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.

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.

El lenguaje de la estructura: Mies van der Rohe y la construcción con acero y hormigón

John Summerson, en El Lenguaje Clásico de la Arquitectura, defiende que los órdenes clásicos que empleaban los arquitectos romanos para decorar sus edificios, no tienen una función estructural pero hacen expresivos a los edificios. Les hacen hablar. Arthur Schopenhauer afirma que “el destino de la Bella Arquitectura es poner de manifiesto la lucha entre el peso y la rigidez de los elementos estructurales”. Y Auguste Perret define la Arquitectura como “el arte de hacer cantar al punto de apoyo”. El objetivo de esta Tesis Doctoral es profundizar en la capacidad de expresión de la estructura. A través del estudio de las estructuras históricas, que se realiza en la primera parte de la Tesis, podemos concluir que existen tres categorías, tres maneras de expresión de la Estructura. Estructuras Vistas, que hablan, Estructuras Ocultas, que se esconden y Estructuras Ilusorias, que fingen. El Partenón y la Sainte Chapelle de París se estudian en el apartado de Estructuras Vistas. El Panteón, el Palacio de Carlos V, la Catedral de San Pablo en Londres, y otras arquitecturas renacentistas y romanas, en el apartado de Estructuras Ocultas. Y como Estructuras Ilusorias, la Alhambra (Dos Hermanas, Comares, el Patio de los Leones), Santa Sofía, y otras arquitecturas del barroco italiano. En la segunda parte de la Tesis se analiza la obra completa de Mies van der Rohe desde el punto de vista de esas tres categorías. Lo visto, lo oculto y lo ilusorio en las estructuras de Mies. Se estudia la evolución en la estructura de la casa, desde las primeras casas con Estructura Oculta de muro de ladrillo, hasta las últimas casas con Estructura Vista y columnas adelantadas, pasando por una etapa intermedia de casas con estructura mixta de muro de ladrillo en la que el acero comienza a hacer su aparición. Se analizan también seis soluciones estructurales en los Bloques y en las Torres: Estructura Vista reverberante, expresiva o inexpresiva vs Estructura Oculta con vestido horizontal, vestido reticular o vestido vertical. Y por último, se estudian las tres soluciones de Estructura Ilusoria que emplea Mies en sus Pabellones. La metodología de trabajo que se ha empleado se divide en cuatro apartados: El análisis bibliográfico; el análisis in situ de los edificios, que nos permite comprobar, por ejemplo, los efectos lumínicos de la columna acanalada del Partenón, o el efecto reverberante de las columnas de la Weissenhofsiedlung; el análisis crítico de planos y detalles constructivos, que nos lleva a concluir que la disposición de pantallas del Pabellón de Barcelona anula la lectura de la crujía estructural, y que la columna del restaurante Cantor se dispone con su alma perpendicular a la cercha, y no paralela, como cabría suponer si se quisiera aprovechar toda la capacidad portante del perfil en H; y por último, el análisis numérico y estructural, que nos lleva a confirmar el sobredimensionado de la Estructura del Patio de los Leones de la Alhambra o el sobredimensionado de la Estructura de la