Graphic Methodology in Structural Analysis of Historical Constructions. Application to Structural Behavior of the Domes’ Backfill

Abstract

This paper presents a graphic methodology for structural analysis of domes and other surfaces of revolution, based on the combined use of funicular and projective geometry. The dome is considered as a network of lines of latitude and longitude, and the equilibrium of this network is analyzed in both horizontal and vertical projection. The equilibrium in the vertical plane is assured by fitting the weight forces polygon to the polar rays, so the dome geometry is a closed antifunicular polygon of the force system. The equilibrium in the horizontal plane is assured by considering the values of the hoop forces in the dual figure, where they form a closed polygon. The new methodology is presented through its application to a hemispherical brick dome of small thickness, considering three structural situations, hemisphere complete, hemisphere with oculus, and hemisphere with lantern; considering different slopes of support reaction; and considering different hypotheses regarding the structural behavior of the haunch filling, in accordance with its morphological characterization. Finally, the minimum thickness required to cancel the tension forces in the dome, is calculated.