Masonry Vaults

Arches, vaults and domes were the most important elements in Iranian buildings until the beginning of the 20 th century. These forms are one of the main features of traditional buildings in small cities and villages in the neighborhood of the desert. The present paper investigates the general performance of arches and domes during the Bam earthquake (December 2003, Ms=6.6). In this earthquake, wide damages to such traditional buildings were observed, especially those located in the vicinity of the fault. The paper reviews the main reasons of failures of such buildings. It also discusses the suitability of these structures in earthquake hazard areas and reviews the main points of weakness of the current construction practices.

Prague is the net vault over the ground level, designed by Peter Parler. Often assumed to have been built after the net vault of Prague Cathedral's choir, this article looks more closely at the masonry, the heraldry and the sculptures of the Tower to suggest that the Bridge Tower vault predates the choir vault. After setting this vault as the first net vault in Bohemia, the article examines how this particular form fits within the evolution of Parlerian vault designs in Prague. In addition, the article explores the larger implications of a design process where smaller spaces are used to experiment and develop new designs before utilising those designs on a larger scale.

This book deals with the general concepts in stereotomy and its connection with descriptive geometry, the social background of its practitioners and theoreticians, the general methods and tools of this technology, and the specific procedures for the members built in hewn stone, including arches, squinches, stairs and vaults, ending with a chapter discussing the open problems in this field. Thus, it can be used as a reference book in the subject, but it can also read as a compelling narrative on this subject, one of the main branches of pre-industrial technology. 

Construction in hewn stone requires the use of geometrical methods and tools to assure that individual stones, either blocks or voussoirs, fit with one another and conform to the general shape of walls, arches or vaults. During the Late Middle Ages and the Renaissance, such techniques and instruments were developed empirically by masons and architects. Later on, learned mathematicians and engineers introduced refinements in these procedures and this branch of knowledge, known as stereotomy, furnished much material to descriptive geometry, a science born with the French Revolution which provided the foundation for projective geometry.

En 1509, Íñigo López de Mendoza, II conde de Tendilla, explicaba que la inclusión del cimborrio en la Capilla Real de Granada era una cosa que da[ba] mucha vista y ahermosea[ba] en gran manera la Capilla y [hacía] el edificio real y magnifico. Para esas fechas tempranas del siglo XVI, el cimborrio se había convertido en un elemento dignificador de la arquitectura religiosa. Al alarde técnico que suponía su construcción, se unía su doble funcionalidad en el templo, ya que permitía aumentar la iluminación interior de los edificios –se trataba, en última instancia, de una figura de luces, tal y como lo definirá Simón García años más tarde–, que servía, a su vez, para subrayar el eje central del espacio religioso allí donde se cruzaban los brazos de la cruz. Estas razones prácticas y simbólicas favorecieron la construcción de este tipo de estructuras en toda la Europa cristiana a lo largo de la Edad Media y parte de la Moderna. El fenómeno también puede observarse en la Península Ibérica, donde comienza muy pronto, y se prolonga hasta fechas muy avanzadas. Trataremos de seguirlo a través de los ejemplos –y de los diseños– conservados.
Íñigo Lopez of Mendoza, the Second count of Tendilla, explained in1509 that the inclusion of the cimborrio in the Royal Chapel of Granada was a thing that gives many sight and embellishes in great way the Chapel and this inclusion transformed the building in to royal and magnificent. At the seearly dates of the 16th century, the cimborio had become a dignifying element of the religious architecture. The advantages were undoubted. First, the technical ostentation that supposed its construction. In addition, it had a double functionality in the temple, since it was allowing to increase the interior lighting and serves to underline the central axis of the religious space where the two parts of the cross were crossing. These practical and symbolic reasons favored the construction of this type of structures throughout the whole Christian Europe during the Middle Ages and part of the Modern one. The phenomenon can also be observed in the Iberian Peninsula; there it begins very early, and continues until very advanced dates. We’ll try to follow it through the examples –and of the designs– preserved.

The research developed in the last years have proved the importance of the Crown of Aragon -and of the Kingdom of Navarra- as a bridge for the spreading of the late Gothic from the other side of the Pyrenees to the Crowns of Castile and Portugal. Isambart, Pedro Jalopa and other professionals of the stone -of different origins and training- played an important part within this process. Their risky life and professional courses lead them to coincide in different points of the European geography before converging on Aragonese land and forming the team which would combine, at least between 1417 and 1422, the refurbishment of the former main chapel -the current chapel of the Corporals- of the collegiate church of Daroca (Zaragoza) and the construction of the chapel of San Agustín in the cathedral of the Aragonese capital, which disappeared sixteen years after its erection. This team dispersed shortly after completing these two contracts and spread the innovations of the flamboyant architecture and of the sculpture of Burgundian ascendant through other peninsular artistic focuses until the central years of the Cuatrocientos, when the arrival of new foreign masters -Flemish and Breton in Toledo, German in Burgos-, ended up making the introduction of new interpretations of the Gothic easier, above all on Castilian land.


