1. INTRODUCTION: THE DOME OF THE BASILICA OF SANTA MARIA DELLA SANITÀ’ IN NAPLES
⌅The church of Santa Maria della Sanità in Naples is part of a religious complex designed by the Dominican friar Giuseppe Nuvolo between 1602-13. Its central plan (1(1) Buccaro, A. (1991). Il borgo dei Vergini. Storia e struttura di un ambito urbano. Napoli: CUEN.
), according to a polycentric scheme which, derived from the examples of San Pietro Church
by Bramante and Michelangelo, integrated “a singular recovery, in an
ideal sense, of the five-nave typology of Constantine’s great basilicas
complex” (2(2) Venditti, A. (1970). Fra’ Nuvolo e l’architettura napoletana tra Cinque e Seicento. In P. F. Palumbo (Ed.), Barocco
europeo, barocco italiano, barocco salentino. Relazioni e comunicazioni
presentate al Congresso internazionale sul barocco, Lecce e Terra
d’Otranto (pp. 195-248). Lecce.
), and from which the friar seems to learn creative ability (Figure 1, a).
In
addition to the church plan design, the Nuovolo’s inventiveness is
expressed in the characteristic structural system of the dome
(accessible from the roof) and its tiled decoration of the extrados with
strong pictorial value. The use of this kind of roof tiles is a very
common practice in the seventeenth century, evidence of Spanish
influences in the Neapolitan context. In fact, it should be considered
that majolica is an ancient craft that was developed along with the
Middle Ages by Muslims and Christians in Spain, and later exported to
Italy. In addition, the considerable elevation of the horizontal plane
which it lies makes this dome one of the most impressive and attractive
on the Neapolitan landscape (3(3) Nicolella, D. (1997). Le cupole di Napoli. Edizioni Scientifiche italiane spa.
). These peculiarities let the dome hire a double role of reference, spiritual and visual (Figure 1, b-c).
The double shell dome of Santa Maria della Sanità
(which can be inspected inside) recalls the masterful example made by
Filippo Brunelleschi (1377-1446) in Florence in the Church of Santa Maria del Fiore (Fig. 2, a),
where the architect, rather than referring to the single-shell Roman
construction method, or the medieval one with the use of ribs, decides
to raise the dome without centering, devising a new technique based on
calculation and balancing it with a self-supporting double shell system,
by means of a frame of vertical and horizontal elements (the main ones
visible on the outside). Furthermore, for a better stability, he uses
various precautions, among which, bricks in a herringbone pattern (4(4) Vasari, M. G. (1568). Le vite de’ più eccellenti pittori, scultori e architettori (pp. 308-311). Firenze.
).
Even if their similar conceptual and structural genesis, the dome of Santa Maria della Sanità presents dimensional and geometric differences compared to Santa Maria del Fiore. The Neapolitan dome is smaller than Brunelleschi’s one and the space in the cavity between the two caps (about 1,5 m) does not allow rapid use of the space. In geometric terms, however, the dome of Santa Maria della Sanità is not set on an octagonal drum but a cylindrical one. This last feature is analogous to the dome of the San Pietro Church in Rome designed by Michelangelo (1475-1564) (Figure 2, b), from whose drum protruding double columns alternating to the windows empty spaces, with a remarkable plastic value. In Santa Maria della Sanità, the double-columns are replaced by buttresses which, although interrupted by the large overhanging cornice of the drum, continue its path also on the dome extrados.
Up to now, that of Santa Maria della Sanità seems to be the first example of a double shell dome in the city of Naples, unless future discoveries (5(5) Minervini, M. T. (2013). Il restauro della cupola maiolicata di Santa Maria della Sanità. Napoli: M. D’Auria Editore.
).
Chosen as a case study for all these peculiarities, through numerous
inspections and the direct architectural survey, it was possible to
carry out a geometric analysis on the dome spatial configuration and the
tiled design decoration, as well as a stability study.
2. THE DOME ARCHITECTURE
⌅The dome of Santa Maria della Sanità
has a circular base. Leaning on four pillars placed at the square
vertices, the connection between the dome impost floor and the square in
which it is inscribed consists of four pendentives. To ensure greater
momentum, the dome rests on a cylindrical windowed drum. The intrados of
the dome is a composed vault, consisting of a simple vault generated by
the rotation around the vertical axis of a curve and intersected by
eight nails located above the windows (6-7(6) Migliari, R. (2009). Geometria descrittiva. Metodi e costruzioni. Milano: CittàStudi.
