Timing performances of a data acquisition system for time of flight PET

We are investigating the performances of a data acquisition system for Time of Flight PET, based on LYSO crystal slabs and 64 channels Silicon Photomultipliers matrices (1.2 cm2 of active area each). Measurements have been performed to test the timing capability of the detection system (SiPM matices coupled to a LYSO slab and the read-out electronics) with both test signal and radioactive source.

Experimental and numerical analysis of reinforced concrete elements subjected to blast loading

El hormigón es uno de los materiales de construcción más empleados en la actualidad debido a sus buenas prestaciones mecánicas, moldeabilidad y economía de obtención, entre otras ventajas. Es bien sabido que tiene una buena resistencia a compresión y una baja resistencia a tracción, por lo que se arma con barras de acero para formar el hormigón armado, material que se ha convertido por méritos propios en la solución constructiva más importante de nuestra época. A pesar de ser un material profusamente utilizado, hay aspectos del comportamiento del hormigón que todavía no son completamente conocidos, como es el caso de su respuesta ante los efectos de una explosión. Este es un campo de especial relevancia, debido a que los eventos, tanto intencionados como accidentales, en los que una estructura se ve sometida a una explosión son, por desgracia, relativamente frecuentes. La solicitación de una estructura ante una explosión se produce por el impacto sobre la misma de la onda de presión generada en la detonación. La aplicación de esta carga sobre la estructura es muy rápida y de muy corta duración. Este tipo de acciones se denominan cargas impulsivas, y pueden ser hasta cuatro órdenes de magnitud más rápidas que las cargas dinámicas impuestas por un terremoto. En consecuencia, no es de extrañar que sus efectos sobre las estructuras y sus materiales sean muy distintos que las que producen las cargas habitualmente consideradas en ingeniería. En la presente tesis doctoral se profundiza en el conocimiento del comportamiento material del hormigón sometido a explosiones. Para ello, es crucial contar con resultados experimentales de estructuras de hormigón sometidas a explosiones. Este tipo de resultados es difícil de encontrar en la literatura científica, ya que estos ensayos han sido tradicionalmente llevados a cabo en el ámbito militar y los resultados obtenidos no son de dominio público. Por otra parte, en las campañas experimentales con explosiones llevadas a cabo por instituciones civiles el elevado coste de acceso a explosivos y a campos de prueba adecuados no permite la realización de ensayos con un elevado número de muestras. Por este motivo, la dispersión experimental no es habitualmente controlada. Sin embargo, en elementos de hormigón armado sometidos a explosiones, la dispersión experimental es muy acusada, en primer lugar, por la propia heterogeneidad del hormigón, y en segundo, por la dificultad inherente a la realización de ensayos con explosiones, por motivos tales como dificultades en las condiciones de contorno, variabilidad del explosivo, o incluso cambios en las condiciones atmosféricas. Para paliar estos inconvenientes, en esta tesis doctoral se ha diseñado un novedoso dispositivo que permite ensayar hasta cuatro losas de hormigón bajo la misma detonación, lo que además de proporcionar un número de muestras estadísticamente representativo, supone un importante ahorro de costes. Con este dispositivo se han ensayado 28 losas de hormigón, tanto armadas como en masa, de dos dosificaciones distintas. Pero además de contar con datos experimentales, también es importante disponer de herramientas de cálculo para el análisis y diseño de estructuras sometidas a explosiones. Aunque existen diversos métodos analíticos, hoy por hoy las técnicas de simulación numérica suponen la alternativa más avanzada y versátil para el cálculo de elementos estructurales sometidos a cargas impulsivas. Sin embargo, para obtener resultados fiables es crucial contar con modelos constitutivos de material que tengan en cuenta los parámetros que gobiernan el comportamiento para el caso de carga en estudio. En este sentido, cabe destacar que la mayoría de los modelos constitutivos desarrollados para el hormigón a altas velocidades de deformación proceden del ámbito balístico, donde dominan las grandes tensiones de compresión en el entorno local de la zona afectada por el impacto. En el caso de los elementos de hormigón sometidos a explosiones, las tensiones de compresión son mucho más moderadas, siendo las tensiones de tracción generalmente las causantes de la rotura del material. En esta tesis doctoral se analiza la validez de algunos de los modelos disponibles, confirmando que los parámetros que gobiernan el fallo de las losas de hormigón armado ante explosiones son la resistencia a tracción y su ablandamiento tras rotura. En base a los resultados anteriores se ha desarrollado un modelo constitutivo para el hormigón ante altas velocidades de deformación, que sólo tiene en cuenta la rotura por tracción. Este modelo parte del de fisura cohesiva embebida con discontinuidad fuerte, desarrollado por Planas y Sancho, que ha demostrado su capacidad en la predicción de la rotura a tracción de elementos de hormigón en masa. El modelo ha sido modificado para su implementación en el programa comercial de integración explícita LS-DYNA, utilizando