Analysis of Combined Bending and Punching Tests of Reinforced Concrete Slabs within IMPACT III Project

The paper reports on a collaborative effort between the Swiss Federal Nuclear Safety Inspectorate (ENSI) and their consultants Principia and Stangenberg. As part of the IMPACT III project, reduced scale impact tests of reinforced concrete structures were carried out. The simulation of test X3 is presented here and the numerical results are compared with those obtained in the test, carried out in August 2013. The general object is to improve the safety of nuclear facilities and, more specifically, to demonstrate the capabilities of current simulation techniques to reproduce the behaviour of a reinforced concrete structure impacted by a soft missile. The missile is a steel tube with a mass of 50 kg and travelling at 140 m/s. The target is a 250 mm thick, 2,1 m by 2,1 m reinforced concrete wall, held in a stiff supporting frame. The reinforcement includes both longitudinal and transverse rebars. Calculations were carried out before and after the test with Abaqus (Principia) and SOFiSTiK (Stangenberg). In the Abaqus simulation the concrete is modelled using solid elements and a damaged plasticity formulation, the rebars with embedded beam elements, and the missile with shell elements. In SOFiSTiK the target is modelled with non-linear, layered shell elements for the reinforcement on both sides; non-linear shear deformations of shell/plate elements are approximately included. The results generally indicate a good agreement between calculations and measurements.

Combined static and dynamic assertion-based debugging of constraint logic programs

We propose a general framework for assertion-based debugging of constraint logic programs. Assertions are linguistic constructions for expressing properties of programs. We define several assertion schemas for writing (partial) specifications for constraint logic programs using quite general properties, including user-defined programs. The framework is aimed at detecting deviations of the program behavior (symptoms) with respect to the given assertions, either at compile-time (i.e., statically) or run-time (i.e., dynamically). We provide techniques for using information from global analysis both to detect at compile-time assertions which do not hold in at least one of the possible executions (i.e., static symptoms) and assertions which hold for all possible executions (i.e., statically proved assertions). We also provide program transformations which introduce tests in the program for checking at run-time those assertions whose status cannot be determined at compile-time. Both the static and the dynamic checking are provably safe in the sense that all errors flagged are definite violations of the pecifications. Finally, we report briefly on the currently implemented instances of the generic framework.

Effectiveness of combined sharing and freeness analysis using abstract interpretation

This paper presents improved unification algorithms, an implementation, and an analysis of the effectiveness of an abstract interpreter based on the sharing + freeness domain presented in a previous paper, which was designed to accurately and concisely represent combined freeness and sharing information for program variables. We first briefly review this domain and the unification algorithms previously proposed. We then improve these algorithms and correct them to deal with some cases which were not well analyzed previously, illustrating the improvement with an example. We then present the implementation of the improved algorithm and evaluate its performance by comparing the effectiveness of the information inferred to that of other interpreters available to us for an application (program parallelization) that is common to all these interpreters. All these systems have been embedded in a real parallelizing compiler. Effectiveness of the analysis is measured in terms of actual final performance of the system: i.e. in terms of the actual speedups obtained. The results show good performance for the combined domain in that it improves the accuracy of both types of information and also in that the analyzer using the combined domain is more effective in the application than any of the other analyzers it is compared to.

Safety and health in forest harvesting operations. Diagnosis and preventive actions. A review

Aim of study: to review the present state of the art in relation to the main labour risks and the most relevant results of recent studies evaluating the safety and health conditions of the forest harvesting work and better ways to reduce accidents. Area of study: It focuses mainly on developed Countries, where the general concern about work risks prevention, together with the complex idiosyncrasy of forest work in forest harvesting operations, has led to a growing interest from the forest scientific and technical community. Material and Methods: The main bibliographic and Internet references have been identified using common reference analysis tools. Their conclusions and recommendations have been comprehensively summarized. Main results: Collection of the principal references and their most important conclusions relating to the main accident risk factors, their causes and consequences, the means used towards their prevention, both instrumental as well as in the aspects of training and business management, besides the influence of the growing mechanization of logging operations on those risks. Research highlights: Accident risk is higher in forest harvesting than in most other work sectors, and the main risk factors such as experience, age, seasonality, training, protective equipment, mechanization degree, etc. have been identified and studied. The paper summarizes some relevant results, one of the principal being that the proper entrepreneurial risk management is a key factor leading to the success in minimizing labour risks..

