Mejora del comportamiento térmico de los morteros de cal aditivados y su empleo en la rehabilitación de inmuebles = Improvement of thermal behaviour of additived lime mortars and their use in rehabilitation of buildings

La envolvente de la edificación es la responsable de equilibrar el intercambio energético entre el interior y el exterior, por lo tanto cualquier actuación encaminada a la reducción del consumo energético ha de establecer, como uno de sus objetivos prioritarios, la mejora del comportamiento de la misma. Las edificaciones anteriores a 1940 constituyen la mayor parte de las existentes en áreas rurales y centros urbanos. En ellas, la repercusión de la fachada sobre las transmitancias globales pone de manifiesto la necesidad de intervención. Sin embargo, su elevada inercia térmica y los importantes saltos térmicos característicos de gran parte de España plantean la importancia de que aquélla se efectúe por el exterior. A tal respecto, la falta de disponibilidad de espesor suficiente para implantar sistemas tipo SATE deriva en que, frecuentemente, la única solución viable sea la de aislar por el interior perdiendo con ello la capacidad de acumulación térmica del muro y con el asociado riesgo de condensaciones. La amplia tradición en el empleo de revestimientos, especialmente en base de cal, permiten que éstos sean utilizados no sólo como elemento estético o de protección de la obra de fábrica antigua sino también para la mejora del comportamiento térmico del soporte, si se aprovecha el mecanismo de transmisión térmica por radiación. Éste es el objetivo de la presente Tesis Doctoral en la que se estudia la modificación de las propiedades radiantes de los morteros de revestimiento para la mejora de la eficiencia energética de las construcciones históricas, principalmente las constituidas por muros monolíticos, aunque podría ser de aplicación a otro tipo de construcciones compuestas por diversas capas. Como punto de partida, se estudió y revisó la documentación disponible sobre las investigaciones de las tres áreas científico-tecnológicas que convergen en la Tesis Doctoral: rehabilitación, material y comportamiento térmico, a partir de lo cual se comprobó la inexistencia de estudios similares al objeto de la presente Tesis Doctoral. Complementariamente, se analizaron los revestimientos en lo concerniente a los materiales que los constituyen, la composición de las mezclas y características de cada una de las capas así como al enfoque que, desde el punto de vista térmico, se estimaba más adecuado para la obtención de los objetivos propuestos. Basándonos en dichos análisis, se preseleccionaron ochenta materiales que fueron ensayados en términos de reflectancia y emisividad para elegir cuatro con los que se continuó la investigación. Éstos, junto con la cal elegida para la investigación y el árido marmóreo característico de la última capa de revestimiento, fueron caracterizados térmicamente, de forma pormenorizada, así como química y físicamente. Los fundamentos teóricos y los estudios preliminares desarrollados con distintos materiales, en estado fresco y endurecido, fueron empleados en la dosificación de componentes de las mezclas, en dos proporciones distintas, para el estudio del efecto del agregado. Éstas se ensayaron en estado fresco, para comprobar su adecuación de puesta en obra y prever su VI adherencia al soporte, así como en estado endurecido a 28 y 90 días de curado, para conocer las propiedades que permitieran prever su compatibilidad con aquél y estimar el alcance de la reducción de transferencias térmicas lograda. Además, se estudiaron las características generales de las mezclas que sirvieron para establecer correlaciones entre distintas propiedades y entender los resultados mecánicos, físicos (comportamiento frente al agua) y energéticos. Del estudio conjunto de las distintas propiedades analizadas se propusieron dos mezclas, una blanca y otra coloreada, cuyas características permiten garantizar la compatibilidad con la obra de fábrica antigua, desde el punto de vista físico y mecánico, y preservar la autenticidad de los revestimientos, en cuanto a la técnica de aplicación tradicional en sistemas multicapa. El comportamiento térmico de las mismas, sobre una obra de fábrica de 40 cm de espesor, se estimó, en estado estacionario y pseudo-transitorio, demostrándose reducciones del flujo térmico entre 16-48%, en condiciones de verano, y entre el 6-11%, en invierno, en función de la coloración y de la rugosidad de la superficie, en comparación con el empleo de la mezcla tradicional. Por lo que, se constata la viabilidad de los materiales compuestos propuestos y su adecuación al objetivo de la investigación. VII ABSTRACT The envelope is responsible for balancing the energy exchange between the inside and outside in buildings. For this reason, any action aimed at reducing energy consumption must establish, as one of its key priorities, its improvement. In rural areas and urban centers, most of the constructions were built before 1940. In them, the impact of the façade on the global transmittance highlights the need for intervention. However, its high thermal inertia and fluctuation of temperatures in the majority of Spain bring up that it should be placed outside the insulation. In this regard, the lack of availability of enough thickness to implement systems such as ETICS results in that often the only viable solution is to isolate the interior, losing thereby the wall’s heat storage capacity with the associated risk of condensation. The tradition in the use of renders, especially lime-based, allows us to use them not only as an aesthetic element or to protect the ancient masonry, but also for improved thermal performance of the support by taking advantage of the heat transfer mechanism by radiation. This is the aim of this Doctoral Thesis in which the modification of the radiative properties of lime mortars for renders to improve the energy efficiency of historic buildings, mainly composed of monolithic walls, is studied, although it could be applied to other structures composed of several layers. As a starting point, the available literature in the three scientific-technological areas that converge at the Doctoral Thesis: rehabilitation, material and thermal behaviour, was reviewed, and confirmed the absence of researches similar to this Doctoral Thesis. Additionally, the renders were studied with regard to the materials that constitute them, the composition of the mixtures and the characteristics of each layer, as well as to the approach which, from a thermal point of view, was deemed the most suitable for achieving the objectives sets. Based on thre aforementioned analysis, eighty materials tested in terms of reflectance and emissivity were pre-selected, to choose four with which the research was continued. Common marble sand, used in the last layer of the renders, together with the appointed materials and hydrated lime were characterized thermally, in detail, as well as chemically and physically. The theoretical bases and preliminary studies with different materials, in fresh and hardened state, were used in the dosage of the composition of the mixtures. In order to study their effect they were used in two different proportions, that is, ten mixtures in total. These were tested in their fresh state to evaluate their setting-up suitability and foresee their adhesion to the support, as well as in their hardened state, at 28 and 90 days of curing, to establish the properties which enabled us to anticipate their compatibility with the old masonry walls and estimate the scope of the reduction of heat transfers achieved. In addition, the general characteristics of the mixtures used to establish correlations and to understand the mechanical, physical and energy results were studied. Two mixtures, one white and one colored, were proposed as the result of the different properties analysed, whose characteristics allow the guarantee of mechanical and physical compatibility VIII with the old masonry and preserve the authenticity of the renders. The thermal behavior of both, applied on a masonry wall 40 cm thick, was estimated at a steady and pseudo-transient state, with heat flow reductions between 16-48% during summertime and 6-11% during wintertime, depending on the color and surface roughness, compared to the use of the traditional mixture. So, the viability of the proposed composite materials and their fitness to the aim of the research are established.