elementos finitos hexaédricos e incorporando la dependencia de la velocidad de deformación para permitir su utilización en el ámbito dinámico. El modelo es estrictamente local y no requiere de remallado ni conocer previamente la trayectoria de la fisura. Este modelo constitutivo ha sido utilizado para simular dos campañas experimentales, probando la hipótesis de que el fallo de elementos de hormigón ante explosiones está gobernado por el comportamiento a tracción, siendo de especial relevancia el ablandamiento del hormigón. Concrete is nowadays one of the most widely used building materials because of its good mechanical properties, moldability and production economy, among other advantages. As it is known, it has high compressive and low tensile strengths and for this reason it is reinforced with steel bars to form reinforced concrete, a material that has become the most important constructive solution of our time. Despite being such a widely used material, there are some aspects of concrete performance that are not yet fully understood, as it is the case of its response to the effects of an explosion. This is a topic of particular relevance because the events, both intentional and accidental, in which a structure is subjected to an explosion are, unfortunately, relatively common. The loading of a structure due to an explosive event occurs due to the impact of the pressure shock wave generated in the detonation. The application of this load on the structure is very fast and of very short duration. Such actions are called impulsive loads, and can be up to four orders of magnitude faster than the dynamic loads imposed by an earthquake. Consequently, it is not surprising that their effects on structures and materials are very different than those that cause the loads usually considered in engineering. This thesis broadens the knowledge about the material behavior of concrete subjected to explosions. To that end, it is crucial to have experimental results of concrete structures subjected to explosions. These types of results are difficult to find in the scientific literature, as these tests have traditionally been carried out by armies of different countries and the results obtained are classified. Moreover, in experimental campaigns with explosives conducted by civil institutions the high cost of accessing explosives and the lack of proper test fields does not allow for the testing of a large number of samples. For this reason, the experimental scatter is usually not controlled. However, in reinforced concrete elements subjected to explosions the experimental dispersion is very pronounced. First, due to the heterogeneity of concrete, and secondly, because of the difficulty inherent to testing with explosions, for reasons such as difficulties in the boundary conditions, variability of the explosive, or even atmospheric changes. To overcome these drawbacks, in this thesis we have designed a novel device that allows for testing up to four concrete slabs under the same detonation, which apart from providing a statistically representative number of samples, represents a significant saving in costs. A number of 28 slabs were tested using this device. The slabs were both reinforced and plain concrete, and two different concrete mixes were used. Besides having experimental data, it is also important to have computational tools for the analysis and design of structures subjected to explosions. Despite the existence of several analytical methods, numerical simulation techniques nowadays represent the most advanced and versatile alternative for the assessment of structural elements subjected to impulsive loading. However, to obtain reliable results it is crucial to have material constitutive models that take into account the parameters that govern the behavior for the load case under study. In this regard it is noteworthy that most of the developed constitutive models for concrete at high strain rates arise from the ballistic field, dominated by large compressive stresses in the local environment of the area affected by the impact. In the case of concrete elements subjected to an explosion, the compressive stresses are much more moderate, while tensile stresses usually cause material failure. This thesis discusses the validity of some of the available models, confirming that the parameters governing the failure of reinforced concrete slabs subjected to blast are the tensile strength and softening behaviour after failure. Based on these results we have developed a constitutive model for concrete at high strain rates, which only takes into account the ultimate tensile strength. This model is based on the embedded Cohesive Crack Model with Strong Discontinuity Approach developed by Planas and Sancho, which has proved its ability in predicting the tensile fracture of plain concrete elements. The model has been modified for its implementation in the commercial explicit integration program LS-DYNA, using hexahedral finite elements and incorporating the dependence of the strain rate, to allow for its use in dynamic domain. The model is strictly local and does not require remeshing nor prior knowledge of the crack path. This constitutive model has been used to simulate two experimental campaigns, confirming the hypothesis that the failure of concrete elements subjected to explosions is governed by their tensile response, being of particular relevance the softening behavior of concrete.

