Influence of the Second Bending Mode on the Response of High-Speed Bridges at Resonance

This paper deals with the assessment of the contribution of the second bending mode to the dynamic behavior of simply supported railway bridges. Traditionally the contributions of modes higher than the fundamental have been considered of little importance for the computation of the magnitudes of interest to structural engineers (vertical deflections, bending moments, etc.). Starting from the dimensionless equations of motion of a simply supported beam subjected to moving loads, the key parameters governing the dynamic behavior are identified. Then, a parametric study over realistic ranges of values of those parameters is conducted, and the influence of the second mode examined in detail. The main purpose is to decide whether the second mode should be taken into account for the determination of the maximum displacement and acceleration in high-speed bridges. In addition, the reasons that cause the contribution of the second bending mode to be relevant in some situations are highlighted, particularly with regard to the computation of the maximum acceleration.

Beitrag zur Entwicklung der Querschnittsgestaltung im Verbundbrückenbau

Die grafische Darstellung des Verbundquerschnittes mit einer oberen Betonplatte und einem darunter liegenden Stahlträger war seit seiner Vorstellung in den 1950er Jahren ein Symbol, das weit über die Theorie hinausging und weite Verbreitung in der Praxis des Verbundbrückenbaus fand. Seit den 1970er bzw. 1980er Jahren hat dieses Bild – bedingt durch neue und freiere Formen, Beton und Stahl miteinander zu kombinieren – seine Symbolhaftigkeit verloren. In Deutschland und Spanien wurde der Doppelverbund mit unten liegenden Betonplatten in Bereichen mit negativen Momenten eingeführt, in Frankreich werden Stahlträger auch in vorgespannten Betonquerschnitten eingebettet. Beide Ansätze haben dazu beigetragen, dass in der Gegenwart die Materialien Stahl und Beton im Verbundbau frei miteinander kombiniert werden können. On the development of sections in composite bridges. A comprehensive theory of composite construction was established in Germany by Sattler in 1953. The theoretical image of the composite section with a superior concrete slab and a lower metallic structure was shaped in addition to the analytical resolution. Theory and graphical representation were going to be known together in Europe. This figure was repeated in all theoretical and academic publications, so becoming an authentic icon of the composite section. Its translation to the bridge deck in flexion was obvious: the superior slab defines the tread platform, while the metallic structure was left off-hook at the bottom. Nevertheless, in continuous decks the section is not optimal at all in zones of negative bending moments. But the overcoming of the graphical representation of the theory did not happen immediately. It was produced after a process in which several European countries played an active role and where different mechanisms of technological transference were developed. One approach to this overcoming is the “double composite action”, with a lower concrete slab in areas of a negative bending moment. The first accomplishments, a bridge in Orasje built in 1968 with 134 m span, as well as the publications of the system proposed by Fabrizio de Miranda in 1971 did not extend nor had continuity. Spanish bridges by Fernández Ordoñez and Martínez Calzón used double composite action for the first time in 1979. The German team of Leonhard, Andrä und partners, has used it since the end of the 1980's to solve bridges of great span. Once the technology has been well known thanks to the ASCE International Congress and the Spanish International Meetings organised by the “Colegio de Ingenieros de Caminos”, double composite action has been integrated well into the structural vocabulary everywhere. In France the approach was different. What Michel Virlogeux calls “double floor composite section” was reached as an evolution of prestressed concrete bridges. In an experimental process widely known, the external prestressing allows weight reduction by diminishing the thickness of the concrete webs. The following step, in the 1980's, was the substitution of the webs by metallic elements: stiffened plates, trusses or folded plates. A direct result of this development is the Brass de la Plaine Bridge in the Reunion Island in 2001 with 280 m span. Both approaches have contributed to a freedom of design in composite construction in steel and concrete today.

Influence of the Second Flexural Mode on the Response of High-Speed Bridges

This paper deals with the assessment of the contribution of the second flexural mode to the dynamic behaviour of simply supported railway bridges. Alluding to the works of other authors, it is suggested in some references that the dynamic behaviour of simply supported bridges could be adequately represented taking into account only the contribution of the fundamental flexural mode. On the other hand, the European Rail Research Institute (ERRI) proposes that the second mode should also be included whenever the associated natural frequency is lower than 30 Hz]. This investigation endeavours to clarify the question as much as possible by establishing whether the maximum response of the bridge, in terms of displacements, accelerations and bending moments, can be computed accurately not taking account of the contribution of the second mode. To this end, a dimensionless formulation of the equations of motion of a simply supported beam traversed by a series of equally spaced moving loads is presented. This formulation brings to light the fundamental parameters governing the behaviour of the beam: damping ratio, dimensionless speed $ \alpha$=VT/L, and L/d ratio (L stands for the span of the beam, V for the speed of the train, T represents the fundamental period of the bridge and d symbolises the distance between consecutive loads). Assuming a damping ratio equal to 1%, which is a usual value for prestressed high-speed bridges, a parametric analysis is conducted over realistic ranges of values of $ \alpha$ and L/d. The results can be extended to any simply supported bridge subjected to a train of equally spaced loads in virtue of the so-called Similarity Formulae. The validity of these formulae can be derived from the dimensionless formulation mentioned above. In the parametric analysis the maximum response of the bridge is obtained for one thousand values of speed that cover the range from the fourth resonance of the first mode to the first resonance of the second mode. The response at twenty-one different locations along the span of the beam is compared in order to decide if the maximum can be accurately computed with the sole contribution of the fundamental mode.