Bovedas Encamonadas: Origen, Evolucion, Geometria y Construccion entre los Siglos XVII y XVIII en el Virreinato de Perú

Desde la creación del Virreinato del Perú, en el siglo XVI, los arcos, bóvedas y cúpulas se acostumbraban a levantar con piedra y fábrica. Sin embargo estas tierras eran sacudidas periodicamente por terremotos, produciendo el colapso de la mayoría de estas edificaciones. Para el siglo XVII los alarifes ya habían experimentado diversas maneras de levantar bóvedas, sin haberse encontrado una respuesta razonable en términos de tiempo, economía y estabilidad frente a los sismos. En medio de este panorama se produjo la introducción de las bóvedas encamonadas a mediados del siglo XVII, consolidandose en el resto de la centuria hasta el punto de terminar convirtiéndose en un recurso tradicional y de estimada elaboración dentro de la arquitectura virreinal peruana. Las bóvedas encamonadas se realizaban con tablas de madera (camones) que se solapaban entre sí para formar arcos (cerchas), los cuales definían la forma que tendrían las bóvedas, y eran estabilizados lateralmente mediante correas. Sobre los arcos y correas se colocaba un cerramiento que podía ser un entablado, unos listones de madera o simplemente un tendido a base de cañas. En la mayoría de casos se finalizaba con un recubrimiento aislante de barro por el extradós y otro decorativo de yeso por el intradós. Precisamente estas bóvedas constituyen el objeto de la presente tesis, específicamente en su devenir histórico entre los siglos XVII y XVIII en el ámbito territorial del Virreinato del Perú, partiendo del examen de los tratados de arquitectura coetáneos y del estudio de las bóvedas de madera en España, para finalizar con el análisis de las características geométricas y constructivas que lograron definir en ellas los alarifes peruanos. Since the creation of the Viceroyalty of Peru, in the sixteenth century, arches, vaults and domes were accustomed to build with stone and masonry. However, these lands were periodically shaken by earthquakes, causing the collapse of most of these buildings. For the seventeenth century the master masons had already experienced several ways to build vaults, without having found a reasonable response in terms of time, economy and stability against earthquakes. Into this context the master carpenters introduced the wooden vaults since seventeenth century, and this constructive system was consolidated around the rest of the century to the end point of becoming a traditional and estimated resource of the Peruvian colonial architecture. The wooden vaults were made with timber planks (camones) that overlapped each other to form arches (cerchas), which defined the shape of the vaults, and were stabilized laterally by purlins. Above the arches and purlins placed planks, wooden strips or just cane. In most cases ended with a mud plaster insulating the extrados and a decorative gypsum plaster on the intrados. Precisely these vaults are the subject of this thesis, specifically in its historical way between the seventeenth and eighteenth centuries in the territory of the Viceroyalty of Peru. Since an examination of the architectural treatises and the Spanish wooden vaults, and concluding with the analysis of the geometric and constructive system that Peruvian builders were able to define on them.