Estudio numérico y experimental del efecto de tamaño en modo mixto de los paneles de yeso laminado y lana de roca

Los paneles sándwich de yeso laminado y lana de roca presentan una abundante patología de fisuración debida a flechas excesivas de forjados. Existe, por tanto, la necesidad de avanzar en la simulación y predicción de comportamiento bajo solicitaciones de tracción y cortante de ese tipo de paneles, a pesar de que en las aplicaciones habituales no tienen responsabilidad estructural. El comportamiento de este material puede ser considerado cuasi-frágil, y en base a ello en este trabajo ha sido estudiado haciendo uso de modelos de fisura cohesiva, cuya aplicación a otros materiales cuasifrágiles, como el hormigón, ha aportado resultados muy satisfactorios. En esta comunicación se presenta el trabajo realizado para estudiar el efecto del tamaño del elemento de yeso laminado y lana de roca en su comportamiento mecánico-resistente. Para ello se diseñó una campaña de ensayos en modo mixto sobre probetas de diferente tamaño. Se han realizado ensayos de flexión en tres puntos en modo mixto de unas probetas entalladas, geométricamente similares y de diferente tamaño, obteniéndose las curvas carga-desplazamiento y cargaabertura de la boca de la entalla. Para simular numéricamente el comportamiento en fractura del panel en modo mixto se ha utilizado un modelo de elementos finitos con fisura embebida basado en la fisura cohesiva en el que se introducen como entrada los parámetros obtenidos a partir de la experimentación de trabajos anteriores, obteniéndose un buen ajuste. En función de estos resultados se analiza el efecto del tamaño en los paneles. Sandwich panels of laminated gypsum and rockwool have an abundant pathology of cracking due to excessive slabs deflection. Therefore, it is necessary to progress in the simulation and prediction of behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability. The behaviour of this material may be considered quasi-brittle and, based on this idea, in this work has been studied using a cohesive crack model that has been applied to other quasi-brittle materials, such as concrete, and has provided very satisfactory results. This communication presents the work carried out to study the size effect of the specimen of plasterboard and rockwool in its mechanical and resistant behaviour. The authors designed an experimental campaign under mixed mode composed by testing specimens of different sizes. Assymetrical three-point bending tests have been performed on notched specimens, geometrically similar and of different size, to obtain load-displacement and load-crack moutn opening displacement curves. To numerically simulate the mixed-mode fracture behaviour of the panels we have used a finite element model with embedded crack, based on the cohesive crack model, using as input the experimental parameters obtained in previous work, obtaining a good adjustment. Based on these results we analyze the size effect of the panels

Estudio de la fisuración de paneles sándwich de yeso laminado y alma de lana de roca = Study of the cracking of sandwich panels of plasterboard and rockwool

Este artículo presenta el estudio de la rotura de paneles sándwich de yeso laminado y lana de roca bajo solicitaciones de flexo-tracción dentro de su plano. Estos paneles se emplean para conformar tabiques interiores de edificación y con frecuencia se fisuran por flechas excesivas en los forjados. Actualmente no hay modelos de cálculo fiables ni datos experimentales que permitan estudiar este problema. Este trabajo presenta los resultados de una campaña experimental encaminada a caracterizar el comportamiento en rotura de los paneles sándwich y de sus componentes individuales. Además, se presenta un modelo cohesivo con fisura embebida que permite simular el comportamiento en rotura del panel sándwich conjunto. Por último se presentan los resultados de los ensayos de fractura en modo mixto (tracción/cortante) de paneles comerciales y se reproduce su comportamiento con el modelo cohesivo propuesto, obteniéndose un buen ajuste. This paper presents the study of plasterboard and rockwool sandwich panels cracking under flexural loading. These panels are usually used to perform interior partition walls and they frequently show cracking pathology due to excessive deflexion of the slabs. There are currently no reliable simulation models and experimental data for the study of this problem. This paper presents the results of an experimental campaign aimed to characterize the fracture behaviour of sandwich panels and their individual components. In addition, the paper presents a cohesive model with embedded crack to simulate the fracture behaviour of the panel. Finally we present the results of tests for mixed mode fracture (tensile / shear) commercial panels and their behaviour is reproduced with the cohesive model proposed, yielding a good fit.

