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Geometrical and Static Aspects of the Cupola of Santa Maria Del Fiore, Florence (Italy)

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Geometrical and Static Aspects of the Cupola of Santa Maria Del Fiore, Florence (Italy) Structural Analysis of Historic Construction – D’Ayala & Fodde (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-46872-5 Geometrical and static aspects of the Cupola of Santa Maria del Fiore, Florence (Italy) A. Cecchi & I. Chiaverini Department of Civil Engineering, University of Florence, Florence, Italy A. Passerini Leonardo Società 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 exten- sion of the ancient church of Santa Reparata: it was designed byArnolfo (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 bap- tistery 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 con- firmed by excavations, that set the date of foundation Figure 1. View of the cathedral of Santa Maria del Fiore. is between the V and IX century (Rocchi 1996). In the second half of the fourteenth century the con- dimension was internally about 45 m, surpassing the struction of the octagonal base was completed; for fifty greatest known, the Pantheon in Rome (43 m about, year about the construction yard stood by,testifying the in concrete) and Hagia Sofia in Constantinople (31 m great uncertainty about the building technique of the about, in masonry); the base itself was laying on four dome, till Brunelleschi’s assignment in 1420. great high piles, so that the height of the top, 90 m We should keep in mind that in that time in Italy about, and the height of the base, 60 m. about, greater there were two other great yards open for the construc- than the Pantheon, made it practically impossible to tion of the cathedrals of Milan and Bologna, but the erect the dome by framework, as was done in Rome. construction of the dome of Florence was so excep- Besides, the Roman dome is a spherical revolution tional to enable the target to appear beyond the human surface, while the Florentine dome has a much more possibilities. complicated geometrical shape, due to its octagonal This is understandable since the dome to be built base. Notice that the Pantheon was built in concrete, a would be the largest ever known (Figure 1,2): its base technique which was probably lost in the Middle Ages 555 perchè 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). 2 AUTHORS WHO DOCUMENTED THE DOME. THE AIMS OF OUR RESEARCH The silence of Filippo is the main cause of the discus- Figure 2. Plan of the cathedral of S. Maria del Fiore sions that followed on the argument. This seems to be (Ximenes). common to all the Middle Ages constructions. Fitchen speaks of “...the total lack of written documentation on both the engineering structure and the erectional procedures...” (Fitchen 1961). and was substituted in the dome of Florence by brick Many authors have related the dome and his mas- masonry. The static function of the flying buttress of ter: among many others let’s remember Giovanni di the Middle Ages cathedrals, to carry the horizontal Gherardo da Prato (1421), Manetti (1480?), Vasari forces to the foundations, (Heyman 1966) was left to (1550), Opera del Duomo (1691) (The Opera del the chapels, which surround the base, much more suit- Duomo was charged by the Duke of Tuscany to write able to the classical tradition of the town, Florentia, down an essay on the stability of the Dome, threatened founded by the Romans in 59 B.C. (Davidsohn by cracks), Guasti (1887), and recently Sanpaolesi 1956). (1962), Fondelli (2004), Rocchi (1994). Sgrilli and Vasari (Vasari 1550) is the main source of infor- Ximenes have rendered the dome accurately in the mation concerning Filippo Brunelleschi’s work. He XVIII century. wrote down an act, collected in the Museum of Nevertheless as a result of this information neither the Cathedral, where the main dimensions of the thorough study on the geometry of the dome, nor on building were specified. We should remember the its statics is carried out. following: Beyond these arguments, the topics which inter- est many researchers, e.g. Di Pasquale (1977), Bartoli – the dome is composed by two cupolas; (1994), are the methods of construction and erection of – the inferior one has a variable thickness from 2.35 m the dome and of the masonry, particularly the special in the bottom to 1.49 m at the top and it is vaulted one called “a spina pesce”. “a quinto acuto negli angoli”. The function of the The survey of Fondelli, based upon photogramme- superior one is: “conservalla dal umido (practical try, must be remembered for its accuracy. It started in function) e perché torni più magnifica e gonfi- 1968 and was carried on for many years. Fondelli’star- ante (esthetical function)”: its thickness varies from get was to render both the outside and the inside of the 0.72 m to 0.43 m; great cathedral and at the same time to link the survey – 24 stone ribs (pietraforte) link the two cupolas, 1 for to the Italian geodetic net. each of the 8 corners and 2 for each web; these ribs The task of this paper is to give a contribution to are tied round by 6 hoops in pietraforte cramped by the knowledge of Filippo’s work on the following four means of iron brackets; topics: – further links between the two cupolas are the “volticciole” (small vaults) chained by means of – based on Brunelleschi’s specifications, the above oak beams; papers and our observations the geometrical shape – the material used is brick masonry, even if at first, of the internal surface of the dome is proposed; stone walls were proposed. – the proposed shape is compared to the results of the survey of the dome; You can note Brunelleschi’s structural intuition, – the differential geometry of the surface is exposed; that is to say the employment of a sandwich ribbed – the statics of a Brunelleschi-like dome is defined structure, in order to lower the load of heavy vaults. and analyzed. Nothing he wrote neither about the methods of erec- tion of the vault, even if he used a cantilever technique Further researches will discuss the masonry, the without frameworks, absolutely new for his times, nor engineering structure, the details and the erectional about the masonry “secondo sara allora consigliato procedures. 556 Figure 4. Surveyed points of the western web of the dome. Figure 3. Geometrical hypothesis on the dome. 4 SURVEY OF THE DOME. COMPARISON BETWEEN SURVEYED AND 3 HYPOTHESIS ON THE GEOMETRICAL GEOMETRICAL POINTS FEATURES OF THE INTERNAL SURFACE OF THE DOME The second aim of our work was to survey one web of the dome so that the hypothesis explained in Chapter Figure 3 shows the geometrical hypothesis, plan and IV IV 3 can be compared. vertical section (AA VF F). The survey was carried out only with topographical The plan of the octagon A, B, D,..., basis of the methods, using an electronic laser total station, a Leica dome, can be observed. C is its centre. The lines TCR 705, 5” angular precision and 2 mm.+2 ppm. lin- A A,B B,D D,..., are the projections of eight cir- ear precision and a digital camera Nikon D300 with a cular arches whose ray is r: they are the rulings of the 12 mega pixel CCD and 50/20 interchangeable Nikkor surfaces. The octagon, represented by A ,B ,D ,..., optics. is the lantern: in section it is represented by the line IV IV It is well known (Cecchi 2006) that the laser tech- A F .According to Brunelleschi’sspecifications the nology permits the direct survey of inaccessible points, arches’centres aren’t in the centre of the octagon: they which is the case of this dome. are in the point “quinto di sesto”. E.g. A A and F F Beyond this the quick acquisition of data in a dig- are the projections of the circular arches AAIV,FFIV, ital format in a reference frame, permits a successive whose centres are respectively the points A ,F such computer elaboration of the data. that, for instance, AF = 1/5 AF. Naturally eight cen- In June 2007 the upper balcony of the cathedral tres form a new octagon A ,B ,D,...,. The points was reached; this one was built on the bottom of the of the webs of the dome represented in the horizontal dome from which the best and nearest view of the plan by the eight quadrilaterals AA B B, BB D D, inside surface of the dome is possible.
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