Casa Farnsworth. Lo que se confirma con esta Tesis Doctoral es que la Estructura es algo más, mucho más, que sólo transmisión de las cargas. ABSTRACT John Summerson, in The Classic Language of Architecture, argues that the classic orders used by Roman architects in the decoration of their buildings did not have a structural function, but made buildings expressive. They make them speak. Arthur Schopenhauer affirms that “the goal of Great Architecture is to highlight the struggle between the gravity and rigidity of structural elements”. And Auguste Perret defines Architecture as “the art of making the points of support sing”. The objective of this Doctoral Thesis is to examine the expressive capacity of structure. Following a study of historic structures in the first part of the thesis, we conclude that three categories exist, three ways of expressing Structure. Visible Structures that speak, Concealed Structures that are hidden and Illusory Structures that pretend. The Parthenon and the Sainte Chapelle in Paris are studied in the section on Visible Structures. The Pantheon, the Palace of Charles V, Saint Paul’s Cathedral in London, and other Renaissance and Roman architectures are dealt with in the Concealed Structures section. And, as examples of Illusory Structures, we focus on the Alhambra (The Hall of the Two Sisters, the Comares and the Court of the Lions), Saint Sophia, and other Italian Baroque architectures. In the second part of the Thesis the complete work of Mies van der Rohe is analysed from the perspective of these three categories. The visible, the concealed and the illusory, in the structures of Mies. We study how the structure of the house evolves, from the first houses with the Hidden Structure of the brick wall, to the later houses with Visible Structures and columns, via an intermediate phase of mixed-structure houses with brick walls, where steel first began to make its appearance. We also analyse six structural solutions in the Blocks and Towers: reverberant, expressive or inexpressive Visible Structure vs Concealed Structure with horizontal cladding, reticular cladding or vertical cladding. And finally, we look at the three Illusory Structure solutions that Mies employs in his Pavilions. The methodology employed is divided into four sections: a bibliographic analysis; an analysis in situ of the buildings, which allows us to test, for example, the lighting effects of the fluted column in the Parthenon, or the reverberant effect of the Weissenhofsiedlung columns; a critical analysis of plans and constructive details, which leads us to conclude that the arrangement of panels in the Barcelona Pavilion cancels out the structural centreline, and that the column in the Cantor restaurant is placed with its web perpendicular to the truss, and not parallel to it, as one might expect if one wanted to avail of all the load-bearing capacity of the H beam; and lastly, a numeric and structural analysis, which confirms the oversizing of the Court of the Lions structure in the Alhambra or the oversized structure of Farnsworth House. All of which confirms in this Doctoral Thesis that structure is something more, much more, than a mere conveyor of loads.