Estudio numérico y experimental del efecto de tamaño en modo mixto de los paneles de yeso laminado y lana de roca

Los paneles sándwich de yeso laminado y lana de roca presentan una abundante patología de fisuración debida a flechas excesivas de forjados. Existe, por tanto, la necesidad de avanzar en la simulación y predicción de comportamiento bajo solicitaciones de tracción y cortante de ese tipo de paneles, a pesar de que en las aplicaciones habituales no tienen responsabilidad estructural. El comportamiento de este material puede ser considerado cuasi-frágil, y en base a ello en este trabajo ha sido estudiado haciendo uso de modelos de fisura cohesiva, cuya aplicación a otros materiales cuasifrágiles, como el hormigón, ha aportado resultados muy satisfactorios. En esta comunicación se presenta el trabajo realizado para estudiar el efecto del tamaño del elemento de yeso laminado y lana de roca en su comportamiento mecánico-resistente. Para ello se diseñó una campaña de ensayos en modo mixto sobre probetas de diferente tamaño. Se han realizado ensayos de flexión en tres puntos en modo mixto de unas probetas entalladas, geométricamente similares y de diferente tamaño, obteniéndose las curvas carga-desplazamiento y cargaabertura de la boca de la entalla. Para simular numéricamente el comportamiento en fractura del panel en modo mixto se ha utilizado un modelo de elementos finitos con fisura embebida basado en la fisura cohesiva en el que se introducen como entrada los parámetros obtenidos a partir de la experimentación de trabajos anteriores, obteniéndose un buen ajuste. En función de estos resultados se analiza el efecto del tamaño en los paneles. Sandwich panels of laminated gypsum and rockwool have an abundant pathology of cracking due to excessive slabs deflection. Therefore, it is necessary to progress in the simulation and prediction of behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability. The behaviour of this material may be considered quasi-brittle and, based on this idea, in this work has been studied using a cohesive crack model that has been applied to other quasi-brittle materials, such as concrete, and has provided very satisfactory results. This communication presents the work carried out to study the size effect of the specimen of plasterboard and rockwool in its mechanical and resistant behaviour. The authors designed an experimental campaign under mixed mode composed by testing specimens of different sizes. Assymetrical three-point bending tests have been performed on notched specimens, geometrically similar and of different size, to obtain load-displacement and load-crack moutn opening displacement curves. To numerically simulate the mixed-mode fracture behaviour of the panels we have used a finite element model with embedded crack, based on the cohesive crack model, using as input the experimental parameters obtained in previous work, obtaining a good adjustment. Based on these results we analyze the size effect of the panels.

Reversible Urban Entities. Improving public-to-private continuity.

The aim of this paper is to call into question those typologies conventionally used in developing the post-industrial urban fabric (streets, cityblocks, slabs, etc.), often catering to urban designs based on speculative interests and completely overlooking community interests. By defining the concepts of ?postpublic space? and ?reversible urban entities? and illustrating them with an exemplary case of Spanish residential architecture from the 1960s, we establish one possible way of tackling contemporary urban-residential projects. This alternative approach considers the relationship between residential systems and open space systems and promotes the continuity and/or alternation of scales between house and city in an effort to improve the urban quality of life for residents and external users.

Modelización y simulación numérica de sistemas geotérmicos planos

En el presente proyecto se estudiará la conveniencia de utilizar simulación numérica para evaluar, diseñar y mejorar el diseño de instalaciones geotérmicas planas. Para ello, se modelizará el conjunto de terreno y sistema geotérmico mediante el acoplamiento de un modelo tridimensional (terreno) y un modelo unidimensional, formado por la red de tubería geotérmica, que estará dispuesta en un plano cuya orientación dependerá de las aplicaciones. Para la simulación numérica se utilizará un software de análisis y resolución por elementos finitos tipo comercial. Finalmente, se definirán unos parámetros geométricos de diseño y, teniendo en cuenta las propiedades térmicas de cada material, se realizarán estudios paramétricos para determinar la influencia de cada grupo de parámetros. Ello requerirá la realización de cientos de simulaciones numéricas que permitirán optimizar el rendimiento de sistemas geotérmicos planos tanto horizontales (soleras), como verticales (muros pantalla). ABSTRACT In this project it is going to be studied the convenience of numerical simulation as to evaluate, design and improve the design of geothermal planar installations. With this purpose, the terrain and the geothermal system will be modeled by coupling a three-dimensional model (terrain) and a one-dimensional model formed by the geothermal piping network disposed in a plane with an orientation which will depend on the applications. For the numerical simulation commercial software of analyzing and resolving by finite elements will be used. Finally, geometric design parameters will be defined, and taking into account the thermal properties of each material, parametric studies will be performed to determine the influence of each group of parameters. This will require the completion of hundreds of numerical simulations which will enhance the performance of both horizontal (slabs) and vertical (diaphragm walls) geothermal systems.