Las investigaciones desarrolladas en los últimos años han venido a demostrar la importancia de la Corona de Aragón –y del Reino de Navarra– como puentes en la difusión del Gótico final desde el otro lado de los Pirineos hasta las Coronas de Castilla y Portugal. Dentro de este proceso desempeñarían un papel determinante, Isambart, Pedro Jalopa y otros profesionales de la piedra de orígenes –y formaciones– diferentes cuyas azarosas trayectorias vitales y profesionales les llevarían a coincidir en distintos puntos de la geografía europea antes de confluir en tierras aragonesas y conformar el equipo que simultanearía, al menos entre 1417 y 1422, la reforma de la antigua capilla mayor –la actual capilla de los Corporales– de la iglesia colegial de Daroca (Zaragoza) y la construcción de la capilla de San Agustín de la catedral de la capital aragonesa, que desaparecería sesenta años después de haberse levantado. Este equipo se dispersaría al poco de concluir estos dos compromisos, difundiendo las novedades de la arquitectura flamígera y de la escultura de ascendente borgoñón por otros focos artísticos peninsulares hasta los años centrales del Cuatrocientos, cuando la llegada de nuevos maestros foráneos –flamencos y bretones a Toledo y alemanes a Burgos–, terminaría facilitando la introducción de nuevas interpretaciones del gótico, sobre todo, en tierras castellanas.

The modular interlocked blocks in flat structures are known in ancient buildings with pure-compression constructions. Over the last two decades, this structural bond has become relevant, studied by mechanical engineers, and material scientists due to the properties and design freedom that modular structures have. The structural hierarchy existing in topologically interlocked structures enhance the performance, allowing to design and fabricate custom block elements. The main reason to consider this system is that, from the architectural perspective, it is composed by identical modular elements, and it discretizes flat or curved surfaces into elements that work only by contact and compression. This article presents preliminary studies for its application and different approaches for designing discrete interlocked assemblies with a focus on the application for architectural structures: studying the structural performance of contact analysis and introducing the combination of topological interlocking with different structural principles.

Crossed-arch domes are a singular type of ribbed vaults. Their characteristic feature is that the ribs that form the vault are intertwined, forming polygons or stars, leaving an empty space in the centre. The fact that the earliest known vaults of this type are found in the Great Mosque of Córdoba, built in the mid 10 th century, has generated a debate on their possible origin. The thesis that appears to have most support is that of the eastern origin. This article describes the different hypothesis, to then proceed with a discussion of the geometry. Geometry is a topic that has been thoroughly studied in Hispanic-Muslim decoration; however, the geometry of domes has very rarely been considered. Also, the function of the ribs has never been discussed, in contrast with the abundant literature on gothic ribs. In what follows, we will give first a historical overview of the evolution of this structural type. Then the geometrical patterns in plan will be examined. Afterwards, the geometric problems of passing from the plan to the three-dimensional space will be considered. Finally, a discussion about the possible structural behavior of these domes will be given.

The tradition of stereotomy developed in the different Christian kingdoms of the Iberian Peninsula between the late XIV and the early XV century will allow to materialize in stone the new Renaissance system which had arrived from Italy. This phenomenon, which represents, without a doubt, one of the greatest Spanish contributions to the “a la Antigua” architecture, will follow two different ways: one, derived from the construction techniques developed in the building of ribbed vaults, and the other one based on the carving and assembly of “piezas enterizas”.




La tradición estereotómica desarrollada en los diferentes reinos cristianos de la Península Ibérica desde finales del siglo XIV y comienzos de la centuria siguiente permitirá afrontar la materialización en piedra del nuevo sistema renacentista llegado desde Italia. Este fenómeno, que constituye, sin lugar a dudas, una de las mayores aportaciones españolas a la arquitectura “a la antigua”, se abordará a partir de dos vías sensiblemente diferentes: una, derivada de las técnicas constructivas desarrolladas en el volteo de las bóvedas de crucería, y otra, basada en la labra y el ensamblado de “piezas enterizas”.