(7) Migliari, R. (2003). Geometria dei modelli. Rappresentazione grafica e informatica per l’architettura e per il design. Roma: Kappa Edizioni.
). The keystone of the dome is replaced by a hole (opaion) surmounted by a lantern with a hemispherical cap.
Access to the dome can be gained consisting in a small spiral staircase that, carved into a side pillar of the church, leads to the dome’s impost floor. Through a cylindrical tunnel in the drum, one its cavity. The space between the double shells is not equidistant from each other, and walls connect them. A ladder has been created in the cavity which, leaning against the intrados line, leads to the base of the lantern. The intrados of the dome has eight-ribs radial design with a decorative and structural role. Eight masonry walls connect the two shells in continuity of the inner ribs.
The extrados of the dome is a
simple vault generated by the rotation of the curve around the vertical
axis and on the outside, it has a radial tiling system with eight green
ribs. Both the dome and the small dome (cupolino) have a
two-color tiled pattern (yellow and green). The chromatic alternation of
the tiles gives a rhomboid pattern. In the drum there are volute
buttresses, originally double and then joined with an alternating rhythm
(apparently for stability needs). Finally, the lantern is the logical
conclusion of the dome, with the same structures below synthetic
aesthetic, in which the eight ribs are occupied by as many coupled
arches, support the final dome and represent the point of maximum gaze
of the observer (8(8) Rossi, A. (2014). The ethos suggested by landscape markers: the tiled dome. Domes and cupolas, an International Journal for Architecture, Engineering, conservation and Culture, vol. 1, n. 1. 2014, p. 85-91. Firenze: Angelo Pontecorboli editore.
).
2.1. The survey methodology
⌅The survey of the dome of Santa Maria della Sanità
(by Pasquale Galdiero and scientifically coordinated by Ornella
Zerlenga and the writer) was carried out both with direct methodology
using Laser rangefinder, and with photographic adjustment at the survey
campaign level. This latter was edited by Igor Todisco, who remotely
supported the dome graphic restitution especially in the presence of
physical obstacles to data acquisition (9(9) Docci, M., Maestri, D.: Il rilevamento architettonico. Storia, metodi e disegno. Laterza, Roma-Bari (1984).
).
The choice to adopt a direct survey methodology is given -despite the
good physical accessibility to the architectural artefact- by the
presence narrow, cramped and dimly lit spaces that would not have
guaranteed the transport and/or the use of advanced instrumentation,
especially in the area between the double shell that barely contained an
operator in its interior in complete safety.
Therefore, the direct survey methodology used required a fundamental critical process of designing horizontal and vertical cross-section planes from which to extrapolate the metric information. The data return took place in the form of planimetric and elevation representations, that allowed a graphic visualization of the various altimetric levels of which the dome is composed (Figure 3).
Then, this survey documentation provided
subsequent thematizations for the realization of 3D geometric models
through the dome configurative and geometric-spatial genesis definition (Figures 4-5) (10-11(10) Giordano, A. (1999). Cupole, volte e altre superfici. La genesi e la forma. Torino: UTET.
(11) Spallone, R. (2019). Geometry of vaulted system in the treatises by Guarino Guarini. EGE - Revista de Expresión Gráfica en la Edificación, n. 11, 2019. ISSN: 2605-082X https://doi.org/10.4995/ege.2019.12872
). Finally, a geometric study of the ornamental
design of the tile roofing system covering the extrados of the dome was
conducted (figure 6).
In this sense, the survey and three-dimensional modeling with a
feedback operation with the existing iconographic documentation allowed
to constantly monitor the results and integrate the methodologies of
knowledge between tradition and innovation (11(11) Spallone, R. (2019). Geometry of vaulted system in the treatises by Guarino Guarini. EGE - Revista de Expresión Gráfica en la Edificación, n. 11, 2019. ISSN: 2605-082X https://doi.org/10.4995/ege.2019.12872
).