Analysis of punching of a reinforced concrete slab within IRIS_2012

As part of the IRIS_2012 international benchmark, simulations were conducted to analyse impacts on reinforced concrete slabs by both rigid and deformable missiles. The analytical results were compared with physical tests conducted by the Technical Research Center VTT of Finland. In the impact discussed here, a rigid missile perforates the concrete slab. The missile is a thick steel tube filled with concrete with a total mass of 47.4 kg and strikes the target at 136 m/s. The target is a 250 mm thick, reinforced concrete slab that spans 2 m by 2 m and is held in a rigid supporting frame. Characterisation tests were provided for calibration of the parameters of the concrete models selected by the participants. Having reproduced those tests, the authors developed models for the slab and the missile. A damaged plasticity model was used for the concrete and the rebars were explicitly represented. The results obtained were very satisfactory in respect of the damage patterns caused in the concrete and the reinforcement; also, the calculated and measured values of the energy spent by the missile in perforating the slab differed by only 4%.

Vulnerability analysis of RC buildings with wide beams located in moderate seismicity regions

A significant number of short-to-mid height RC buildings with wide beams have been constructed in areas of moderate seismicity of Spain, mainly for housing and administrative use. The buildings have a framed structure with one-way slabs; the wide beams constitute the distinctive characteristic, their depth being equal to that of the rest of the slab, thus providing a flat lower surface, convenient for construction and the layout of facilities. Seismic behavior in the direction of the wide beams appears to be deficient because of: (i) low lateral strength, mainly because of the small effective depth of the beams, (ii) inherent low ductility of the wide beams, generated by high amount of reinforcement, (iii) the big strut compressive forces developed inside the column-beam connections due to the low height of the beams, and (iv) the fact that the wide beams are wider than the columns, meaning that the contribution of the outer zones to the resistance of the beam-column joints is unreliable because there is no torsion reinforcement. In the orthogonal direction, the behavior is worse since the only members of the slabs that contribute to the lateral resistance are the joists and the façade beams. Moreover, these buildings were designed with codes that did not include ductility requirements and required only a low lateral resistance; indeed, in many cases, seismic action was not considered at all. Consequently, the seismic capacity of these structures is not reliable. The objective of this research is to assess numerically this capability, whereas further research will aim to propose retrofit strategies. The research approach consists of: (i) selecting a number of 3-story and 6-story buildings that represent the vast majority of the existing ones and (ii) evaluating their vulnerability through three types of analyses, namely: code-type, push-over and nonlinear dynamic analysis. Given the low lateral resistance of the main frames, the cooperation of the masonry infill walls is accounted for; for each representative building, three wall densities are considered. The results of the analyses show that the buildings in question exhibit inadequate seismic behavior in most of the examined situations. In general, the relative performance is less deficient for Target Drift CP (Collapse Prevention) than for IO (Immediate Occupancy). Since these buildings are selected to be representative of the vast majority of buildings with wide beams that were constructed in Spain without accounting for any seismic consideration, our conclusions can be extrapolated to a broader scenario.

Finite element simulation of sandwich panels of laminated plaster and rockwool under mixed mode fracture

Sandwich panels of laminated gypsum and rock wool have shown large pathology of cracking due to excessive slabs deflection. Currently the most widespread use of this material is as vertical elements of division or partition, with no structural function, what justifies that there are no studies on the mechanism of fracture and mechanical properties related to it. Therefore, and in order to reduce the cracking problem, it is necessary to progress in the simulation and prediction of the behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability.

Cover cracking of the reinforced concrete due to rebar corrosion induced by chloride penetration

This paper is focused on the problem of the chloride-induced corrosion of the rebar in reinforced concrete, with special application to the slabs and decks of the bridges. High superficial concentrations may be usual in these structures (marine environments or de-icing salts in roadway bridges, e.g.). Like any aggressive agent such as water, gases or other dissolved ions, chloride induced deterioration is very conditioned by possibilities of transport through concrete mass.

Fracture of concrete structural members subjected to blast

If reinforced concrete structures are to be safe under extreme impulsive loadings such as explosions, a broad understanding of the fracture mechanics of concrete under such events is needed. Most buildings and infrastructures which are likely to be subjected to terrorist attacks are borne by a reinforced concrete (RC) structure. Up to some years ago, the traditional method used to study the ability of RC structures to withstand explosions consisted on a choice between handmade calculations, affordable but inaccurate and unreliable, and full scale experimental tests involving explosions, expensive and not available for many civil institutions. In this context, during the last years numerical simulations have arisen as the most effective method to analyze structures under such events. However, for accurate numerical simulations, reliable constitutive models are needed. Assuming that failure of concrete elements subjected to blast is primarily governed by the tensile behavior, a constitutive model has been built that accounts only for failure under tension while it behaves as elastic without failure under compression. Failure under tension is based on the Cohesive Crack Model. Moreover, the constitutive model has been used to simulate the experimental structural response of reinforced concrete slabs subjected to blast. The results of the numerical simulations with the aforementioned constitutive model show its ability of representing accurately the structural response of the RC elements under study. The simplicity of the model, which does not account for failure under compression, as already mentioned, confirms that the ability of reinforced concrete structures to withstand blast loads is primarily governed by tensile strength.

