Procedimiento De Amplificador De Envolvente De Señales Moduladas En RF Para Técnicas EER Y ET

An envelope amplifier for an EER (Envelope Elimination and Restoration) and ET (Envelope Tracking) techniques is shown in this paper. The amplifier is based on a high speed two phases buck converter and employs RF LDMOS technology for the switching stage. A DPWM (Digital Pulse With Modulation) signal is used to control the amplifier by means of a functions generator. Simulations and measurements on a circuit prototype are presented showing a good agreement. Up to 125W output peak power can be delivered over a 5Ω load resistor. About 80% efficiency has been obtained. And at the two tone test, the third order intermodulation products (IP3) remain below 45dBc over a 2MHz bandwidth.

Multi-microphone recordings (EigenMike32) inside a WFS system (Iosono) through Ambisonics techniques using Matlab

El audio multicanal ha avanzado a pasos agigantados en los últimos años, y no solo en las técnicas de reproducción, sino que en las de capitación también. Por eso en este proyecto se encuentran ambas cosas: un array microfónico, EigenMike32 de MH Acoustics, y un sistema de reproducción con tecnología Wave Field Synthesis, instalado Iosono en la Jade Höchscule Oldenburg. Para enlazar estos dos puntos de la cadena de audio se proponen dos tipos distintos de codificación: la reproducción de la toma horizontal del EigenMike32; y el 3er orden de Ambisonics (High Order Ambisonics, HOA), una técnica de codificación basada en Armónicos Esféricos mediante la cual se simula el campo acústico en vez de simular las distintas fuentes. Ambas se desarrollaron en el entorno Matlab y apoyadas por la colección de scripts de Isophonics llamada Spatial Audio Matlab Toolbox. Para probar éstas se llevaron a cabo una serie de test en los que se las comparó con las grabaciones realizadas a la vez con un Dummy Head, a la que se supone el método más aproximado a nuestro modo de escucha. Estas pruebas incluían otras grabaciones hechas con un Doble MS de Schoeps que se explican en el proyecto “Sally”. La forma de realizar éstas fue, una batería de 4 audios repetida 4 veces para cada una de las situaciones garbadas (una conversación, una clase, una calle y un comedor universitario). Los resultados fueron inesperados, ya que la codificación del tercer orden de HOA quedo por debajo de la valoración Buena, posiblemente debido a la introducción de material hecho para un array tridimensional dentro de uno de 2 dimensiones. Por el otro lado, la codificación que consistía en extraer los micrófonos del plano horizontal se mantuvo en el nivel de Buena en todas las situaciones. Se concluye que HOA debe seguir siendo probado con mayores conocimientos sobre Armónicos Esféricos; mientras que el otro codificador, mucho más sencillo, puede ser usado para situaciones sin mucha complejidad en cuanto a espacialidad. In the last years the multichannel audio has increased in leaps and bounds and not only in the playback techniques, but also in the recording ones. That is the reason of both things being in this project: a microphone array, EigenMike32 from MH Acoustics; and a playback system with Wave Field Synthesis technology, installed by Iosono in Jade Höchscule Oldenburg. To link these two points of the audio chain, 2 different kinds of codification are proposed: the reproduction of the EigenMike32´s horizontal take, and the Ambisonics´ third order (High Order Ambisonics, HOA), a codification technique based in Spherical Harmonics through which the acoustic field is simulated instead of the different sound sources. Both have been developed inside Matlab´s environment and supported by the Isophonics´ scripts collection called Spatial Audio Matlab Toolbox. To test these, a serial of tests were made in which they were compared with recordings made at the time by a Dummy Head, which is supposed to be the closest method to our hearing way. These tests included other recording and codifications made by a Double MS (DMS) from Schoeps which are explained in the project named “3D audio rendering through Ambisonics techniques: from multi-microphone recordings (DMS Schoeps) to a WFS system, through Matlab”. The way to perform the tests was, a collection made of 4 audios repeated 4 times for each recorded situation (a chat, a class, a street and college canteen or Mensa). The results were unexpected, because the HOA´s third order stood under the Well valuation, possibly caused by introducing material made for a tridimensional array inside one made only by 2 dimensions. On the other hand, the codification that consisted of extracting the horizontal plane microphones kept the Well valuation in all the situations. It is concluded that HOA should keep being tested with larger knowledge about Spherical Harmonics; while the other coder, quite simpler, can be used for situations without a lot of complexity with regards to spatiality.

Simulación de componentes no estacionarias de viento en orografías complejas

Realistic operation of helicopter flight simulators in complex topographies (such as urban environments) requires appropriate prediction of the incoming wind, and this prediction should be made in real time. Unfortunately, the wind topology around complex topographies shows time-dependent, fully nonlinear, turbulent patterns (i.e., wakes) whose simulation cannot be made using computationally inexpensive tools based on corrected potential approximations. Instead, the full Navier-Stokes plus some kind of turbulent modeling is necessary, which is quite computationally expensive. The complete unsteady flow depends on two parameters, namely the velocity and orientation of the free stream flow. The aim of this MSc thesis is to develop a methodology for the real time simulation of these complex flows. For simplicity, the flow around a single building (20 mx20 m cross section and 100 m height) is considered, with free stream velocity in the range 5-25 m/s. Because of the square cross section, the problem shows two reflection symmetries, which allows for restricting the orientations to the range 0° < a. < 45°. The methodology includes an offline preprocess and the online operation. The preprocess consists in three steps: An appropriate, unstructured mesh is selected in which the flow is sim¬ulated using OpenFOAM, and this is done for 33 combinations of 3 free stream intensities and 11 orientations. For each of these, the simulation proceeds for a sufficiently large time as to eliminate transients. This step is quite computationally expensive. Each flow field is post-processed using a combination of proper orthogonal decomposition, fast Fourier transform, and a convenient optimization tool, which identifies the relevant frequencies (namely, both the basic frequencies and their harmonics) and modes in the computational mesh. This combination includes several new ingredients to filter errors out and identify the relevant spatio-temporal patterns. Note that, in principle, the basic frequencies depend on both the intensity and the orientation of the free stream flow. The outcome of this step is a set of modes (vectors containing the three velocity components at all mesh points) for the various Fourier components, intensities, and orientations, which can be organized as a third order tensor. This step is fairly computationally inexpensive. The above mentioned tensor is treated using a combination of truncated high order singular value, decomposition and appropriate one-dimensional interpolation (as in Lorente, Velazquez, Vega, J. Aircraft, 45 (2008) 1779-1788). The outcome is a tensor representation of both the relevant fre¬quencies and the associated Fourier modes for a given pair of values of the free stream flow intensity and orientation. This step is fairly compu¬tationally inexpensive. The online, operation requires just reconstructing the time-dependent flow field from its Fourier representation, which is extremely computationally inex¬pensive. The whole method is quite robust.

Use of Headed Reinforcement Bars in Contruction. A Theoretical Approach to Determine the Dimensions of Anchorage Plates and Experimental Tests on Knee Joints Subjected to a Closing Moment

In order to reduce costs and time while improving quality, durability and sustainability in structural concrete constructions, a widely used material nowadays, special care must be taken in some crucial phases of the project and execution, including the structure design and calculation, the dosage, dumping and curing of concrete: another important aspect is the proper design and execution of assembly plans and construction details. The framework, a name designating the whole reinforcement bars cage already assembled as shown in the drawings, can be made up of several components and implies higher or lower industrialization degree. The framework costs constitute about one third of the price per cubic meter placed in concrete works. The best solutions from all points of view are clearly those involving an easier processing to achieve the same goal, and consequently carrying a high degree of industrialization, meaning quality and safety in the work. This thesis aims to provide an indepth analysis of a relatively new type of anchoring by plate known as headed reinforcement bars, which can potentially replace standard or L-shaped hooks, improving the cleaning of construction details and enabling a faster, more flexible, and therefore a more economical assembly. A literature review on the topic and an overview of typical applications is provided, followed by some examples of specific applications in real projects. Since a strict theoretical formulation used to provide the design plate dimensions has not yet been put forward, an equation is proposed for the side-face blowout strength of the anchorage, based on the capacity of concrete to carry concentrated loads in cases in which no transverse reinforcement is provided. The correlation of the calculated ultimate load with experimental results available in the literature is given. Besides, the proposed formulation can be expanded to cases in which a certain development length is available: using a software for nonlinear finite element analysis oriented to the study of reinforced concrete, numerical tests on the bond-bearing interaction are performed. The thesis ends with a testing of eight corner joints subjected to a closing moment, held in the Structures Laboratory of the Polytechnic University of Madrid, aiming to check whether the design of such plates as stated is adequate for these elements and whether an element with plate-anchored reinforcement is equivalent to one with a traditional construction detail.

The PSE-3D instability analysis methodology for flows depending strongly on two and weakly on the third spatial dimension

The present contribution discusses the development of a PSE-3D instability analysis algorithm, in which a matrix forming and storing approach is followed. Alternatively to the typically used in stability calculations spectral methods, new stable high-order finitedifference-based numerical schemes for spatial discretization 1 are employed. Attention is paid to the issue of efficiency, which is critical for the success of the overall algorithm. To this end, use is made of a parallelizable sparse matrix linear algebra package which takes advantage of the sparsity offered by the finite-difference scheme and, as expected, is shown to perform substantially more efficiently than when spectral collocation methods are used. The building blocks of the algorithm have been implemented and extensively validated, focusing on classic PSE analysis of instability on the flow-plate boundary layer, temporal and spatial BiGlobal EVP solutions (the latter necessary for the initialization of the PSE-3D), as well as standard PSE in a cylindrical coordinates using the nonparallel Batchelor vortex basic flow model, such that comparisons between PSE and PSE-3D be possible; excellent agreement is shown in all aforementioned comparisons. Finally, the linear PSE-3D instability analysis is applied to a fully three-dimensional flow composed of a counter-rotating pair of nonparallel Batchelor vortices.

