Engineering concepts behind the stability of famous masonry domes confirmed

*Brunelleschi's dome of Florence Cathedral (Credits: Wikipedia)*

Research conducted at Princeton University and the University of Bergamo unearths the technical secrets behind famous self-supporting masonry domes such as the dome of the duomo of Maria del Fiore in Florence.

For more than half a century, engineers were puzzled on how Filippo Brunelleschi constructed the Florence Cathedral’s dome, which is characterized as the largest standing masonry dome at present. Moreover, an issue of interest for the researchers was the determination of how the famous cupola was built without any temporary support.

The engineers developed detailed computational models in order to derive how forces are successfully being distributed achieving equilibrium. For the analysis, the Discrete Element Modeling (DEM) technique was used to simulate the dome's behavior at several construction phases. Apart from providing proof of the structural engineering behind the dome’s stability, the limit state analysis results are aiming in establishing ways to recreate the construction techniques today.

The most challenging part of the analysis was the modeling of the geometry pattern of the bricks of the interior dome, which is the key for the structure to remain self-supporting. A herringbone is formed between the field bricks of the horizontal direction and the vertical bricks at the beginning and the end of the horizontal rows. This placement creates step-wise lines of vertical bricks that continue across the curvature of the cupola, in a diagonal direction. In that way a complex cross-herringbone spiraling pattern is developed, providing stability for the interior bricks and maintaining the curvature of the dome. Based on the analysis, it was shown that this double-helix support, called double loxodrome, achieves to successfully distribute the weight of the cupola.

Each horizontal row of bricks puts transverse pressure on the vertical herringbone bricks, forming rows of structural elements known as plate-bandes, or straight arches inside the loxodrome. This physical pressure toward the vertical bricks results in cupola’s stability. One of the main conclusions of the research team is that the herringbone pattern causes the bricks to be lodged as plate-bandes, preventing the dome's collapse during construction. A famous dome built with such double loxodrome technique is St. Peter’s Basilica in the Vatican.

The double loxodrome technique (Credits: Princeton University)

Filippo Brunelleschi used only a single helix (original single loxodrome structure) in the placement of the bricks for the famous dome of Maria del Fiore in Florence. In that way the lines of vertical bricks do not cross one another and stay parallel instead, a geometry which also achieves stability and enables construction without shoring.

The research team, consisting of Sigrid Adriaenssens, Professor of civil and environmental engineering at Princeton, Vittorio Paris , a graduate student at the University of Bergamo and Attilio Pizzigoni, Professor of Engineering and Applied Sciences at the University of Bergamo, believes that the results of this study could benefit innovative remote construction techniques, e.g. construction via aerial drones or robots. These techniques could lead to enhanced working safety, increased construction speed and reduced cost.

Pizzigoni stated: “With these studies, we aim to approach moments in history when the sole form of technology available to man was the abstract rationality of geometry. […] What we as designers, architects and builders can learn from the past is the knowledge of a structural equilibrium of form based on the geometry of materials and of their reciprocal measurements in three-dimensional space.”

The findings of the research will be published in the July 2020 issue of Engineering Structures journal.

Source: Princeton University