Technical Challenges in the Construction of Gothic Vaults: The Gothic Theory of Structural Design

The construction of a Gothic vault implied the solution of several technical challenges. The literature on Gothic vault construction is quite large and its growth continues steadily. The main challenge of any structure is that, during and after construction, it must be "safe", that is, it must not collapse. Indeed, it must be amply safe, able to support different loads for long periods of time. Masonry architecture has shown its structural safety for centuries or millennia. The Pantheon of Rome stands today after almost 2,000 years without having needed any structural reinforcement (of course, the survival of any building implies continuous maintenance) . Hagia Sophia in Istanbul, finished in the 6th century AD, has withstood not only the dead loads but also many severe earthquakes . Finally, the Gothic cathedrals, with their appearance of weakness, are• more than a half millennium old. The question arises of what the source of this amazing strength is and how the illiterate master masons were able to design such daring and safe structures . This question is usually evaded in manuals of Gothic architecture. This is quite surprising, the structure being a fundamental part of Gothic buildings. The present article aims to give such an explanation, which has been studied in detail elsewhere. In the first part, the Gothic design methods "V ill be discussed. In the second part, the validity of these methods wi11 be verified within the frame of the modern theory of masonry structures . References have been reduced to a minimum to make the text simpler and more direct.

The Gothic Ribbed vaults in Rodrigo Gil de Hontañón

The Gothic Ribbed vaults in Rodrigo Gil de Hontañón. Second International Congress on Construction History. Construction History Society. Cambridge. Reino Unido. Vol: III. Pags: 2415-2431. ISBN. 0-7017-0205-2

Technological development in Spanish gothic vaults design

The principle of complexity as the evolution vector of the gothic style was an idea largely developed by Paul Frankl. The high complexity reached in the 15th and 16th centuries was possible thanks to the geometrical resources developed in the workshops of the medieval stonemasons. The search for more sophisticated designs was possible also with the higher standardization, so that the most complex ribbed vault could be built with ribs that had all the same curvature and with voussoirs that were therefore identical. Spanish Gothic architecture has been deeply studied from a historical and artistic point of view. The present paper, as a complement to these analyses, aims to point out some of the geometrical methods and technological improvements that late medieval masons were able to develop. In that way, some selected vaults have been measured, in order to study their geometry and design process. Also scale models of some vaults have been built at the Escuela de Arquitectura (Madrid) to validate these geometrical principles. More than just a research method, the scale models allow to understand the medieval construction techniques, and they are a powerful pedagogical tool with which pupils can reach a rewarding experience based on the “medieval-way” praxis.

Las teorías del gótico y su representación gráfica en España el último tercio del siglo XIX. Un estudio sobre: Some Account of Gothic Architecture in Spain, de George Edmund Street

