Cecchi I Chiaverini

Department of Civil Engineering, University of Florence, Florence, Italy A. Passerini

Leonardo Societa di Ingegneria S.r.l., Florence, Italy

ABSTRACT: The purpose of this research is to clarify, in the language of differential geometry, the geometry of the internal surface of Brunelleschi's dome, in the Cathedral of Santa Maria del Fiore, Florence; the statics of a Brunelleschi-like dome have also been taken into consideration. The masonry, and, in particular, the "lisca pesce" one, together with the construction and layout technologies, have been main topics of interest for many researchers: they will be the subjects of further research.

1 INTRODUCTION: THE DOME OF THE CATHEDRAL OF FLORENCE

The construction of the cathedral of Firenze was begun in the year 1296, with the works related to the extension of the ancient church of Santa Reparata: it was designed by Arnolfo (1240,1302). The design included a great dome, based on an octagonal base, to be erected in the eastern end of the church. The dome is an unusual construction of the Middle Ages, (Wittkower 1962): Arnolfo certainly referred to the nearby octagonal baptistery San Giovanni, so ancient and revered that the Florentines believed it was built by the Romans, as the temple of Ares, hypothesis which was not confirmed by excavations, that set the date of foundation is between the V and IX century (Rocchi 1996).

In the second half of the fourteenth century the construction of the octagonal base was completed; for fifty year about the construction yard stood by, testifying the great uncertainty about the building technique of the dome, till Brunelleschi's assignment in 1420.

We should keep in mind that in that time in Italy there were two other great yards open for the construction of the cathedrals of Milan and Bologna, but the construction of the dome of Florence was so exceptional to enable the target to appear beyond the human possibilities.

This is understandable since the dome to be built would be the largest ever known (Figure 1,2): its base

Figure 1. View of the cathedral of Santa Maria del Fiore.

dimension was internally about 45 m, surpassing the greatest known, the Pantheon in Rome (43 m about, in concrete) and Hagia Sofia in Constantinople (31m about, in masonry); the base itself was laying on four great high piles, so that the height of the top, 90 m about, and the height of the base, 60 m. about, greater than the Pantheon, made it practically impossible to erect the dome by framework, as was done in Rome. Besides, the Roman dome is a spherical revolution surface, while the Florentine dome has a much more complicated geometrical shape, due to its octagonal base. Notice that the Pantheon was built in concrete, a technique which was probably lost in the Middle Ages iliyS

Figure 2. Plan of the cathedral of S. Maria del Fiore (Ximenes).

and was substituted in the dome of Florence by brick masonry. The static function of the flying buttress of the Middle Ages cathedrals, to carry the horizontal forces to the foundations, (Heyman 1966) was left to the chapels, which surround the base, much more suitable to the classical tradition of the town, Florentia, founded by the Romans in 59 B.C. (Davidsohn 1956).

Vasari (Vasari 1550) is the main source of information concerning Filippo Brunelleschi's work. He wrote down an act, collected in the Museum of the Cathedral, where the main dimensions of the building were specified. We should remember the following:

- the dome is composed by two cupolas;

- the inferior one has a variable thickness from 2.35m in the bottom to 1.49 m at the top and it is vaulted "a quinto acuto negli angoli". The function of the superior one is: "conservalla dal umido (practical function) e perché torni piu magnifica e gonfi-ante (esthetical function)": its thickness varies from 0.72 m to 0.43 m;

- 24 stone ribs (pietraforte) link the two cupolas, 1 for each of the 8 corners and 2 for each web; these ribs are tied round by 6 hoops in pietraforte cramped by means of iron brackets;

- further links between the two cupolas are the "volticciole" (small vaults) chained by means of oak beams;

- the material used is brick masonry, even if at first, stone walls were proposed.

You can note Brunelleschi's structural intuition, that is to say the employment of a sandwich ribbed structure, in order to lower the load of heavy vaults.

Nothing he wrote neither about the methods oferec-tion of the vault, even if he used a cantilever technique without frameworks, absolutely new for his times, nor about the masonry "secondo sara allora consigliato perche nel murare la praticha insegnera quello ches-sara a seguire" (Brunelleschi's specifications), nor about the mechanical apparatus he would have used later to raise the heavy weights "tirare i pesi per via di contrappesi e ruote, che un sol bue tirava quanto avrebbero appena tirato sei paia" (Vasari 1550).

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