6. Conclusion. The origin of the catenary arch in Spain

The assessment of some drawings of gunpowder warehouses, found in the collection of Mapas planos y Dibujos (MPD) of the General Archive of Simancas (Archivo General de Simancas, AGS) (AGS 2014), has revealed the use of the chain theory in Miguel Marín's projects for Barcelona (1731) and Tortosa (1733) and Juan de la Feriére ones in A Coruña (1736). A built evidence has also been found: the Carlón wine cellars in Benicarló, built by the O'Connors family from Ireland (1757). The analysis of these examples proved the theory of the chain arrival to Spain during the first half of the eighteenth century. However, 50 years before Antoni Gaudí, Catholic families emigrating from Scotland and Ireland already initiated some of the catenary's form mathematical theory in some practical uses, a theory that begun to be taught at the Mathematics Academy of Barcelona in 1720.

This paper addresses the introduction of the concept of the catenary arch in Spain before the nineteenth century. After an exhaustive review of the theoretical framework, some cases are assessed. The aim of the research is to find out if the mechanical concept of the chain was used by the Spanish military engineers and by the exiled English engineers, who built several wine cellars in Spain. Thus, we intend to determine whether there is any geometrical relationship between the layout of several gunpowder magazines made by Spanish military engineers in the 1730s and the construction of a civil building—the Carlón wine cellar in Benicarló (1757)—in which catenary arches may have been used.

The assessments of the gunpowder warehouses by Miguel Marín for Barcelona (1731) and Tortosa (1733) and by Juan de la Feriére y Valentín in A Coruña (1736) are only a mere 4.05% of the projects analysed. However, they prove the intention to lay out the vault as a catenary. These authors knew that in a catenary the tensility in the shape of a hanging chain has the same compression values in the inverted geometrical figure. These engineers had a vast knowledge of the mechanical principles of the modern theory for masonry. From a scientific perspective, catenary vaults are the most interesting because they introduce the principles established by Hooke (1676). Both the arches of gunpowder magazines and the arches a(2–8) of Benicarló were laid out using the geometrical construction of an oval. Otherwise, the location of the horizontal axis of the ovals under the springline reveals the application of one of the characteristics of the catenary. This causes that the vertical line which is tangent to the curve in the springing does not form a right angle with the horizontal, so they used the chain's theory in the layout of the projects.

Formally, if the distance between the axes and the springline of the arch is small, then the angle of incidence has a minimum influence on the thrust and the line of pressure. Otherwise, the location of the axis under the springline reveals the intention to minimize stresses in this point and in the neighbouring areas, even though the final mechanical influence is small.

Although there is no evidence of the construction of the gunpowder warehouses, it is possible to confirm the use of catenary arches in the construction of the Carlón cellars of the O'Connor in Benicarló (1757). There are significant differences between the measures of the arches of the gunpowder magazines (maximum span: 22 feet; maximum rise: 14 feet) and the arches of the Benicarló cellar (span: 30 feet; rise: between 17 and 18 "toise" feet, until the springline). In addition, the span-to-rise ratio

Thus, arch a1 resembles a catenary arch, whereas the other seven arches a2–<sup>8</sup> tend to be ellipses. These seven arches do not have a vertical tangent on the springline because their horizontal axis has been moved 1 foot below the arch's springline. As defined by Frézier (1738), the shape of the catenary has the following essential property: the vertical line which is tangent to the curve at the springline does not form a right angle with the horizontal plane. Therefore, geometrically, the catenary can be understood as any curve that does not have a vertical tangent at its springline. This is what happens in the springline of St. Paul's dome in London [11], which was designed by Christopher Wren in collaboration with Robert Hooke [46]. Otherwise, it should be noted that from a mechanical perspective, catenary arches are an optimal solution to build masonry arches, since the material has very low

Finally, from the construction point of view, the catenary shape can be approximated using other geometric forms such as ovals or ellipses, under the condition that there is not a vertical tangent at the springline. The catenary shape forms a barycentric axis, which minimizes the tensions on a linear element that is subject to only vertical loads. In the arch, the inverted catenary shape prevents the appearance

Thus, there are two hypotheses regarding the construction of the wine cellar. The first one is that the construction work was started from the inside toward the façade; thus, arches a(2–8) were constructed before the catenary arch a1. The second hypothesis is that the construction work began with arch a1. According to the second hypothesis, there is also a difference between both types of arches: on the first brick courses from the springline of arch a1 (the first 9 courses on 1 side and the

tensile strength.