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.

Fisuración y deformaciones en tabiquerías

A diferencia de otros parámetros, el efecto de la existencia de huecos en la aparición y desarrollo de los procesos de fisuración en los paños de fábrica no ha sido considerado por las distintas normativas existentes en la actualidad. En nuestros días se emplea una variada gama de tipologías de elementos de cerramiento para realizar las particiones en las obras de edificación, cada una de ellas con características mecánicas diferentes y distinta metodología de ejecución, siendo de aplicación la misma normativa relativa al cálculo y control de las deformaciones. Tal y como expresamos en el Capitulo 1, en el que se analiza el Estado del Conocimiento, los códigos actuales determinan de forma analítica la flecha probable que se alcanza en los elementos portantes estructurales bajo diferentes condiciones de servicio. Las distintas propuestas que existen respecto para la limitación de la flecha activa, una vez realizado el cálculo de las deformaciones, bien por el método de Branson ó mediante los métodos de integración de curvaturas, no contemplan como parámetro a considerar en la limitación de la flecha activa la existencia y tipología de huecos en un paño de fábrica soportado por la estructura. Sin embargo se intuye y podríamos afirmar que una discontinuidad en cualquier elemento sometido a esfuerzos tiene influencia en el estado tensional del mismo. Si consideramos que, de forma general, los procesos de fisuración se producen al superarse la resistencia a tracción de material constitutivo de la fábrica soportada, es claro que la variación tensional inducida por la existencia de huecos ha de tener cierta influencia en la aparición y desarrollo de los procesos de fisuración en los elementos de partición o de cerramiento de las obras de edificación. En los Capítulos 2 y 3 tras justificar la necesidad de realizar una investigación encaminada a confirmar la relación entre la existencia de huecos en un paño de fábrica y el desarrollo de procesos de fisuración en el mismo, se establece este aspecto como principal Objetivo y se expone la Metodología para su análisis. Hemos definido y justificado en el Capítulo 4 el modelo de cálculo que hemos utilizado para determinar las deformaciones y los procesos de fisuración que se producen en los casos a analizar, en los que se han considerado como variables: los valores de la luz del modelo, el estado de fisuración de los elementos portantes, los efectos de la fluencia y el porcentaje de transmisión de cargas desde el forjado superior al paño de fábrica en estudio. Además se adoptan dos valores de la resistencia a tracción de las fábricas, 0.75MPa y 1.00MPa. La capacidad de representar la fisuración, así como la robustez y fiabilidad ha condicionado y justificado la selección del programa de elementos finitos que se ha utilizado para realizar los cálculos. Aprovechando la posibilidad de reproducir de forma ajustada las características introducidas para cada parámetro, hemos planteado y realizado un análisis paramétricos que considera 360 cálculos iterativos, de cuya exposición es objeto el Capítulo 5, para obtener una serie representativa de resultados sobre los que se realizará el análisis posterior. En el Capítulo 6, de análisis de los resultados, hemos estudiado los valores de deformaciones y estados de fisuración obtenidos para los casos analizados. Hemos determinado la influencia que tiene la presencia de huecos en la aparición de los procesos de fisuración y en las deformaciones que se producen en las diferentes configuraciones estructurales. Las conclusiones que hemos obtenido tras analizar los resultados, incluidas en el Capítulo 7, no dejan lugar a dudas: la presencia, la posición y la tipología de los huecos en los elementos de fábricas soportadas sobre estructuras deformables son factores determinantes respecto de la fisuración y pueden tener influencia en las deformaciones que constituyen la flecha activa del elemento, lo que obliga a plantear una serie de recomendaciones frente al proyecto y frente a la reglamentación técnica. La investigación desarrollada para esta Tesis Doctoral y la metodología aplicada para su desarrollo abre nuevas líneas de estudio, que se esbozan en el Capítulo 8, para el análisis de otros aspectos que no han sido cubiertos por esta investigación a fin de mejorar las limitaciones que deberían establecerse para los Estados Límite de Servicio de Deformaciones correspondientes a las estructuras de edificación. SUMMARY. Unlike other parameters, the effect of the existence of voids in the arising and development of cracking processes in the masonry walls has not been considered by current Codes. Nowadays, a huge variety of enclosure elements types is used to execute partitions in buildings, each one with different mechanical characteristics and different execution methodology, being applied the same rules concerning deflection calculation and control. As indicated in Chapter 1, which analyzes the State of Art, current codes analytically determine the deflection likely to be achieved in structural supporting elements under different service conditions. The different proposals that exist related to live deflection limitation, once performed deformations calculation, either by Branson´s method or considering curvatures integration methods, do not consider in deflection limitation the existence and typology of voids in a masonry wall structured supported. But is sensed and it can be affirmed that a discontinuity in any element under stress influences the stress state of it. If we consider that, in general, cracking processes occur when masonry material tensile strength is exceeded, it is clear that tension variation induced by the existence of voids must have some influence on the emergence and development of cracking processes in enclosure elements of building works. In Chapters 2 and 3, after justifying the need for an investigation to confirm the relationship between the existence of voids in a masonry wall and the development of cracking process in it, is set as the main objective and it is shown the analysis Methodology. We have defined and justified in Chapter 4 the calculation model used to determine the deformation and cracking processes that occur in the cases analyzed, in which were considered as variables: model span values, bearing elements cracking state, creep effects and load transmission percentage from the upper floor to the studied masonry wall. In addition, two masonry tensile strength values 0.75MPa and 1.00MPa have been considered. The cracking consideration ability, robustness and reliability has determined and justified the selection of the finite element program that was used for the calculations. Taking advantage of the ability of accurately consider the characteristics introduced for each parameter, we have performed a parametric analyses that considers 360 iterative calculations, whose results are included in Chapter 5, in order to obtain a representative results set that will be analyzed later. In Chapter 6, results analysis, we studied the obtained values of deformation and cracking configurations for the cases analyzed. We determined the influence of the voids presence in the occurrence of cracking processes and deformations in different structural configurations. The conclusions we have obtained after analyzing the results, included in Chapter 7, leave no doubt: the presence, position and type of holes in masonry elements supported on deformable structures are determinative of cracking and can influence deformations which are the element live deflection, making necessary to raise a number of recommendations related to project and technical regulation. The research undertaken for this Doctoral Thesis and the applied methodology for its development opens up new lines of study, outlined in Chapter 8, for the analysis of other aspects that are not covered by this research, in order to improve the limitations that should be established for Deflections Serviceability Limit States related to building structures.