Los tratados y el jardín renacentista en Italia. Principios, metodologías y técnicas

La tesis destaca la influencia que ejerció la teoría, las técnicas y la metodología de proyecto de los principales tratados de la época renacentista en la concepción, diseño y realización de algunos de los más importantes jardines de la época. Los tratados de Vitruvio, Alberti, Filarete, Di Giorgio, Serlio, Palladio, Colonna y Del Riccio establecen una nueva estética y una nueva visión del mundo, basadas en la geometría elemental y en los números simples. En la Grecia antigua, Platón y Pitágoras intuyeron la necesidad existencial del hombre de apoyarse en unas leyes seguras de orden superior. Sus teorías sobre las leyes del Universo son retomadas y aplicadas en el arte y en el jardín por Vitruvio y por los tratadistas del Renacimiento. Según los tratadistas, la estética es el núcleo generador del que se activan la información y las leyes hacia todos los campos del conocimiento y de la vida social y, por lo tanto, la finalidad de los tratados es buscar, a través de un procedimiento científico y racional, las reglas de la belleza. Las leyes estéticas formuladas por los tratadistas examinados se aplican con el mismo rigor y respeto ya sea al paisaje que al jardín, exaltando el elemento natural al igual que el construido (la ciudad y la arquitectura). De los tratados renacentistas se han extraídos términos y conceptos que ayudan a revalorizar, reinterpretar e integrar en el debate los temas del paisaje y del jardín. La tesis sostiene que: 1) una idea moderna de jardín se tiene que fundar en la historia; 2) que la historia es indispensable incluso para enfrentar el problema del mantenimiento y de la restauración de los jardines históricos; 3) que la teoría y las ideas que tienen valor, así como nos enseña Alberti, producen obras que también tienen valor; 4) la influencia de la estética de los tratadistas se encuentra incluso en algunos importantes jardines de época moderna y contemporánea. El capítulo 1 contiene la definición de tratado y la concepción estética del Renacimiento, analizada por medio de: a) la idea de ciencia y b) a través de las pinturas. Los capítulos 2 y 3 contienen respectivamente los principios teóricos de los tratados y el diseño, la metodología, las técnicas constructivas y los métodos de representación del proyecto según los tratadistas. Estos capítulos resultan propedéuticos de los capítulos siguientes por proporcionar el instrumento de lectura e interpretación de los jardines renacentistas y modernos. El capítulo 4 destaca la gran influencia de los tratados sobre las villas y jardines renacentistas y describe sus elementos. El último capítulo, el quinto, contiene un análisis de algunos jardines modernos. Entre ellos: Chiswick, la Villa “I Tatti”, Sutton Place, y la Villa “Il Roseto” que renuevan y prosiguen, en nuestra opinión, la lección de los tratadistas. El primer anexo contiene la propuesta de líneas de investigación que surgen a la luz de la tesis, y el segundo anexo contiene las noticias biográficas de los tratadistas examinados. ABSTRACT The thesis investigates the influence exercised by the theory, techniques and project methodology contained in the most relevant essays on art and architecture of the Renaissance on the concept, design and making of some of the most important gardens of that time. The essays of Vitruvius, Alberti, Filarete, Di Giorgio, Serlio, Palladio, Colonna y Del Riccio established a new concept of aesthetics and a vision of the world based on basic geometry and simple numbers. In ancient Greece, Plato and Pythagoras understood that humans needed “superior laws” to anchor their existences. Their theories on laws of the Universe were adopted and applied in art and gardening by Vitruvius and Renaissance essays authors. According to the authors of these essays, aesthetics represents the core generating information and laws that branch out toward all the fields of knowledge and social life. Therefore, the purpose of art and architecture essays consists in exploring, through a scientific and rational process, the rules of beauty. The laws of aesthetics proposed by the authors apply to landscaping and gardening with the same rigor and exalt the natural component as much as the artificial one (city and architecture). Several terms and concepts are also extracted that, despite their age, still help us to understand and enrich the contemporary debate revolving around landscaping and gardening. The thesis argues that: 1) the modern idea of gardening must be based on history; 2) history is fundamental even to address the topics of maintenance and restoration of historical gardens; 3) like Leon Battista Alberti maintains, valid theory and ideas produce valuable works; 4) the influence played by aesthetics on authors can be found in many important modern and contemporary gardens. Chapter 1 contains the definition of essay and of the Renaissance concept of aesthetics, analyzed by: a) the idea of science and 2) the analysis of some paintings of the period. Chapters 2 and 3 discuss respectively the theoretical principles of the essays and the design, methodology, construction techniques and the methods of representation of the project according to the authors. These chapters are preparatory toward the following chapters and provide us with the keys necessary to read and interpret Renaissance and modern gardens. Chapter 4 highlights the great influence exercised by those authors on the planning of important villas and gardens from the Renaissance while describing their elements. The 5th and final chapter analyzes some modern gardens among which Chiswick, Villa “I Tatti”, Sutton Place, Villa “Il Roseto”. These villas renew and in our opinion carry on the lesson of the essays written in the Renaissance. The first addendum suggests future lines of research derived from the thesis, while the second addendum contains biographical information regarding the authors examined.