La tesis se centra en el estudio, descripción y análisis del libro publicado por el arquitecto británico George Edmund Street en 1865, bajo el título Some Account of Gothic Architecture in Spain. El libro dio a conocer una de la colecciones más importantes de dibujos realizada en el siglo XIX sobre la arquitectura gótica española, y por lo tanto fue una primera referencia para su estudio, hasta bien entrado el siglo veinte. El volumen incluyó 107 grabados de diversos tipos de edificios con perspectivas y detalles, y 25 láminas con 45 planos de plantas de iglesias y claustros, muchos de ellos publicados por primera vez. Gracias a varias campañas de verano por la mitad norte del país, la casi inexplorada -desde un punto de vista académico- arquitectura española medieval fue finalmente descubierta. Este hecho conduce a una pregunta intrigante que está en el origen de esta investigación ¿cómo pudo Street en pocos viajes sentar las bases de la historia del gótico español que hasta entonces los estudiosos españoles no habían sido capaces de definir? Esta tesis comienza describiendo la obra de Street en su contexto cultural con un breve repaso a su biografía y a su posición profesional y teórica. También su relación con las personas más representativas que participaron en el estudio de la arquitectura gótica, como Robert Willis, William Whewell, Augustus Pugin, o George G. Scott. Se ha prestado especial atención, en explicar su papel relevante en el Gothic Revival, para entender el significado de su interés en la arquitectura gótica continental. Estos capítulos preliminares son seguidos por una revisión del papel del dibujo como herramienta para la arquitectura de los viajeros en sus rutas en busca de la arquitectura gótica. También se trata la influencia de la Royal Academy y sus académicos, (entre los cuales estuvo Street) y su formación académica. Finalmente la tesis entra en el estudio de los planos arquitectónicos que Street hizo durante sus viajes continentales de arquitectura, seguido por una descripción detallada de sus dibujos de España, analizando su método, su técnica, y las nuevas características aportadas, que fueron una novedad en el contexto español. También se lleva a cabo algunos estudios comparativos de los dibujos de España, gracias a una recopilación exhaustiva de bocetos y dibujos originales de Street, que en su gran mayoría se conservan en los archivos del RIBA, cotejándolos con sus versiones finales, con dibujos de la época de otros autores sobre los mismos edificios, y con fotos recientes. La tesis deja claro por qué y cómo Street, gracias a su soporte teórico y habilidades para el dibujo, pudo realizar algo que había pasado desapercibido para los estudiosos españoles de la época (construcción, historia de los estilos, señalamiento de períodos constructivos), lo que le permitió encontrar el lugar adecuado de la arquitectura gótica española en la historia y en el mapa de la arquitectura gótica europea. ABSTRACT This thesis focuses on the study, description and analysis of the book published by the British architect George Edmund Street in 1865, under the title Some Account of Gothic Architecture in Spain. The book displayed one of the most significant collections of drawings on Spanish Gothic Architecture made in the nineteenth century, and therefore was a first reference for its study, until well into the twentieth century. The book included 107 engravings, the surveying of various types of buildings with perspectives and details, and 25 sheets containing 45 ground plans of churches and cloisters, many of them new and published for the first time. Thanks to several summer campaigns in the north half of the country, the almost unexplored -from a scholar point of view- medieval Spanish architecture was eventually revealed. This fact lead to an intriguing question that is at the origin of this research: how could Street in a few trips lay the foundations of the history of Spanish Gothic that until then Spanish scholars had not been able to define? This thesis begins inscribing this Street's work in his cultural context. A brief review of his biography and professional and theoretical positions has been seen as necessary. Also his debts and relationship with the most representative people involved in the study of Gothic architecture, like Robert Willis, William Whewell, Augustus Pugin, or George G. Scott are discussed. Special attention has been paid, taken into account his relevant role in the Gothic Revival, to understand the significance of his interest in continental Gothic architecture. These preliminary chapters are followed by a review of role of drawing as a tool for Architectural travellers in their Tours in search of the Gothic architecture. The influence of the Royal Academy and its academicians, (among which was Street) and his educational background are here tackled. Eventually this thesis enters into the study of the architectural drawings Street made during his continental architectural journeys, which is followed by a detailed description and analysis of the Spanish ones: his methods, his technique, and the new features which were a novelty in the Spanish context are explored. Also in this thesis is carried out some comparative studies thanks to a previous exhaustive gathering of Street's sketches and original drawings, most of which are preserved in the RIBA archives. Their final versions, drawings of the same buildings from other contemporary draughtsman and pictures of their current state are compared with them. This thesis makes clear why and how Street thanks to his theoretical back-ground and portraying skills could realize what have passed unnoticed by contemporary Spanish scholars (construction, genealogy of forms, dating of periods) allowing him to find the proper place of the Spanish architecture in the history and the map of European Gothic architecture.