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.

Structural Analysis of Thin Tile Vaults and Domes: The Inner Oval Dome of the Basilica de los Desamparados in Valencia

The inner oval dome of the Basílica de la Virgen los Desamparados, built in 1701, is one of the most slender masonry vaults ever built. It is a tile dome with a total thickness of 80 mm and a main span of 18.50 m. It was built without centering with great ingenuity and economy of means, thirty three years after the termination of the building in 1667. The dome is in contact with the external dome only in the inferior part with the projecting ribs of the intrados, the lunettes of the windows, and, in the upper part, through 126 inclined iron bars. This unique construction was revealed in the 1990's in the studies previous to the restoration of the Basílica, and has given rise to different theories about the mode of construction and the structural behaviour and safety of the dome. The present contribution aims to provide a plausible hypothesis about the mode of construction and to explain the safety of the inner dome which has stood, without need of repairs or reinforcement, for 300 hundred years.

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.

The Ciborium or Lantern Tower of Valencia Cathedral: Geometry, Construction and Stability

Early 18th century treatise writer Tomas Vicente Tosca1 includes in his Tratado de la montea y cortes de Canteria [On Masonry Design and Stone Cutting], what is an important documentary source about the lantern of Valencia Cathedral. Tosca writes about this lantern as an example of vaulting over cross arches without the need of buttresses. A geometrical description is followed by an explanation of the structural behavior which manifests his deep understanding of the mechanics of masonry structures. He tries to demonstrate the absence of buttresses supporting his thesis on the appropriate distribution of loads which will reduce the "empujos" [horizontal thrusts] to the point of not requiring more than the thickness of the walls to stand (Tosca [1727] 1992, 227-230). The present article2 assesses T osca' s appreciation studying how loads and the thrusts they generate are transmitted through the different masonry elements that constitute this ciborium. In order to do so, we first present a geometrical analysis and make considerations regarding its materials and construction methods to, subsequently, analyze its stability adopting an equilibrium approach within the theoretical framework of the lower bound limit analysis.