The impact of the economic crisis and policy actions on GHG emissions from road transport in Spain

Road traffic is the greatest contributor to the carbon footprint of the transport sector and reducing it has become one of the main targets of sustainable transport policies. An analysis of the main factors influencing greenhouse gas (GHG) emissions is essential for designing new energy- and environmentally efficient strategies for the road transport. This paper addresses this need by (i) identifying factors which influence the carbon footprint, including traffic activity, fuel economy and socioeconomic development; and (ii) proposing a methodological framework which uses Modified Laspeyres Index decomposition to analyze the effect of important drivers on the changes in emissions of road transport in Spain during the period from 1990 to 2010. The results demonstrate that the country׳s economic growth has been closely linked to the rise in GHG emissions. The innovative contribution of this paper is the special analysis of the changes in mobility patterns and GHG emissions during the economic crisis, when, for the first time, Spanish road traffic emissions decreased. The reduction of road transport and improved energy efficiency has been powerful contributors to this decrease, demonstrating the effectiveness of energy-saving measures. On the basis of this analysis, several tailored policy recommendations have been suggested for future implementation.

Characteristics of the turbulent/nonturbulent interface in boundary layers, jets and shear-free turbulence

The characteristics of turbulent/nonturbulent interfaces (TNTI) from boundary layers, jets and shear-free turbulence are compared using direct numerical simulations. The TNTI location is detected by assessing the volume of turbulent flow as function of the vorticity magnitude and is shown to be equivalent to other procedures using a scalar field. Vorticity maps show that the boundary layer contains a larger range of scales at the interface than in jets and shear-free turbulence where the change in vorticity characteristics across the TNTI is much more dramatic. The intermittency parameter shows that the extent of the intermittency region for jets and boundary layers is similar and is much bigger than in shear-free turbulence, and can be used to compute the vorticity threshold defining the TNTI location. The statistics of the vorticity jump across the TNTI exhibit the imprint of a large range of scales, from the Kolmogorov micro-scale to scales much bigger than the Taylor scale. Finally, it is shown that contrary to the classical view, the low-vorticity spots inside the jet are statistically similar to isotropic turbulence, suggesting that engulfing pockets simply do not exist in jets

Combined determination of sharing and freeness of program variables through abstract interpretation

In this paper, abstract interpretation algorithms are described for computing the sharmg as well as the freeness information about the run-time instantiations of program variables. An abstract domain is proposed which accurately and concisely represents combined freeness and sharing information for program variables. Abstract unification and all other domain-specific functions for an abstract interpreter working on this domain are presented. These functions are illustrated with an example. The importance of inferring freeness is stressed by showing (1) the central role it plays in non-strict goal independence, and (2) the improved accuracy it brings to the analysis of sharing information when both are computed together. Conversely, it is shown that keeping accurate track of sharing allows more precise inference of freeness, thus resulting in an overall much more powerful abstract interpreter.

Comportamiento estructural de elementos de fábrica reforzados con materiales compuestos avanzados solicitados a flexión y flexocompresión

