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2022 | Buch

From Corbel Arches to Double Curvature Vaults

Analysis, Conservation and Restoration of Architectural Heritage Masonry Structures


Über dieses Buch

The book focuses on all typological aspects of arches and vaults within the heritage of design and construction, while bringing attention to new “green” materials, promoting a circular economy informed by limitations caused by global warming. The multidisciplinary approach involves several different competences in architecture, structural engineering, conservation and restoration, geomatics, BIM, building engineering, the technology and history of construction, graphical methods of assessment, and innovative design that utilizes non-polluting materials. After an overview of the technical and aesthetic advantages of masonry vaults, there is a review of the most up-to-date trends in historic preservation. Classic methods of static assessment and innovative building technologies are detailed. Surveying methods and data acquisition are discussed, particularly laser scanning technology and its applications in heritage masonry curved structures. Next comes the experimental static and dymanic behavior of masonry vaults, followed by a critical revision of Distinct Element innovative computerized Methods. An explanation as to how to pass from classic stability analysis to an adaptive Finite Element Method limit analysis procedure is offered. Reinterpretation of the past is then undertaken, with an eye towards emphasizing sustainability. Finally, the conclusion examines still existing gaps in knowledge and recommends avenues of future research.


Structures of architectural heritage have inevitably suffered damage with time, and this is particularly true for vaults and domes. Earthquakes, soil settlements, material degradation and lack of maintenance are the main reasons for that. With Sustainable Development Goal 11 (SDG 11), countries have pledged to “make cities and human settlements inclusive, safe, resilient and sustainable”. Within this goal, Target 11.4 aims to “strengthen efforts to protect and safeguard the world’s cultural heritage”. In Europe, inside cathedrals, churches in general, common buildings, castles, towers and palaces the role played by curved masonry and wood structures, in the form of arches, vaults and domes are among the most well recognized. Arches are also very common and of major importance in Roman and Medieval bridges, as well as in aqueducts. The evolution from trilithons to arches, passing through corbel vaults was a Roman intuition; the further refinement of the idea, achieved in the Middle Age and Renaissance, to conceive structures resistant thanks to their geometry led in Europe to build double curvature structures and domes with impressive artistic value. There is an imperative need to ensure that these outstanding structures continue to be an integral part of local life, given the increasing level of support and expertise required to maintain them at a time when the limited resources in communities are becoming ever more stretched.
Gabriele Milani, Vasilis Sarhosis
Historical Review of Masonry Arches and Vaults. Trends in Historic Preservation and the Relevance of Understanding Curved Masonry Structures
This work took origin from the inspiring didactic teaching experienced during a summer school course organized in the huge context of Como Lake. The main task, addressed to the study of masonry vaults, gave the possibility to open a wide reflection on building techniques and the differences characterizing the construction traditions diffused in peculiar areas. Como Lake, well-known for the various examples of medieval architectures considered to be a fundamental step for the further diffusion of the Romanesque style, becomes an interesting study field for observing the evolution of building techniques respect to its surroundings, considering the basin of the lake, the near valleys (Intelvi and Valtellina), and the context of Milan, the main town of the region and the influences that it had on the development of the building traditions in this restricted area. The carried-out review shows an optimization process, in which the builders learned how to select natural stones according to the needs of a high strength or low weight.
Stefano Della Torre, Lorenzo Cantini
Survey and Monitoring Methods for Masonry Arches and Vaults
The conservation and utilization of masonry constructions would not be achieved without precise descriptions provided by surveys, or the information provided by the monitoring of their current state. This chapter summarizes the contents and non-destructive methods of survey and monitoring regarding curved masonry structures, including arches and vaults appearing in buildings and arch bridges belonging to infrastructure. Some applications and progress in practical engineering are introduced here, and prospects are proposed based on current engineering needs.
Yu Yuan, Gabriel Stockdale, Gabriele Milani
Digital Setting Out Techniques for Tile Vaults Without Formwork
A short introduction to tile vault construction without formwork is provided, with emphasis on provisional equilibrium. The general problems of setting out complex forms when no formwork is available will then be discussed. A digital method for setting out these forms, including markers detection systems and optical tracking through cameras, is later proposed and studied.
Julián García, Carlos Martín, Roberto Molinos, Joaquín Grau, Juan Manuel Pérez
Experimental Behaviour of Masonry: Static and Dynamic Behaviour of Arches and Vaults