Technical evaluation of a third generation optical pose tracker for motion analysis and image-guided surgery

Laparoscopic instrument tracking systems are an essential component in image-guided interventions and offer new possibilities to improve and automate objective assessment methods of surgical skills. In this study we present our system design to apply a third generation optical pose tracker (Micron- Tracker®) to laparoscopic practice. A technical evaluation of this design is performed in order to analyze its accuracy in computing the laparoscopic instrument tip position. Results show a stable fluctuation error over the entire analyzed workspace. The relative position errors are 1.776±1.675 mm, 1.817±1.762 mm, 1.854±1.740 mm, 2.455±2.164 mm, 2.545±2.496 mm, 2.764±2.342 mm, 2.512±2.493 mm for distances of 50, 100, 150, 200, 250, 300, and 350 mm, respectively. The accumulated distance error increases with the measured distance. The instrument inclination covered by the system is high, from 90 to 7.5 degrees. The system reports a low positional accuracy for the instrument tip.

Cine en 3D

Este proyecto pretende documentar el proceso completo de una producción audiovisual en 3D. Para ello, se hace un recorrido por cada una de sus etapas, desde los primeros pasos de la escritura hasta que la película llega a los espectadores. Como el flujo de trabajo para realizar una película es enorme, el estudio se centra exclusivamente en las peculiaridades estereoscópicas, dejando al margen los procesos habituales de una producción convencional. El proyecto está dividido en cinco grandes bloques, centrados en cada etapa de producción. El primer capítulo es una introducción al mundo tridimensional, que sienta las bases de la percepción humana para entender cómo funcionan todas las demás etapas. Además, se hace un repaso por los distintos avances producidos en el campo estereoscópico a lo largo de la historia. El segundo capítulo se centra en la pre-producción, el primer paso para llevar a cabo cualquier proyecto audiovisual, consistente en la planificación del trabajo a realizar y la organización de los distintos elementos que serán necesarios durante el rodaje, teniendo en cuenta desde el primer momento la tercera dimensión. El tercer capítulo está dedicado a la grabación de las imágenes, centrándose principalmente en las características y configuraciones de las cámaras o rigs con los que se obtienen las dos secuencias. El cuarto capítulo aborda la percepción de la película 3D, explicando las características de los variados sistemas de visualización de las imágenes grabadas, que dan a su vez diferentes sistemas de proyección estereoscópica. El quinto y último capítulo se centra en el procesado digital de las imágenes estéreo, que permite juntar el material grabado, corregirlo o perfeccionarlo, y darle la forma adecuada de película que llega al público final. La documentación escrita en español sobre todas estas fases es algo escasa, centrándose normalmente en alguna parte concreta de la cadena, por lo que el proyecto trata también de llenar ese vacío, explicándolo de manera sencilla para hacerlo accesible y factible para toda persona interesada. ABSTRACT. This project has the intention of document the complete process of 3D audiovisual production. For that reason, we make a journey through each of its stages, from the first steps of writing until the film reaches the final viewers. Since the workflow for a film is huge, the study focuses exclusively on the stereoscopic peculiarities, leaving aside the usual processes of conventional production. The Project is divided into five major sections focused on each stage of production. The first chapter is an introduction to three-dimensional world, which lays the foundation of human perception to understand how the other stages work. In addition, we review the various advances in the stereoscopic field throughout history. The second chapter focuses on the pre-production, the first step in carrying out any audiovisual project, including the design of all the works to do and the organization of the different elements that will be needed during filming, taking into account the third dimension from the first moment. The third chapter is devoted to the image recording, focusing mainly on the features and the settings of the cameras or rigs used to obtain the two sequences. The fourth chapter deals with the 3D film perception, explaining the characteristics of the various systems used for displaying the recorded images, which, in turn, give different stereoscopic projection systems. The fifth and final chapter focuses on the digital processing of stereo images, which allows collecting all the recorded material, correcting or improving it, and giving it the proper style for a film that reaches the end consumer. The documents written in Spanish about all these phases are somewhat sparse, usually focusing on a particular part of the chain, so the project also aims to fill that gap, with simple explanations in order to make it accessible and doable for anyone interested.

Localization and Tracking in Energy-Constrained Networks with Dynamic Connectivity

Systems used for target localization, such as goods, individuals, or animals, commonly rely on operational means to meet the final application demands. However, what would happen if some means were powered up randomly by harvesting systems? And what if those devices not randomly powered had their duty cycles restricted? Under what conditions would such an operation be tolerable in localization services? What if the references provided by nodes in a tracking problem were distorted? Moreover, there is an underlying topic common to the previous questions regarding the transfer of conceptual models to reality in field tests: what challenges are faced upon deploying a localization network that integrates energy harvesting modules? The application scenario of the system studied is a traditional herding environment of semi domesticated reindeer (Rangifer tarandus tarandus) in northern Scandinavia. In these conditions, information on approximate locations of reindeer is as important as environmental preservation. Herders also need cost-effective devices capable of operating unattended in, sometimes, extreme weather conditions. The analyses developed are worthy not only for the specific application environment presented, but also because they may serve as an approach to performance of navigation systems in absence of reasonably accurate references like the ones of the Global Positioning System (GPS). A number of energy-harvesting solutions, like thermal and radio-frequency harvesting, do not commonly provide power beyond one milliwatt. When they do, battery buffers may be needed (as it happens with solar energy) which may raise costs and make systems more dependent on environmental temperatures. In general, given our problem, a harvesting system is needed that be capable of providing energy bursts of, at least, some milliwatts. Many works on localization problems assume that devices have certain capabilities to determine unknown locations based on range-based techniques or fingerprinting which cannot be assumed in the approach considered herein. The system presented is akin to range-free techniques, but goes to the extent of considering very low node densities: most range-free techniques are, therefore, not applicable. Animal localization, in particular, uses to be supported by accurate devices such as GPS collars which deplete batteries in, maximum, a few days. Such short-life solutions are not particularly desirable in the framework considered. In tracking, the challenge may times addressed aims at attaining high precision levels from complex reliable hardware and thorough processing techniques. One of the challenges in this Thesis is the use of equipment with just part of its facilities in permanent operation, which may yield high input noise levels in the form of distorted reference points. The solution presented integrates a kinetic harvesting module in some nodes which are expected to be a majority in the network. These modules are capable of providing power bursts of some milliwatts which suffice to meet node energy demands. The usage of harvesting modules in the aforementioned conditions makes the system less dependent on environmental temperatures as no batteries are used in nodes with harvesters--it may be also an advantage in economic terms. There is a second kind of nodes. They are battery powered (without kinetic energy harvesters), and are, therefore, dependent on temperature and battery replacements. In addition, their operation is constrained by duty cycles in order to extend node lifetime and, consequently, their autonomy. There is, in turn, a third type of nodes (hotspots) which can be static or mobile. They are also battery-powered, and are used to retrieve information from the network so that it is presented to users. The system operational chain starts at the kinetic-powered nodes broadcasting their own identifier. If an identifier is received at a battery-powered node, the latter stores it for its records. Later, as the recording node meets a hotspot, its full record of detections is transferred to the hotspot. Every detection registry comprises, at least, a node identifier and the position read from its GPS module by the battery-operated node previously to detection. The characteristics of the system presented make the aforementioned operation own certain particularities which are also studied. First, identifier transmissions are random as they depend on movements at kinetic modules--reindeer movements in our application. Not every movement suffices since it must overcome a certain energy threshold. Second, identifier transmissions may not be heard unless there is a battery-powered node in the surroundings. Third, battery-powered nodes do not poll continuously their GPS module, hence localization errors rise even more. Let's recall at this point that such behavior is tight to the aforementioned power saving policies to extend node lifetime. Last, some time is elapsed between the instant an identifier random transmission is detected and the moment the user is aware of such a detection: it takes some time to find a hotspot. Tracking is posed as a problem of a single kinetically-powered target and a population of battery-operated nodes with higher densities than before in localization. Since the latter provide their approximate positions as reference locations, the study is again focused on assessing the impact of such distorted references on performance. Unlike in localization, distance-estimation capabilities based on signal parameters are assumed in this problem. Three variants of the Kalman filter family are applied in this context: the regular Kalman filter, the alpha-beta filter, and the unscented Kalman filter. The study enclosed hereafter comprises both field tests and simulations. Field tests were used mainly to assess the challenges related to power supply and operation in extreme conditions as well as to model nodes and some aspects of their operation in the application scenario. These models are the basics of the simulations developed later. The overall system performance is analyzed according to three metrics: number of detections per kinetic node, accuracy, and latency. The links between these metrics and the operational conditions are also discussed and characterized statistically. Subsequently, such statistical characterization is used to forecast performance figures given specific operational parameters. In tracking, also studied via simulations, nonlinear relationships are found between accuracy and duty cycles and cluster sizes of battery-operated nodes. The solution presented may be more complex in terms of network structure than existing solutions based on GPS collars. However, its main gain lies on taking advantage of users' error tolerance to reduce costs and become more environmentally friendly by diminishing the potential amount of batteries that can be lost. Whether it is applicable or not depends ultimately on the conditions and requirements imposed by users' needs and operational environments, which is, as it has been explained, one of the topics of this Thesis.