2.2. Graphical analysis, 3D modeling and tiled pattern of the dome
⌅The graphical analysis and three-dimensional modeling of the dome of Santa Maria della Sanità enabled us to represent the intrados and extrados geometric-configurative matrices (Figure 4, a-d) and give a synthesis of spatial visualization (12-13(12) De Rubertis, R. editor: Dossier rilievo. XY dimensioni del disegno. 17-18-19 (1993).
(13)
Zerlenga, O., Cirillo, V. (2018). Curves and Surfaces in the churches
with ovate plant in Naples. geometric analogies and differences. In L.
Cocchiarella (Ed.), ICGG 2018- Proceedings of the 18th International Conference on Geometry and Graphics. Vol. 809, pp. 514-525, BERLIN: Springer.
).
The dome geometric configuration is regulated by a symmetry of order
eight; therefore, the 3D modeling (for intrados and extrados) was done
by iterating the base module eight times (Figure 4, a, b).
In particular, the intrados base module was configured according to the
dome model with eight ribs and eight nails. Instead, the extrados base
module was configured according to the dome model with eight double ribs
(Fig. 4, c, d).
The 3D view of the dome was made by completing the model with the
addition of the drum on which the dome lies, and the lantern, which
stands on the opaion.
The geometric model of the drum is a straight cylinder with a circular base in which eight windows are placed. The large windows are interspersed with buttresses, simple and double (alternated), to which eight twin ribs correspond to the extrados of the dome. The lantern is also geometrically regulated by a radial symmetry of order eight. Therefore, the dome three-dimensional model was made by iterating eight times the base module (drum, dome, lantern), bearing in mind the alternation of buttresses placed at the height of the drum (Figure 5).
Of
great geometric interest is the ornamental solution to the dome
extrados obtained by the application of majolica tiles in the
characteristic Neapolitan yellow and green colors (14(14) Capone, M., Lanzara, E. (2019). 3D data interpretation using treatises geometric rules to built coffered domes. ISPRS. Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., Vol. XLII-2/W15, pp. 231 - 238.
).
The roof tiles used have an elongated shape along the vertical axis and
end in the lower part with a semi-circumference. Specifically, from the
roof tiles architectural survey it appears that the vertical
measurement corresponds to 30 cm while the width to 20 cm. To be fixed
with nails on the dome mantle, the roof tiles have a small hole along
the vertical axis (Figure 6, a).
From the geometrical point of view, the roof tiles installation is
regulated by a rectangular grid where the rows of tiles along the
horizontal direction are alternately arranged (Figure 6, b) (15(15) Penta, I. (1999). Gli embrici maiolicati. In A. Baculo, A., di Luggo, A. e Florio, R. (Eds.), Napoli versus coelum. La città e le sue cupole. Napoli: Electa.
).
From the ornamental point of view, the roof tiles returned a rhomboid
pattern obtained with the use of yellow and green colors.
From the geometric point of view, this ornamental design is obtained by superimposing another rhomboid grid on the rectangular ones (Figure 6, c). This rhomboid grid allows the identification of the directions in which the yellow tiles are placed and the consequent fields in which to collocate the green tiles (Figure 6, d). In this sense, the set of the two ordering grids (rectangular and rhomboid) perceptually returns an aggregation of tiles characterized by yellow ochre, for the tiles arranged along the perimeter of the rhombuses and by the green “ramina” for those placed in the rhombuses center (Figure 6, e). This geometric arrangement adapted to the dome extrados follows the radial sectors course and therefore in the dome planimetric and altimetric development it is progressively reduced towards the lantern.
3. STRUCTURAL STUDIES
⌅3.1. Limit state analysis of masonry
⌅In
this research work, the limit state analysis of masonry has been
applied. This theory was originally introduced for the evaluation of the
collapse load of elastic-perfectly-plastic structures with unlimited
ductility, such as those made of steel, and later extended to the study
of the behavior of masonry constructions, as has already been
demonstrated by Kooharian (17(17) Kooharian, A. (1952). Limit analysis of voussoir (segmental) and concrete arches. Journal of the American Concrete Institute, 24(4).
) and Heyman (18(18) Heyman, J. (1966). The stone skeleton. International Journal of Solids and Structures, 2(2), 249-279.
).
