Structural Analysis of Historical Constructions by Graphic Methodologies based on Funicular and Projective Geometry

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. INTRODUCTIONThis paper presents a new graphic methodology for the structural analysis of domes and other surfaces of revolution, based on a combined use of funicular and projective geometry.