Comportamiento a fatiga por cortante de elementos lineales de hormigón armado sin cercos

Las estructuras de hormigón son susceptibles de sufrir los efectos asociados a las acciones de fatiga cuando estas se ven sometidas a un elevado número de cargas repetidas. Muchas de estas estructuras no requieren armadura transversal para cumplir los condicionantes de dimensionamiento estático como por ejemplo las losas superiores de tableros de puentes, los muros de contención, las losas de transición de puentes, las torres eólicas o las estructuras marítimas. La mayor parte de los códigos de diseño vigentes no incluyen una comprobación específica del nivel de seguridad a cortante de estas estructuras para acciones de fatiga, y aquellas que lo hacen prefieren utilizar expresiones de tipo empírico basadas en curvas S-N que relacionan el número de ciclos resistentes con el valor de la carga aplicada. A pesar de que el empleo de curvas S-N es de gran utilidad desde un punto de vista práctico, estas curvas no permiten comprender el proceso de rotura por cortante para cargas repetidas. El objetivo principal de esta Tesis es el de estudiar el comportamiento a cortante de elementos de hormigón armado sin cercos sometidos a fatiga. Además, el análisis es ampliado al estudio del comportamiento transversal de los voladizos de las losas superiores de tableros de puentes de hormigón que de forma habitual son diseñados sin armadura de cortante. De forma habitual estos elementos se diseñan atendiendo a criterios de dimensionamiento estáticos sin tener en cuenta la resistencia a cortante cuando se ven sometidos a cargas cíclicas. A pesar de que las cargas de fatiga son inferiores a aquellas que producen el fallo estático, es importante tener en cuenta el comportamiento de estos elementos ante cargas repetidas. Los trabajos experimentales existentes en vigas de hormigón armado sin cercos evidenciaron diferencias significativas entre los modos de fallo ante cargas estáticas y cíclicas. Estos trabajos llegaron a la conclusión de que estos elementos diseñados para tener un fallo dúctil por flexión pueden llegar a desarrollar un tipo de fallo frágil por cortante cuando se ven sometidos a cargas repetidas. El proceso de rotura por cortante en elementos de hormigón armado sin cercos sometidos a fatiga es un proceso complejo que debe ser estudiado en profundidad debido al carácter frágil de este tipo de fallo. Los trabajos experimentales permitieron comprobar que el origen de este fallo tiene lugar tras la formación de una fisura de cortante a partir de una fisura de flexión formada durante los primeros ciclos en el vano de cortante. Tras la formación de esta fisura, esta se va propagando hacia la cabeza de compresión hasta que finalmente se produce el fallo como consecuencia de la destrucción de la cabeza de compresión cuando la altura alcanzada por esta es insuficiente para resistir la fuerza de compresión aplicada en esta zona. Por otra parte, la propagación de esta fisura diagonal puede desarrollarse por completo en el instante en el que esta se forma derivando en un tipo de fallo por cortante más frágil que el anterior. El proceso de fatiga es estudiado en esta Tesis mediante un modelo mecánico. Por una parte, se propone un modelo predictivo para determinar el número de ciclos acumulados hasta que se forma la fisura diagonal en función del estado tensional que se tiene en la punta de una fisura crítica de flexión formada en los primeros ciclos. Por otra parte, la resistencia a fatiga tras la formación de la fisura diagonal se analiza teniendo en cuenta el daño por fatiga acumulado en la cabeza de compresión y las variables que afectan a la propagación de esta fisura de cortante. Para la evaluación de la resistencia a fatiga tras la formación de la fisura crítica de cortante en este tipo de elementos, se plantea un modelo teórico basado en conceptos de Mecánica de la Fractura adaptados al hormigón. Este modelo puede ser aplicado a vigas de hormigón armado sin cercos de canto constante o variable siguiendo diferentes procedimientos. Una campaña experimental ha sido llevada a cabo con el objetivo de estudiar el comportamiento a cortante de vigas de hormigón armado sin cercos de canto variable sometidas a cargas estáticas y de fatiga. Se han desarrollado un total de diez ensayos estáticos y de fatiga para diferentes niveles de carga y esbelteces de cortante, teniendo lugar diferentes modos de fallo. Estos elementos fueron diseñados para reproducir, a escala real y de forma simplificada, los voladizos laterales de las losas superiores de tableros de puentes de carretera de hormigón. Los resultados experimentales demostraron que el tipo de fallo desarrollado depende de varios parámetros como por ejemplo el nivel de carga máxima, el nivel de oscilación de tensiones en la armadura longitudinal, la esbeltez de cortante o la calidad del hormigón utilizado entre otros. Para