical stone arch bridge. Ancient stone or masonry arch bridges are still a useful and a not rare engineering road in Italy, as well as in other parts of Europe. Some of the most ancient arch bridges are concentrated in Italy and constitute an integral part of the Italian transportation system. They also represent a valuable engineering achievement of the people that have lived in Italy for centuries and a cultural heritage of the world. A finite element modal analysis and seismic load evaluation has been performed building a suitable program code. The assessment of the collapse and shakedown states, related to a nonlinear constrained optimization problems, has been analyzed using lower bound and Bleich-Melan theorems of limit analysis. Whereas the retrofitting of this stone structure cannot be executed in the intrados surface of the stone vault, so that an application of CFRP strips on the arch extrados is a more useful constructive technique, especially if a significant increase of the limit and shakedown load multipliers occurs.