El refuerzo de estructuras existentes mediante el encolado exterior de láminas de polímeros reforzados con fibras (FRP) se ha convertido en la aplicación más común de los materiales compuestos avanzados en construcción. Estos materiales presentan muchas ventajas frente a los materiales convencionales (sin corrosión, ligeros, de fácil aplicación, etc.). Pero a pesar de las numerosas investigaciones realizadas, aún persisten ciertas dudas sobre algunos aspectos de su comportamiento y las aplicaciones prácticas se llevan a cabo sólo con la ayuda de guías, sin que haya una normativa oficial. El objetivo de este trabajo es incrementar el conocimiento sobre esta técnica de refuerzo, y más concretamente, sobre el refuerzo a flexión de estructuras de fábrica. Con frecuencia el elemento reforzado es de hormigón armado y las láminas de FRP encoladas al exterior sirven para mejorar su resistencia a flexión, cortante o compresión (encamisados). Sin embargo su empleo en otros materiales como las estructuras de fábrica resulta muy prometedor. Las fábricas se caracterizan por soportar muy bien los esfuerzos de compresión pero bastante mal los de tracción. Adherir láminas de materiales compuestos puede servir para mejorar la capacidad resistente de elementos de fábrica sometidos a esfuerzos de flexión. Pero para ello, debe quedar garantizada una correcta adherencia entre el FRP y la fábrica, especialmente en edificios antiguos cuya superficie puede estar deteriorada por encontrarse a la intemperie o por el propio paso del tiempo. En el capítulo II se describen los objetivos fundamentales del trabajo y el método seguido. En el capítulo III se hace una amplia revisión del estado de conocimiento sobre el tema. En el apartado III.1 se detallan las principales características y propiedades mecánicas de fibras, matrices y materiales compuestos así como sus principales aplicaciones, haciendo especial hincapié en aspectos relativos a su durabilidad. En el apartado III.2 se incluye una revisión histórica de las líneas de investigación, tanto teóricas como empíricas, publicadas sobre estructuras de hormigón reforzadas a flexión encolando materiales compuestos. El apartado III.3 se centra en el aspecto fundamental de la adherencia refuerzo-soporte. Se hace un repaso a distintos modelos propuestos para prevenir el despegue distinguiendo si éste se inicia en la zona de anclaje o si está inducido por fisuras en la zona interior del elemento. Se observa falta de consenso en las propuestas. Además en este punto se relatan las campañas experimentales publicadas acerca de la adherencia entre materiales compuestos y fábricas. En el apartado III.4 se analizan las particularidades de las estructuras de fábrica. Además, se revisan algunas de las investigaciones relativas a la mejora de su comportamiento a flexión mediante láminas de FRP. El comportamiento mecánico de muros reforzados solicitados a flexión pura (sin compresión) ha sido documentado por varios autores, si bien es una situación poco frecuente en fábricas reales. Ni el comportamiento mecánico de muros reforzados solicitados a flexocompresión ni la incidencia que el nivel de compresión soportado por la fábrica tiene sobre la capacidad resistente del elemento reforzado han sido suficientemente tratados. En cuanto a los trabajos teóricos, las diferentes propuestas se basan en los métodos utilizados para hormigón armado y comparten los principios habituales de cálculo. Sin embargo, presentan diferencias relativas, sobre todo, a tres aspectos: 1) la forma de modelar el comportamiento de la fábrica, 2) el valor de deformación de cálculo del refuerzo, y 3) el modo de fallo que se considera recomendable buscar con el diseño. A pesar de ello, el ajuste con la parte experimental de cada trabajo suele ser bueno debido a una enorme disparidad en las variables consideradas. Cada campaña presenta un modo de fallo característico y la formulación que se propone resulta apropiada para él. Parece necesario desarrollar un método de cálculo para fábricas flexocomprimidas reforzadas con FRP que pueda ser utilizado para todos los posibles fallos, tanto atribuibles a la lámina como a la fábrica. En el apartado III.4 se repasan algunas lesiones habituales en fábricas solicitadas a flexión y se recogen ejemplos de refuerzos