Military Engineering

Figure 21.

50

Springing of arches no. 1 and no. 2 in the O'Connor cellar.

of stresses other than compression stresses.

of the oval arches in the gunpowder magazine studies is [1.39:1.57], whereas in Benicarló, this ratio is [1.67:1.76]. It can be concluded that arch a1 is a catenary arch, whereas arches a(2–8) tend to be elliptical. Arches a(2–8) show the special feature that their (x) axis is located below the springline; therefore, the tangent of the curve on the springline does not form a right angle with the horizontal. This is a feature of the definition of the catenary.

References

329-342

523-558

1900. pp. 37-48

pp. 137-145

53

1848. pp. 472-477

[1] Huerta S. Structural design in the work of Gaudí. Architectural Science

DOI: http://dx.doi.org/10.5772/intechopen.87060

Scientific Knowledge of Spanish Military Engineers in the Seventeenth Century

Instruments. London: Printed by T.R.

Proceedings of the First International Congress on Construction History. Madrid: Instituto Juan de Herrera; 2003.

[12] Stevin S. Het Eerste Bovck van de Beghinselen der weegcons. In: De Beghinselen der Weeghconst. Beschreven duer Simon Stevin van Brugghe. Leyden: Inde Druckerye van Cristoffel Plantijn, By Françoys van

[13] Bernoulli J. Analysis problematic antehac propositi de inventions lineae descensus a copore gravi percurrendae

[14] Bernoulli J. Solutio problematis funicaularii. Actae Eruditorum. 1691;

[15] Huygens C. Dynastae Zulichemii, solutio problematis funicularii. Actae Eruditorum. 1691; Mensis Junii:

[16] Gregory D. Catenaria. Philosophical Transactions of the Royal Society. 1697;

[17] Stirling J. Lineae Tertii Ordinis Neutonianae. Oxonia: Whistler; 1717.

[18] Poleni G. Memorie istoriche della Gran Cupola del Tempio Vaticano. Padua: Stamperia del Seminario; 1748.

[19] Heyman J. Poleni's problema. Proceedings of the Institution of Civil

Engineers. 1988;84:737-759

uniformiter, sic ut temporibus aequalibus aequales altitudines emetiaatur. Actae Eruditorum. 1690;

Mensis Maji: pp. 217-219

Mensis Junii: pp. 274-276

pp. 281-282

19:637-652

pp. 11-14

pp. 30-50

Raphelinghen. 1586. p. 41

for John Martyn; 1676. p. 31

pp. 1-11

[11] Heyman J. Wren, Hooke and Partners. In: Huerta S, editor.

[2] Llorens JI. Wine cathedrals: Making the most of masonry. Proceedings of the

Review. 20004;49:324-339

Institution of Civil Engineers: Construction Materials. 2013;166:

[3] Martinell C. Gaudí i la Sagrada Familia comentada per ell mateix. Barcelona: Ayamà; 1951. p. 29

de Catalunya. 2002. p. 120

[5] Alsina C, Serrano G. Gaudí, Geometricamente. Gaceta de la Real Sociedad Matemática Española. 2002;5:

[4] Lacuesta R. Gaudi a través de Cèsar Martinell, la relación personal entre Antoni Gaudí i Cèsar Martinell. In: VV AA, editor. Els arquitectes de Gaudí Barcelona: Collegi Oficial d'Arquitectes

[6] Domenech J. La fábrica del ladrillo en la construcción catalana. Anuario de la Asociación de Arquitecto de Cataluña.

[7] Rondelet JB. Traité théorique et pratique de l'art de bâtir, V2. Paris: Chez l'auteur, en clos du Panthéon. 1804.

[8] Millintong J. Elementos de

[9] Graus R, Martín-Nieva H. The beauty of a beam: The continuity of Joan Torra's beam of equal strength in the work of his disciples-Guastavino. Gaudi and Jujol International Journal of Architectural Heritage. 2013;9:341-351

[10] Hooke R. A Description of Helioscopes, and Some Other

Arquitectura, escritos en ingles por John Millington,V2. Madrid: Imprenta Real;

The theory of the equilibrium curve, followed by most of the British engineers, became known to the Bourbon military engineers through the academy of mathematics in the eighteenth century, and it was used by some immigrants of English origin, such as the O'Connors, a century before the modernist architecture of Antoni Gaudí.