As
known, the basic criteria for the analysis of a masonry structures
concern the material properties. Masonry construction is built with a
material that fulfills three conditions. Firstly, it works in
compression: the tensions are very low and this implies the possibility
to assume that the compressive strength is infinite. In almost all
cases, there is no problem with the compressive strength of the
material. Secondly, the tensile strength is zero, and this is in favor
of security whereas there is always a certain adherence to the mortar.
Finally, no sliding occurs. Under these conditions, the material is
standard, and the principles of Limit Analysis can be demonstrated for
masonry (18(18) Heyman, J. (1966). The stone skeleton. International Journal of Solids and Structures, 2(2), 249-279.
).
The hypotheses made, allow schematizing the masonry construction as a
set of rigid and mono-dimensional blocks held together by compressive
forces. According to this approach, the collapse occurs for the
formation of non-dissipative hinges. When the number of hinges is high
enough to convert the structure into a mechanism, the collapse takes
place.
Since the Church dome of Santa Maria della Sanità is a masonry structure, the three key assumptions on material properties of no tensile strength (i), infinite compressive strength (ii), no yield through sliding (iii) formulated by Heyman (18(18) Heyman, J. (1966). The stone skeleton. International Journal of Solids and Structures, 2(2), 249-279.
)
for the simply voussoir arch, but applicable to any masonry structural
forms, have been taken into account. By applying the Safe Theorem,
static graphical analysis has been carried out in the point 4.
3.2. Dome behavior and graphic statics
⌅A
dome is a three-dimensional element of revolution obtained by rotating a
semi-arch around an axis, although octagonal domes also exist. Any
complex shapes can be studied starting from the behavior of the arch. In
fact, a dome, however complex it may be, can always be traced back to
as a set of arches. It can be studied with the slicing technique, a
quite ancient method that consists in imagining the dome cut for
meridian planes: every two-sliced obtained, form an arch that rests on a
common key. For the Safe Theorem, if a thrust line fits within the
thickness of the structure, the arch is stable and the dome will be too (19-20(19) Huerta, S. (2008). The analysis of masonry architecture: A historical approach. Architectural Science Review, 51(4), 297-328.
(20) Huerta, S. (2004). Arcos bóvedas y cúpulas. Geometría y equilibrio en el cálculo tradicional de estructuras de fábrica. Madrid: Instituto Juan de Herrera.
).
The
thrust line theory and graphic statics arrived during the 19th c.
Graphic statics supplies a practical method to assess the stability of
ancient constructions, and it systematically based on the catenary
principle introduced by Robert Hooke in 1676. Hooke’s inversion law
stating that “as hangs the flexible line, so but inverted, will stand
the rigid arch” refers to the ideal shape of a stone arch whose
equilibrium is that of the inverted catenary curve traced by a chain
subjected to the same weight distribution (21(21)
Cennamo, C., Cusano, C. & Guerriero, L. (2017). The slicing
technique for the evaluation of the formal efficiency: a comparative
study. In Proceedings of the XXIII Conference of the Italian Association of Theoretical and Applied Mechanics (pp. 1500-1511). Mediglia (MI): Gechi Edizioni, Salerno.
).
In other words, the idea is that if something hangs under a certain
loading condition under pure tension, if you only look at static
equilibrium, you can flip this geometry and this geometry will be in
perfect compression (22(22)
Roca, P., Cervera, M., Gariup, G., & Pela, L. 2010. Structural
Analysis of Masonry Historical Constructions. Classical and Advanced
Approaches. Archives of Computational Methods in Engineering, 17(3), 299-325.
). This paragraph quotes Figure 7, shown on the right.
).
This is a very important concept. You could explain the stability of a masonry structure by making hanging models, as ancient architects and engineers did. Alternatively, more simply, by using graphic statics as a paper version of hanging models. Diagrams using force vectors and closed force polygons represent nothing more than the equilibrium in a hanging system (Figure 8).
). Graphical design of the retaining walls of the Parque Güell in Barcelona (25(25) Rubió i Bellver, J. (1912). Conferencia acerca de l0s conceptos orgánicos, mecánicos y constructivos de la Catedral de Mallorca. Anuario de la Asociación de Arquitectos de Catalunia (pp.87-140).