con FRP para reparar o prevenir estos daños. Para mejorar el conocimiento sobre el tema, se llevan a cabo dos pequeñas campañas experimentales realizadas en el Instituto de Ciencias de la Construcción Eduardo Torroja. La primera acerca de la adherencia de materiales compuestos encolados a fábricas deterioradas (apartado IV.1) y la segunda sobre el comportamiento estructural a flexocompresión de probetas de fábrica reforzadas con estos materiales (apartado IV.2). En el capítulo V se analizan algunos de los modelos de adherencia propuestos para prevenir el despegue del extremo del refuerzo. Se confirma que las predicciones obtenidas con ellos resultan muy dispares. Se recopila una base de datos con los resultados experimentales de campañas sobre adherencia de FRP a fábricas extraídas de la literatura y de los resultados propios de la campaña descrita en el punto IV.1. Esta base de datos permite conocer cual de los métodos analizados resulta más adecuado para dimensionar el anclaje de láminas de FRP adheridas a fábricas. En el capítulo VI se propone un método para la comprobación en agotamiento de secciones de fábrica reforzadas con materiales compuestos sometidas a esfuerzos combinados de flexión y compresión. Está basado en el procedimiento de cálculo de la capacidad resistente de secciones de hormigón armado pero adaptado a las fábricas reforzadas. Para ello, se utiliza un diagrama de cálculo tensión deformación de la fábrica de tipo bilineal (acorde con el CTE DB SE-F) cuya simplicidad facilita el desarrollo de toda la formulación al tiempo que resulta adecuado para predecir la capacidad resistente a flexión tanto para fallos debidos al refuerzo como a la fábrica. Además se limita la deformación de cálculo del refuerzo teniendo en consideración ciertos aspectos que provocan que la lámina adherida no pueda desarrollar toda su resistencia, como el desprendimiento inducido por fisuras en el interior del elemento o el deterioro medioambiental. En concreto, se propone un “coeficiente reductor por adherencia” que se determina a partir de una base de datos con 68 resultados experimentales procedentes de publicaciones de varios autores y de los ensayos propios de la campaña descrita en el punto IV.2. También se revisa la formulación propuesta con ayuda de la base de datos. En el capítulo VII se estudia la incidencia de las principales variables, como el axil, la deformación de cálculo del refuerzo o su rigidez, en la capacidad final del elemento. Las conclusiones del trabajo realizado y las posibles líneas futuras de investigación se exponen en el capítulo VIII. ABSTRACT Strengthening of existing structures with externally bonded fiber reinforced polymers (FRP) has become the most common application of advanced composite materials in construction. These materials exhibit many advantages in comparison with traditional ones (corrosion resistance, light weight, easy to apply, etc.). But despite countless researches have been done, there are still doubts about some aspects of their behaviour and applications are carried out only with the help of guidelines, without official regulations. The aim of this work is to improve the knowledge on this retrofitting technique, particularly in regard to flexural strengthening of masonry structures. Reinforced concrete is often the strengthened material and external glued FRP plates are used to improve its flexural, shear or compressive (by wrapping) capacity. However the use of this technique on other materials like masonry structures looks promising. Unreinforced masonry is characterized for being a good material to support compressive stresses but really bad to withstand tensile ones. Glue composite plates can improve the flexural capacity of masonry elements subject to bending. But a proper bond between FRP sheet and masonry must be ensured to do that, especially in old buildings whose surface can be damaged due to being outside or ageing. The main objectives of the work and the methodology carried out are described In Chapter II. An extensive overview of the state of art is done in Chapter III. In Section III.1 physical and mechanical properties of fibers, matrix and composites and their main applications are related. Durability aspects are especially emphasized. Section III.2 includes an historical