The Ciborium or Lantern Tower of Valencia Cathedral: Geometry, Construction and Stability

Early 18th century treatise writer Tomas Vicente Tosca1 includes in his Tratado de la montea y cortes de Canteria [On Masonry Design and Stone Cutting], what is an important documentary source about the lantern of Valencia Cathedral. Tosca writes about this lantern as an example of vaulting over cross arches without the need of buttresses. A geometrical description is followed by an explanation of the structural behavior which manifests his deep understanding of the mechanics of masonry structures. He tries to demonstrate the absence of buttresses supporting his thesis on the appropriate distribution of loads which will reduce the "empujos" [horizontal thrusts] to the point of not requiring more than the thickness of the walls to stand (Tosca [1727] 1992, 227-230). The present article2 assesses T osca' s appreciation studying how loads and the thrusts they generate are transmitted through the different masonry elements that constitute this ciborium. In order to do so, we first present a geometrical analysis and make considerations regarding its materials and construction methods to, subsequently, analyze its stability adopting an equilibrium approach within the theoretical framework of the lower bound limit analysis.

Ethics and materials: Some Spanish Cases

The problem is general: modern architects and engineers are trying to understand historic structures using the wrong theoretical frame, the classic (elastic) thery of structures developed in the 19th Century for iron and stell, and in the 20th century for reinforced concrete, disguised with "modern" computer packages, mainly FEM, but also others. Masonry is an essentially different material, and the structural equations must be adapted accordingly. It is not a matter of "taste" or "opinion", and the consequences are before us. Since, say 1920s, historic monuments have suffered the aggression of generations of archietcts and engineers, trying to transform masonry in reinfored concrete or steel. The damage to the monuments and the expense has been, and is, enormous. However, as we have an adequate theory (modern limit analysis of masonry structures, Heyman 1966) which encompasses the "old theory" used successfully by the 18th and 19th Century practical engineers (from Perronet to Sejourné), it is a matter of "Ethics" not to use the wrong approach. It is also "contra natura" to modify the material masonry with indiscriminate injections, stitchings, etc. It is insane to consider, suddenly, that buildings which are Centuries or milennia old, are suddenly in danger of collapse. Maintenance is necessary but not the actual destruction of the constructive essence of the monument. A cocktail of "ignorance, fear and greed" is acting under the best of intentions.

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.

Bóvedas y contrarresto del Colegio de Nuestra Señora de la Antigua de Monforte de Lemos : geometría, construcción y mecánica

