Some of the highest and widest vault constructions produced in the Middle Ages are located in the Mediterranean area. Outstanding buildings with remarkable vaults and buttressing, such as the ...Cathedral of Majorca, are evidence of a lively technology transfer and contemporary developments. International experts trace the complex processes of Medieval design and construction. They research structural patterns in the processes involved, analyze building methods, and relate their findings to historic documents. The approach of combining field research with the study of literary sources provides a fresh look at the impressive monuments and shines new light on technological advances and construction technology of the time.
•From the NURBS 3D model of a generic masonry vault to a rigid body assembly.•Kinematic limit analysis based on a homogenized upper bound formulation.•Dissipation allowed along element edges ...only.•Optimization of the rigid body assembly through a suitable Genetic Algorithm.•Fast determination of the load bearing capacity and failure mechanism of the masonry vault.
The present paper proposes a new Genetic Algorithm NURBS-based approach for the limit analysis of masonry vaults based on an upper bound formulation. A given masonry vault geometry can be represented by a NURBS (Non-Uniform Rational B-Spline) parametric surface and a NURBS mesh of the given surface can be generated. Each element of the mesh is a NURBS surface itself and can be idealized as a rigid body. An upper bound limit analysis formulation, which takes into account the main characteristics of masonry material is deduced, with internal dissipation allowed exclusively along element edges. The approach is capable of well predicting the load bearing capacity of any masonry vault of generic shape. It is proved that, even by using a mesh constituted by very few elements, a good estimate of the collapse load multiplier is obtained provided that the initial mesh is adjusted by means of a meta-heuristic approach (i.e. a Genetic Algorithm, GA) in order to enforce that element edges accurately represent the actual failure mechanism. The proposed method turns out to be both accurate and much less computationally expensive than existing methods for the limit analysis of masonry vaults.
A numerical method is implemented to cope with the funicular analysis of ribbed masonry vaults under self-weight. A two-layer spatial network with given plan geometry is adopted to account for the ...load path in the overlying vault and in the supporting ribs. The minimization of the horizontal thrusts is formulated in terms of an independent set of force densities, and in the vertical coordinates of the restrained nodes. Constraints are enforced on the height of the nodes and on the sign of the force densities, to seek anti-funicular networks in equilibrium with the loading that lie within the envelope of the ribbed vault. A stellar masonry vault originally built in the ancient church of Tereske (Hungary) is investigated, comparing results achieved by using either single-layer or two-layer spatial networks.
The aim of this paper is to present an in-depth numerical investigation on the statics of historical masonry stellar vaults, a special class of masonry ribbed vaults whose three-dimensional geometry ...features a star-shaped projection on the horizontal plane. In particular, the mechanical behavior of the masonry stellar vault belonging to the church of Santa Maria del Monte in Cagliari (Italy) is analyzed and illustrated as an especially meaningful case study. This church, which was built during the second half of the sixteenth century, is a beautiful example of Gothic-Catalan style, and its ribbed stellar vault is one of the most representative of this type in the town of Cagliari. The geometric outline of the vault has been obtained through laser scanning techniques and a procedure of
reverse engineering
. Starting from a three-dimensional representation of its geometry, the ultimate load-bearing capacity of the stellar vault can be accurately estimated through a recently developed, NURBS-based upper-bound limit analysis scheme. A comparison with incremental nonlinear analyses carried out with the commercial finite element code DIANA is presented. Furthermore, the paper also includes a sensitivity study aimed at investigating the role of ribs on the ultimate load-bearing capacity of the structure.
•Comprehensively description of the procedure for the analysing of thrust networks with free edges and holes.•Extension of the method to the cases of networks subject to the combined action of ...vertical and horizontal loads so as to include seismic actions.•Reformulation of the method to enhance computational performances: efficient branch assemblage, flexible node numbering, reduction of the number of conditions involved in the optimization process.•Analysis of real vaults subjected to combined vertical and horizontal loads, modeled by network with complex geometry and high number of free edges.