overview of theoretical and empirical researches on concrete structures strengthened gluing FRP plates to improve their flexural behaviour. Section III.3 focuses on the critical point of bonding between FRP and substrate. Some theoretical models to prevent debonding of FRP laminate are reviewed, it has made a distinction between models for detachment at the end of the plate or debonding in the intermediate zones due to the effects of cracks. It is observed a lack of agreement in the proposals. Some experimental studies on bonding between masonry and FRP are also related in this chapter. The particular characteristics of masonry structures are analyzed in Section III.4. Besides some empirical and theoretical investigations relative to improve their flexural capacity with FRP sheets are reviewed. The mechanical behaviour of strengthened walls subject to pure bending (without compression) has been established by several authors, but this is an unusual situation for real masonry. Neither mechanical behaviour of walls subject to bending and compression nor influence of axial load in the final capacity of the strengthened element are adequately studied. In regard to theoretical studies, the different proposals are based on reinforced concrete analytical methods and share common design principles. However, they present differences, especially, about three aspects: 1) the constitutive law of masonry, 2) the value of ultimate FRP strain and 3) the desirable failure mode that must be looked for. In spite of them, a good agreement between each experimental program and its theoretical study is often exhibited due to enormous disparity in considered test parameters. Each experimental program usually presents a characteristic failure mode and the proposed formulation results appropriate for this one. It seems necessary to develop a method for FRP strengthened walls subject to bending and compression enable for all failure modes (due to FRP or masonry). Some common damages in masonry subject to bending are explained in Section III.4. Examples of FRP strengthening to repair or prevent these damages are also written. Two small experimental programs are carried out in Eduardo Torroja Institute to improve the knowledge on this topic. The first one is concerned about the bond between FRP plates and damaged masonry (section IV.1) and the second one is related to the mechanical behaviour of the strengthened masonry specimens subject to out of plane bending combined with axial force (section IV.2). In the Chapter V some bond models to prevent the debonding at the FRP plate end are checked. It is confirmed that their predictions are so different. A pure-shear test database is compiled with results from the existing literature and others from the experimental program described in section IV.1. This database lets know which of the considered model is more suitable to design anchorage lengths of glued FRP to masonry. In the Chapter VI a method to check unreinforced masonry sections with external FRP strengthening subject to bending and compression to the ultimate limit state is proposed. This method is based on concrete reinforced one, but it is adapted to strengthened masonry. A bilinear constitutive law is used for masonry (according to CTE DB SE-F). Its simplicity helps to develop the model formulation and it has proven to be suitable to predict bending capacity either for FRP failures or masonry crushing. With regard to FRP, the design strain is limited. It is taken into account different aspects which cause the plate can’t reach its ultimate strength, like intermediate FRP debonding induced by opening cracking or environmental damage. A “bond factor” is proposed. It is obtained by means of an experimental bending test database that includes 68 results from the existing literature and from the experimental program described in section IV.2. The proposed formulation has also been checked with the help of bending database. The effects of the main parameters, like axial load, FRP design effective strain or FRP stiffness, on the bending capacity of the strengthened element are studied in Chapter VII. Finally, the main conclusions from the work carried out are summarized in Chapter VIII. Future lines of research to be explored are suggested as well.