La luz natural como generadora del espacio arquitectónico de la catedral gótica

La historia de la construcción de las catedrales góticas es la historia de la búsqueda de la luz. Esta afirmación casi metafísica, recoge una realidad asumida por todos los historiadores tanto de la arquitectura antigua como del resto de las artes. La luz en el gótico ha sido descrita bajo múltiples matices como son su carácter simbólico, cromático e incluso místico, sin embargo no existe, en el estudio del conocimiento de la luz gótica, ninguna referencia a la misma como realidad física cuantificable, cualificable y por tanto, clasificable. La presente tesis doctoral aborda el concepto de la iluminación gótica desde una perspectiva nueva. Demuestra, con un método analítico inédito, que la iluminación gótica es cuantificable y cualificable. Para ello analiza en profundidad la iluminación de una selección de 6 edificios muestra, las catedrales de Gerona, Toledo, Sevilla y León, la basílica de Santa María del Mar y la capilla de la Sainte Chapelle de París, mediante una toma de datos “in situ” de iluminación y su comparación con los datos lumínicos obtenidos por un programa de soleamiento de la simulación en tres dimensiones de los distintos proyectos originales góticos. El análisis exhaustivo de las muestras y su introducción en el método analítico descrito, permite determinar, en primer lugar, unas cualidades inéditas que identifican la luz de los espacios góticos según unos parámetros nuevos como son la intensidad, expresividad, recorrido, distorsión y color. También describe cuales son los factores determinantes, de nuevo inéditos, que modulan cada una de las cualidades y en que proporción lo hacen cada uno de ellos. Una vez establecidas las cualidades y los factores que las definen, la tesis doctoral establece los rangos en los que se mueven las distintas cualidades y que conformarán la definitiva clasificación según “tipos de cualidad lumínica”. Adicionalmente, la tesis propone un procedimiento abreviado de acercamiento a la realidad de la iluminación gótica a través de unas fórmulas matemáticas que relacionan los factores geométricos detectados y descritos en la tesis con el resultado luminoso del espacio en lo que concierne a las dos cualidades más importantes de las reflejadas, la intensidad y la expresividad. Gracias a este método y su procedimiento abreviado, la clasificación se hace extensible al resto de catedrales góticas del panorama español y europeo y abre el camino a nuevas clasificaciones de edificios históricos de distintas épocas, iniciando un apasionante camino por recorrer en la recuperación de “la luz original”. Esta clasificación y sus cualidades podrán a su vez, ser utilizadas como herramientas de conocimiento de un factor determinante a la hora de describir cualquier espacio gótico y su aportación pretende ser un nuevo condicionante a tener en cuenta en el futuro, ayudando a entender y respetar, en las posibles intervenciones a realizar sobre el patrimonio arquitectónico, aquello que fue en su inicio motor principal del proyecto arquitectónico y que hoy día no se valora suficientemente tan solo por falta de conocimiento: su luz. The history of the construction of the Gothic cathedrals is the history of the search for light. This almost etaphysical statement reflects a reality accepted by all historians both of ancient architecture and other arts. Light in the Gothic period has been described under multiple approaches such as its symbolic, chromatic and even mystical character. However, in the study of the Gothic light, no references exist to it as a physical quantifiable and qualifiable reality and therefore, classifiable. This dissertation deals with the concept of Gothic light from a new perspective. With a new analytical method, it shows that Gothic lighting is quantifiable and can be classified regarding quality. To this end, a selection of 6 buildings light samples are analyzed; the cathedrals of Gerona, Toledo, Seville and León, the basilica of Santa María of the Sea and the Sainte Chapelle in Paris. "In situ" lighting data is collected and it is compared with lighting data obtained by a program of sunlight of the 3D simulation of various Gothic original projects. The comprehensive analysis of the samples and the data introduced in the analytical method described, allows determining, first, important qualities that identify the light of Gothic spaces according to new parameters such as intensity, expressiveness, trajectory, distortion and color. It also describes the determinant factors, which modulate each of the qualities and in what proportion they do it. Once the qualities and factors that define them have been established, in this doctoral dissertation the ranges regarding different qualities are set, which will make up the final classification according to "types of light quality". In addition, this work proposes an abbreviated procedure approach to the reality of the Gothic lighting through some mathematical formulae, relating the geometric factors identified and described in the study with the bright result of space regarding the two most important qualities of the light,intensity and expressiveness. Thanks to this method and to the abbreviated procedure, the classification can be applied to other Spanish and European Gothic cathedrals and opens up the way to new classifications of historic buildings from different eras, starting an exciting road ahead in the recovery of the "original light". This classification and its qualities may in turn be used as tools to know a determinant factor when describing any Gothic space. Its contribution is intended to be a new conditioning factor to keep in mind in the future, helping to understand and respect, in possible interventions on the architectural heritage, what was the main engine to start the architectural project and which today is not valued enough due to the lack knowledge: the light.

Geometric tools in Juan de Álava's stonecutting workshop

Stonemasonry of the Gothic vault in its totality is based upon geometry of the line, whereas classic stereotomy relies on the comprehensive knowledge of the surface and the highly sophisticated sides of the voussoirs necessary for its vaults. It is obvious that this leap in the art of construction was paralleled and accompanied by an extension of the horizons of geometry. In Spain, it was made possible thanks to the centuries-old tradition of stone building begun in the most remote medieval times and to the presence of outstanding architects or stonemasons such as Juan de Álava, whose professional work surpassed the established limits and provided the art of building with new instruments.