Modelización tridimensional de ensayos de adherencia tipo viga del refuerzo NSM-FRP en hormigón

El uso de refuerzos NSM‐FRP en estructuras de hormigón armado se ha incrementado considerablemente en los últimos años como método de refuerzo estructural. Los ensayos de arrancamiento en viga de los refuerzos NSM‐FRP permiten el estudio del comportamiento de la unión pegada. El principal objetivo del presente trabajo aborda la simulación numérica de este tipo de ensayos, con el propósito de caracterizar correctamente la adherencia entre las barras de NSM‐FRP y el hormigón. En una fase inicial se simuló un modelo bidimensional para conseguir evaluar y verificar el comportamiento de los elementos cohesivos y ver su comportamiento primero ante diferentes modelos de material y segundo ante un modo mixto de fallo, debido a la aplicación simultanea de carga axial y carga cortante. En una segunda fase se creó un modelo tridimensional para estudiar el arrancamiento de una barra de material compuesto insertada en hormigón, creando un modelo de material de hormigón y viendo el comportamiento cualitativo del sistema ante variaciones en los parámetros de los diferentes materiales. En la tercera fase, la más importante del presente trabajo, se abordó la simulación numérica del ensayo de arrancamiento en viga. Se simularon todos los componentes del ensayo y se evaluaron diferentes alternativas para representar la interfase NSM‐FRP ‐ hormigón, usando elementos cohesivos y diferentes distribuciones de los mismos en la interfase. Para conseguir representar lo más fielmente posible las condiciones del ensayo, se diseñó también un controlador PID que permite realizar las simulaciones numéricas mediante un control en desplazamientos, lo cual permite capturar más correctamente el comportamiento de reblandecimiento de la unión pegada. El controlador PID aplica técnicas de ingeniería de control para conseguir calcular a priori la amplitud necesaria del desplazamiento impuesto que provoque una evolución establecida en una variable interna del sistema. La variable usada para correlacionar los ensayos es la diferencia en desplazamientos entre dos puntos y se escoge una evolución lineal de la misma, pero en la tesis también se exponen los resultados de escoger otras posibles variables internas con diferentes evoluciones. Se compararon las simulaciones numéricas con resultados de mediciones experimentales previamente publicadas. Los resultados carga‐deslizamiento obtenidos encajan bien con los datos experimentales. El modelo propuesto es también capaz de predecir el modo de fallo en la interfase NSM‐FRP ‐ hormigón. Finalmente, también se han llevado a cabo estudios paramétricos, para evaluar la influencia de cada parámetro en los resultados. También se realizó un estudio cualitativo de cómo se comporta la unión pegada en cada momento de la simulación, mediante el uso macros y gráficas tridimensionales, para conseguir una mejor visualización y facilitar el análisis de los resultados. ABSTRACT The use of near‐surface mounted FRP reinforcement in reinforced concrete structures has seen a considerable increase in recent years as a strengthening method. Beam pull‐out tests for near‐surface reinforcement allow obtaining the local bond‐slip behavior of a bonded joint. The main objective of the current work deals with the three‐dimensional modeling of this kind of test with the purpose of characterizing suitably the mechanics of bond between FRP rods and concrete. In an initial stage, a two bidimensional in order to evaluate and to verify the behavior of the cohesive elements. Its behavior was evaluated first testing different material models and second testing the behavior when mixed mode failure appears, due to simultaneous axial and shear load. In a second stage a tridimensional model was created in order to study the pull‐out of an inserted beam of composite material in concrete. A concrete material model was created and the influence of each material parameter was studied qualitatively. The third part, the most relevant of the present work, the numerical simulation of the Beam Pull‐Out test was faced. All the parts of the Beam Pull‐Out test were included inthe simulation and different alternatives to represent the FRP bar – concrete interface have been evaluated, using cohesive elements and different distributions of them. In order to reproduce the test conditions more reliably, a PID controller has also been designed to conduct suitably the numerical tests in order to properly capture the softening branch of the load‐slip behaviour. The PID controller applies control techniques to calculate a priori the necessary amplitude of the load in order to achieve a given evolution through the simulation of an internal variable previously chosen. The variable used in order to correlate the simulation with the test results is the difference in displacements between two points and a linear evolution was chosen, but in the thesis the results of choosing other possible internal variables with different evolutions are also shown. The numerical FE simulations were compared with experimental measurements previously published. Load‐slip predictions compare well with the corresponding experimental data. The proposed model is also able to predict the failure mode at the FRP‐concrete interface. Some parametric studies have also been carried out, in order to evaluate the influence of each material parameter in the results. A qualitative study of the behaviour of the joint was also performed, using the results of the numeric simulations and through the use of macros and 3D graphs, the tensional state of each point of the joint can be visualized in each moment of the simulation.

Dilemas modernos: el proyecto urbano en Montevideo y la costa balnearia

Para analizar este complejo proceso se ha ensayado un recorrido que sigue los avatares y alternativas que se producen en la incorporación de las ideas que se gestaron en el urbanismo moderno en el Uruguay de la primera mitad del siglo XX. Ideas que se intensifican a partir de los años veinte. A través de una primer parte, se analizan las ideas que transitan los primeros años del urbanismo hasta los años treinta. Este es un período de preconstitución disciplinaria y búsqueda de imágenes urbanas análogas que por afinidad cultural, en general, recurren al repertorio europeo. Es un momento de constitución ciudadana y de su espacio cívico y, para ello, se responde al imaginario colectivo con propuestas urbanas que reflejan las ideas de ciudad presentes en el panorama internacional. Al aplicarse a un territorio sin tensiones sociales, las ideas y propuestas urbanas se presentan como una oportunidad de ensayo para los técnicos extranjeros y nacionales. El mito de la oportunidad que ofrece el Nuevo Mundo hace que un personaje reconocido llegue, casi sin prefigurarlo, a hacer una breve visita por Montevideo. La segunda parte describe al viajero Le Corbusier con sus ideas, sus propuestas sudamericanas y el Plan de Montevideo. La fugaz visita deja huellas indelebles, en el huésped y en sus anfitriones. Los caminos rápidamente se bifurcan pese a eventuales reencuentros. En Le Corbusier, Montevideo implica un punto de inflexión en la serie de planes que va a gestar. En los anfitriones abrazando aun más la bandera de la renovación desplegada antes de la visita, pese a no compartir el plan corbusiano para Montevideo, los impulsa a seguir el proceso de construcción moderna. A partir de la tercera parte, se indaga en el impulso moderno dejado por Le Corbusier, junto a la casi coincidente “celebración del futuro” donde se propone el Plan del Centenario para Montevideo. A partir del plan y su debate, sus consiguientes marchas y contramarchas, se muestra que las ideas modernas al igual que en toda celebración tuvieron momentos de apoteosis y entusiasmo, quedando luego, tan sólo las cenizas y los resplandores de la celebración, materializadas en algunos fragmentos de ideas urbanas. En la cuarta parte se analizan las ideas y propuestas en torno al proyecto urbano de la centralidad capitalina. Marchas y contramarchas, protagonizadas por anfitriones e integrantes del auditorio de Le Corbusier muestran un devenir donde se entrecruza la ciudad moderna, el crecimiento real, con las ideas urbanas que el amplio espectro cultural arquitectónico uruguayo conserva desde su constitución. La quinta parte desarrolla las propuestas estructuradas en torno a la expansión del balneario verificando las ideas de urbanismo que con naturalidad evaden la transposición literal o acrítica y se acondicionan y acomodan al territorio, conservando con intensidad, la esencia del pensamiento moderno. La relación entre la urbanidad y el horizonte marino permite el ensayo de una serie de estrategias proyectuales para la urbanización del borde costero que caracterizan y definen a la rambla montevideana y al conjunto de proyectos balnearios modernos. ABSTRACT In order to analyze this complex process, we have pursued a path that takes into consideration the vicissitudes and alternatives produced in the incorporation of the ideas conceived in modern urbanism in Uruguay in the first half of the twentieth century. These ideas have been intensified since the 1920s. The first part of the thesis analyzes the ideas of the first years of urbanism until the 1930s. This was a period of disciplinary pre-constitution and search of analogous urban images which, due to their cultural affinity, in general, resorted to the European repertoire. It was a moment of citizen constitution and the establishment of its civic space, and for that the collective imagination was responded with urban designs that reflected the ideas of the city, which could also be found in the international scene. As they were applied to a territory without social tensions, the ideas and urban designs were presented as an opportunity for rehearsal to foreign and national technicians. The myth of the opportunity offered by the New World caused the arrival of a well-known character that, almost without foreshadowing it, paid a short visit to Montevideo. The second part describes Le Corbusier, the traveler, with his ideas, his South American schemes and the Plan for Montevideo. His fleeting visit left a deep mark on the guest and on his hosts. The paths rapidly forked despite the sporadic reunions. For Le Corbusier, Montevideo marked a turning point in the series of plans that he would conceive. The hosts, who embraced the flag of renovation raised prior to his arrival, in spite of not sharing Le Corbusier’s plan for Montevideo, were encouraged to follow the process of modern construction. The third part of the thesis explores the modern impulse left by Le Corbusier, as well as the almost coincidental “celebration of the future” in which the Plan for the Centenary of Montevideo was proposed. From the plan and its discussion, its consequent progress and obstacles, it was shown that the modern ideas, as in any other celebration, had its moments of apotheosis and enthusiasm, only remaining the ashes and the glow of the celebration, materialized in some fragments of the urban design ideas. The fourth part discusses the ideas and schemes on the urban project of the centrality of the capital. Progress and obstacles, led by the hosts and the members of the auditorium of Le Corbusier, showed a development in which the modern city and the actual growth merged with the urban design ideas preserved, since its constitution, by the wide spectrum of the Uruguayan architectonic culture. Finally, the fifth part develops the schemes formulated for the expansion of the resort and verifies the ideas of urbanism which naturally avoid the literal or uncritical transposition and adjust and accommodate to the territory, preserving with intensity the essence of modern thought. The relation between urbanity and the marine horizon allowed the rehearsal of a series of design strategies for the urbanization of coastal areas which characterize and define the promenade of Montevideo and the whole set of projects of modern resorts.

Providing 30Mbit/s to Spain’s final third. -A techno-economic assessment.

