Structural Investigation of 18th-Century Ogival Masonry Domes: From Carlo Fontana to Bernardo Vittone

In this study a structural investigation on the ogival masonry domes is performed with particular attention to the significant debate between mathematicians and architects mainly of the French and Italian schools that characterized the 18th century. In this period, analytical approaches to investigate the static of dome structures were developed concurrently for the affirmation of the proportional methods, as reported in several architectural treatises in which graphical constructions for the design of masonry domes can be found. It is well known that Carlo Fontana, in 1694, was the first to show in detail the geometrical rules for the design of a masonry dome. Later, in 1760, the Italian architect Bernardo Antonio Vittone proposed some variations to the rules written by Fontana in order to increase the height of the dome and the slope of the meridian section at the intersection with the lantern. In this study, Vittone’s dome has been analyzed and compared with Fontana’s dome by means of an analytical approach that also considers the influence of the lantern at the top. The obtained results confirm that Vittone’s rules lead not only to architectural, but also structural improvements.     

Dome Strengthening By Encircling Ties: A Monitored Experiment

This study describes a new strategy of conservation of historical monuments based on the combined use of monitoring analysis and empiric reappraisal. Over time, the mechanical behavior of domes—their lack of stability due to the horizontal thrusts generated by their self-weight—has been analyzed by architects and engineers, starting from the observation of damage. This process, which was mathematically demonstrated for the first time by the famous Viviani’s analysis of Santa Maria del Fiore in Florence, has provided over the centuries a number of enhancements in dome structural conception, thus leading to the final solution, referred to as encircling tie rod intervention. Based on these premises, the experimental case of Santa Maria del Quartiere dome in Parma, Italy, is discussed herein. Indeed, it has been considered a good opportunity to present the method used in its strengthening-intervention assessment, further validated by the monitoring system installed. In this monitored in-scale experiment, the empiric classical solution to the primeval dome’s thrust finds its confirmation and offers further possibilities of recalibration during time, thus indicating structural monitoring that may be described as a possible and desirable “alternative to intervention”, in step with “minimum intervention” and “reversibility” principles.     

A Procedure to Investigate the Collapse Behavior of Masonry Domes: Some Meaningful Cases

Masonry domes represent an important part of the architectural heritage. However, the literature about domes analysis seems less consistent than that referred to other masonry structures. The collapses that have happened in recent years as a consequence of seismic actions or lack of maintenance show the need for detailed studies. Here a limit analysis to evaluate the masonry domes behavior is presented. An algorithm based on the kinematic approach has been developed to evaluate the geometric position of the hinges that determine the minimum collapse load multiplier. The proposed procedure is validated by a comparison with some meaningful cases—the collapse of Anime Sante Church in L’Aquila, the collapse of San Nicolò Cathedral in Noto, the crack pattern of San Carlo Alle Quattro Fontane Church in Rome, and the analysis developed on Hagia Sofia in Istanbul. The comparison with real cases shows a good agreement between the model results and the phenomenological crack patterns.     

Nonlinear Structural Performance of a Historical Brick Masonry Inverted Dome

ABSTRACT

Traditional domes are obtained by double curvature shells, which can be rotationally formed by any curved geometrical plane figure rotating about a central vertical axis. They are self-supported and stabilized by the force of gravity acting on their weight to hold them in compression. However, the behavior of inverted domes is different since the dome is downward and masonry inverted domes and their structural behaviors in the literature received limited attention. This article presents a nonlinear finite element analysis of historical brick masonry inverted domes under static and seismic loads. The brick masonry inverted dome in the tomb of scholar Ahmed-El Cezeri, town of Cizre, Turkey, constructed in 1508 is selected as an application. First, a detailed literature review on the masonry domes is given and the selected inverted dome is described briefly. 3D solid and continuum finite element models of the inverted masonry dome are obtained from the surveys. An isotropic Concrete Damage Plasticity (CDP) material model adjusted to masonry structures with the same tensile strength assumed along the parallel and meridian directions of the inverted dome is considered. The nonlinear static analyses and a parametric study by changing the mechanical properties of the brick unit of the inverted masonry dome are performed under gravity loads. The acceleration records of vertical and horizontal components of May 1, 2003 Bingöl earthquake (Mw = 6.4), Turkey, occurred near the region, are chosen for the nonlinear seismic analyses. Nonlinear step by step seismic analyses of the inverted dome are implemented under the vertical and horizontal components of the earthquake, separately. Static modal and seismic responses of the inverted masonry dome are evaluated using mode shapes, minimum and maximum principal strains and stresses, and damage propagations.     

Results of a 60-Year Monitoring System for Santa Maria del Fiore Dome in Florence

This study aims to present the results of the historical and statistical analysis carried out on the monitoring systems that control one of the most studied domes in the world: Santa Maria del Fiore in Florence, Italy. An accurate analysis of the dome crack widths and of its global displacements (horizontal and vertical), both considering the historical data and more recent data, has allowed detection of the static movements developed in the monument over time as well as in context of their relationship to environmental and seismic phenomena. Thanks to the large amount of measured data (from 1955 to 2010), some previous conclusions on the dome damage trend are updated herein. Moreover, in light of the experimental results, some issues on the dome stability—as the principal hypotheses advanced during centuries about the main cause of Brunelleschi’s dome crack pattern—are reconsidered, including the horizontal thrusts due to the dome’s self-weight characterized by Viviani in 1695 and Chiarugi in 1985, the differential settlement of pillars detailed by Cecchini in 1698, Ximenes in 1757 and Borga in 1975 and the influence of temperature variations investigated by Nervi in 1934. The final aim of this study is to show the great utility of modern and historical monitoring in setting up a reliable forecasting model of the monument.     

Dome of the Basilica of Santa Maria Degli Angeli in Assisi: Static and Dynamic Assessment

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 of the structure that can be attributed to the dynamic properties of the slender drum-dome system. This finding justifies the good performance of the structure during the seismic events of 1832 and 1997.