).
Equilibrium in a masonry arch, and thus of a dome, can be visualized using a line of thrust, the trajectory of the resultant of the compressive forces within the structure. This line is nothing but the inverted catenary.
4. STABILITY ANALYSIS
⌅4.1. Assumptions on the geometrical parameters used and on the applied loads
⌅Geometry
is the most important factor in determining the structural behavior of a
dome. Stability methods consider only the geometry of the structure,
and feasibility is assessed based on conditions of equilibrium; material
failure is not considered (26(26) Huerta, S. (2006). Structural Design in the Work of Gaudí. Architectural Science Review, (49)4.
).
The main dome of the Church is a double-shelled dome that spans approximately 16.42m, with a rise of 9.41m from the dome base. This structural analysis assumes that the dome is simply supported on the vertical cylinder wall of the drum, whose continuous support is only provided in the vertical direction with no transfer of bending forces. The internal radius of the outer shell, a, measures 8.21m while the radius of the inner shell, b, measures 6.93m. The thickness of the external shell is 0.40m, constant for all the section, and the thickness of the internal shell grows from 0.40m at the springing to about 1.30m to the crown. Figure 9 and Table 1 show the main parameters for the dome.
| Dome geometry | ||
|---|---|---|
| Parameter | Value | Symbol |
| Span (m) | 16,42 | |
| Rise (m) | 9,41 | |
| Outer shell | ||
| Dome radius (m) | 8,21 | a |
| Dome thickness (m) | 0,40 | to |
| Skylight radius (m) | 1,85 | ro |
| Radius to thickness ratio | 20,5 | a/ to |
| Inner shell | ||
| Dome radius (m) | 6,93 | b |
| Dome thickness (m) | 0,90-1,40 | ti |
| Skylight radius (m) | 1,10 | ri |
| Diameter (m) | 13,85 | di |
| Lantern | ||
| Diameter (m) | 2,7 | dl |
| Elevation (m) | 7,87 | Hl |
| Lantern thickness (m) | 0,26 | tl |
Figure 10 shows the studies on the geometry of the dome, which have been conducted to determine the shape and curvature of both outer and inner shells.
Once identified the geometry, a preliminary structural analysis of the dome has been performed to assess its stability. The structure has been disassembled by elements whose weight has been individually calculated. On this basis, the dome has been sliced into spherical sectors having an angle of 45º in plan, and a generic cross-section of the structure has been studied.
Each slice obtained has been then subdivided into 6 ideal voussoirs to discretize the calculation of the load due to self-weight, to estimate the final thrust of the dome transmitted to the supports, and to define the possible trajectories of the pressure line inside the masonry. A specific weight of the masonry equal to 17 kN/m3 has been considered.
Firstly, the weight of the lantern has been calculated taking into account that the lantern is composed of 8 windows and that it mostly stands on the inner shell; only the volute buttresses of the lantern rest on the outer shell. The estimated total weight of the lantern is equal to Wltot = 334.22 kN and the weight of the lantern buttresses is equal to Wlb = 76,16 kN.
Secondly, the weight of the 8 masonry walls pierced by windows that connect the two shells has been calculated, obtaining a value equal to Wp = 720,08 kN.
Subsequently, the weight of the dome has been calculated as follows. The weight of the outer shell estimated taking into account the own weight of the structure, the tiled covering and the contribution of the lantern buttresses is equal to Wetot = 2961,14 kN (Figure 11, a). The weight of the inner shell calculated considering the weight of the lantern and the weight of masonry partitions is equal to Witot = 3734,06 kN (Figure 11, b). Summing the two values, the total weight of the dome equals to Wtot = 6695,20 kN (Figure 11, c) is obtained. Figure 11 shows the graphical computation of the total weight of the dome with lantern. Notice that only the self-weight has been considered in the analysis.
4.2. Thrust of the dome
⌅This section focuses on calculating the total thrust of the dome from the slicing method while the next section centers on checking the stability of the abutments.
Based on the slicing illustrated in Figure 11c, for each of the voussoirs the area and the horizontal distance to the symmetry axis have been determined.
Considering the weights of the voussoirs on the entire surface of revolution, the value obtained for the horizontal thrust is H = 1987.60 kN. At the base of the dome, the vertical reaction, calculated directly from the weight of the dome equals to V = 6695.20 kN.
