Graphical Methodology for Structural Analysis of Historical Constructions by Combined Use of Funicular and Projective Geometry

This paper presents a new graphic methodology for the structural analysis of domes and other surfaces of revolution, based on the combined use of funicular and projective geometry. The methodology is presented through its application to a hemispherical brick dome with a small thickness. The dome is considered a network of lines of latitude and longitude, and the equilibrium of this network is analyzed in both horizontal and vertical projections. To contrast the results obtained, the methodology has been applied to different structural situations whose analytical solution is known: complete hemisphere, hemisphere with oculus on the top, and hemisphere with lantern. The new methodology has also been applied to the analysis of structural situations different from the previous ones, by combining the following considerations: presence of the backfilling on the extrados of the dome, small inclinations of the reaction in the support, and small variations in the vertical position of the nodes in the simplified model considered. The tests included in the article have been selected to show all the possibilities of this methodology. Multiple solutions for the internal forces are obtained, whose equilibrium is guaranteed by this graphic methodology.