We address the Thrust Network Analysis (TNA), i.e. the methodology for modeling masonry vaults as a discrete network of forces in equilibrium with gravitational loads, first contributed by O’Dwyer and fully developed by Block and coworkers. Reducing the bias by the quoted authors in favor of a graphical interpretation of the method, we reformulate the original version of the TNA by discarding the dual grid and focusing only on the primal grid, thus significantly enhancing the computational performances. The proposed reformulation of the TNA is also extended by including horizontal forces in the analysis as well as holes or free edges in the vault. Furthermore, the coefficient matrices entering the solution scheme are obtained by assembling the separate contribution of each branch, thus avoiding the ad hoc node numbering and branch orientation required by alternative implementations. Numerical examples, some of which referred to vaults having a particularly complex geometry, show the effectiveness and robustness of the proposed approach in assessing the safety conditions of existing masonry vaults or in designing new ones.
This paper deals with the study of a rectangular plan sail vault built by brick slices in the Roman villa of Carranque in Spain in the fifth century, in the context of a research project on the ...constructive configuration of Mediterranean vaults of this kind. The project aims to identify technical links to trace their expansion and examine the possibilities of using this technique in present-day building practice. The case at Carranque confirms the arrival of this vaulting technique to the Iberian Peninsula prior to a possible diffusion through the Arab world. The analysis of a 3d photogrammetric model of the remains allows posing that the solution used to solve the slices meeting at the diagonal is different from Byzantine ones; the large perimetral arches were lowered, almost matching the height of the small ones, and a vertical area was placed, being arranged as if it were part of the vault itself. With this design, it is not easy to notice the rectangular form of the vault.
Catalan vaults have always been popular in many countries. Architects such as Gaudi have made the Catalan vault a success worldwide. Substantially these vaults are built with bricks such as the ...“raisilla”, a thin brick that can have a thickness of one centimeter. The basic idea of Catalan vaulting technique is that a center is not necessary because, given the reduced weight of the rasilla and the nature of the mortar used for joints (often rich in gypsum), the first layer of the vault will be quickly assembled and will support the further layers and the workers. While the idea of having the joint of each new layer of the vault rotated of 45 degrees with respect to the previous layer’s joint has generally been kept, in the modern Catalan vault a mesh (steel or composite) it is often introduced, between the two external layers of bricks. This mesh operates by distributing the loads and increasing the strength against the effect of asymmetric or concentrated loads. This paper presents a study made on a new type of Catalan vault made with much thicker and stronger bricks that abandon the idea of rotating the joint direction. The vaults were firstly studied using a FEM model and then specimens of the vaults were tested in compression, flexion and shear. The results obtained were compared with more classical Catalan vault. The results seem to confirm that the Catalan technique is a fast and interesting vaulting method for modern construction.
Brick Vaults by Slices in Choisy and Paredes Rabasa Díaz, Enrique; López-Mozo, Ana; Alonso-Rodríguez, Miguel Ángel
Nexus network journal,
12/2020, Volume:
22, Issue:
4
Journal Article
Peer reviewed
A brick barrel vault can be bonded basically according to three techniques depending on the arrangement of the bricks main planes: they can be radially orientated with respect to the vault axis (
...radial brick vault
); they can be aligned with the vault surface (
tile vault
) or they can be vertical or slightly inclined, forming slices (
vault by slices
). The last two types do not require any formwork to be built. This work deals with the last case,
vaults by slices
, focusing on the study and comparison of two late nineteenth-century texts in France and Spain that go deeply into the geometry of this type of vault and still remain unstudied from this point of view: that of Choisy (Annales des Ponts et Chaussées 12: 439–449, 1876 and L’Art de bâtir chez les Byzantins. Librairie de la Société Anonyme de Publications Periodiques, Paris, 1883), who addresses the study of this type of vault in Byzantium, and that of Paredes (ca. 1883), who analyses the Spanish vault building tradition of this type in the region of Extremadura.
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