valores similares de esbeltez de cortante, los ensayos de fatiga realizados permitieron comprobar que la rotura por cortante de estos elementos está asociada a niveles de carga máxima elevados, mientras que el fallo por fatiga de la armadura longitudinal tiene mayor probabilidad de ocurrir en elementos sometidos a elevados niveles de oscilación de tensiones en esta armadura. Además, estos ensayos han sido analizados a través del modelo propuesto para tratar de comprender el comportamiento resistente de estos elementos sometidos a cargas de fatiga. Concrete structures are able to suffer fatigue when they are subjected to high number of cyclic loads. Many of these need not shear reinforcement to satisfy static design requirements, such as bridge deck slabs, retaining walls, bridge approach slabs, wind towers or maritime structures among others. Many codes of practice do not include a verification of the shear fatigue safety. Moreover, those which include it still prefer empirical S-N-based approaches that provide the number of cycles as a function of applied forces. S-N models are practical but they do not provide information to understand the shear fatigue process. The main objective of this Thesis is to study shear behaviour of reinforced concrete elements without stirrups subjected to fatigue loads. In addition, the analysis is extended in order to study the transverse behaviour of cantilever slabs of concrete bridges that traditionally are designed without shear reinforcement. These elements usually are designed on the basis of static strength and it is unusual that codes consider fatigue strength of concrete in shear. Accordingly, it is important to take into account the fatigue behaviour of structural members subjected to cyclic loads although these loads are lower than those which produce the static failure. Existing experimental works show important differences between the static and cyclic failure modes of reinforced concrete beams without stirrups. These works concluded that beams without transverse reinforcement, designed to have a ductile failure mode in flexure, can submit a brittle shear failure mode when they are subjected to repeated loads. Shear fatigue failure of reinforced concrete beams without stirrups is a rather complex process from the mechanical viewpoint. Since it leads to a brittle failure mode it should be better understood. Experimental evidence indicates that a diagonal crack first develops from the inclination of flexural cracks in the shear span. Thereafter, the diagonal crack propagates into the compression zone. Failure normally takes place by the destruction of the compression zone when its depth is too small to resist the applied force. The propagation of the diagonal crack can also be instantaneous, leading to sudden diagonal cracking fatigue failure rather than shear-compression failure. Fatigue process is studied in this Thesis on a mechanical basis. On the one hand, a predictive model is derived to obtain the number of cycles up to diagonal cracking, as a function of the stress state at the tip of a critical flexural crack. On the other hand, the residual fatigue strength after diagonal cracking is analyzed taking into account the fatigue damage accumulated by the compression zone and the variables affecting the propagation of the diagonal crack. In order to assess the residual fatigue strength after diagonal cracking of such elements, a theoretical model is proposed based on concepts from fracture mechanics adapted to concrete. This model can be successfully applied for straight or haunched reinforced concrete beams without stirrups following different procedures. In order to achieve a more advanced knowledge in this subject, an experimental campaign has been carried out with the aim of study the shear behaviour of reinforced concrete haunched beams without stirrups subjected to static and fatigue loads. A total of ten static and fatigue tests have been performed with distinct load levels and shear span-to-depth ratios, presenting different failures modes. These elements were designed to reproduce in a simplified form the cantilever slab of concrete bridges at real scale. Experimental results showed that the type of failure depends on several parameters as for example the maximum load level, the stress oscillation level on the longitudinal reinforcement, the shear span-to-depth ratio or the quality of the concrete used among others. For a similar value of the shear span-to-depth ratio, tests evidenced that shear fatigue failure is related to high maximum load levels, while steel fatigue failure is easier to occur in elements subjected to high stress oscillation level on the reinforcement bars. Besides, these tests have been analyzed through the proposed model in order to clarify the structural behaviour of such elements subjected to fatigue loads.

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.