Simplified longitudinal seismic analysis of buried tunnels

In this paper an analytical static approach to analyse buried tunnels under seismic surface waves (Rayleigh and Love waves), propagating parallel to the tunnels axis, is provided. In the proposed method, the tunnel is considered as a beam on elastic foundation by using a Winkler model to represent the subgrade reaction and the soil-structure interaction. The seismic load is imposed by giving at the base of the soil springs a determined configuration corresponding to the free-field motion. From the solution of the differential governing equations of the problem, results are obtained in form of relative displacements between points of tunnel, and therefore the seismic bending moments and shearing forces, acting on the tunnel cross section, can be computed.

A nonlinear analysis of laying a floating pipeline on the seabed

In this article, a model for the determination of displacements, strains, and stresses of a submarine pipeline during its construction is presented. Typically, polyethylene outfall pipelines are the ones treated by this model. The process is carried out from an initial floating situation to the final laying position on the seabed. The following control variables are considered in the laying process: the axial load in the pipe, the flooded inner length, and the distance of the control barge from the coast. External loads such as self-weight, dead loads, and forces due to currents and small waves are also taken into account.This paper describes both the conceptual framework for the proposed model and its practical application in a real engineering situation. The authors also consider how the model might be used as a tool to study how sensitive the behavior of the pipeline is to small changes in the values of the control variables. A detailed description of the actions is considered, especially the ones related to the marine environment such as buoyancy, current, and sea waves. The structural behavior of the pipeline is simulated in the framework of a geometrically nonlinear dynamic analysis. The pipeline is assumed to be a two-dimensional Navier_Bernoulli beam. In the nonlinear analysis an updated Lagrangian formulation is used, and special care is taken regarding the numerical aspects of sea bed contact, follower forces due to external water pressures, and dynamic actions. The paper concludes by describing the implementation of the proposed techniques, using the ANSYS computer program with a number of subroutines developed by the authors. This implementation permits simulation of the two-dimensional structural pipe behavior of the whole construction process. A sensitivity analysis of the bending moments, axial forces, and stresses for different values of the control variables is carried out. Using the techniques described, the engineer may optimize the construction steps in the pipe laying process

Refuerzo de vigas de hormigón armado mediante la aplicación de fuerzas exteriores introducidas por predeformación de perfiles metálicos