La escalera de caracol con ojo a finales del S.XV y comienzos del S.XVI: el caso de la ciudad y tierra de Segovia

Este trabajo de investigación se ha centrado en la escalera de caracol con ojo también denominado caracol de mallorca, en sus primeras apariciones a finales del s.XV y comienzos del s.XVI durante el llamado periodo tardogótico. Este elemento aparentemente sencillo presenta, sin embargo, una gran diversidad de esquemas geométricos. Todavía a día de hoy, no hay explicación del por qué de la mayor difusión de unos con respecto a otros. El objetivo de este trabajo ha sido valorar el papel que el confort/seguridad de uso así como la economía en el trabajo –sencillez de ejecución y coste económico– tuvieron en el contexto de la difusión de este elemento arquitectónico. Este estudio ha analizado en base a estos criterios objetivos, la geometría de cada uno de los esquemas tipo que resuelven la formación del hueco central característico este tipo de escaleras, con la intención de determinar las causas objetivas que pudieron motivar la desigual expansión de los mismos. Una vez determinado el marco teórico, se han establecido dos líneas para abordar el problema. Por un lado se ha planteado el análisis de los modelos teóricos recogidos en los distintos textos de cantería escritos por autores españoles desde finales del s.XVI. Si bien en la época en que se escribieron, la arquitectura gótica como sistema había desaparecido, alguno de sus elementos más característicos, como la escalera de caracol, continuaban empleándose. Las trazas del caracol con ojo recogidas en estos textos, describen habitualmente las soluciones geométricas más frecuentes e incluso los ejemplos construidos más conocidos, los cuales fueron levantados en su mayoría en el período en el cual se desarrolla esta investigación. Por otro lado, este estudio se plantea el análisis de modelos construidos existentes en la Ciudad y Tierra de Segovia. La razón que justifica dichos límites geográficos, la encontramos en que la mayor parte del patrimonio gótico existente en este área fue construido entre finales del s.XV y comienzos del s. XVI. Ambos grupos, modelos teóricos y modelos construidos, recogen la herencia gótica heredada en la construcción de este elemento arquitectónico. Cada una de estas dos líneas establecidas han seguido una metodología específica adaptada al objeto de análisis, si bien ambas se basan en un primer análisis individual y posterior análisis comparativo de los modelos seleccionados. Estos análisis han permitido identificar los distintos esquemas empleados para resolver el hueco central, lo que ha posibilitado establecer una clasificación general de los mismos en tres grupos: caracol con ojo de solución radial, el caracol con ojo de solución no radial y el caracol con ojo de solución tangencial. A partir de los datos y resultados obtenidos del análisis comparativo de los parámetros geométricos que afectan al confort/seguridad de uso y economía en el trabajo de dichos esquemas, podemos concluir que a pesar que los tres esquemas identificados resuelven el caracol con ojo de forma muy similar, el predominio de la solución radial y la caída en el olvido de las soluciones tangencial y no radial estuvieron justificados. ABSTRACT This work focused on the helical staircase, also known as mallorca staircase, in the late 15th and the early 16th centuries. This seemingly simple element, presents however a wide variety of geometrical designs. Still to date, there is no explanation of why some of them were limited use, while others had a wide impact. The aim of this study was to assess the influence which comfort, safety and work economy –ease of construction and financial cost– had on their widespread. This study analysed, following these objective criteria, the geometry of the different designs, which solve the characteristic inner aperture of this type of staircase. And thus, find the reasons, which motivated their uneven spread. Once the theoretical framework was developed, two research lines were set up to address the problem. On one hand, this study analysed the theoretical helical staircases described in the early Spanish texts, which were written since the end of the 16th century. Although these texts were written after the Gothic Architecture system had already disappeared, some of its more representative elements like the helical staircase were still in use. The traces of the helical stair, which are included in these texts, describe the most frequently-used designs and even the most famous real examples which were usually constructed in the Late Gothic period. On the other hand, this study analysed some real helical staircases, which were constructed in the Ciudad y Tierra de Segovia. The reason for choosing these geographical limits is that most of the Gothic buildings of this area were constructed between the end of the 15th and the early 16th centuries, during the Late Gothic period. Both groups, theoretical and constructed samples, collect the Gothic construction tradition of the helical stair. Each of these research lines followed a specific methodology, which was adapted to the research object. Nevertheless, both are based on a first individual analysis of each selected example and a later on comparative one. These analysis allowed the identification of the different layouts which solve the inner aperture of the helical staircase, what made possible to set up a broad classification in three groups, according to the geometrical design strategy that solves the central aperture: the helical staircase by radial solution, the helical staircase by non-radial solution and the helical staircase by tangent solution. The research findings of the comparative analysis of their geometrical parameters, which have an impact in the comfort, safety and work economy, have shown that although all of them solve the helical staircase in a really similar way, the fade into oblivion of the non-radial and tangent approaches was objectively motivated.