Bóvedas de crucería rebajadas hispanas: geometría, estructura y construcción

La arquitectura histórica constituye un ámbito de notable singularidad dentro del patrimonio cultural, ya que representa uno de los máximos exponentes de la cultura material de las sociedades precedentes. Su adecuada conservación y preservación debe ir necesariamente precedida de un riguroso y profundo conocimiento de sus valores culturales, de ahí la importancia de las investigaciones en este campo. Entre todos los elementos que configuran las edificaciones históricas, son probablemente las bóvedas los elementos más singulares, dada su relevancia desde un punto de vista tanto estético como estructural y constructivo. Hasta la fecha, los estudios centrados en los abovedamientos medievales góticos han aportado visiones generales del conjunto de obras, estableciendo las pertinentes clasificaciones y poniendo de manifiesto la notable variedad de tipos de bóvedas de crucería. La presente investigación tiene su origen en la necesidad de profundizar en el conocimiento de este sistema constructivo mediante el estudio específico y sistemático de un tipo concreto de abovedamiento: las bóvedas de crucería rebajadas que sustentan los coros altos de los templos. En concreto, el análisis se ha centrado en aquellos abovedamientos construidos en la Corona de Castilla durante los reinados de los Reyes Católicos y Carlos I, puesto que es en este momento de transición entre el mundo medieval y la Edad Moderna con una coexistencia de la tradición medieval y las nuevas ideas renacentistas cuando se crean las más singulares obras. Por lo tanto, el trabajo desarrollado se ha centrado en el estudio e interpretación de los procesos de diseño, trazado y construcción específicos de cada una de las bóvedas. Más allá de un enfoque descriptivo o basado en una visión actual, se ha tratado de profundizar en los métodos, sistemas y recursos que los maestros canteros emplearon, lo que ha obligado a adoptar en la medida de lo posible la mentalidad y conocimiento bajomedievales. Con estas premisas se ha desarrollado una investigación que necesariamente se ha apoyado en la contextualización histórica de cada una de las bóvedas, generándose un catálogo completo de las obras. Posteriormente, se ha desarrollado una toma de datos y un análisis individualizado de cada una de ellas, para poder obtener una interpretación de su proceso de diseño y construcción. Finalmente, se ha abordado un estudio comparativo del conjunto de las obras, poniendo en relación sus características históricas, geométricas, constructivas y estructurales. Ello ha permitido obtener unos resultados novedosos respecto a las principales cuestiones sobre el diseño y construcción de las bóvedas de crucería rebajadas, poniendo de relieve su singularidad y el profundo conocimiento de los maestros canteros que las crearon. De este modo, se ha pretendido avanzar en la investigación y sentar las bases para posteriores trabajos en el ámbito de los abovedamientos de crucería. Historical architecture is a quite singular field when considering cultural heritage, because it is one of the most important exponents of the material culture previous societies. Its proper conservation and restoration must be preceded of a rigorous and deep knowledge of the cultural values, and that is why researches in this fi eld are very important. The study of historical architecture has been developed traditionally from the viewpoint of History of Art and Architecture. Thanks to such discipline, it has been possible to establish and systematize several architectonical types and styles. However, there has been a lack in relationship with the analyses focused on the structural and constructive historical systems, which has been recently compensated by the gradual development of the discipline of Construction History. Among the several elements which form the historical buildings, the vaults are probably the most singular elements, thanks to their aesthetic, constructive and structural relevance. To date, the studies focused on the medieval gothic vaults have provided general visions of the whole group of works, which has allowed defi ning the proper classifi cations and underlining the great variety of kinds of ribbed vaults. The present research has its origin in the need of a deeper knowledge of this specific constructive system. For that reason, a specifi c and systematic analysis of a particular kind of vaults has been developed. It is focused on the surbased ribbed vaults which support the elevated choirs of some churches. In particular, it includes the works built in the Crown of Castille during the kingdoms of Catholic Kings and Carlos I, because at this precise moment of transition from the medieval world into de Modern Age with a coexistence of the medieval tradition and the new classicistic ideas the most singular and relevant surbased vaults were built. In this way, the analysis has been focused in the study and interpretation of the design, tracing and construction methods of each vault. More than a descriptive approach or an analysis based on our contemporary point of view and knowledge, this research has studied the methods, systems and resources of master masons in depth. Then, it has been necessary to adopt as much as possible their mentality, as well as the late medieval knowledge. With the above mentioned premises, the research has been developed including the historical contextualization of each vault, providing also a complete catalogue of such works. After obtaining the proper survey, measurements and other complementary data, each one has been analyzed in order to develop a hypothesis of the design and construction process. Finally, a comparative study has been carried out, which has allowed putting in relationship the historical, geometrical, constructive and structural features of the whole group of vaults. This research has provided novel results about de design and construction of surbased ribbed vaults, underlining their singularity as well as the deep knowledge of master masons who created them. In this way, we have tried to go further in this scientific field and to set the basis for latter researches focused on ribbed vaults.