Crack width control in RC elements with recycled steel fibres and applications to integral structures : theoretical and experimental study

El presente trabajo trata de elementos reforzados con barras de armadura y Fibras Metálicas Recicladas (FMR). El objetivo principal es mejorar el comportamiento a fisuración de elementos sometidos a flexión pura y a flexión compuesta, aumentando en consecuencia las prestaciones en servicio de aquellas estructuras con requerimientos estrictos con respecto al control de fisuración. Entre éstas últimas se encuentran las estructuras integrales, es decir aquellas estructuras sin juntas (puentes o edificios), sometidas a cargas gravitatorias y deformaciones impuestas en los elementos horizontales debidas a retracción, fluencia y temperatura. Las FMR son obtenidas a partir de los neumáticos fuera de uso, y puesto que el procedimiento de reciclado se centra en el caucho en vez que en el acero, su forma es aleatoria y con longitud variable. A pesar de que la eficacia del fibrorefuerzo mediante FMR ha sido demostrada en investigaciones anteriores, la innovación que representa este trabajo consiste en proponer la acción combinada de barras convencionales y FMR en la mejora del comportamiento a fisuración. El objetivo es por tanto mejorar la sostenibilidad del proyecto de la estructura en HA al utilizar materiales reciclados por un lado, y aumentando por el otro la durabilidad. En primer lugar, se presenta el estado del arte con respecto a la fisuración en elementos de HA, que sucesivamente se amplía a elementos reforzados con barras y fibras. Asimismo, se resume el método simplificado para el análisis de columnas de estructuras sin juntas ya propuesto por Pérez et al., con particular énfasis en aquellos aspectos que son incompatibles con la acción de las fibras a nivel seccional. A continuación, se presenta un modelo para describir la deformabilidad seccional y la fisuración en elementos en HA, que luego se amplía a aquellos elementos reforzados con barras y fibras, teniendo en cuenta también los efectos debidos a la retracción (tension stiffening negativo). El modelo es luego empleado para ampliar el método simplificado para el análisis de columnas. La aportación consiste por tanto en contar con una metodología amplia de análisis para este tipo de elementos. Seguidamente, se presenta la campaña experimental preliminar que ha involucrado vigas a escala reducida sometidas a flexión simple, con el objetivo de validar la eficiencia y la usabilidad en el hormigón de las FMR de dos diferentes tipos, y su comportamiento con respecto a fibras de acero comerciales. Se describe a continuación la campaña principal, consistente en ensayos sobre ocho vigas en flexión simple a escala 1:1 (variando contenido en FRM, Ø/s,eff y recubrimiento) y doce columnas a flexión compuesta (variando contenido en FMR, Ø/s,eff y nivel de fuerza axil). Los resultados obtenidos en la campaña principal son presentados y comentados, resaltando las mejoras obtenidas en el comportamiento a fisuración de las vigas y columnas, y la rigidez estructural de las columnas. Estos resultados se comparan con las predicciones del modelo propuesto. Los principales parámetros estudiados para describir la fisuración y el comportamiento seccional de las vigas son: la separación entre fisuras, el alargamiento medio de las armaduras y la abertura de fisura, mientras que en los ensayos de las columnas se ha contrastado las leyes momento/curvatura, la tensión en las barras de armadura y la abertura de fisura en el empotramiento en la base. La comparación muestra un buen acuerdo entre las predicciones y los resultados experimentales. Asimismo, se nota la mejora en el comportamiento a fisuración debido a la incorporación de FMR en aquellos elementos con cuantías de armadura bajas en flexión simple, en elementos con axiles bajos y para el control de la fisuración en elementos con grandes recubrimientos, siendo por tanto resultados de inmediato impacto en la práctica ingenieril (diseño de losas, tanques, estructuras integrales, etc.). VIIIComo punto final, se presentan aplicaciones de las FMR en estructuras reales. Se discuten dos casos de elementos sometidos a flexión pura, en particular una viga simplemente apoyada y un tanque para el tratamiento de agua. En ambos casos la adicción de FMR al hormigón lleva a mejoras en el comportamiento a fisuración. Luego, utilizando el método simplificado para el análisis en servicio de columnas de estructuras sin juntas, se calcula la máxima longitud admisible en casos típicos de puentes y edificación. En particular, se demuestra que las limitaciones de la práctica ingenieril