Since the Digital Agenda for Europe released the Europe2020 flagship, Member States are looking for ways of fulfilling their agreed commitments to fast and ultrafast internet deployment. However, Europe is not a homogenous reality. The economic, geographic, social and demographic features of each country make it a highly diverse region to develop best practices over Next Generation Access Networks (NGAN) deployments. There are special concerns about NGAN deployments for “the final third”, as referred to the last 25% of the country’s population who, usually, live in rural areas. This paper assesses, through a techno-economic analysis, the access cost of providing over 30 Mbps broadband for the final third of Spain`s population in municipalities, which are classified into area types, referred to as geotypes. Fixed and mobile technologies are compared in order to determine which is the most cost-effective technology for each geotype. The demographic limit for fixed networks (cable, fibre and copper) is also discussed. The assessment focuses on the supply side and the results show the access network cost only. The research completes a previous published assessment (Techno-economic analysis of next generation access networks roll-out. The case of platform competition, regulation and public policy in Spain) by including the LTE scenario. The LTE scenario is dimensioned to provide 30 Mbps (best effort) broadband, considering a network take-up of 25%. The Rocket techno-economic model is used to assess a ten-year study period deployment. Nevertheless, the deployment must start in 2014 and be completed by 2020, in order to fulfil the Digital Agenda’s goals. The feasibility of the deployment is defined as the ability to recoup the investment at the end of the study period. This ability is highly related to network take-up and, therefore, to service adoption. Network deployment in each geotype is compared with the cost of the deployment in the Urban geotype and broadband expected penetration rates for clarity and simplicity. Debating the cost-effective deployments for each geotype, while addressing the Digital Agenda’s goals regarding fast and ultrafast internet, is the main purpose of this paper. At the end of the last year, the independent Spanish regulation agency released the Spain broadband coverage report at the first half of 2013. This document claimed that 59% and 52% of Spain’s population was already covered by NGAN capable of providing 30 Mbps and 100 Mbps broadband respectively. HFC, with 47% of population coverage, and FTTH, with 14%, were considered as a 100 Mbps capable NGAN. Meanwhile VDSL, with 12% of the population covered, was the only NGAN network considered for the 30 Mbps segment. Despite not being an NGAN, the 99% population coverage of HSPA networks was also noted in the report. Since mobile operators are also required to provide 30 Mbps broadband to 90% of the population in rural areas by the end of 2020, mobile networks will play a significant role on the achievement of the 30 Mbps goal in Spain’s final third. The assessment indicates the cost of the deployment per cumulative households coverage with 4 different NGANs: FTTH, HFC, VDSL and LTE. Research shows that an investment ranging from €2,700 (VDSL) to €5,400 (HFC) million will be needed to cover the first half of the population with any fixed technology assessed. The results state that at least €3,000 million will be required to cover these areas with the least expensive technology (LTE). However, if we consider the throughput that fixed networks could provide and achievement of the Digital Agenda’s objectives, fixed network deployments are recommended for up to 90% of the population. Fibre and cable deployments could cover up to a maximum of 88% of the Spanish population cost efficiently. As there are some concerns about the service adoption, we recommend VDSL and mobile network deployments for the final third of the population. Despite LTE being able to provide the most economical roll-out, VDSL could also provide 50 Mbps from 75% to 90% of the Spanish population cost efficiently. For this population gap, facility based competition between VDSL providers and LTE providers must be encouraged. Regarding 90% to 98.5% of the Spanish population, LTE deployment is the most appropriate. Since costumers in less populated the municipalities are more sensitive to the cost of the service, we consider that a single network deployment could be most appropriate. Finally, it has become clear that it is not possible to deliver 30Mbps to the final 1.5% of the population cost-efficiently and adoption predictions are not optimistic either. As there are other broadband alternatives able to deliver up to 20 Mbps, in the authors’ opinion, it is not necessary to cover the extreme rural areas, where public financing would be required.

Caracterización de un robot para aplicaciones de mecanizado con requerimientos de tolerancias

