Static analysis of masonry vaults, constitutive model and numerical analysis

Abstract

The paper deals with some of the explicit and numerical methods used for modeling the mechanical behavior of masonry vaults and domes. After a brief description of the constitutive equation of masonrylike materials, a numerical method for the structural analysis of masonry vaults is presented. Then, the concept of maximum modulus eccentricity surface for masonry vaults is recalled. Subsequently, the collapse load and the corresponding mechanism are explicitly calculated for two particular cases: a circular plate subjected to a permanent load acting on the lateral surface and a variable vertical load applied to the extrados, and a spherical dome subjected to its own weight and variable point load applied to the keystone. The exact solutions are compared to the numerical results obtained via finite element analysis. Lastly, a study of the dome of the church of Santa Maria Maddalena in Morano Calabro is described. The method has enabled the stress field and the fractures distribution in the dome to be determined and the maximum modulus eccentricity surface to be evaluated.

Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches

“…Lucchesi et al [77] have generalized the static approach for arches to the case of masonry vaults through a maximum modulus eccentricities surface, a concept analogous to the line of thrust in the case of arches. Andreu et al [2,3] have developed a computer technique for the assessment of complex masonry constructions, including 3D framed structures and shells, inspired on Gaudi's hanging models (Fig.…”

Processes in Masonry Bodies and the Dynamical Significance of Collapse

“…Let 5 1 , let 1 5 be given by (28) and let where 7 W is defined in (21). Then for any two positive numbers 1 K we have infI 3u4 : u 9 1 U : dist H 3u1 1 54 1 u W K 6 I 0 2…”

“…The code has been successfully applied to the analysis of some buildings of historical interest [21]. The equations of motion must be integrated directly.…”

A Procedure to Investigate the Collapse Behavior of Masonry Domes: Some Meaningful Cases

“…Along the wedges act meridian forces which are always compressive under vertical loads, while along the parallel bands act hoop forces which are perpendicular to the meridian forces. Hoop forces, that restrain the out-of-plane movement of the wedges, are compressive in the upper zone of the dome and tensile in the lower zone, in most cases the passage from compressive to tensile forces occurs between 45 and 60 degrees respect to the vertical axis (Heymann, 1982;Como, 2011;Lucchesi, 2007), as shown in figure 1, that reports results obtained by membrane analysis of a semi-circular masonry dome (Pavlovic, 2013). Therefore, the load bearing capacity of masonry domes is related to their shape: a dome is a double-curved shell that thanks to its shape exhibits an optimal structural behaviour under axialsymmetric loads.…”

“…The greater part of these models (Lucchesi et al, 2007) is devoted to the definition of the stresses distribution in parallels and meridians at varying the geometrical shape of masonry dome, the loading or the boundary conditions. Masonry material is modelled as isotropic or orthotropic material depending on the sophistication of modelling A c c e p t e d M a n u s c r i p t 8 approach.…”