El vidrio y sus máscaras : el sueño de la arquitectura de cristal

Según Heidegger, la esencia de la arquitectura, de la construcción, descansa en un no espacio: en la materia con que se construyen las fronteras que otorgan espacios, irradiando sobre ellos aquello que los caracteriza. Si hay alguna materia, de las utilizadas por la arquitectura a lo largo de su historia para construir fronteras, que haya mantenido una especial relación con la luz y la visión, dando un carácter inconfundible a los espacios aviados por ellas, esta es el vidrio; algunas de las etimologías de su nombre: zakû (ser claro), hyalos (diáfano) o vitrum (ver), así lo evidencian. Posiblemente, sea la pregnancia de este modo fascinante de relacionarse con la luz, la que ha hecho del vidrio, a lo largo del tiempo que lleva siendo usado en arquitectura, y aún antes, el material que ha provocado en el imaginario humano la ilusión de ser aquel en que, en último término, podrían llegar a sublimarse todos los demás, dando lugar con ello a lo que en la tesis hemos denominado el sueño de la arquitectura de cristal. Siendo la luz, siempre, energía, consideraremos en la tesis luz-energía, a aquella que ilumina y calienta; es una luz científica y mesurable. Cuando la luz se “hace visible”, desvelando un mensaje “contenido” en el vidrio, hablaremos de luz-información. Esta luz, no puede medirse científicamente. La luz-energía y la luz-información, se manifiestan al conjuro de la arquitectura de vidrio. Es la segunda la que ha conformado las fronteras de vidrio enmascarado, y la que se estudia con más detenimiento en la tesis. Los distintos modos de usar en arquitectura la infinita combinatoria de las propiedades de absortancia, reflectancia, transmitancia y translucencia del vidrio, ha condicionado al hombre en su manera de “ver” el mundo. Unas veces, “inmerso” en él, puesto que solo lo separa del mismo, una frontera transparente, y “deseadamente” invisible: ese modo de usar el vidrio, ha sido el sueño imposible de una parte importante de la arquitectura del siglo XX. Otras veces, para “aislarse” de él, el hombre ha manipulado la luz y el vidrio para construir mundos diferentes. Las fronteras de vidrio enmascarado de color, mosaicos, vidrieras, pantallas y lo que hemos llamado vidrios complejos (con un cometido similar al que Schiller atribuía al coro en la tragedia griega, aislar a esta del “mundo real”, para mantener su libertad poética), son las fronteras que han construido el sueño posible de la arquitectura de cristal. Ambas actitudes, en distintos momentos de la historia de la arquitectura, han sido dos formas de querer materializar un mismo sueño. La capacidad del vidrio para adaptarse a tantos modos de presentarse ante nosotros, y a poder ser interpretado de tantas formas diferentes, es la que ha servido para dar título a la tesis, pues hasta en su faceta más transparente, el vidrio, de una forma o de otra, se ha mostrado siempre como un material enmascarado en el más amplio sentido de la palabra: se enmascara, incluso cuando apela a la transparencia o se convierte en espejo, para hacernos caer en la ilusión de que no está presente. Cuando el hombre construyó fronteras de vidrio e incluso antes, cuando soñó que con él podría llegar a construirlas, condensó en ellas toda la mítica, la mística y la epistemología en torno a la luz y la visión, dando lugar a una serie de arquetipos arquitectónicos. En la iglesia bizantina, la luz sobre, o la luz desde, los mosaicos, construyó una frontera titilante; y en la catedral gótica, la luz a través de las vidrieras construyó una frontera radiante; en ambos casos con el fin de alcanzar anagógicamente lo Inteligible. En el siglo XIX, con el descubrimiento de la electricidad y su incorporación a la arquitectura, las fronteras se vuelven fulgurantes, aviando, en este caso, el espacio urbano. Poco antes, en este mismo siglo, el espíritu del gótico tiene un efímero resurgir del que se nutrirá, a comienzos del siglo XX, el expresionismo cristalino, en el que la luz anagógica se hace laica. El espacio urbano fulgurante