El Colegio de Nuestra Señora de la Antigua de Monforte de Lemos (1593-1619) constituye el principal ejemplo del clasicismo herreriano de Galicia. Esta tesis analiza los aspectos técnicos de la construcción de sus bóvedas de cantería, en el marco disciplinar de la Historia de la Construcción. El Colegio contiene varios tipos de bóvedas entre las que destacan su cúpula trasdosada y su escalera monumental. Además, se conservan los documentos notariales históricos que describen las obras y una de las monteas más importantes de Galicia. Las bóvedas han sufrido movimientos y algunas presentan importantes deformaciones, que han suscitado preocupación sobre su estabilidad. El estudio se organiza en tres epígrafes: geometría, construcción y mecánica, tres aspectos estrechamente interrelacionados en este tipo de estructuras. La parte de estudio geométrico parte de un levantamiento en el que se emplea una estación total sin reflectante, una técnica que permite una medición muy precisa de la forma real de las bóvedas. Como complemento se ha recurrido a técnicas de escáner fotográfico. Con los datos de las mediciones se han elaborado los dibujos de las bóvedas, y analizado sus medidas e irregularidades. Se ha incluido un análisis metrológico por métodos inductivos, que ha puesto de manifiesto la unidad utilizada en la construcción. El estudio se completa con la recopilación de las reglas de dimensionamiento que figuran en los tratados, que se comparan con las dimensiones de las bóvedas analizadas. En el estudio constructivo se registran los despieces y la configuración constructiva y se contrastan, por un lado, con las soluciones que aparecen en los principales tratados de los siglos XVI, XVII y XVIII, y por otro, con las descripciones que se encuentran en los documentos históricos del Colegio. Se ha prestado especial atención al estudio de estos documentos, que han permitido conocer algunos aspectos originales del proceso de construcción de estas bóvedas. En una de las paredes del claustro se ha identificado una montea inédita cuyo levantamiento y análisis se incorpora en esta parte. En el estudio mecánico se analiza la estabilidad dentro del marco teórico del Moderno Análisis Límite de Estructuras de Fábricas. La comprensión del comportamiento estructural, unida a la precisión de los levantamientos, ha permitido explicar los movimientos de las fábricas e inferir la geometría original de algunas de las bóvedas, no siempre evidente en los casos de fuertes deformaciones. Los estudios realizados hasta ahora en bóvedas de los siglos XVI y XVII permiten vislumbrar un panorama de soluciones constructivas más rico que el que recogen los tratados históricos. Las nuevas técnicas de medición sin contacto abren nuevas posibilidades para analizar estas estructuras. Los casos estudiados todavía son escasos y se necesita un conjunto más amplio para poder realizar un análisis general. Esta tesis aporta el estudio de uno de esos casos con el fin de contribuir al mejor conocimiento de la construcción en España en los siglos XVI y XVII. ABSTRACT The Colegio de Nuestra Señora de la Antigua (1593-1619), in Monforte de Lemos, Spain, is the best example in Galicia of the classicism influenced by the Monastery of El Escorial and his architect, Juan de Herrera. This thesis analyzes the technical aspects of the construction of its masonry vaults within the discipline of Construction History. The Colegio exhibits various types of vaults, among which the extradosed ashlar dome and the grand staircase are particularly worth mentioning. In addition, the legal documents containing thorough specifications of the work, as well as one of the construction drawings at actual size —one of the best examples in Galicia—, have both been preserved to this date. Some of the vaults have undergone important deformations that have raised concerns about their stability. The study is organized in three sections: geometry, construction, and mechanics, the three clearly interrelated in this type of structures. The geometrical study starts out with a metric survey using a reflectorless total station, a technique that allows a very precise measurement of the actual shape of the vault. This technique was complemented with the use of a photo-based 3D scanner. The resulting measurements were used to draw the vaults, and analyze their dimensions and irregularities. An inductive metrological analysis, which was able to reveal the exact metric unit utilized during the construction, is included in this section. The section is completed with the gathering of the dimensional rules appearing in the various historical treatises, which are compared with the dimensions of the actual vaults. The construction study deals with the quartering of the structure, whose results are compared, on the one hand, with the approaches appearing in the main treatises of the 16th- 18th centuries, and on the other, with the descriptions in the historical documents of the Colegio itself. Special attention has been paid to the study of these documents, which have revealed some original aspects in the construction process of the vaults. In one of the cloister’s walls, a hitherto unheard-of construction drawing at actual size was found. Its survey and analysis is included in this section. The mechanical study analyzes the Colegio's vaults stability within the theoretical frame of the Modern Limit Analysis of Masonry Structures. The interpretation of the structural behavior, coupled with the precision of the surveys, has allowed a deep understanding of the masonry���s movements and the original geometry of some of the vaults —not always evident in the case of strong deformations— has been inferred. The studies dealing with XVI and XVII century vaults conducted up to this date show a landscape of constructive solutions far richer than the one suggested in the historical treatises. The new contactless measuring techniques offer exciting possibilities for the analysis of these structures. The cases studied are still few and more would be needed before a general analysis can be attempted. This thesis constitutes one such additional case and its goal is to improve our understanding of Spanish construction in the 16th-17th centuries.

El problema del rozamiento en el análisis de estructuras de fábrica mediante modelos de sólidos rígidos

