Graphic Methodology Based on Funicular and Projective Geometry, in Structural Analysis of Historical Constructions

A graphic methodology for the structural analysis of domes and other surfaces of revolution, based in the combined use of funicular and projective geometry, is presented. It is considered a dome as a network of lines of latitude and longitude and it is analyzed the equilibrium of this network 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. The equilibrium can be enforced at each node, that is, at each intersection of latitude and longitude lines. 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). By considering their horizontal projection, and its dual form, it is possible to choose the shape of the radial force diagram (the vertical projection of 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 model of hemispherical dome analyzed has been referenced to a real dome: the hemispherical dome of brick over the transept, in Basilica of San Juan de Dios in Granada (Spain). The hemispherical brick dome has been also analyzed by applying the slicing technique in the frame of limit analysis. The structural analysis of the brick dome using both methodologies allow us the contrasting of the results obtained.