From the application of the loads to their vector graphic expression it has been observed that the thrust line is contained within the masonry (Figure 12), and the dome is stable, as postulated by the Fundamental Theorem of the Limit Analysis (Safe Theorem).
The power of this Theorem is that the thrust line, namely the equilibrium condition, can be freely chosen. In fact, considering that the line of thrust is nothing else than the graphical representation of the equilibrium equations, the structural analysis via graphic statics illustrated in Figure 12, represents one of the possible equilibrium states in compression for the dome.
4.3. Safety assessment of the dome-buttress system
⌅The support system of the dome consists of the drum that stands on a circular base and of the four central pillars of the Greek cross plan of the Church, sustaining the tambour.
After obtaining the thrust values of the dome, the horizontal (H) and vertical (V) components have been applied to the support system. The thrust dome combines with the total weight of the drum and the abutment. On the basis of the thrust values and weights shown in Figure 13a, by using the overturning moment, the distance d of the reaction X from the wall boundary is calculated. Table 2 below shows, in the summary, the computation of the loads and thrusts in the analysis of the dome-buttress system.
| weight [kN] | Xgi [m] | Wi· xgi [kNm] | d [m] | xg [m] | s.c.s. | |
|---|---|---|---|---|---|---|
| W8 | 1575,73 | |||||
| W9 | 5698,74 | |||||
| Wc | 29097,88 | 2,31 | 86985,54 | |||
| Wb | 1285,20 | 4,14 | 6885,65 | |||
| Wd | 17436,43 | 5,59 | 126137,18 | |||
| dome | 6695,20 | 5,58 | 58275,68 | |||
| X | 54514,71 | |||||
| sum | 278284,05 | |||||
| 3,92 | ||||||
| H | 1987,60 | 34,13 | 105707,44 | |||
| xd | 172576,62 | 2,56 | ||||
| s.c.s. | 2,88 |
The analysis carried out graphically in Figure 13b shows that the diaphragm of the support system conveniently provides the necessary counterweight. A geometric safety coefficient of the structure equals 2,88 is obtained.
The analysis carried out shows
that the structure is stable and that the geometric safety coefficient
calculated is a good value for these kinds of constructions (27(27)
Ferrero, C., Cusano, C., Dell’Endice, A., Yavuzer, M. N., Wu, Y. X.
& Iannuzzo, A. (2020). When cracks are (not) a structural concern:
the case study of “Giovanni Vinciguerra” school in Anagni. In:
Proceedings of the SAHC Symposium, Barcelona.
). Even
if the geometry of the dome is peculiar, the global equilibrium is
guarantee. Although at this stage, the role and the behavior of the
internal walls have not been studied.
As already explained above,
only the stability of the dome has been evaluated, and no vulnerability
analysis of the dome has been performed, on which topic two of the
authors have provided relevant scientific contributions (28-31(28)
Cennamo, C., Cusano, C. & Angelillo, M. (2019). A limit analysis
approach for masonry domes: the basilica of San Francesco di Paola in
Naples. International Journal of Masonry Research and Innovation, 4,227-242.
(29) Cennamo, C., Cusano, C. & Angelillo, M. (2019). Stability Analysis and Seismic Vulnerability of Large Masonry Domes. MI - Masonry International, (32)2.
(30) Cennamo, C., Cusano, C. & Angelillo, M. (2018). Seismic vulnerability of domes: a case study. Journal Of Mechanics of Materials and Structures, 13,679-689.
(31)
Cennamo, C., Cusano, C., Angelillo, M. & Fortunato, A. (2018). A
study on form and seismic vulnerability of the Dome of San Francesco di
Paola in Naples. Ingegneria Sismica, 35, 88-108.
).
5. CONCLUSIONS
⌅The geometric analysis carried out on the architectural survey of the church of Santa Maria della Sanità dome in Naples allowed a study on its spatial configuration, majolica tiles decoration and stability1This contribution is the result of a multidisciplinary team. The chapter 1 was written by Ornella Zerlenga; the chapter 2 by Vincenzo Cirillo; the chapters 3 and 4 by Claudia Cennamo and Concetta Cusano. The conclusions were written by Ornella Zerlenga and Claudia Cennamo..