actual (sobre todo en edificación) pueden ser aumentadas considerando el comportamiento real de las columnas en HA. Finalmente, los mismos casos son modificados para considerar el uso de MFR, y se presentan las mejoras tanto en la máxima longitud admisible como en la abertura de fisura para una longitud y deformación impuesta. This work deals with elements reinforced with both rebars and Recycled Steel Fibres (RSFs). Its main objective is to improve cracking behaviour of elements subjected to pure bending and bending and axial force, resulting in better serviceability conditions for these structures demanding keen crack width control. Among these structures a particularly interesting type are the so-called integral structures, i.e. long jointless structures (bridges and buildings) subjected to gravitational loads and imposed deformations due to shrinkage, creep and temperature. RSFs are obtained from End of Life Tyres, and due to the recycling process that is focused on the rubber rather than on the steel they come out crooked and with variable length. Although the effectiveness of RSFs had already been proven by previous research, the innovation of this work consists in the proposing the combined action of conventional rebars and RSFs to improve cracking behaviour. Therefore, the objective is to improve the sustainability of RC structures by, on the one hand, using recycled materials, and on the other improving their durability. A state of the art on cracking in RC elements is firstly drawn. It is then expanded to elements reinforced with both rebars and fibres (R/FRC elements). Finally, the simplified method for analysis of columns of long jointless structures already proposed by Pérez et al. is resumed, with a special focus on the points that conflict when taking into account the action of fibres. Afterwards, a model to describe sectional deformability and cracking of R/FRC elements is presented, taking also into account the effect of shrinkage (negative tension stiffening). The model is then used to implement the simplified method for columns. The novelty represented by this is that a comprehensive methodology to analyse this type of elements is presented. A preliminary experimental campaign consisting in small beams subjected to pure bending is described, with the objective of validating the effectiveness and usability in concrete of RSFs of two different types, and their behaviour when compared with commercial steel fibres. With the results and lessons learnt from this campaign in mind, the main experimental campaign is then described, consisting in cracking tests of eight unscaled beams in pure bending (varying RSF content, Ø/s,eff and concrete cover) and twelve columns subjected to imposed displacement and axial force (varying RSF content, Ø/s,eff and squashing load ratio). The results obtained from the main campaign are presented and discussed, with particular focus on the improvement in cracking behaviour for the beams and columns, and structural stiffness for the columns. They are then compared with the proposed model. The main parameters studied to describe cracking and sectional behaviours of the beam tests are crack spacing, mean steel strain and crack width, while for the column tests these were moment/curvature, stress in rebars and crack with at column embedment. The comparison showed satisfactory agreement between experimental results and model predictions. Moreover, it is pointed out the improvement in cracking behaviour due to the addition of RSF for elements with low reinforcement ratios, elements with low squashing load ratios and for crack width control of elements with large concrete covers, thus representing results with a immediate impact in engineering practice (slab design, tanks, integral structures, etc.). Applications of RSF to actual structures are finally presented. Two cases of elements in pure bending are presented, namely a simple supported beam and a water treatment tank. In both cases the addition of RSF to concrete leads to improvements in cracking behaviour. Then, using the simplified model for the serviceability analysis of columns of jointless structures, the maximum achievable jointless length of typical cases of a bridge and building is obtained. In XIIparticular, it is shown how the limitations of current engineering practice (this is especially the case of buildings) can be increased by considering the actual behaviour of RC supports. Then, the same cases are modified considering the use of RSF, and the improvements both in maximum achievable length and in crack width for a given length and imposed strain at the deck/first floor are shown.