El presente Trabajo fin Fin de Máster, versa sobre una caracterización preliminar del comportamiento de un robot de tipo industrial, configurado por 4 eslabones y 4 grados de libertad, y sometido a fuerzas de mecanizado en su extremo. El entorno de trabajo planteado es el de plantas de fabricación de piezas de aleaciones de aluminio para automoción. Este tipo de componentes parte de un primer proceso de fundición que saca la pieza en bruto. Para series medias y altas, en función de las propiedades mecánicas y plásticas requeridas y los costes de producción, la inyección a alta presión (HPDC) y la fundición a baja presión (LPC) son las dos tecnologías más usadas en esta primera fase. Para inyección a alta presión, las aleaciones de aluminio más empleadas son, en designación simbólica según norma EN 1706 (entre paréntesis su designación numérica); EN AC AlSi9Cu3(Fe) (EN AC 46000) , EN AC AlSi9Cu3(Fe)(Zn) (EN AC 46500), y EN AC AlSi12Cu1(Fe) (EN AC 47100). Para baja presión, EN AC AlSi7Mg0,3 (EN AC 42100). En los 3 primeros casos, los límites de Silicio permitidos pueden superan el 10%. En el cuarto caso, es inferior al 10% por lo que, a los efectos de ser sometidas a mecanizados, las piezas fabricadas en aleaciones con Si superior al 10%, se puede considerar que son equivalentes, diferenciándolas de la cuarta. Las tolerancias geométricas y dimensionales conseguibles directamente de fundición, recogidas en normas como ISO 8062 o DIN 1688-1, establecen límites para este proceso. Fuera de esos límites, las garantías en conseguir producciones con los objetivos de ppms aceptados en la actualidad por el mercado, obligan a ir a fases posteriores de mecanizado. Aquellas geometrías que, funcionalmente, necesitan disponer de unas tolerancias geométricas y/o dimensionales definidas acorde a ISO 1101, y no capaces por este proceso inicial de moldeado a presión, deben ser procesadas en una fase posterior en células de mecanizado. En este caso, las tolerancias alcanzables para procesos de arranque de viruta se recogen en normas como ISO 2768. Las células de mecanizado se componen, por lo general, de varios centros de control numérico interrelacionados y comunicados entre sí por robots que manipulan las piezas en proceso de uno a otro. Dichos robots, disponen en su extremo de una pinza utillada para poder coger y soltar las piezas en los útiles de mecanizado, las mesas de intercambio para cambiar la pieza de posición o en utillajes de equipos de medición y prueba, o en cintas de entrada o salida. La repetibilidad es alta, de centésimas incluso, definida según norma ISO 9283. El problema es que, estos rangos de repetibilidad sólo se garantizan si no se hacen esfuerzos o éstos son despreciables (caso de mover piezas). Aunque las inercias de mover piezas a altas velocidades hacen que la trayectoria intermedia tenga poca precisión, al inicio y al final (al coger y dejar pieza, p.e.) se hacen a velocidades relativamente bajas que hacen que el efecto de las fuerzas de inercia sean menores y que permiten garantizar la repetibilidad anteriormente indicada. No ocurre así si se quitara la garra y se intercambia con un cabezal motorizado con una herramienta como broca, mandrino, plato de cuchillas, fresas frontales o tangenciales… Las fuerzas ejercidas de mecanizado generarían unos pares en las uniones tan grandes y tan variables que el control del robot no sería capaz de responder (o no está preparado, en un principio) y generaría una desviación en la trayectoria, realizada a baja velocidad, que desencadenaría en un error de posición (ver norma ISO 5458) no asumible para la funcionalidad deseada. Se podría llegar al caso de que la tolerancia alcanzada por un pretendido proceso más exacto diera una dimensión peor que la que daría el proceso de fundición, en principio con mayor variabilidad dimensional en proceso (y por ende con mayor intervalo de tolerancia garantizable). De hecho, en los CNCs, la precisión es muy elevada, (pudiéndose despreciar en la mayoría de los casos) y no es la responsable de, por ejemplo la tolerancia de posición al taladrar un agujero. Factores como, temperatura de la sala y de la pieza, calidad constructiva de los utillajes y rigidez en el amarre, error en el giro de mesas y de colocación de pieza, si lleva agujeros previos o no, si la herramienta está bien equilibrada y el cono es el adecuado para el tipo de mecanizado… influyen más. Es interesante que, un elemento no específico tan común en una planta industrial, en el entorno anteriormente descrito, como es un robot, el cual no sería necesario añadir por disponer de él ya (y por lo tanto la inversión sería muy pequeña), puede mejorar la cadena de valor disminuyendo el costo de fabricación. Y si se pudiera conjugar que ese robot destinado a tareas de manipulación, en los muchos tiempos de espera que va a disfrutar mientras el CNC arranca viruta, pudiese coger un cabezal y apoyar ese mecanizado; sería doblemente interesante. Por lo tanto, se antoja sugestivo poder conocer su comportamiento e intentar explicar qué sería necesario para llevar esto a cabo, motivo de este trabajo. La arquitectura de robot seleccionada es de tipo SCARA. La búsqueda de un robot cómodo de modelar y de analizar cinemática y dinámicamente, sin limitaciones relevantes en la multifuncionalidad de trabajos solicitados, ha llevado a esta elección, frente a otras arquitecturas como por ejemplo los robots antropomórficos de 6 grados de libertad, muy populares a nivel industrial. Este robot dispone de 3 uniones, de las cuales 2 son de tipo par de revolución (1 grado de libertad cada una) y la tercera es de tipo corredera o par cilíndrico (2 grados de libertad). La primera unión, de tipo par de revolución, sirve para unir el suelo (considerado como eslabón número 1) con el eslabón número 2. La segunda unión, también de ese tipo, une el eslabón número 2 con el eslabón número 3. Estos 2 brazos, pueden describir un movimiento horizontal, en el plano X-Y. El tercer eslabón, está unido al eslabón número 4 por la unión de tipo corredera. El movimiento que puede describir es paralelo al eje Z. El robot es de 4 grados de libertad (4 motores). En relación a los posibles trabajos que puede realizar este tipo de robot, su versatilidad abarca tanto operaciones típicas de manipulación como operaciones de arranque de viruta. Uno de los mecanizados más usuales es el taladrado, por lo cual se elige éste para su modelización y análisis. Dentro del taladrado se elegirá para acotar las fuerzas, taladrado en macizo con broca de diámetro 9 mm. El robot se ha considerado por el momento que tenga comportamiento de sólido rígido, por ser el mayor efecto esperado el de los pares en las uniones. Para modelar el robot se utiliza el método de los sistemas multicuerpos. Dentro de este método existen diversos tipos de formulaciones (p.e. Denavit-Hartenberg). D-H genera una cantidad muy grande de ecuaciones e incógnitas. Esas incógnitas son de difícil comprensión y, para cada posición, hay que detenerse a pensar qué significado tienen. Se ha optado por la formulación de coordenadas naturales. Este sistema utiliza puntos y vectores unitarios para definir la posición de los distintos cuerpos, y permite compartir, cuando es posible y se quiere, para definir los pares cinemáticos y reducir al mismo tiempo el número de variables. Las incógnitas son intuitivas, las ecuaciones de restricción muy sencillas y se reduce considerablemente el número de ecuaciones e incógnitas. Sin embargo, las coordenadas naturales “puras” tienen 2 problemas. El primero, que 2 elementos con un ángulo de 0 o 180 grados, dan lugar a puntos singulares que pueden crear problemas en las ecuaciones de restricción y por lo tanto han de evitarse. El segundo, que tampoco inciden directamente sobre la definición o el origen de los movimientos. Por lo tanto, es muy conveniente complementar esta formulación con ángulos y distancias (coordenadas relativas). Esto da lugar a las coordenadas naturales mixtas, que es la formulación final elegida para este TFM. Las coordenadas naturales mixtas no tienen el problema de los puntos singulares. Y la ventaja más importante reside en su utilidad a la hora de aplicar fuerzas motrices, momentos o evaluar errores. Al incidir sobre la incógnita origen (ángulos o distancias) controla los motores de manera directa. El algoritmo, la simulación y la obtención de resultados se ha programado mediante Matlab. Para realizar el modelo en coordenadas naturales mixtas, es preciso modelar en 2 pasos el robot a estudio. El primer modelo se basa en coordenadas naturales. Para su validación, se plantea una trayectoria definida y se analiza cinemáticamente si el robot satisface el movimiento solicitado, manteniendo su integridad como sistema multicuerpo. Se cuantifican los puntos (en este caso inicial y final) que configuran el robot. Al tratarse de sólidos rígidos, cada eslabón queda definido por sus respectivos puntos inicial y final (que son los más interesantes para la cinemática y la dinámica) y por un vector unitario no colineal a esos 2 puntos. Los vectores unitarios se colocan en los lugares en los que se tenga un eje de rotación o cuando se desee obtener información de un ángulo. No son necesarios vectores unitarios para medir distancias. Tampoco tienen por qué coincidir los grados de libertad con el número de vectores unitarios. Las longitudes de cada eslabón quedan definidas como constantes geométricas. Se establecen las restricciones que definen la naturaleza del robot y las relaciones entre los diferentes elementos y su entorno. La trayectoria se genera por una nube de puntos continua, definidos en coordenadas independientes. Cada conjunto de coordenadas independientes define, en un instante concreto, una posición y postura de robot determinada. Para conocerla, es necesario saber qué coordenadas dependientes hay en ese instante, y se obtienen resolviendo por el método de Newton-Rhapson las ecuaciones de restricción en función de las coordenadas independientes. El motivo de hacerlo así es porque las coordenadas dependientes deben satisfacer las restricciones, cosa que no ocurre con las coordenadas independientes. Cuando la validez del modelo se ha probado (primera validación), se pasa al modelo 2. El modelo número 2, incorpora a las coordenadas naturales del modelo número 1, las coordenadas relativas en forma de ángulos en los pares de revolución (3 ángulos; ϕ1, ϕ 2 y ϕ3) y distancias en los pares prismáticos (1 distancia; s). Estas coordenadas relativas pasan a ser las nuevas coordenadas independientes (sustituyendo a las coordenadas independientes cartesianas del modelo primero, que eran coordenadas naturales). Es necesario revisar si el sistema de vectores unitarios del modelo 1 es suficiente o no. Para este caso concreto, se han necesitado añadir 1 vector unitario adicional con objeto de que los ángulos queden perfectamente determinados con las correspondientes ecuaciones de producto escalar y/o vectorial. Las restricciones habrán de ser incrementadas en, al menos, 4 ecuaciones; una por cada nueva incógnita. La validación del modelo número 2, tiene 2 fases. La primera, al igual que se hizo en el modelo número 1, a través del análisis cinemático del comportamiento con una trayectoria definida. Podrían obtenerse del modelo 2 en este análisis, velocidades y aceleraciones, pero no son necesarios. Tan sólo interesan los movimientos o desplazamientos finitos. Comprobada la coherencia de movimientos (segunda validación), se pasa a analizar cinemáticamente el comportamiento con trayectorias interpoladas. El análisis cinemático con trayectorias interpoladas, trabaja con un número mínimo de 3 puntos máster. En este caso se han elegido 3; punto inicial, punto intermedio y punto final. El número de interpolaciones con el que se actúa es de 50 interpolaciones en cada tramo (cada 2 puntos máster hay un tramo), resultando un total de 100 interpolaciones. El método de interpolación utilizado es el de splines cúbicas con condición de aceleración inicial y final constantes, que genera las coordenadas independientes de los puntos interpolados de cada tramo. Las coordenadas dependientes se obtienen resolviendo las ecuaciones de restricción no lineales con el método de Newton-Rhapson. El método de las splines cúbicas es muy continuo, por lo que si se desea modelar una trayectoria en el que haya al menos 2 movimientos claramente diferenciados, es preciso hacerlo en 2 tramos y unirlos posteriormente. Sería el caso en el que alguno de los motores se desee expresamente que esté parado durante el primer movimiento y otro distinto lo esté durante el segundo movimiento (y así sucesivamente). Obtenido el movimiento, se calculan, también mediante fórmulas de diferenciación numérica, las velocidades y aceleraciones independientes. El proceso es análogo al anteriormente explicado, recordando la condición impuesta de que la aceleración en el instante t= 0 y en instante t= final, se ha tomado como 0. Las velocidades y aceleraciones dependientes se calculan resolviendo las correspondientes derivadas de las ecuaciones de restricción. Se comprueba, de nuevo, en una tercera validación del modelo, la coherencia del movimiento interpolado. La dinámica inversa calcula, para un movimiento definido -conocidas la posición, velocidad y la aceleración en cada instante de tiempo-, y conocidas las fuerzas externas que actúan (por ejemplo el peso); qué fuerzas hay que aplicar en los motores (donde hay control) para que se obtenga el citado movimiento. En la dinámica inversa, cada instante del tiempo es independiente de los demás y tiene una posición, una velocidad y una aceleración y unas fuerzas conocidas. En este caso concreto, se desean aplicar, de momento, sólo las fuerzas debidas al peso, aunque se podrían haber incorporado fuerzas de otra naturaleza si se hubiese deseado. Las posiciones, velocidades y aceleraciones, proceden del cálculo cinemático. El efecto inercial de las fuerzas tenidas en cuenta (el peso) es calculado. Como resultado final del análisis dinámico inverso, se obtienen los pares que han de ejercer los cuatro motores para replicar el movimiento prescrito con las fuerzas que estaban actuando. La cuarta validación del modelo consiste en confirmar que el movimiento obtenido por aplicar los pares obtenidos en la dinámica inversa, coinciden con el obtenido en el análisis cinemático (movimiento teórico). Para ello, es necesario acudir a la dinámica directa. La dinámica directa se encarga de calcular el movimiento del robot, resultante de aplicar unos pares en motores y unas fuerzas en el robot. Por lo tanto, el movimiento real resultante, al no haber cambiado ninguna condición de las obtenidas en la dinámica inversa (pares de motor y fuerzas inerciales debidas al peso de los eslabones) ha de ser el mismo al movimiento teórico. Siendo así, se considera que el robot está listo para trabajar. Si se introduce una fuerza exterior de mecanizado no contemplada en la dinámica inversa y se asigna en los motores los mismos pares resultantes de la resolución del problema dinámico inverso, el movimiento real obtenido no es igual al movimiento teórico. El control de lazo cerrado se basa en ir comparando el movimiento real con el deseado e introducir las correcciones necesarias para minimizar o anular las diferencias. Se aplican ganancias en forma de correcciones en posición y/o velocidad para eliminar esas diferencias. Se evalúa el error de posición como la diferencia, en cada punto, entre el movimiento teórico deseado en el análisis cinemático y el movimiento real obtenido para cada fuerza de mecanizado y una ganancia concreta. Finalmente, se mapea el error de posición obtenido para cada fuerza de mecanizado y las diferentes ganancias previstas, graficando la mejor precisión que puede dar el robot para cada operación que se le requiere, y en qué condiciones. -------------- This Master´s Thesis deals with a preliminary characterization of the behaviour for an industrial robot, configured with 4 elements and 4 degrees of freedoms, and subjected to machining forces at its end. Proposed working conditions are those typical from manufacturing plants with aluminium alloys for automotive industry. This type of components comes from a first casting process that produces rough parts. For medium and high volumes, high pressure die casting (HPDC) and low pressure die casting (LPC) are the most used technologies in this first phase. For high pressure die casting processes, most used aluminium alloys are, in simbolic designation according EN 1706 standard (between brackets, its numerical designation); EN AC AlSi9Cu3(Fe) (EN AC 46000) , EN AC AlSi9Cu3(Fe)(Zn) (EN AC 46500), y EN AC AlSi12Cu1(Fe) (EN AC 47100). For low pressure, EN AC AlSi7Mg0,3 (EN AC 42100). For the 3 first alloys, Si allowed limits can exceed 10% content. Fourth alloy has admisible limits under 10% Si. That means, from the point of view of machining, that components made of alloys with Si content above 10% can be considered as equivalent, and the fourth one must be studied separately. Geometrical and dimensional tolerances directly achievables from casting, gathered in standards such as ISO 8062 or DIN 1688-1, establish a limit for this process. Out from those limits, guarantees to achieve batches with objetive ppms currently accepted by market, force to go to subsequent machining process. Those geometries that functionally require a geometrical and/or dimensional tolerance defined according ISO 1101, not capable with initial moulding process, must be obtained afterwards in a machining phase with machining cells. In this case, tolerances achievables with cutting processes are gathered in standards such as ISO 2768. In general terms, machining cells contain several CNCs that they are interrelated and connected by robots that handle parts in process among them. Those robots have at their end a gripper in order to take/remove parts in machining fixtures, in interchange tables to modify position of part, in measurement and control tooling devices, or in entrance/exit conveyors. Repeatibility for robot is tight, even few hundredths of mm, defined according ISO 9283. Problem is like this; those repeatibilty ranks are only guaranteed when there are no stresses or they are not significant (f.e. due to only movement of parts). Although inertias due to moving parts at a high speed make that intermediate paths have little accuracy, at the beginning and at the end of trajectories (f.e, when picking part or leaving it) movement is made with very slow speeds that make lower the effect of inertias forces and allow to achieve repeatibility before mentioned. It does not happens the same if gripper is removed and it is exchanged by an spindle with a machining tool such as a drilling tool, a pcd boring tool, a face or a tangential milling cutter… Forces due to machining would create such big and variable torques in joints that control from the robot would not be able to react (or it is not prepared in principle) and would produce a deviation in working trajectory, made at a low speed, that would trigger a position error (see ISO 5458 standard) not assumable for requested function. Then it could be possible that tolerance achieved by a more exact expected process would turn out into a worst dimension than the one that could be achieved with casting process, in principle with a larger dimensional variability in process (and hence with a larger tolerance range reachable). As a matter of fact, accuracy is very tight in CNC, (its influence can be ignored in most cases) and it is not the responsible of, for example position tolerance when drilling a hole. Factors as, room and part temperature, manufacturing quality of machining fixtures, stiffness at clamping system, rotating error in 4th axis and part positioning error, if there are previous holes, if machining tool is properly balanced, if shank is suitable for that machining type… have more influence. It is interesting to know that, a non specific element as common, at a manufacturing plant in the enviroment above described, as a robot (not needed to be added, therefore with an additional minimum investment), can improve value chain decreasing manufacturing costs. And when it would be possible to combine that the robot dedicated to handling works could support CNCs´ works in its many waiting time while CNCs cut, and could take an spindle and help to cut; it would be double interesting. So according to all this, it would be interesting to be able to know its behaviour and try to explain what would be necessary to make this possible, reason of this work. Selected robot architecture is SCARA type. The search for a robot easy to be modeled and kinematically and dinamically analyzed, without significant limits in the multifunctionality of requested operations, has lead to this choice. Due to that, other very popular architectures in the industry, f.e. 6 DOFs anthropomorphic robots, have been discarded. This robot has 3 joints, 2 of them are revolute joints (1 DOF each one) and the third one is a cylindrical joint (2 DOFs). The first joint, a revolute one, is used to join floor (body 1) with body 2. The second one, a revolute joint too, joins body 2 with body 3. These 2 bodies can move horizontally in X-Y plane. Body 3 is linked to body 4 with a cylindrical joint. Movement that can be made is paralell to Z axis. The robt has 4 degrees of freedom (4 motors). Regarding potential works that this type of robot can make, its versatility covers either typical handling operations or cutting operations. One of the most common machinings is to drill. That is the reason why it has been chosen for the model and analysis. Within drilling, in order to enclose spectrum force, a typical solid drilling with 9 mm diameter. The robot is considered, at the moment, to have a behaviour as rigid body, as biggest expected influence is the one due to torques at joints. In order to modelize robot, it is used multibodies system method. There are under this heading different sorts of formulations (f.e. Denavit-Hartenberg). D-H creates a great amount of equations and unknown quantities. Those unknown quatities are of a difficult understanding and, for each position, one must stop to think about which meaning they have. The choice made is therefore one of formulation in natural coordinates. This system uses points and unit vectors to define position of each different elements, and allow to share, when it is possible and wished, to define kinematic torques and reduce number of variables at the same time. Unknown quantities are intuitive, constrain equations are easy and number of equations and variables are strongly reduced. However, “pure” natural coordinates suffer 2 problems. The first one is that 2 elements with an angle of 0° or 180°, give rise to singular positions that can create problems in constrain equations and therefore they must be avoided. The second problem is that they do not work directly over the definition or the origin of movements. Given that, it is highly recommended to complement this formulation with angles and distances (relative coordinates). This leads to mixed natural coordinates, and they are the final formulation chosen for this MTh. Mixed natural coordinates have not the problem of singular positions. And the most important advantage lies in their usefulness when applying driving forces, torques or evaluating errors. As they influence directly over origin variable (angles or distances), they control motors directly. The algorithm, simulation and obtaining of results has been programmed with Matlab. To design the model in mixed natural coordinates, it is necessary to model the robot to be studied in 2 steps. The first model is based in natural coordinates. To validate it, it is raised a defined trajectory and it is kinematically analyzed if robot fulfils requested movement, keeping its integrity as multibody system. The points (in this case starting and ending points) that configure the robot are quantified. As the elements are considered as rigid bodies, each of them is defined by its respectively starting and ending point (those points are the most interesting ones from the point of view of kinematics and dynamics) and by a non-colinear unit vector to those points. Unit vectors are placed where there is a rotating axis or when it is needed information of an angle. Unit vectors are not needed to measure distances. Neither DOFs must coincide with the number of unit vectors. Lengths of each arm are defined as geometrical constants. The constrains that define the nature of the robot and relationships among different elements and its enviroment are set. Path is generated by a cloud of continuous points, defined in independent coordinates. Each group of independent coordinates define, in an specific instant, a defined position and posture for the robot. In order to know it, it is needed to know which dependent coordinates there are in that instant, and they are obtained solving the constraint equations with Newton-Rhapson method according to independent coordinates. The reason to make it like this is because dependent coordinates must meet constraints, and this is not the case with independent coordinates. When suitability of model is checked (first approval), it is given next step to model 2. Model 2 adds to natural coordinates from model 1, the relative coordinates in the shape of angles in revoluting torques (3 angles; ϕ1, ϕ 2 and ϕ3) and distances in prismatic torques (1 distance; s). These relative coordinates become the new independent coordinates (replacing to cartesian independent coordinates from model 1, that they were natural coordinates). It is needed to review if unit vector system from model 1 is enough or not . For this specific case, it was necessary to add 1 additional unit vector to define perfectly angles with their related equations of dot and/or cross product. Constrains must be increased in, at least, 4 equations; one per each new variable. The approval of model 2 has two phases. The first one, same as made with model 1, through kinematic analysis of behaviour with a defined path. During this analysis, it could be obtained from model 2, velocities and accelerations, but they are not needed. They are only interesting movements and finite displacements. Once that the consistence of movements has been checked (second approval), it comes when the behaviour with interpolated trajectories must be kinematically analyzed. Kinematic analysis with interpolated trajectories work with a minimum number of 3 master points. In this case, 3 points have been chosen; starting point, middle point and ending point. The number of interpolations has been of 50 ones in each strecht (each 2 master points there is an strecht), turning into a total of 100 interpolations. The interpolation method used is the cubic splines one with condition of constant acceleration both at the starting and at the ending point. This method creates the independent coordinates of interpolated points of each strecht. The dependent coordinates are achieved solving the non-linear constrain equations with Newton-Rhapson method. The method of cubic splines is very continuous, therefore when it is needed to design a trajectory in which there are at least 2 movements clearly differents, it is required to make it in 2 steps and join them later. That would be the case when any of the motors would keep stopped during the first movement, and another different motor would remain stopped during the second movement (and so on). Once that movement is obtained, they are calculated, also with numerical differenciation formulas, the independent velocities and accelerations. This process is analogous to the one before explained, reminding condition that acceleration when t=0 and t=end are 0. Dependent velocities and accelerations are calculated solving related derivatives of constrain equations. In a third approval of the model it is checked, again, consistence of interpolated movement. Inverse dynamics calculates, for a defined movement –knowing position, velocity and acceleration in each instant of time-, and knowing external forces that act (f.e. weights); which forces must be applied in motors (where there is control) in order to obtain requested movement. In inverse dynamics, each instant of time is independent of the others and it has a position, a velocity, an acceleration and known forces. In this specific case, it is intended to apply, at the moment, only forces due to the weight, though forces of another nature could have been added if it would have been preferred. The positions, velocities and accelerations, come from kinematic calculation. The inertial effect of forces taken into account (weight) is calculated. As final result of the inverse dynamic analysis, the are obtained torques that the 4 motors must apply to repeat requested movement with the forces that were acting. The fourth approval of the model consists on confirming that the achieved movement due to the use of the torques obtained in the inverse dynamics, are in accordance with movements from kinematic analysis (theoretical movement). For this, it is necessary to work with direct dynamics. Direct dynamic is in charge of calculating the movements of robot that results from applying torques at motors and forces at the robot. Therefore, the resultant real movement, as there was no change in any condition of the ones obtained at the inverse dynamics (motor torques and inertial forces due to weight of elements) must be the same than theoretical movement. When these results are achieved, it is considered that robot is ready to work. When a machining external force is introduced and it was not taken into account before during the inverse dynamics, and torques at motors considered are the ones of the inverse dynamics, the real movement obtained is not the same than the theoretical movement. Closed loop control is based on comparing real movement with expected movement and introducing required corrrections to minimize or cancel differences. They are applied gains in the way of corrections for position and/or tolerance to remove those differences. Position error is evaluated as the difference, in each point, between theoretical movemment (calculated in the kinematic analysis) and the real movement achieved for each machining force and for an specific gain. Finally, the position error obtained for each machining force and gains are mapped, giving a chart with the best accuracy that the robot can give for each operation that has been requested and which conditions must be provided.

