Latest revision as of 14:48, 30 November 2021

Abstract

This paper presents a graphic methodology for the structural analysis of domes and other surfaces of revolution, based on a combined use of funicular and projective geometry. By considering a dome as a network of lines of latitude and longitude, the equilibrium of the network is analyzed in both horizontal and vertical projection. The resulting dual configuration is also a spatial system that can be considered by its projection in a horizontal and a vertical plane. The dome is divided by latitude and longitude into an arbitrary number of sectors, and the equilibrium is enforced at each node. The tangential forces can be considered for their net effect at each node; the net effect of two tangential forces, equal in magnitude, at a node is a radially directed force in the plane of the line of latitude, acting outwards (compression) or inwards (tension). Considering their horizontal projection, and its dual form, it is possible to choose the shape of the radial force diagram (the vertical projection and the force diagram), and identify the radial forces associated with it, and thus the tangential forces. The new methodology is presented through its application to a hemispherical brick dome of small thickness. The hemispherical brick dome has been also analyzed by applying the slicing technique, considering different hypotheses regarding the structural behavior of the haunch filling, according to its morphological characterization. The structural analysis of the brick dome using both methodologies allows us to contrast the results obtained.

Full document

References

[1] Suarez Medina, F.J, Bravo Pareja, R., González Casares, J. A., Structural and Constructive Analysis of a Faux Vault, the Dome of San Juan de Dios Church, in Granada (SPAIN). International Journal of Architectural Heritage. (2019). https://doi.org/10.1080/15583058.2019.1645242.

[2] Bouguer, P., Sur les lignes courbes qui sont propres à former les voûtes en dôme. Mémoires de l'Académie Royale de Sciences de Paris, (1734), 149-66.

[3] Frézier, A. F., La théorie et la pratique de la coupe des pierres et des bois, pour la construction des voûtes... ou Traité de stéréotomie à l'usage de l'architecture (Vol.1). JeanDaniel Doulsseker. (1737).

[4] Le Seur, T., Jacquier, F., & Boscovich, R. G. Parere di Tre Matematici Sopra i danni, che si sono trovati nella cupola di San Pietro. (1742).

[5] Poleni, J. Memorie istoriche della gran cupola del tempio Vaticano e de'danni di essa e detristoramenti loro, divisi in libri 5. Nella Stamperia del seminario. (1748).

[6] Gauthey, E. M., Mémoire sur l'application des principes de la mécanique a la construction des voutes et des dômes, dans lequel on examine le problème proposé par M. Patte, relativement a la construction de la coupole de l'église Sainte-Geneviève de Paris. Par M. Gauthey de l'imprimerie de louis-Nicolas Frantin. (1771).

[7] Navier, C. L. M. H., Résumé des leçons données à l'école royale des Ponts et chaussées sur l'application de la mécanique à l'établissement des constructions et des machines (Vol. 1). Didot. (1826).

[8] Poncelet, J., Traité des propriétés projectives des figures, deux volumes. Bachelier, Paris, 2. (1822).

[9] Culmann, K., Die Graphische Statik, Meyer und Zeller. Zürich. (1865).

[10] Körner, C., "Gewölbte Decken." Handbuch der Architectur, Third part 2 (1901): 141-553.

[11] Rankine, W. J. M., A Manual of Applied Mechanics. Charles Griffin, London (1858).

[12] Eddy, Henry T., Research in Graphical Statics, New York, Van Nostrand. (1878).

[13] Föppl, A., Ausgewählte Capitel der mathematischen Theorie der Bauconstructionen. 1. Theorie der Gewölbe: mit vier Tafeln und vielen Holzschnitten. (1881).

[14] Dunn, W., Notes on the stress in Framed Spires and Domes. Journal of the Royal Institute of British Architects. Third Series, vol. 11; (1904). 401- 412.

[15] Dunn, W., The Principles of Dome Construction. Architectural Review. (1908). Vol 23: 63-73; 108-112.

[16] Pieper, K., Sicherung historischer Bauten. W. Ernst, (1983).

[17] Heyman, J., “On shell solutions of masonry domes”. International Journal of Solids and Structures, vol. 3, (1967), pp 227.

[18] Heyman, J., Equilibrium of shell structures. Oxford University Press, (1977).

[19] Fray Lorenzo de, S.N., Arte y uso de arquitectura, Madrid, (1639) first book; (1665) second book.

[20] Isla Mingorance, E., José de Bada y Navajas, arquitecto andaluz (1691-1755). Granada, (1977).

[21] Heyman, J., The Stone Skeleton. International Journal of Solids and Structures, 2 (2) (1966) 249-279.

[22] Heyman, J., The Stone Skeleton. Structural Engineering of Masonry Architecture, Cambridge University Press, Cambridge, (1995).

[23] Huerta Fernández, S., La mecánica de las bóvedas tabicadas en su contexto histórico: la aportación de los Guastavino, Las bóvedas de Guastavino en América, Instituto Juan de Herrera. Madrid, (1999).

[24] Redondo Martínez, E., La bóveda tabicada en España en el siglo XIX: la transformación de un sistema constructivo. (PhD Thesis). Polytechnique University of Madrid, (2013).

[25] Ramos León, J., Clasificación morfológica de los rellenos en el trasdós de bóvedas de fábrica. Informes de la Construcción, 65 (532) (2013). 471-480; https://doi.org/10.3989/ic.12.062.

[26] Block, P. & Ochsendorf, J., Thrust Network Analysis: A new methodology for threedimensional equilibrium. Journal of the international association for shell and spatial structures. Vol. 48. (2007).

[27] Huerta Fernández, S., The Mechanics of Timbrel Vaults: A Historical outline, in Essays on the History of Mechanics, ed. Becchi et al. Basel Birkhauser Verlang. (2003).

[28] Bow, R.H., Economics of construction in relation to frame structures, Spon, London, (1873).

[29] Huerta Fernández, S., Arcos, bóvedas y cúpulas. Geometría y equilibrio en el cálculo tradicional de estructuras de fábrica, Juan de Herrera Instituto, Madrid, (2004).

[30] Lourenço, P., Experimental and numerical issues in the modelling of the mechanical behavior of masonry. Structural Analysis of Historical Constructions II. Barcelona: P. Roca, J.L. González, E. Oñate and P.B. Lourenço (Eds.) CIMNE. (1998).

[31] Pluijm, V. d., Out of plane bending of masonry: behaviour and strength. doi:10.6100/IR528212. (1999).