La evaluación de la seguridad de estructuras antiguas de fábrica es un problema abierto.El material es heterogéneo y anisótropo, el estado previo de tensiones difícil de conocer y las condiciones de contorno inciertas. A comienzos de los años 50 se demostró que el análisis límite era aplicable a este tipo de estructuras, considerándose desde entonces como una herramienta adecuada. En los casos en los que no se produce deslizamiento la aplicación de los teoremas del análisis límite estándar constituye una herramienta formidable por su simplicidad y robustez. No es necesario conocer el estado real de tensiones. Basta con encontrar cualquier solución de equilibrio, y que satisfaga las condiciones de límite del material, en la seguridad de que su carga será igual o inferior a la carga real de inicio de colapso. Además esta carga de inicio de colapso es única (teorema de la unicidad) y se puede obtener como el óptimo de uno cualquiera entre un par de programas matemáticos convexos duales. Sin embargo, cuando puedan existir mecanismos de inicio de colapso que impliquen deslizamientos, cualquier solución debe satisfacer tanto las restricciones estáticas como las cinemáticas, así como un tipo especial de restricciones disyuntivas que ligan las anteriores y que pueden plantearse como de complementariedad. En este último caso no está asegurada la existencia de una solución única, por lo que es necesaria la búsqueda de otros métodos para tratar la incertidumbre asociada a su multiplicidad. En los últimos años, la investigación se ha centrado en la búsqueda de un mínimo absoluto por debajo del cual el colapso sea imposible. Este método es fácil de plantear desde el punto de vista matemático, pero intratable computacionalmente, debido a las restricciones de complementariedad 0 y z 0 que no son ni convexas ni suaves. El problema de decisión resultante es de complejidad computacional No determinista Polinomial (NP)- completo y el problema de optimización global NP-difícil. A pesar de ello, obtener una solución (sin garantía de exito) es un problema asequible. La presente tesis propone resolver el problema mediante Programación Lineal Secuencial, aprovechando las especiales características de las restricciones de complementariedad, que escritas en forma bilineal son del tipo y z = 0; y 0; z 0 , y aprovechando que el error de complementariedad (en forma bilineal) es una función de penalización exacta. Pero cuando se trata de encontrar la peor solución, el problema de optimización global equivalente es intratable (NP-difícil). Además, en tanto no se demuestre la existencia de un principio de máximo o mínimo, existe la duda de que el esfuerzo empleado en aproximar este mínimo esté justificado. En el capítulo 5, se propone hallar la distribución de frecuencias del factor de carga, para todas las soluciones de inicio de colapso posibles, sobre un sencillo ejemplo. Para ello, se realiza un muestreo de soluciones mediante el método de Monte Carlo, utilizando como contraste un método exacto de computación de politopos. El objetivo final es plantear hasta que punto está justificada la busqueda del mínimo absoluto y proponer un método alternativo de evaluación de la seguridad basado en probabilidades. Las distribuciones de frecuencias, de los factores de carga correspondientes a las soluciones de inicio de colapso obtenidas para el caso estudiado, muestran que tanto el valor máximo como el mínimo de los factores de carga son muy infrecuentes, y tanto más, cuanto más perfecto y contínuo es el contacto. Los resultados obtenidos confirman el interés de desarrollar nuevos métodos probabilistas. En el capítulo 6, se propone un método de este tipo basado en la obtención de múltiples soluciones, desde puntos de partida aleatorios y calificando los resultados mediante la Estadística de Orden. El propósito es determinar la probabilidad de inicio de colapso para cada solución.El método se aplica (de acuerdo a la reducción de expectativas propuesta por la Optimización Ordinal) para obtener una solución que se encuentre en un porcentaje determinado de las peores. Finalmente, en el capítulo 7, se proponen métodos híbridos, incorporando metaheurísticas, para los casos en que la búsqueda del mínimo global esté justificada. Abstract Safety assessment of the historic masonry structures is an open problem. The material is heterogeneous and anisotropic, the previous state of stress is hard to know and the boundary conditions are uncertain. In the early 50's it was proven that limit analysis was applicable to this kind of structures, being considered a suitable tool since then. In cases where no slip occurs, the application of the standard limit analysis theorems constitutes an excellent tool due to its simplicity and robustness. It is enough find any equilibrium solution which satisfy the limit constraints of the material. As we are certain that this load will be equal to or less than the actual load of the onset of collapse, it is not necessary to know the actual stresses state. Furthermore this load for the onset of collapse is unique (uniqueness theorem), and it can be obtained as the optimal from any of two mathematical convex duals programs However, if the mechanisms of the onset of collapse involve sliding, any solution must satisfy both static and kinematic constraints, and also a special kind of disjunctive constraints linking the previous ones, which can be formulated as complementarity constraints. In the latter case, it is not guaranted the existence of a single solution, so it is necessary to look for other ways to treat the uncertainty associated with its multiplicity. In recent years, research has been focused on finding an absolute minimum below which collapse is impossible. This method is easy to set from a mathematical point of view, but computationally intractable. This is due to the complementarity constraints 0 y z 0 , which are neither convex nor smooth. The computational complexity of the resulting decision problem is "Not-deterministic Polynomialcomplete" (NP-complete), and the corresponding global optimization problem is NP-hard. However, obtaining a solution (success is not guaranteed) is an affordable problem. This thesis proposes solve that problem through Successive Linear Programming: taking advantage of the special characteristics of complementarity constraints, which written in bilinear form are y z = 0; y 0; z 0 ; and taking advantage of the fact that the complementarity error (bilinear form) is an exact penalty function. But when it comes to finding the worst solution, the (equivalent) global optimization problem is intractable (NP-hard). Furthermore, until a minimum or maximum principle is not demonstrated, it is questionable that the effort expended in approximating this minimum is justified. XIV In chapter 5, it is proposed find the frequency distribution of the load factor, for all possible solutions of the onset of collapse, on a simple example. For this purpose, a Monte Carlo sampling of solutions is performed using a contrast method "exact computation of polytopes". The ultimate goal is to determine to which extent the search of the global minimum is justified, and to propose an alternative approach to safety assessment based on probabilities. The frequency distributions for the case study show that both the maximum and the minimum load factors are very infrequent, especially when the contact gets more perfect and more continuous. The results indicates the interest of developing new probabilistic methods. In Chapter 6, is proposed a method based on multiple solutions obtained from random starting points, and qualifying the results through Order Statistics. The purpose is to determine the probability for each solution of the onset of collapse. The method is applied (according to expectations reduction given by the Ordinal Optimization) to obtain a solution that is in a certain percentage of the worst. Finally, in Chapter 7, hybrid methods incorporating metaheuristics are proposed for cases in which the search for the global minimum is justified.

