Masonry Dome Behavior under Gravity Loads Based on the Support Condition by Considering Variable Curves and Thicknesses

It is necessary to recognize masonry domes’ behavior under gravity loads in order to strengthen, restore, and conserve them. The neutral hoop plays a crucial role in identifying the masonry dome’s behavior to distinguish between its tensile and compressive regions. When it comes to determining the neutral hoop position in a dome with the same brick material, in addition to determining the dome’s curve and thickness, the support condition located on the boundary line is a significant parameter that has received less attention in the past. Therefore, this research aims to comprehensively define masonry dome behaviors based on the support condition’s effect on the masonry dome’s behavior, in addition to thickness and curve parameters, by determining neutral hoop(s). The method is a graphical and numerical analysis to define the sign-changing positioning in the first principal stress (hoop stress), based on the shell theory and extracted from a finite element method (FEM) Karamba3D analysis of a macro-model. The case studies are in four types of supports: condition fixed, free in the X- and Y-axes, free in all axes (domes placed on a drum), and free in all axes (domes placed on a pendentive and a drum). For each support condition, twelve curves and four varied thicknesses for each curve are considered. Results based on the dome’s variables show that, in general, four types of masonry domes behavior can be identified: single-masonry dome behavior with no neutral hoop; double-masonry dome behavior where all hoops are compressive with a single neutral hoop; double-masonry dome behavior where hoops are compressive and tensile with a single neutral hoop; and treble-masonry dome behavior with double neutral hoops.

On Collapse Behavior of Reinforced Masonry Domes under Seismic Loads

In this paper, the first result on the collapse behavior of reinforced masonry domes under seismic loads is presented. A certain masonry dome is modeled through NURBS surfaces, which have the great advantage to represent accurately complex geometries. The obtained NURBS model is imported in the MATLAB® environment, in which an initial NURBS mesh is defined. An upper bound limit analysis is applied: each element is idealized as rigid block and eventual plastic dissipation is allowed only along element edges. The minimum of the kinematic multipliers is found by optimizing the NURBS mesh (i.e. modifying the position of fracture lines) through a meta-heuristic algorithm (e.g. a Genetic Algorithm). A reinforcing system made by FRCM fibers is included through additional NURBS surfaces: each new surface represents a strip and exhibits only a tensile contribute in the evaluation of plastic dissipation. The dome of the church of Anime Sante, which collapsed during the L’Aquila earthquake in 2009, is considered as meaningful case study. A standard disposition of FRCM fibers, typically designed for incrementing the vertical load bearing capacity, has been hypothesized. The reinforced dome is analyzed under a horizontal acceleration linear in height and constant in plane and a comparison between the unreinforced and the reinforced case is presented.

Finite Element Thrust Line Analysis (FETLA) of Axisymmetric Masonry Dome with Meridian Cracks

Many masonry domes in their lower portion are subjected to hoop tensile forces which mostly lead to vertical cracks appearing along the dome's meridian planes. A close inspection of any such dome reveals these hoop tension cracks. The dome stands as a series of arches with common key stone, with cracks as a matter of non-structural consequences. Different strategies have been considered historically to arrest these cracks. The provision of tension ring mechanism adds to the stability of these domes, and hence many masonry domes are retrofitted with the provision of the tension rings using steel and FRP rings. The challenge in such retrofitting will remain to analyze its effect on stability of these masonry domes, more specifically in absence of reliable mechanical properties of such masonry domes. This paper presents a simplified analysis procedure combining thrust line analysis with the finite element analysis called here as Finite Element Thrust Line Analysis (FETLA). The development of a new element suitable for masonry dome analysis to include the effect of hoop tension cracks is demonstrated. The orthotropic material properties are utilized for penalty approach to allow redistribution of the forces from meridian direction to the hooping rings, with thrust line approaching the extrados or intrados of the dome. The analysis results of FETLA are validated with the previously available results. The analysis method proposed in this paper gives the rational estimates for the failure load without utilizing inelastic properties of the material to model the hoop tension cracks and its propagation.