Wedges and plate-bandes: mechanical theories after De la Hire

Plate-bandes are straight masonry arches (they are called, also, flat arches or lintel arches). Ideally they have the surfaces of extrados and intrados plane and horizontal. The stones or bricks have radial joints converging usually in one centre. The voussoirs have the form of wedges and in French they are called "claveaux". A plate-bande is, in fact, a lintel made of several stones and the proportions of lintels and plate-bandes are similar. Proportions of plate-bandes, that is the relationship between the thickness t and the span s (t/s)varies, typically between 1/4–1/3 in thick plate-bandes, and is less than 1/20 in the most slender ones. A ratio of circa 1/8 was usual in the 18th Century and follows a simple geometrical rule: the centre form with the intrados an equilateral triangle and the plate-bande should contain an arc of circle. The joints are usually plane, but in some cases present a «rebated» or «stepped» form. Plate-bandes exert an inclined thrust as any masonry arch. This thrust is usually very high and it requires either massive buttresses, or to be built in the middle of thick walls. Master builders and architects have tried since antiquity to calculate the abutment necessary for any arch. A modern architect or engineer will measure the arch thrust in units of force, kN or tons. Traditionally, the thrust has been measured as the size of the buttresses to resist it safely. Old structural rules, then, addressed the design problem establishing a relationship between the span and the depth of the buttress. These were empirical rules, particular for every type of arch or structure in every epoch. Thus, the typical gothic buttress is 1/4 of the vault span, but a Renaissance or baroque barrel vault will need more than 1/3 of the span. A plate-bande would require more than one half of the span; this is precisely the rule cited by the French engineer Gautier, who tried unsuccessfully to justify it by static reasons. They were used, typically, to form the lintels of windows or doors (1-2 m, typically); in Antiquity they were used, also, though rarely, at the gates of city walls or in niches (ca. 2 m, reaching 5.2 m). Plate-bandes may show particular problems: it is not unusual that some sliding of the voussoirs can be observed, particularly in thick plate-bandes. The stepped joints on Fig. 1, left, were used to avoid this problem. There are other «hidden» methods, like iron cramps or the use of stone wedges, etc. In seismic zones these devices were usual. Another problem relates to the deformation; a slight yielding of the abutments, or even the compression of the mortar joints, may lead to some cracking and the descent of the central keystone. Even a tiny descent will convert the original straight line of the intrados in a broken line with a visible «kink» or angle in the middle. Of course, both problems should be avoided. Finally, the wedge form of the voussoirs lead to acute angles in the stones and this can produce partial fractures; this occurs usually at the inferior border of the springers at the abutments. It follows, that to build a successful plate-bande is not an easy matter. Also, the structural study of plate-bandes is far from simple, and mechanics and geometry are related in a particular way. In the present paper we will concentrate on the structural aspects and their constructive consequences, with a historical approach. We will outline the development of structural analysis of plate-bandes from ca. 1700 until today. This brief history has a more than purely academic interest. Different approaches and theories pointed to particular problem, and though the solution given may have been incorrect, the question posed was often pertinent. The paper ends with the application of modern Limit Analysis of Masonry Structures, developed mainly by professor Heyman in the last fifty years. The work aims, also, to give some clues for the actual architect and engineer involved in the analysis or restoration of masonry buildings.

Dynamic Studies of Shell and Spatial Structures

For the past 20 years, dynamic analysis of shells has been one of the most fascinating fields for research. Using the new light materials the building engineer soon discovered that the subsequent reduction of gravity forces produced not only the desired shape freedom but the appearance of ecologic loads as the first factor of design; loads which present strong random properties and marked dynamic influence. On the other hand, the technological advance in the aeronautical and astronautical field placed the engineers in front of shell structures of nonconventional shape and able to sustain substantialy dynamic loads. The response to the increasingly challenger problems of the last two decades has been very bright; new forms, new materials and new methods of analysis have arosen in the design of off-shore platforms, nuclear vessels, space crafts, etc. Thanks to the intensity of the lived years we have at our disposition a coherent and homogeneous amount of knowledge which enable us to face problems of inconceivable complexity when IASS was founded. The open minded approach to classical problems and the impact of the computer are, probably, important factors in the Renaissance we have enjoyed these years, and a good proof of this are the papers presented to the previous IASS meetings as well as that we are going to consider in this one. Particularly striking is the great number of papers based on a mathematical modeling in front of the meagerness of those treating laboratory experiments on physical models. The universal entering of the computer into almost every phase of our lifes, and the cost of physical models, are –may be- reasons for this lack of experimental methods. Nevertheless they continue offering useful results as are those obtained with the shaking-table in which the computer plays an essential role in the application of loads as well as in the instantaneous treatment of control data. Plates 1 and 2 record the papers presented under dynamic heading, 40% of them are from Japan in good correlation with the relevance that Japanese research has traditionally showed in this area. Also interesting is to find old friends as profesors Tanaka, Nishimura and Kostem who presented valuable papers in previous IASS conferences. As we see there are papers representative of all tendencies, even purely analytical! Better than discuss them in detail, which can be done after the authors presentation, I think we can comment in the general pattern of the dynamical approach are summarized in plate 3.

Crossing trellis vaults in Spain and México

The general aim of this study can be summarized in contributin gempirical evidence on the existence, design, fabrication and functioning of the crossing trellis vaults asa constructive expression of the Spanish renaissance moved to the New Spain, today México, and their mutual relation.