Graphical Modelling of Hoop Force Distribution for Equilibrium Analysis of Masonry Domes

Abstract

The behaviour of axisymmetric masonry shells can be simulated by a system of forces constituted by meridian forces acting in the vertical planes, and by hoop forces acting circumferentially. A crucial component for the assessment of these structures using the Modified Thrust Line Method (MTLM) is the determination of hoop forces, whose computation is strenuous, limiting the practical application of MTLM. Working around this limitation, the current research introduces a strategy to manipulate the hoop forces by graphically implementing a function describing their distribution. The adaptiveness of this distribution function not only allows the application of MTLM for the analysis of a range of geometries, but also enables the simulation of membrane behaviour, arch behaviour and their combination, for considering partially cracked structures. Taking this into account, the approach is applied in the case studies illustrated within the current research.

Limit analysis of masonry arches and domes with finite strength: funicular analysis versus stability area method

“…Eddy [23] made the first graphical analysis contribution to masonry domes, studying the equilibrium of a hemispherical dome through graphical reinterpretation of membrane theory. Lévy [39] and Wolfe [57] followed, with recent contributions revisiting these methods, including [29,50,58].…”

A Virtual Reconstruction of Gaudi’s Skyscraper Hotel Attraction Using Physics-Based Simulation

“…The resulting form is known as a catenary, which, when inverted, functions mainly through compression, eliminating bending moments (Hooke 1675;Heyman 1999;Huerta 2006a). Equilibrium in a masonry arch can be visualized using a line of thrust, which represents the path of the resultant of the compressive forces through the stone structure (Block et al 2006;Paris et al 2021). This is a rational design process in which the resulting form is a structure optimized to work under compression, and explains why stone materials with high compressive strength are especially useful.…”

THE STONE ROOF OF THE THOLOS OF ATHENA PRONAIA IN DELPHI: STRUCTURAL HYPOTHESES STARTING FROM FRAGMENTS OF MARBLE TILES

“…As regards the upper portion of the dome, it should be observed that the thrust line related to the independent lune would exit at some joints. Considering the action of hoop forces, for example, according to the procedure described in (Aita, Barsotti, and Bennati, 2019b) or in (Paris, Ruscica, and Mirabella Roberti, 2021), allows for finding fully statically admissible solutions for the conical dome. On the contrary, the results related to the systems formed by the conical dome and the external colonnade (or the vertical loadbearing structure), show that these structures would collapse according to the collapse mode 1, since the horizontal thrust deriving from the meridian cracking of the dome is not compatible with the rotational equilibrium.…”