Urbanism and dictatorship: perspectives of the field of urban studies

In 1933 public letter to Wilhelm Furtwängler, Joseph Goebbels synthesized the official understanding of the link between politics, art and society in the early steps of the Third Reich. By assuming the ethos of art, politics acquired a plastic agency to mold its objects —population and the state— as a unified entity in the form of a ‘national-popular community’ (Volksgemeinschaft); in turn, by infusing art with a political valence, it became part of a wider governmental apparatus that reshaped aesthetic discourses and practices. Similar remarks could be made about the ordering of cities and territories in this period. Dictatorial imaginations mobilized urbanism —including urban theory, urban design and planning— as a fundamental tool for social organization. Under their aegis the production of space became a moment in a wider production of society. Many authors suggest that this political-spatial nexus is intrinsic to modernity itself, beyond dictatorial regimes. In this light, I propose to use dictatorial urbanisms as an analytical opportunity to delve into some concealed features of modern urban design and planning. This chapter explores some of these aspects from a theoretical standpoint, focusing on the development of dictatorial planning mentalities and spatial rationalities and drawing links to other historical episodes in order to inscribe the former in a broader genealogy of urbanism. Needless to say, I don’t suggest that we use dictatorships as mere templates to understand modern productions of space. Instead, these cases provide a crude version of some fundamental drives in the operationalization of urbanism as an instrument of social regulation, showing how far the modern imagination of sociospatial orderings can go. Dictatorial urbanisms constituted a set of experiences where many dreams and aspirations of modern planning went to die. But not, as the conventional account would have it, because the former were the antithesis of the latter, but rather because they worked as the excess of a particular orientation of modern spatial governmentalities — namely, their focus on calculation, social engineering and disciplinary spatialities, and their attempt to subsume a wide range of everyday practices under institutional structuration by means of spatial mediations. In my opinion the interest of dictatorial urbanisms lies in their role as key regulatory episodes in a longer history of our urban present. They stand as a threshold between the advent of planning in the late 19th and early 20th century, and its final consolidation as a crucial state instrument after World War II. We need, therefore, to pay attention to these experiences vis-à-vis the alleged ‘normal’ development of the field in contemporary democratic countries in order to develop a full comprehension thereof.