Análisis de elementos viga-columna en régimen no lineal con deformación por cortante

El hormigón estructural sigue siendo sin duda uno de los materiales más utilizados en construcción debido a su resistencia, rigidez y flexibilidad para diseñar estructuras. El cálculo de estructuras de hormigón, utilizando vigas y vigas-columna, es complejo debido a los fenómenos de acoplamiento entre esfuerzos y al comportamiento no lineal del material. Los modelos más empleados para su análisis son el de Bernoulli-Euler y el de Timoshenko, indicándose en la literatura la conveniencia de usar el segundo cuando la relación canto/luz no es pequeña o los elementos están fuertemente armados. El objetivo fundamental de esta tesis es el análisis de elementos viga y viga-columna en régimen no lineal con deformación por cortante, aplicando el concepto de Pieza Lineal Equivalente (PLE). Concepto éste que consiste básicamente en resolver el problema de una pieza en régimen no lineal, transformándolo en uno lineal equivalente, de modo que ambas piezas tengan la misma deformada y los mismos esfuerzos. Para ello, se hizo en primer lugar un estudio comparado de: las distintas propuestas que aplican la deformación por cortante, de los distintos modelos constitutivos y seccionales del hormigón estructural y de los métodos de cálculo no lineal aplicando el método de elementos finitos (MEF). Teniendo en cuenta que la resolución del problema no lineal se basa en la resolución de sucesivos problemas lineales empleando un proceso de homotopía, los problemas lineales de la viga y viga-columna de Timoshenko, se resuelven mediante MEF, utilizando soluciones nodalmente exactas (SNE) y acción repartida equivalente de cualquier orden. Se obtiene así, con muy pocos elementos finitos, una excelente aproximación de la solución, no sólo en los nodos sino en el interior de los elementos. Se introduce el concepto PLE para el análisis de una barra, de material no lineal, sometida a acciones axiales, y se extiende el mismo para el análisis no lineal de vigas y vigas-columna con deformación por cortante. Cabe señalar que para estos últimos, la solución de una pieza en régimen no lineal es igual a la de una en régimen lineal, cuyas rigideces son constantes a trozos, y donde además hay que añadir momentos y cargas puntuales ficticias en los nodos, así como, un momento distribuido ficticio en toda la pieza. Se han desarrollado dos métodos para el análisis: uno para problemas isostáticos y otro general, aplicable tanto a problemas isostáticos como hiperestáticos. El primero determina de entrada la PLE, realizándose a continuación el cálculo por MEF-SNE de dicha pieza, que ahora está en régimen lineal. El general utiliza una homotopía que transforma de manera iterativa, unas leyes constitutivas lineales en las leyes no lineales del material. Cuando se combina con el MEF, la pieza lineal equivalente y la solución del problema original quedan determinadas al final de todo el proceso. Si bien el método general es un procedimiento próximo al de Newton- Raphson, presenta sobre éste la ventaja de permitir visualizar las deformaciones de la pieza en régimen no lineal, de manera tanto cualitativa como cuantitativa, ya que es posible observar en cada paso del proceso la modificación de rigideces (a flexión y cortante) y asimismo la evolución de las acciones ficticias. Por otra parte, los resultados obtenidos comparados con los publicados en la literatura, indican que el concepto PLE ofrece una forma directa y eficiente para analizar con muy buena precisión los problemas asociados a vigas y vigas-columna en las que por su tipología los efectos del cortante no pueden ser despreciados. ABSTRACT The structural concrete clearly remains the most used material in construction due to its strength, rigidity and structural design flexibility. The calculation of concrete structures using beams and beam-column is complex as consequence of the coupling phenomena between stresses and of its nonlinear behaviour. The models most commonly used for analysis are the Bernoulli-Euler and Timoshenko. The second model is strongly recommended when the relationship thickness/span is not small or in case the elements are heavily reinforced. The main objective of this thesis is to analyse the beam and beam-column elements with shear deformation in nonlinear regime, applying the concept of Equivalent Linear Structural Element (ELSE). This concept is basically to solve the problem of a structural element in nonlinear regime, transforming it into an equivalent linear structural element, so that both elements have the same deformations and the same stresses. Firstly, a comparative study of the various proposals of applying shear deformation, of various constitutive and sectional models of structural concrete, and of the nonlinear calculation methods (using finite element methods) was carried out. Considering that the resolution of nonlinear problem is based on solving the successive linear problem, using homotopy process, the linear problem of Timoshenko beam and beam-columns is resolved by FEM, using the exact nodal solutions (ENS) and equivalent distributed load of any order. Thus, the accurate solution approximation can be obtained with very few finite elements for not only nodes, but also for inside of elements. The concept ELSE is introduced to analyse a bar of nonlinear material, subjected to axial forces. The same bar is then used for other nonlinear beam and beam-column analysis with shear deformation. It is noted that, for the last analyses, the solution of a structural element in nonlinear regime is equal to that of linear regime, in which the piecewise-stiffness is constant, the moments and fictitious point loads need to be added at nodes of each element, as well as the fictitious distributed moment on element. Two methods have been developed for analysis: one for isostatic problem and other more general, applicable for both isostatic and hiperstatic problem. The first method determines the ELSE, and then the calculation of this piece is performed by FEM-ENS that now is in linear regime. The general method uses the homotopy that transforms iteratively linear constitutive laws into nonlinear laws of material. When combined with FEM, the ELSE and the solution of the original problem are determined at the end of the whole process. The general method is well known as a procedure closed to Newton-Raphson procedure but presents an advantage that allows displaying deformations of the piece in nonlinear regime, in both qualitative and quantitative way. Since it is possible to observe the modification of stiffness (flexural and shear) in each step of process and also the evolution of the fictitious actions. Moreover, the results compared with those published in the literature indicate that the ELSE concept offers a direct and efficient way to analyze with very good accuracy the problems associated with beams and beams columns in which, by typology, the effects of shear cannot be neglected.