Regarding the geometric analysis, the dome, a surface of revolution, has the following characteristics: different curvature for the intrados and extrados, the structure is regulated by a symmetry of order eight; the double bands of ribs delimit eight surfaces sectors. The distribution of modular roof tiles requires a support distribution network consisting of two groups of curves which are mutually orthogonal; the roof tiles ornamental design is an adaptation of prefabricated modules.
From the structural studies illustrated to point 3 and from the analysis performed to point 4, some remarks can be outlined.
Safety in masonry constructions is a matter of geometry (32(32) Huerta, S. (2013). Ethics and materials: Some Spanish Case Studies. Déontologie de la pierre. Stratégies d’intervention pour la cathédrale de Lausanne. Lausanne.
).
As deeply discussed, the material imposes that the thrust line, namely
the locus of the position of the resultant of the compressive forces,
must be contained within the thickness of the structure as it appears.
The
equilibrium approach, which comes directly from the Safe Theorem of
Limit Analysis, has demonstrated to be the most adequate for the
analysis of masonry structures (33(33) Huerta, S. (2008). The analysis of masonry architecture: A historical approach. Architectural Science Review, 51(4), 297.
),
also considering that the geometrical design of such ancient buildings
embeds rules used by old master builders over centuries. Some of the
authors emphasized the importance of the use of compressive thrust line
analysis, via graphic statics, to explore the range of possible
equilibrium states both for 2d and 3D structures (34-39(34) Cennamo, C. & Cusano, C. (2018). The gothic arcade of Santa Maria Incoronata in Naples. Equilibrium of gothic arches. International Journal of Masonry Research and Innovation, 3,92-107.
(35)
Cennamo, C., Cusano, C., & Di Santo, D. (2019). Stability of the
Abbey of San Lorenzo ad Septimum cloister in Aversa. In Carmine
Gambardella (ed), Proceedings of the XVII International Forum Le vie dei Mercanti, Architecture, Heritage and Design. World Heritage and Legacy. Rome: Gangemi Editor International Publishing.
(36)
Cennamo, C., Cusano, C., & Angelillo, M. (2018). On the statics of
large domes: a static and kinematic approach for San Francesco di Paola
in Naples. In Proceedings of the British Masonry Society (pp. 504-517). Milan: The International Masonry Society (IMS).
(37)
Cennamo, C., Cusano, C., & Angelillo, M. (2017). The Neoclassical
Dome of San Francesco di Paola in Naples. A study on form and stability.
In Proceedings of the XXIII Conference of the Italian Association of Theoretical and Applied Mechanics (pp. 1500-1511). Mediglia (MI): Gechi Edizioni, Salerno.
(38)
Fuentes González, P., Huerta, S. (2016). Geometry, Construction and
Structural Analysis of the Crossed-Arch Vault of the Chapel of
Villaviciosa, in the Mosque of Córdoba. International Journal of Architectural Heritage, 10(5):150506103629008.
(39)
Huerta, S., Fuentes González, P. (2010). Analysis and Demolition of
Some Vaults of the Church of La Peregrina in Sahagun (Spain). Advanced Materials Research, 133-134.
).
This
work contributes, on the one hand, to explore unsolved matters
concerning the examined case study of the Neapolitan dome of Santa Maria della Sanità.
On the other hand, from a wider perspective, it provides an even more
important contribution to a potential way of approaching the study of
historical constructions (40(40)
López Manzanares, G. (1998). Estabilidad y construcción de cúpulas de
fábrica: el nacimiento de la teoría y su relación con la práctica, Tesis
Doctoral, ETS de Arquitectura, Universidad Politécnica de Madrid.
).
Therefore, in conclusion, a multidisciplinary approach that includes
in-depth studies on the geometry and construction aspects of historical
buildings is a topic of great relevance when dealing with architectural
heritage (41(41) Cennamo, C. & Di Fiore, M. (2013). Best practice of structural retrofit: the SS. Rosario Church in Gesualdo, Italy. International Journal of Disaster Resilience in the Built Environment, (4)2,215-235.
), both to assess its stability and to prevent inappropriate or, in most cases, unnecessary interventions.