prefigurado por este movimiento y presente en las ciudades desde principios del siglo XX, fue potenciado a mediados de ese siglo con la aparición de las pantallas, extendiéndose desde entonces, imparable, por todo el planeta. La reciente emergencia de los vidrios complejos, ha abierto la posibilidad de construir fronteras a la carta (de vidrios de propiedades múltiples, seleccionadas de forma voluntaria y variable en cada momento). En principio, se pensó que, el uso de estos vidrios como cerramiento, podría llegar a constituirse como la panacea de los problemas del material relacionados con la luz-energía, sin necesidad de recurrir a “prótesis”, y manteniendo por tanto la seductora tersura de la fachada; aunque parece que, por ahora, esa posibilidad es, cuando menos, lejana. Sin embargo, en el campo de las megapantallas urbanas (y ,en general, en el de las pantallas de información), ubicuas actualmente en nuestras vidas, los vidrios complejos ayudan a construir los espesos velos de ilusión, que según Lefebvre sirven para mantener el capitalismo, siendo el último estadio de un desarrollo tecnológico, impuesto por el principio de economía del hombre, que como un metrónomo inexorable, y a modo de contrapunto, ha acompañado siempre (de nuevo en palabras de Lefebvre), a la necesidad del gasto, del juego, de la lucha, del arte, de la fiesta. La tecnología y el arte forman parte de la cultura producida por la sociedad y como señala Lévi-Strauss, esa cultura imprime orden; por el contrario, la sociedad, entendida como el conjunto de relaciones que los hombres mantienen entre sí, produce desorden. Del equilibrio entre esos extremos, surge el progreso, incluido el de la arquitectura. Las fronteras de vidrio que analizamos en la tesis –que avían espacios para la espiritualidad, el fasto y el espectáculo o, desde otro punto de vista, para las distintas manifestaciones del poder: la iglesia, la monarquía, el estado o el mercado– también han surgido de esa concomitancia entre el desorden y el orden; y forma parte de ese desorden, la aventura que ha impulsado al genio individual de místicos, alquimistas, geómetras, abades, reyes, inventores, poetas y arquitectos, a explorar, como escribe Apollinaire, vastos y extraños territorios donde el misterio en flor, se ofrece a quien quiera cogerlo, hogueras nuevas de colores nunca vistos, mil fantasmas imponderables a los que dar cuerpo. ABSTRACT According to Heidegger, the essence of architecture, building, lies in a non-space: the material that creates the boundaries from which something begins its presencing, radiating onto them that which characterizes them. If there is any single material amongst all those used throughout the history of architecture to build boundaries which has maintained a special relationship with light and vision, which has bestowed a distinctive character on spaces avid for them, it is glass. This is evidenced in some of its etymologies: zakû (to be clear), hyalos (transparent), vitrum (see). The rich potential of this fascinating way of relating to light in the history of the architectural use of glass, and even before, is possibly what has triggered the illusion in human imagination of being something that can ultimately sublimate all others, giving rise to what in this thesis we call The Dream of Crystal Architecture. Given that light is always energy, in this thesis we consider energy-light to be that which illuminates and warms. This is scientific, measurable light. When light "becomes visible" and reveals a message “contained” in glass, we speak of information-light. This light cannot be measured scientifically. Energy-light and information-light are manifested under the spell of glass architecture. The latter is what has shaped the boundaries of coloured glass, which is studied in this thesis. Architecture's different ways of using the infinite combinations of the absorptance, reflectance, transmittance and translucency of glass has affected the way we humans "see" the world. Sometimes we are "immersed" in it, since only an invisible, transparent boundary separates