Una técnica de refuerzo de elementos flectados en general y, en particular, de vigas y forjados de hormigón armado, consiste en la disposición de perfiles metálicos por debajo de los elementos a reforzar y retacados a ellos. En muchos casos este refuerzo se diseña con un planteamiento pasivo, es decir, los perfiles no entran en carga hasta que no se incrementan las acciones sobre el elemento reforzado, o lo hacen sólo ligeramente y de forma cuantitativamente no controlada efectuando el retacado mediante cuñas metálicas. En el presente trabajo se estudia la alternativa del refuerzo de vigas de hormigón armado frente a momentos flectores con un planteamiento activo, introduciendo unas fuerzas (por ejemplo, mediante gatos o barras roscadas) entre el perfil y el elemento a reforzar, y retacando posteriormente el perfil a la viga en los puntos de introducción de las fuerzas, mediante cuñas metálicas, mortero, etc. La propuesta que formulamos en el presente trabajo de investigación para el control de las fuerzas introducidas consiste en la medida de las flechas que se producen en el perfil metálico al hacerlo reaccionar contra la viga. Esto permite el empleo de procedimientos sencillos para la predeformación del perfil que no dispongan de dispositivos de medida de la carga introducida, o bien controlar la veracidad de las medidas de las fuerzas que dan tales dispositivos. La gran fiabilidad que tiene el cálculo de flechas en jácenas metálicas hace que con este procedimiento se puedan conocer con gran precisión las fuerzas introducidas. Las medidas de las flechas se pueden llevar a cabo mediante los procedimientos de instrumentación habituales en pruebas de carga, con una precisión más que suficiente para conocer y controlar con fiabilidad el valor de las fuerzas que el perfil ejerce sobre la viga. Los perfiles necesarios para el refuerzo con esta técnica son netamente inferiores a los que se precisarían con el planteamiento pasivo antes indicado. En el trabajo de investigación se recoge un estudio sobre el número, posición y valor de las fuerzas de refuerzo a introducir, en función de la carga para la que se diseña el refuerzo y la capacidad resistente del elemento a reforzar, y se analizan los valores máximos que pueden tener dichas fuerzas, en función de la capacidad de la pieza frente a momentos de signo contrario a los debidos a las cargas gravitatorias. A continuación se analiza la interacción viga-perfil al incrementarse las cargas sobre la viga desde el instante de la ejecución del refuerzo, interacción que hace variar el valor de las fuerzas que el perfil ejerce sobre la viga. Esta variación permite contar con un incremento en las fuerzas de refuerzo si, con las cargas permanentes presentes al reforzar, no podemos introducirlas inicialmente con el valor necesario, o si se producen pérdidas en las propias fuerzas. Este es uno de los criterios a la hora de seleccionar las características del perfil. Por el contrario, dicha variación puede suponer que en algunos puntos a lo largo del vano se supere la capacidad a flexión frente a momentos de signo contrario a los debidos a las cargas gravitatorias, lo que también debe ser tenido en cuenta. Seguidamente se analizan diferentes aspectos que producen una variación en el valor de las fuerzas de refuerzo, como son las deformaciones diferidas del hormigón (fluencia y retracción), los gradientes de temperatura en la pieza, o la actuación de sobrecargas en los vanos adyacentes. Se concluye los efectos de estos fenómenos, que en ocasiones tienen gran influencia, pueden ser cuantificados por el proyectista, recogiéndose propuestas sencillas para su consideración en casos habituales. Posteriormente recogemos una propuesta de metodología de comprobación del refuerzo, en cuanto a cómo considerar la fisuración y evolución del módulo de deformación de la viga, la introducción de la seguridad, la influencia de las tolerancias de laminación en el perfil sobre el valor calculado de las flechas necesarias en el perfil para introducir las fuerzas iniciales proyectadas, o la situación accidental de fuego, entre otros aspectos. Por último, se exponen las conclusiones más relevantes de la investigación realizada, y se proponen futuras líneas de investigación. One technique for strengthening flexural members in general, and reinforced concrete beams and slabs in particular, entails caulking the underside of these members with steel shapes. This sort of strengthening is often designed from a passive approach; i.e., until the load is increased, the shapes are either not loaded or are only slightly loaded to some unquantified extent by caulking with steel shims. The present study explored the possibility of actively strengthening the capacity of reinforced concrete beams to resist bending moments by applying forces (with jacks or threaded bars, for instance) between the shape and the member to be strengthened. The shape is subsequently caulked under the beam at the points where the forces are applied with steel shims, mortar or similar. The proposal put forward in the present study to monitor the forces applied consists in measuring the deflection on the steel shape as it reacts against the beam. With this technique, the shape can be pre-strained using simple procedures that do not call for devices to measure the force applied, or the accurancy of the respective measurements can be verified. As deflection calculations in steel girders are extremely reliable, the forces applied with this procedure can be very precisely determined. Standard instrumental procedures for load testing can be used to measure deflection with more than sufficient precision to reliably determine and monitor the value of the forces exerted on the beam by the shape. Moreover, the shapes required to strengthen members with this technique are substantially smaller than the ones needed in the aforementioned passive approach. This study addressed the number, position and value of the strengthening forces to be applied in terms of the load for which strengthening was designed and the bearing capacity of the member to be strengthened. The maximum value of such forces was also analysed as a function of the capacity of the member to resist counter-gravity moments. An analysis was then conducted of beam-shape interaction when the load on the beam raises since the instant that strengthening is applied, interaction that alters the forces applied to the beam by the shape. This variation can provide an increment in the forces if we cannot introduce them initially with the value calculated as necessary because they were limited by the permanent loads existing when strengthening, or if losses occur in the forces themselves. This is one of the criteria for defining shape specifications. Conversely, such variation may cause the forces to exceed beam counter-gravity bending strength at some points in the span, a development that must also be taken into consideration. Other factors inducing variations in the strengthening force values were then analysed, including deferred concrete strain (creep and shrinkage), temperature gradients in the member and the live loads acting on adjacent spans. The inference drawn was that these developments, which may on occasion have a heavy impact, can be quantified by the design engineer, particularly in ordinary situations, for which simple procedures are proposed. Methodology is likewise proposed for verifying strength in terms of how to appraise beam's cracking and variations in modulus of deformation; safety concerns; the effect of shape lamination tolerance on the calculated deflection necessary for the shape to apply the design forces; and fire-induced situations, among others. Lastly, the most prominent conclusions are discussed and future lines of research are suggested.