La arquitectura de José M. García de Paredes ideario de una obra

Acercarse a las obras de José M. García de Paredes, y mirarlas como un conjunto de ideas que nos indican una manera de pensar y de hacer arquitectura, nos explica un ideario que persiste en el tiempo. Tomando prestado el término “explicar” en el sentido que Stravinski le da en su Poética musical1: desplegar, desarrollar, describir una cosa, descubrir y aclarar su génesis, se comprueban las relaciones que cosas aparentemente dispersas tienen entre si, cómo se originan las obras para saber cómo determinan la arquitectura, una vez que ésta tiene vida propia y uso, pasado el tiempo. El motivo de esta tesis se encuentra en el orden, análisis y estudio de su archivo, realizado a partir del año 1990. García de Paredes, titulado en Madrid, fue arquitecto entre 1950 y 1990 y se inició en la arquitectura en un tiempo tan complejo como el actual. No fue un teórico de la arquitectura, si bien conoció en profundidad su teoría y dejó escritos y reflexiones sobre la manera de abordar el proyecto. Quizás no fue un arquitecto radicalmente innovador y sus obras son silenciosas, aunque muchas encierran planteamientos rotundos que permanecen voluntariamente en penumbra. Sin embargo sus obras son nítidas, tienen el valor de la coherencia y son valiosas por el conocimiento y por los valores que transmiten. Han cumplido su objetivo y ahora son parte de los lugares para los que se construyeron y parte de la vida de las personas para las que se proyectaron. En gran medida, poseen ya la pátina del tiempo. Su obra, no muy extensa, aúna ideas necesarias para abordar la práctica del proyecto y para llegar a ese voluntario resultado final en el que la arquitectura sea, además de una expresión personal, una actividad social capaz de hacer mejor la vida de las personas. Mirar la arquitectura de García de Paredes a través del estudio de todas las cuestiones que intervienen en ella y convertir su conocimiento en un instrumento útil de trabajo en el proyecto, es el objetivo de esta tesis. Así se analizan determinadas obras para exponer temas de antes y de ahora, ideas que son a la vez antiguas y contemporáneas. Este ideario sobre la arquitectura de García de Paredes no pertenece sólo a un tiempo, pues la bella utilidad social de la arquitectura y cómo llegar a ella a través del conocimiento y de la economía intelectual, sigue vigente. Y este objetivo tiene claramente una segunda lectura, pues al poner en valor el ideario de su obra, la presente tesis constituye tanto un homenaje como un agradecimiento al arquitecto. Sintetizar este ideario ha necesitado tanto del tiempo para organizar un archivo como de la práctica de la arquitectura para constatarlo. Durante una década, entre 1981 y 1990, trabajé en el estudio de José M. García de Paredes, con la mirada enfocada hacia los proyectos que entonces se desarrollaban en su estudio. En esos años, la música y las secciones de las salas de concierto llenaban las mesas de dibujo. En 1990, tras su inesperada marcha, me encontré con un legado de documentos que constituyen un fragmento de la arquitectura contemporánea española, que encierran la explicación de proyectos y planteamientos que son respuesta clara a la realidad de su momento. La preparación entonces de la documentación para las tres monografías sobre su obra me llevó a ordenar, clasificar y a documentar los fondos del estudio de manera sistemática y cronológicamente. Los documentos, conservados en archivadores y tubos sin numerar, desvelaban una obra en un momento en el cual el escenario de fondo del debate sobre arquitectura era ético. De manera casi artesanal y próximo de un grupo coherente de arquitectos, algunos vinculados también a las artes plásticas, García de Paredes utiliza los medios materiales a su alcance, interpretando la realidad de una forma personal, alejada de la frialdad del movimiento moderno estricto, con una voluntad de mejorarla y de prescindir de todo aquello que no fuera necesario. Las obras dan respuesta a esa realidad de tal manera que la transforman, como si de un “mágico realismo” se tratara. Estos documentos con olor a antiguo, más que narrar una historia, explican la manera en que se ha hecho esa historia, cómo las biografías y los acontecimientos se entrelazan para llegar al conocido resultado final. Y de un primer análisis, disponiéndolos a la vista de un mismo tiempo, va surgiendo otro interés que no es el de explicar su obra sino el de observar el proceso de trabajo de un arquitecto para desvelar un método de proyecto. Sobre el método de trabajo de un músico, Azorín se pregunta en su artículo “Vida imaginaria de Falla”: “Es fácil ver trabajar a un pintor, no es tan fácil ver enfrascado en su labor a un literato, aunque en las redacciones solamos ver cómo escribe un poeta que hace artículos para un periódico. ¿Pero cómo imaginamos a un músico en su tarea?. ¿Cómo escribe un músico?. ¿Es que siente de pronto un arrebato lírico y un poco desmelenado, los músicos deben llevar el pelo largo, se sienta al piano y comienza a tañer como una inspirada pitonisa?. ¿es que se levanta a media noche y, arrebatado por la inspiración y a la luz de la luna, si la hay, escribe febrilmente esas garrapatitas que vemos en los hilos telegráficos de la música?" Manuel de Falla en una carta le responde: “Nada de eso, mi querido amigo, mi trabajo de compositor no es tan misterioso como usted imagina: podría compararse al de un escritor que fuera a la vez arquitecto”. ¿Y cómo trabaja un arquitecto?. La complejidad del proceso arquitectónico nos presenta sin embargo resultados finales que sólo a través de una observación minuciosa permiten entrever el recorrido desde el pensamiento hasta la obra acabada. El escritor narra lo que ve o imagina y el arquitecto construye y da forma a esa realidad o a esos deseos y para ello debe mirar, escuchar y debe saber hacer. Analizar este proceso nos lleva inexorablemente a desvelar las claves que hacen valiosas determinadas arquitecturas. En junio de 1986 García de Paredes escribe el texto “Tres paisajes con arquitecturas”4. El texto describe tres paisajes culturales diferentes en distintos tiempos. El primero que describe es el Madrid neoclásico y el significado que tiene en este paisaje el Museo del Prado. El segundo paisaje se denomina “Alhambra versus Carlos V” y en él relata un delicado escenario donde se entrelazan distintas cuestiones relativas a la intervención en lugares históricos. En el tercer paisaje “Paisaje con Ruinas” tras describir las hermosas ruinas físicas del pasado concluye con una reflexión: “Hay ruinas y ruinas… Pero quizá no sean estas las verdaderas ruinas de nuestro tiempo. Qué clase de ruina producirá nuestra modesta arquitectura del siglo XX?. Nuestro legado no debería leerse en clave de piedras como las de otras épocas que no disponían de otro lenguaje que el de construir para los tiempos. Sin embargo es posible que surjan otras claves, quizá aún no bien conocidas, que sean para las generaciones futuras de tan clara lectura como la de este tercer Paisaje”. Encontrar esas claves contemporáneas, es el objeto de este paseo por las obras y escritos de García de Paredes. Mirar, suprimido el tiempo, los planos, dibujos, escritos, libros y fotografías del archivo del arquitecto, ordenando y comprendiendo los motivos que propiciaron cada obra, nos lleva a pensar que la arquitectura de cada momento es sólo un desplazamiento de los anteriores. Nada ahora es completamente distinto de lo que era entonces y la arquitectura de antes puede ser interpretada, más allá de aspectos formales, por otras generaciones, desdibujándose el tiempo donde pretendemos ordenarla. Este legado de claves conceptuales nos es útil ahora para conocer lo que permanece en la arquitectura pensando en cuestiones actuales a través de papeles antiguos. El legado de esa “modesta arquitectura” no se debe leer pues en clave de “piedras”, como expresaba García de Paredes. Gran parte de sus obras se construyen con materiales sencillos y la lectura de su valor no es directa. Sin embargo explican en qué momento la arquitectura pasa a ser un hecho capaz de transmitir intenciones ocultas y convertirse en una actividad social en sintonía con la realidad. Desvelar esta colección de ideas para enfocar cuestiones de arquitectura, en el convencimiento de que este ideario es tan válido hoy como entonces, nos acerca a ese utópico método de trabajo del arquitecto. En este ciclo abierto se han seleccionado determinadas obras que permiten plantear mejor las cuestiones que ilustran su razón de ser y así pues se suceden lugares y personas, números y geometrías, música, artes plásticas y arquitecturas. ABSTRACT Looking at the work of José M. García de Paredes as a set of ideas that outline a way of imagining and producing architecture, explains a vision that has persisted in time. Employing the word “explain” in the same sense as Stravinsky in his Poetics of Music: deploying, developing and describing something, discovering and clarifying its origins as a way of observing the relationships between things and the way designs originate in order to understand how they determine the architecture, once it has a life and use of its own after time has passed. This thesis is based on an analysis of the archives of José M. Garcia de Paredes, which began in 1990. After graduating from the Madrid School in 1950 —an equally complex time as today— he continued to practise architecture until 1990. He was not an architectural theorist but he had a deep understanding of theory and left essays and ideas on the way to tackle projects. Although he may not have been a radically innovative architect and his work may seem subdued, much of it embodies categorical approaches, which are deliberately overshadowed. Nevertheless, his work is sharp, consistent and is valuable for the knowledge and values it transmits. It has served its purpose, it now forms part of the places for which it was built and has become part of the lives of the people it was designed for. To a large extent, his buildings already show the patina of time. While not large in number, they bring together the ideas needed to put a project into practice and arrive at an end result in which the architecture is also a personal expression, a social activity that makes life better for people. The discourse takes a new look at the architecture of Garcia de Paredes through an analysis of all the issues involved in order to turn the resulting knowledge into a useful tool for project work. It therefore now, ideas that are old but at the same time contemporary. This vision time. The beautiful social utility of his architecture and the way he arrived at it through knowledge and intellectual economy still remain valid. The synthesis of this vision has required much time to organize the archive and also a professional architectural practice to put it into perspective. The preserved documents reveal a body of work that was designed at a time when ethics shaped the underlying scenario of the Relación de architectural debate. The architect used the material resources at his disposal in an almost craftsman-like way, in the company of a congruent group of architects. He interpreted reality in a personal way, removed from the coldness of the strict Modern Movement, striving to improve it and strip off anything that was unnecessary. His buildings responded to their context in such a way that transformed it, as if they were “magical realism”. Another line of analysis emerged from an initial analysis, with all the documents in view at the same time: not to explain his work but rather to study the design process of an architect in order to discover a method. In 1986, García de Paredes wrote “Three landscapes with architectures”, which describes three cultural landscapes in different times. After describing the beauty of the physical ruins of the past, the third landscape, “Landscape with Ruins”, concludes with this observation: “There are ruins and ruins ... But these might not be the real ruins of our time. What kind of ruin will be produced by our modest 20th century architecture? Our legacy should not be interpreted in the key of mere stones, like those of past eras which had access to no other language than construction for all times. Other keys, perhaps not yet familiar, may well emerge and be as legible for future generations as this third Landscape”. This tour of the work and writings of Garcia de Paredes is aimed at discovering these contemporary keys. The legacy of such keys can now help us to know what endures in architecture; thinking about current issues through the perspective of old papers. Having set aside the time factor, looking at the drawings, essays, books and photographs from the architect’s archives, organising and understanding the reasons that gave rise to each work, I now believe that the architecture of each moment is only previous work that has been shifted. Nothing is completely different now from what it was back then. The architecture of the past can be interpreted by other generations, looking beyond the aspects of form, blurring the time factor when we want to order it. For this purpose I have selected particular works that permit a better enunciation of the issues that illustrate their rationale, hence the succession of places and people, numbers and geometries, music, art and architectures.