us from it: this use of glass has characterized a considerable part of 20th century architecture. In other cases, in order to "isolate" us from it, we have manipulated light and glass to build different worlds: the boundaries of glass "masked" by colour, mosaics, stained glass, screens and what we have called complex glazing, which plays a similar role to what Schiller attributed to the chorus in Greek tragedy, isolating it from the "real world" in order to maintain its poetic license. These are the boundaries that have built the viable dream of crystal architecture. These two approaches have been different ways of making same dream come true at different times in the history of architecture. The ability of glass to adapt to so many forms of manifestation, and interpretation, is what has given rise to the title of the thesis. Even in its most transparent facet, glass has one way or another always been a masking material in the broadest sense of the word: it is masked even when it invites transparency or becomes a mirror, triggering the illusion that it is not present. When man began to build glass boundaries, and even before, when he dreamed that he could build them, he condensed in them all the mythology, mysticism and epistemology concerning light and vision, which gave rise to a series of architectural archetypes. In the Byzantine church, light on or from mosaics created tenuous boundaries. In Gothic cathedrals, the light through the stained glass windows constructed radiant boundaries. In both cases the aim was to achieve, in an anagogical way, the Intelligible. In the 19th, the discovery of electricity and its use in architecture led to the production of dazzling boundaries, in this case employed in urban spaces. Earlier in the same century, the Gothic spirit had a short-lived revival, which in the early 20th century drew from crystalline expressionism in which anagogic light became secular. The dazzling urban space prefigured by this movement, present in cities since the early 20th century, was intensified in the mid-century with the emergence of screens, and since then it has spread unstoppably across the world. The recent emergence of complex glasses has made it possible to build boundaries on demand in glass with multiple properties, chosen at will and at whim at any time. Initially it was thought that the use of this glass as a wall could eventually become the panacea for the material problems related to energy-light, without needing to resort to "prosthesis" and thereby maintain the seductive smoothness of the facade. For now, that possibility seems remote, to say the least. In the realm of urban megascreens and information screens in general, now ubiquitous in our lives, complex glasses help to build the thick veils of illusion which, according to Lefebvre, serve to maintain capitalism. Like an inexorable metronome, in counterpoint, this ultimate state of technological development imposed by man's principle of economy has in fact always accompanied (again in the words of Lefebvre), the need to spend, play, fight, art, and party. Technology and art are part of the culture produced by society. As Levi-Strauss says, this culture imposes order. On the contrary, society, understood as a set of relationships amongst people, produces disorder. Progress, including that of architecture, arises from the balance between these two extremes. The glass boundaries analyzed in this thesis, which propitiate spaces for spirituality, pomp and spectacle or, from a different perspective, for the various manifestations of power: the church, the monarchy, the state and the market, have also emerged from the concomitance of order and disorder. One aspect of this disorder is the adventure that has inspired the individual genius of mystics, alchemists, surveyors, abbots, kings, inventors, poets and architects to explore, as Apollinaire says, vast, strange domains where flowering mystery offers itself to whoever wishes to pluck it, new fires, colours you have never seen before, a thousand intangible phantasms still awaiting reality.