La tradizione stereotomica sviluppata nei vari regni cristiani della Penisola Iberica tra la fine del XIV secolo e gli inizi del secolo successivo permetterà di affrontare la materializzazione in pietra del nuovo sistema rinascimentale giunto dall’Italia. Questo fenomeno, che rappresenta, senza alcun dubbio, uno dei maggiori contributi spagnoli all’architettura “a la antigua”, seguirà due vie profondamente differenti: una, derivata dalle tecniche costruttive sviluppate nella costruzione di volte a crociera, e l’altra basata sulla lavorazione e l’assemblaggio di “piezas enterizas”.

The current Special Issue focuses both on recent advances in graphic statics and on the examination of the old graphical methods from a more modern viewpoint. Suitable topics include but are not limited to the following:
Applications of graphic statics to the mechanics of
historic masonry constructions;
Historical approaches using graphic statics to
design structures;
Thrust network analysis;
Extension of graphic statics to 3D structures;
Recent advances in graphic statics;
Applications of graphic statics to the mechanics of
trusses;
Applications of graphic statics to bending analysis
and design;
Applications of graphic statics to concrete
structures;
Applications of graphic statics to timber structures;
Numerical tools using graphic statics;
Analytical and computational graphic statics;
Structural optimization using graphic statics;
Design of funicular forms;
A modern interpretation of the historical method of
graphic statics.
We would be grateful to you if you could spread this
information to anyone who might be interested.
Deadline for manuscript submissions: 30 June 2021

Благовещенский храм XIV в. не сохранил первоначальное завершение, отдельные следы арок зафиксированы при натурных исследованиях. По мнению Л. Е. Красноречьева, Г.М. Штендера и др. храм перекрывался с помощью ступенчатых арок и сводов. Данные реставрационных исследований показывают, что в постройке была сложная система арок и сводов; пят подпружных арок и сводов, которые опирались на эти арки, не найдено; схема расположения арок и сводов Благовещенской церкви не может быть достоверно реконструирована. Наиболее вероятно, что в храме существовала система чередующихся пониженных арок, на которых лежали своды. Ближайший аналог подобному решению — церковь Николы в Изборске 1330–1340-х гг.

The cathedral of Zagreb is the most important and the largest Gothic building in Croatia: ca 75 m long, ca 35 m wide, with vaults of the nave and choir spanning 13 m. Its eastern part (presbytery with three apses) was begun in the 13 th century, following the model of the church of Saint-Urbain in Troyes (Champagne). According to historical documents, the two aisles of the presbytery (i.e. of the eastern part of the edifice) were vaulted by the end of the 13 th century, but there are no historical sources on the construction of the first choir vault. Survey drawings from mid-19 th century show a vault with late Gothic stylistic characteristics, with ribs forming patterns typical of Central-European late Gothic vaults. However, it was not constructed in the Gothic period: from the contract with master Hans Alberthal in 17 th century it is known that he built this vault "exactly following the form of the old vault" which had collapsed shortly before. This was the only vault of the Zagreb cathedral with the late Gothic formal characteristics. All the other vaults of the cathedral were of the quadripartite type, typical of early and high Gothic. Therefore it might be concluded that the choir vault was built later than the other vaults of the cathedral – even later than the vaults of the hall-type nave, constructed in the 15 th c. Also, the choir vault is the only vault of the Zagreb cathedral which collapsed in the earthquake in 1880 (Torbar 1882). Interestingly, from the historical sources it can be concluded that it collapsed several times before the 1880 earthquake – while the other vaults of the cathedral had never had serious structural problems. The cross section of the presbytery has unusual proportion of the heights of its central and lateral vessels: the springings of its choir vault are higher than the springings of its aisle vaults, but not enough high to enable high clerestory windows-as it was the rule in aisled early and high Gothic cathedrals. However, the choir vault is still considerably higher than the aisle vaults. Astoundingly, the eastern part of the cathedral does not have flying buttresses. On the basis of historical and structural analysis of the building a hypothesis was made that the lack of flying buttresses caused structural weakness of this part of the church. Due to the inadequate buttressing system, the original Gothic vault of the choir probably collapsed soon after the construction, and the eastern part of the edifice was never built as it must have been planned: as a real basilican type structure, with the choir considerably higher than the aisles.