Masonry is a heterogeneous material that consists of units and joints displaying a complex mechanical behaviour. In the present chapter, the experimental behaviour of masonry is briefly reviewed considering an advanced mechanical characterization of components (namely, units and mortar) and of masonry as a composite. Moving to vaulted structures, although a certain consensus has been reached in the masonry community regarding their static behaviour, ongoing research is still investigating their dynamic one. In this respect, the present chapter describes two paradigmatic case studies for two- and three-dimensional elements. First, the shaking table tests performed on a scaled dry‐joint arch undergoing windowed sine pulses is presented. A feature tracking‐based measuring technique, employed to evaluate the displacement of selected points, was used to analyse the failure mechanisms. Secondly, a scaled dry‐joint cross vault and a full‐scale mortared cross vault tested on the shaking table are presented. Finally, two engineering applications related to the safety assessment of vaulted structures are examined.
Nicoletta Bianchini, Angelo Gaetani, Nuno Mendes, Paulo B. Lourenço
Revisiting Classic Methods for the Equilibrium Analysis of Masonry Arches and Domes
The Chapter revisits classic analytical approaches based on equilibrium and admissibility to assess the stability of masonry arches and vaults. A particular focus is given to Durand-Claye’s method and its modern re-interpretations developed in recent years. Durand-Claye proposed an original graphical method for assessing the stability of masonry arches and vaults. The procedure proposed by Durand-Claye is aimed at determining all the thrusts that allow for verifying the equilibrium of any given part of the arch and are at the same time compatible with the masonry strength, by drawing a particular plane figure, the stability area. In 1880 Durand-Claye extended his stability area method to assess the equilibrium of domes of revolution. The Chapter ends revisiting some recent methods of graphical stability analysis coupled with computerization, focusing in particular on the thrust network analysis, directly related to the thrust line method.
Danila Aita
Rigid Block Limit Analysis of Masonry Arches with Associated and Non-associated Slides
Heterogeneous limit analysis with infinitely resistant blocks and rigid-plastic joints reduced to interfaces is a powerful tool for the prediction of the collapse behavior of historical arch and vault masonry structures. Such analysis not only can provide the collapse mechanism and ultimate load of the structures in a quick and direct manner in a single step, but can precisely take into account the heterogeneous nature of the masonry in the most precise way. This chapter deliberates the theoretical background of such a powerful tool. First, the governing theoretical formulation of the collapse is elaborated, including the equilibrium conditions, the compatibility conditions, the constitutive and flow laws, the non-negative external work condition, and the complementary condition. After that, the solution of the collapse problem employing associated or non-associated flow rules for the joints is discussed respectively. Finally, a simple approach to consider the strengthening effect in the frame of limit analysis is proposed. Several examples and parametric studies are given to show the implementation of the theory and put at disposal to the reader an operative tool for design and assessment.
Yiwei Hua, Gabriele Milani
NURBS-Based Limit Analysis of Masonry Vaults
Limit analysis is currently one of the most used approaches for the stability assessment of masonry arches and vaults. The lower and upper bound theorems allow easy and practical identification of the load-bearing capacity, the stress pattern, and the mechanism at the collapse. Novel lower and upper bound numerical approaches based on an exact representation of curved geometries via NURBS (Non-Uniform Rational B-Spline) are here described. The presentation is enriched with some numerical examples concerning masonry arches and historical vaults.
Nicola Grillanda, Andrea Chiozzi, Gabriele Milani
Discrete Element Modelling of Masonry Arch Bridges, Arches and Vaults
Discrete element models provide a numerical representation of masonry structures as an assembly of discrete units interacting along joints. The essential concepts of this numerical method are presented herein, namely the choice of rigid or deformable blocks for the units, the assumptions governing contact mechanics, and the solution algorithms. The application of discrete element to masonry arches and vaults is discussed and illustrated with various examples. Practical application issues are examined by means of simple arch models, considering static and dynamic loads.
José V. Lemos, Francesca Gobbin, Tamás Forgács, Vasilis Sarhosis
Complex Simplicity—Design of Innovative Sustainable Thin-Shell Masonry Structures
The relationship between structural form and natural force allowed medieval master builders to construct spaces that still inspire awe today, many of which would be difficult to recreate. But with an understanding of antique knowledge, traditional construction, and contemporary computation we can once again explore the form and structure of centuries ago in contemporary architecture and engineering. Combining historic wisdom with the latest natural material technology offers the promise of novel and sustainable building solutions, especially as far as curved structures are concerned. We discuss developments from our research at Cambridge and our practice Light Earth Designs on curved structures that draw on learning from ancient traditions for contemporary sustainable architecture and engineering.
Michael H. Ramage, Ana Gatóo, M. Wesam Al Asali
From Corbel Arches to Double Curvature Vaults
herausgegeben von
Gabriele Milani
Vasilis Sarhosis
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