Functionalism and Caprice in Stonecutting. The Case of the Nativity Chapel in Burgos Cathedral

Starting from the inaugural text of Philibert de L'Orme, stereotomic treatises and manuscripts are subject to the opposing forces of reason and fancy. The Nativity Chapel in Burgos Cathedral provides an outstanding case study on this subject. It was built in 1571-1582 by Martín de Bérriz and Martín de la Haya, using an oval vault resting on trumpet squinches to span a rectangular bay. Bed joints and rib axes are not planar curves, as usual in oval vaults. This warping is not capricious; we shall argue that it is the outcome of a systematic tracing method. As a result of this process, the slope of the bed joints increases slightly in the first courses, but stays fairly constant after the third course; this solution prevents the upper courses from slipping. Thus, in the Nativity Chapel of Burgos Cathedral, the constraints of masonry construction fostered a singular solution verging on capriccio. It is also worthwhile to remark that the warping of the joints is not easily appreciable to the eye and that the tracing process does not seem to start from a previous conception of the resulting form. All this suggests that we should be quite careful when talking about the whimsical character of Late Gothic and Early Renaissance; in some occasions, apparent caprice is the offspring of practical thinking.

The Islamic Crossed-Arch Domes in Cordoba: Geometry and Structural Analysis of the “Capilla de Villaviciosa”

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 earliest known vaults of this type are found in the Great Mosque of Córdoba, built ca. 960 a.C. The type spread through Spain, and the north of Africa in the 10th to the 16th Centuries, and was used by Guarini and Vittone in the 17th and 18th Centuries in Italy. However, it was used only in a few buildings. Though the literature about the structural behaviour of ribbed Gothic vaults is extensive, so far no structural analysis of crossed arch domes has been made. The purpose of this work is, first to show the way to attack such an analysis within the frame of Modern Limit Analysis of Masonry Structures (Heyman 1995), and then to apply the approach to study the stability of the dome of the Capilla de Villaviciosa. The work may give some clues to art and architectural historians to understand better the origin and development of Islamic dome architecture.

Late Gothic German Vault Design Methods and Its Relationship with Spanish Ribbed Vaults

The arrival of European master masons to Burgos and Toledo during the mid-fifteenth century was essential for the promotion of the late Gothic ribbed vault design techniques in Spain. The Antigua Chapel in Seville Cathedral, designed by the Spanish master mason Simón de Colonia on 1497, provides an outstanding case study on this subject. This vault is characterized by the interlacing of the ribs near the springing, reflecting the influence of German ribbed vault designs. This paper analyses the relationship between German ribbed vaults and their design methods with those of Spanish ribbed vaults; with particular attention to the presence of ribs that cut through one another above the springing, materialized in the work of Simón de Colonia. This characteristic is reflected in some manuscripts in the German area, like the Wiener Sammlungen (15th-16th centuries) and the Codex Miniatus 3 (ca. 1560-1570), but no Spanish documents of the same period make reference to it.

The Irregular Ribbed Vault of the Sacristy of the Cathedral of Saint-Jean Baptiste in Perpignan

The vault of the sacristy of the Cathedral of Saint-Jean Baptiste in Perpignan (France), constructed by the Majorcan architect Guillem Sagrera between 1433 and 1447, is an outstanding, yet strikingly unknown, example of rib vaulting. This paper analyzes the overall construction of the form of the vault, characterized by its highly irregular perimeter, with particular attention to an isolated decorated corbel which solves the problem of the wall support of a group of six ribs and is in stark contrast with the rest of the supports, which are completely unadorned. Given the extreme rigour of Sagrera in all his works (and this one in particular), this apparent “capriccio” must be justified not only by decorative or formal requirements, but also by the constructive logic of Gothic vaulting system

Crossed-arch vaults in late-gothic and early Renaissance vaulting: a problem in building technology transfer

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, 11th_13th 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, Leonardo 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.

The construction of sexpartite vaults in Europe

Sexpartite vaults constitute one of the most interesting chapters in European Gothic architecture. Originally, the use of the square cross-ribbed vault was limited to relatively small spaces, but when the need arose to cover spaces of considerable size, a new vault with very peculiar characteristics appeared. This new vault was a cross-ribbed vault that was reinforced in the centre by a rib that was parallel to the transverse ribs which effectively divided the vault in half. This configuration breaks the side arch into two fragments, creating a pair of windows on each side. The volumetrics of these vaults is extremely complex and the difficulties involved in their construction perhaps explain why they were abandoned in favour of the simple cross ribbed vault, now with rectangular sections. The existence of the sexpartite vault barely lasted more than fifty years, from the end of the XII century and the beginning of the XIII. Towards the end of the 19th century Viollet-le-Duc gave a succinct explanation of this type of vault. A. Choisy also, later, devotes some pages to the French sexpartite vault; since then, the subject has only been broached in a few references in later studies on Gothic architecture. However, despite its short period of existence, the sexpartite vault spread throughout Europe and was used to build important vaulting. Viollet-le-Duc's sexpartite vault could be considered to be the prototype of them all, while it is true that the studies that we have conducted so far lead us to affirm that there is a wide variety of vaults, with different volumetric spaces and different construction strategies. Therefore, we believe that this chapter of international Gothic deserves further study applying the knowledge and resources that are available today. This paper has been written to explore the most significant European sexpartite vaults. New measurement technology has led to a revolution in research into the history of construction, allowing studies to be conducted that were hitherto impossible. Thorough data collection using total station and photogrammetry has enabled us to identify the stereotomy of the voussoirs, tas-de-charges and keystones, as well as the bonding of the surfaces of the severies. A comparison of the construction techniques employed in the different vaults studied reveals common construction features and aspects that are specific to each country. Thus we are able to establish the relationship between sexpartite vaults in different European countries and their influence on each other.