La catedral de Ávila : evolución constructiva y análisis estructural

Esta tesis se enmarca en el ámbito de la Historia de la Construcción, se estudia la Catedral de Ávila desde un punto de vista técnico, necesario para completar la visión que de esta catedral se tenía. La interpretación de la documentación de archivo, que se encontraba dispersa e inconexa, ha permitido realizar una cronología revisada y completa de las campañas constructivas para el conjunto de la Catedral, desde el siglo XI al XXI. Mediante el análisis de los Contratos de Obra e Informes, se ha puesto de relieve conocimientos de técnicas constructivas medievales. Se plantean dos hipótesis para el orden en el proceso constructivo. En la zona del Cimorro, en relación con la supresión de la tribuna, colocación de los arbotantes y construcción de la fortificación y triple almenado. En el cuerpo de las naves, referida a la posible existencia de una tribuna, colocación del sistema de contrarresto que vemos actualmente y misión del arco entibo del coro. Se ha analizado la estabilidad estructural de la Catedral bajo el marco teórico del Análisis Límite para Estructuras de Fábrica, utilizando la restitución gráfica procedente del levantamiento topográfico realizado. Estos análisis han servido como comprobación de las hipótesis planteadas, por realizarse tanto para la situación actual como para las diferentes campañas constructivas propuestas. Se ha comprobado la validez de las reglas geométricas tradicionales para el análisis de la estructuras de fábrica en los elementos principales de la estructura gótica. Esta tesis incrementa el conocimiento de la historia mecánica del edificio interpretando el funcionamiento mecánico de sus arbotantes, proyectados de forma atípica, y la colocación de los arcos entibo y codales para conseguir la estabilidad del conjunto. La tesis cuenta con un anexo que recopila una extensa documentación gráfica: planimetría, iconografía y fotografía histórica; la trascripción inédita del Contrato de obra para la Capilla de San Segundo y un anexo de cálculo de la zona del Cimorro y del Cuerpo de Naves. This thesis aims to the field of Construction History. The Cathedral of Ávila is studied from a technical point of view, which was necessary to complete the existing knowledge about this Cathedral. The interpretation of archive documentation, which was disperse and unconnected before this work, has allowed the proposal of a revised and complete chronology of the diverse building stages of the Cathedral, dating from the XI century to the XXI century. The analysis of work contracts and of reports has revealed knowledge of medieval construction techniques. Two hypotheses are presented about the order in the construction process. The first hypothesis concerning the destruction of the tribune, the placing of the flying buttress and the building of the fortification and triple system of battlement in the area of the “Cimorro”. The second hypothesis regarding the naves: the possible existence of a tribune, the placing of the system of counterthrust, which can currently be seen, and the function of the “entibo” arch in the choir. The Structural Stability of the Cathedral has been analysed within the theoretical Framework of Limit Analysis to Masonry Structure, by using of the drawing proceeding from our lifting topographical. These analyses have proven the presented hypotheses, since they have been applied to the current situation as well as to the several building stage proposed in the chronology. The validity of the traditional geometric rules for the analysis of the masonry structure in the core elements of Gothic structures has been verified. This thesis increases the knowledge of the mechanical history of the building by interpreting the mechanical working of the flying buttress in an atypical arrangement and the placing of the “entibo” arch and “codal” arch in order to obtain the stability of the monument. The thesis incorporates supplementary material which can be categorized in three groups: 1) extensive graphic documentation (planning, iconography and history photography); 2) the hitherto unknown transcription of the “CONTRATO DE OBRA PARA LA CAPILLA DE SAN SEGUNDO”; 3) an appendix of Analysis of Calculation for the “Cimorro” and the naves.

Seismic vulnerability analysis of wide-beam buildings in Spain

A number of short-to-mid height RC buildings with wide beams have been constructed in moderate-seismicity areas of Spain. The seismic behavior in the direction of the wide beams appears to be deficient because of low lateral strength, low ductility of the wide beams, big strut compressive forces inside the column-beam connections, and unreliable contribution of the spandrel zones of the wide beams. In the orthogonal direction, the behavior is worse since only the joists and the façade beams contribute to the lateral resistance. The objective is to assess the seismic capability of these structures; further research will involve proposing retrofit strategies. The research approach consists of selecting a number of representative buildings and evaluating their vulnerability by code-type, push-over and dynamic analyses. The cooperation of the masonry infill walls is accounted for. The main conclusion is that the seismic behavior of these buildings is inadequate in most of the situations.