Crossed-arch vaults are a particular type of ribbed vaults. Their main feature is that the ribs that form the vault are intertwined, forming polygons or stars and leaving an empty space in the middle. The firsts appear in Córdoba in the second half of the 10th Century. Afterwards, the type diffused through Spain and North Africa, 11 th-13 th Centuries. These vaults reappear in Armenia in the 13th Century. In the 14th and 15th Century a few examples are found both in England (Durham, Raby) and Central Europe (Prague, Landshut, Vienna). At about the same time, Leo-nardo da Vinci produced designs for the Tiburio (Ciborium) of Milan cathedral with a cross-arched structure and proposed tests to assess the strength; he also, made use of the same pattern of vault for Renaissance centralized churches. Eventually, the type can be tracked through the 17th (Guarini) and 18th (Vittone) Centuries, until Spanish post war architecture in the 1940-60s (Moya). Some questions arose, which so far, have not been answered. How was it possible that a particular type of vault had such enormous geographical spread? How was it transmitted from Córdoba to the Caucasus? The matter is one of transfer of knowledge, ideas, and technology; it relates both aesthetics and construction.

Virtual reconstruction of the vaults of the nave of the church of San Domenico in Cagliari (16th cent.).

This paper focuses on the 3D virtual reconstruction of the star-shaped rib vaulting of the nave of the church of San Domenico in Cagliari (Sardinia), destroyed in 1943 by a large-scale bombing of the city. Virtual reconstruction, combining historical research tools and digital representation technologies, was employed to understand the constructive process of the disappeared coverage of the nave. It also allowed a proper interpretation of the linguistic details and constructive features in order to elaborate new dating hypotheses through a comparison with the coeval religious architecture.

The present paper summarizes a study on masonry vaults, with the purpose of understanding their building aspects, interpreting their actual structural behavior, and identifying proper interventions which are compatible with the typical characteristics of historical constructions. The interpretation of the historical technical literature, the formulation of a rigorous theory of structural analysis, and the critical study on the possible strengthening techniques and thrust containment methods have led to verify the efficiency of some types of intervention on masonry vaults, with particular reference to the insertion of tie rods.

Folia Historiae Artium Seria Nowa, t. 13: 2015 / PL ISSN 0071-6723 Wśród dzieł polskiej architektury gotyckiej nie ma chyba takiego, o którym napisano by więcej, niż o katedrze na Wawelu w Krakowie. Pierwsze studium monograficzne poświęcił jej już w roku 1900 Tadeusz Wojciechowski 2 , później zaś wiedzę o tej budowli znacznie poszerzyli m.in.

The Biblioteca Nacional de España in Madrid holds a fair number of stonecutting manuscripts. One of them, MS 12686, including 31 sheets in parchment binding, and bearing no author mention, title or date, has not been studied from a geometrical point of view. In this paper, we present a preliminary study of the manuscript, analysing the graphical techniques and construction methods used in the drawings, dealing in particular with projection types and graphical resources such as developments and triangulations. Such research approach furnishes valuable data about the connections of the manuscript with other important stonecutting texts in the Iberian area, such as the ones by Hernán Hernán Ruiz el Joven (c. 1550), Alonso de Vandelvira (c. 1580), Ginés Martínez de Aranda (c. 1600) and Juan de Portor y Castro (1708), supporting the attribution posited by Gómez Martínez (1998) to Pedro de Alviz, a stonemason active around 1540 in the Cuenca area.

Masonry churches are effectively studied by means of kinematic analyses on macro-elements. This paper presents a procedure to recognize and evaluate the contribution to the dynamic response of such macro-elements by means of nonlinear transient analyses. In particular, it consists in evaluating damages occurred by applying accelerograms of the Emilia Romagna earthquake (Italy, 2012) to a small church characterized by a complex damage pattern. First, a modal analysis furnished qualitative information about vulnerable macro-elements of the chapel, stressing the high vulnerability of the central vault, actually collapsed, and that of the façade, subjected by an incipient overturning and in plane mechanism. Afterwards, a more sophisticated approach was performed, considering the nonlinear behavior of masonry, capable to evaluate the damage evolution or the degradation of elastic stiffness. The density of energy dissipated by damages for each macro-element was computed for three sets of natural accelerograms, applied in transient analysis. The rates of dissipated energy densities with respect to the total dissipated energy helped to identify the macro-elements subjected to more severe damages. Such structural elements were demonstrated to be effectively the most damaged under the considered main shock. A similar procedure can be applied in a preventive perspective to judge the critical parts of a church or a historic building, upon a correct evaluation of the post-elastic behavior of masonry and a proper choice of acceleration time-histories.

I prepare high-quality illustrations of art objects or historical buildings for museums and academics to use in publications and related work. You can appreciate a small selection of my works at: https://sites.google.com/site/matildegrimaldi/
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The paper describes the traditional technology used, in the reign of two Sicilies,  to produce light vaults including hollow ceramic components, such as terracotta jugs, in the mortar fill.
It further analyzes the problems generated trying to apply, as is, the new national seismic regulations that do not contemplate such technologies.