Mathematicians revealed secrets of the domes of Renaissance Cathedrals

(ORDO NEWS) — Mathematicians found out how the brick dome of the Cathedral of Santa Maria del Fiore in Florence, created in the 15th century, supported its own weight and did not collapse under the influence of gravity during construction without external support. The results of their work were published by the scientific journal Engineering Structures.

“The most interesting thing for me was how such beautiful and large domes were built without any formwork, what innovations helped their builders achieve such success. This knowledge, in turn, will help us understand how to adapt such forgotten technologies for use in modern construction,” said Sigrid Adriaenssens, one of the authors of the study, a professor at Princeton University (USA).

One of the domes of St. Peter’s Basilica in the Vatican, as well as the vaults of many other temples of Italy from the early Renaissance, were built using a unique technology, thanks to which the masters of that time built them from the bottom up without formwork and other devices that would not allow the dome to collapse before completion the buildings.

A similar technique was invented by Italian architect of the 15th century Filippo Brunelleschi during the construction of the cathedral of Florence – Santa Maria del Fiore. It consists in the fact that the dome consists of two types of masonry – a kind of “grid” of vertically laid bricks, which is rotated relative to the Earth’s surface at an angle of 45 degrees, and horizontal layers of bricks that fill the voids inside the cells of this grid.

New Renaissance Heritage

Adriaenssens and her colleagues note that understanding how such masterpieces were built does not explain how such a structure can not be destroyed both after the construction was completed and when the dome was assembled. For decades, engineers, physicists and mathematicians have been trying to figure this out, but so far they have not had an answer to this question.

American and Italian mathematicians solved this problem by calculating how the distribution of forces and stresses inside an unfinished dome changes as each new layer of bricks is added. In addition, they studied how the structural properties of the top of the cathedral were affected by the periodic addition of so-called borders – special ledges made of bricks.

These calculations helped scientists to find out what these “borders” the architect inserted into the dome at a certain angle, which was always more than 10 degrees. In this case, these inserts themselves, and the entire structure were always stable and never moved. Thanks to this, the dome of the cathedral did not collapse, and he did not need support during all 89 stages of its construction. Thanks to this, Brunelleschi and his students could build such churches without formwork and a large number of workers.

Similar principles, scientists suggest, can be used to reduce the cost of building materials and other resources when building domes in modern temples and other buildings, as well as to create fully automated building methods using drones or robots.

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