Análisis del comportamiento de uniones metálicas viga-soporte mediante modelo de elementos finitos y comparación de resultados con el modelo de nudos y barras

Para el proyecto y cálculo de estructuras metálicas, fundamentalmente pórticos y celosías de cubierta, la herramienta más comúnmente utilizada son los programas informáticos de nudos y barras. En estos programas se define la geometría y sección de las barras, cuyas características mecánicas son perfectamente conocidas, y sobre las cuales obtenemos unos resultados de cálculo concretos en cuanto a estados tensionales y de deformación. Sin embargo el otro componente del modelo, los nudos, presenta mucha mayor complejidad a la hora de establecer sus propiedades mecánicas, fundamentalmente su rigidez al giro, así como de obtener unos resultados de estados tensionales y de deformación en los mismos. Esta “ignorancia” sobre el comportamiento real de los nudos, se salva generalmente asimilando a los nudos del modelo la condición de rígidos o articulados. Si bien los programas de cálculo ofrecen la posibilidad de introducir nudos con una rigidez intermedia (nudos semirrígidos), la rigidez de cada nudo dependerá de la geometría real de la unión, lo cual, dada la gran variedad de geometrías de uniones que en cualquier proyecto se nos presentan, hace prácticamente inviable introducir los coeficientes correspondientes a cada nudo en los modelos de nudos y barras. Tanto el Eurocódigo como el CTE, establecen que cada unión tendrá asociada una curva momento-rotación característica, que deberá ser determinada por los proyectistas mediante herramientas de cálculo o procedimientos experimentales. No obstante, este es un planteamiento difícil de llevar a cabo para cada proyecto. La consecuencia de esto es, que en la práctica, se realizan extensas comprobaciones y justificaciones de cálculo para las barras de las estructuras, dejando en manos de la práctica común la solución y puesta en obra de las uniones, quedando sin justificar ni comprobar la seguridad y el comportamiento real de estas. Otro aspecto que conlleva la falta de caracterización de las uniones, es que desconocemos como afecta el comportamiento real de éstas en los estados tensionales y de deformación de las barras que acometen a ellas, dudas que con frecuencia nos asaltan, no sólo en la fase de proyecto, sino también a la hora de resolver los problemas de ejecución que inevitablemente se nos presentan en el desarrollo de las obras. El cálculo mediante el método de los elementos finitos, es una herramienta que nos permite introducir la geometría real de perfiles y uniones, y nos permite por tanto abordar el comportamiento real de las uniones, y que está condicionado por su geometría. Por ejemplo, un caso típico es el de la unión de una viga a una placa o a un soporte soldando sólo el alma. Es habitual asimilar esta unión a una articulación. Sin embargo, el modelo por elementos finitos nos ofrece su comportamiento real, que es intermedio entre articulado y empotrado, ya que se transmite un momento y el giro es menor que el del apoyo simple. No obstante, la aplicación del modelo de elementos finitos, introduciendo la geometría de todos los elementos estructurales de un entramado metálico, tampoco resulta en general viable desde un punto de vista práctico, dado que requiere invertir mucho tiempo en comparación con el aumento de precisión que obtenemos respecto a los programas de nudos y barras, mucho más rápidos en la fase de modelización de la estructura. En esta tesis se ha abordado, mediante la modelización por elementos finitos, la resolución de una serie de casos tipo representativos de las uniones más comúnmente ejecutadas en obras de edificación, como son las uniones viga-pilar, estableciendo el comportamiento de estas uniones en función de las variables que comúnmente se presentan, y que son: •Ejecución de uniones viga-pilar soldando solo por el alma (unión por el alma), o bien soldando la viga al pilar por todo su perímetro (unión total). •Disposición o no de rigidizadores en los pilares •Uso de pilares de sección 2UPN en cajón o de tipo HEB, que son los tipos de soporte utilizados en casi el 100% de los casos en edificación. Para establecer la influencia de estas variables en el comportamiento de las uniones, y su repercusión en las vigas, se ha realizado un análisis comparativo entre las variables de resultado de los casos estudiados:•Estados tensionales en vigas y uniones. •Momentos en extremo de vigas •Giros totales y relativos en nudos. •Flechas. Otro de los aspectos que nos permite analizar la casuística planteada, es la valoración, desde un punto de vista de costos de ejecución, de la realización de uniones por todo el perímetro frente a las uniones por el alma, o de la disposición o no de rigidizadores en las uniones por todo el perímetro. Los resultados a este respecto, son estrictamente desde un punto de vista económico, sin perjuicio de que la seguridad o las preferencias de los proyectistas aconsejen una solución determinada. Finalmente, un tercer aspecto que nos ha permitido abordar el estudio planteado, es la comparación de resultados que se obtienen por el método de los elementos finitos, más próximos a la realidad, ya que se tiene en cuenta los giros relativos en las uniones, frente a los resultados obtenidos con programas de nudos y barras. De esta forma, podemos seguir usando el modelo de nudos y barras, más versátil y rápido, pero conociendo cuáles son sus limitaciones, y en qué aspectos y en qué medida, debemos ponderar sus resultados. En el último apartado de la tesis se apuntan una serie de temas sobre los que sería interesante profundizar en posteriores estudios, mediante modelos de elementos finitos, con el objeto de conocer mejor el comportamiento de las uniones estructurales metálicas, en aspectos que no se pueden abordar con los programas de nudos y barras. For the project and calculation of steel structures, mainly building frames and cover lattices, the tool more commonly used are the node and bars model computer programs. In these programs we define the geometry and section of the bars, whose mechanical characteristics are perfectly known, and from which we obtain the all calculation results of stresses and displacements. Nevertheless, the other component of the model, the nodes, are much more difficulty for establishing their mechanical properties, mainly the rotation fixity coefficients, as well as the stresses and displacements. This "ignorance" about the real performance of the nodes, is commonly saved by assimilating to them the condition of fixed or articulated. Though the calculation programs offer the possibility to introducing nodes with an intermediate fixity (half-fixed nodes), the fixity of every node will depend on the real connection’s geometry, which, given the great variety of connections geometries that in a project exist, makes practically unviable to introduce the coefficients corresponding to every node in the models of nodes and bars. Both Eurocode and the CTE, establish that every connection will have a typical moment-rotation associated curve, which will have to be determined for the designers by calculation tools or experimental procedures. Nevertheless, this one is an exposition difficult to carry out for each project. The consequence of this, is that in the practice, in projects are extensive checking and calculation reports about the bars of the structures, trusting in hands of the common practice the solution and execution of the connections, resulting without justification and verification their safety and their real behaviour. Another aspect that carries the lack of the connections characterization, is that we don´t know how affects the connections real behaviour in the stresses and displacements of the bars that attack them, doubts that often assault us, not only in the project phase, but also at the moment of solving the execution problems that inevitably happen in the development of the construction works. The calculation by finite element model is a tool that allows us to introduce the real profiles and connections geometry, and allows us to know about the real behaviour of the connections, which is determined by their geometry. Typical example is a beam-plate or beam-support connection welding only by the web. It is usual to assimilate this connection to an articulation or simple support. Nevertheless, the finite element model determines its real performance, which is between articulated and fixed, since a moment is transmitted and the relative rotation is less than the articulation’s rotation. Nevertheless, the application of the finite element model, introducing the geometry of all the structural elements of a metallic structure, does not also turn out to be viable from a practical point of view, provided that it needs to invest a lot of time in comparison with the precision increase that we obtain opposite the node and bars programs, which are much more faster in the structure modelling phase. In this thesis it has been approached, by finite element modelling, the resolution of a representative type cases of the connections commonly used in works of building, since are the beam-support connections, establishing the performance of these connections depending on the variables that commonly are present, which are: •Execution of beam-support connections welding only the web, or welding the beam to the support for the whole perimeter. •Disposition of stiffeners in the supports •Use 2UPN in box section or HEB section, which are the support types used in almost 100% building cases. To establish the influence of these variables in the connections performance, and the repercussion in the beams, a comparative analyse has been made with the resulting variables of the studied cases: •Stresses states in beams and connections. •Bending moments in beam ends. •Total and relative rotations in nodes. •Deflections in beams. Another aspect that the study allows us to analyze, is the valuation, from a costs point of view, of the execution of connections for the whole perimeter opposite to the web connections, or the execution of stiffeners. The results of this analyse, are strictly from an economic point of view, without prejudice that the safety or the preferences of the designers advise a certain solution. Finally, the third aspect that the study has allowed us to approach, is the comparison of the results that are obtained by the finite element model, nearer to the real behaviour, since the relative rotations in the connections are known, opposite to the results obtained with nodes and bars programs. So that, we can use the nodes and bars models, more versatile and quick, but knowing which are its limitations, and in which aspects and measures, we must weight the results. In the last part of the tesis, are relationated some of the topics on which it would be interesting to approach in later studies, with finite elements models, in order to know better the behaviour of the structural steel connections, in aspects that cannot be approached by the nodes and bars programs.