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.

Parametric analysis on bridge reinforced concrete elevated pile-cap foundations

Current design practices recommend to comply with the capacity protection principle, which pays special attention to ensuring an elastic response of the foundations under ground motion events. However, in cases such as elevated reinforced concrete (RC) pile-cap foundation typologies, this design criterion may lead to conservative designs, with excessively high construction costs. Reinforced concrete elevated pile-cap foundations is a system formed by a group of partially embedded piles connected through an aboveground stayed cap and embedded in soil. In the cases when they are subjected to ground motions, the piles suffer large bending moments that make it difficult to maintain their behavior within the elastic range of deformations. Aiming to make an in-depth analysis of the nonlinear behavior of elevated pile-cap foundations, a cyclic loading test was performed on a concrete 2x3 pile configuration specimen of elevated pile-cap foundation. Two results of this test, the failure mechanism and the ductile behavior, were used for the calibration of a numerical model built in OpenSees framework, by using a pushover analysis. The calibration of the numerical model enabled an in-depth study of the seismic nonlinear response of this kind of foundations. A parametric analysis was carried for this purpose, aiming to study how sensitive RC elevated pile-cap foundations are, when subjected to variations in the diameter of piles, reinforcement ratios, external loads, soil density or multilayer configurations. This analysis provided a set of ductility factors that can be used as a reference for design practices and which correspond to each of the cases analyzed.

Sobre el comportamiento de micropilotes trabajando a flexión y/o cortante en estructuras de tierra

El empleo de los micropilotes en la ingeniería civil ha revolucionado las técnicas de estabilización de terraplenes a media ladera, ya que aunque los pilotes pueden ser la opción más económica, el uso de micropilotes permite llegar a sitios inaccesibles con menor coste de movimientos de tierras, realización de plataformas de trabajo de dimensiones reducidas, maquinaria necesaria es mucho más pequeña, liviana y versátil en su uso, incluyendo la posibilidad de situar la fabricación de morteros o lechadas a distancias de varias decenas de metros del elemento a ejecutar. Sin embargo, realizando una revisión de la documentación técnica que se tiene en el ámbito ingenieril, se comprobó que los sistemas de diseño de algunos casos (micropilotes en terraplenes a media ladera, micropilotes en pantallas verticales, micropilotes como “paraguas” en túneles, etc.) eran bastante deficientes o poco desarrollados. Premisa que permite concluir que el constructor ha ido por delante (como suele ocurrir en ingeniería geotécnica) del cálculo o de su análisis teórico. Del mismo modo se determinó que en su mayoría los micropilotes se utilizan en labores de recalce o como nueva solución de cimentación en condiciones de difícil acceso, casos en los que el diseño de los micropilotes viene definido por cargas axiales, de compresión o de tracción, consideraciones que se contemplan en reglamentaciones como la “Guía para el proyecto y la ejecución de micropilotes en obras de carretera” del Ministerio de Fomento. En los micropilotes utilizados para estabilizar terraplenes a media ladera y micropilotes actuando como muros pantalla, en los que éstos trabajan a esfuerzo cortante y flexión, no se dispone de sistemas de análisis fiables o no se introduce adecuadamente el problema de interacción terreno-micropilote. Además en muchos casos, los parámetros geotécnicos que se utilizan no tienen una base técnico-teórica adecuada por lo que los diseños pueden quedar excesivamente del lado de la seguridad, en la mayoría de los casos, o todo lo contrario. Uno de los objetivos principales de esta investigación es estudiar el comportamiento de los micropilotes que están sometidos a esfuerzos de flexión y cortante, además de otros objetivos de gran importancia que se describen en el apartado correspondiente de esta tesis. Cabe indicar que en este estudio no se ha incluido el caso de micropilotes quasi-horizontales trabajando a flexion (como los “paraguas” en túneles), por considerarse que estos tienen un comportamiento y un cálculo diferente, que está fuera del alcance de esta investigación. Se ha profundizado en el estudio del empleo de micropilotes en taludes, presentando casos reales de obras ejecutadas, datos estadísticos, problemas de diseño y ejecución, métodos de cálculo simplificados y modelación teórica en cada caso, efectuada mediante el empleo de elementos finitos con el Código Plaxis 2D. Para llevar a cabo los objetivos que se buscan con esta investigación, se ha iniciado con el desarrollo del “Estado del Arte” que ha permitido establecer tipología, aplicaciones, características y cálculo de los micropilotes que se emplean habitualmente. Seguidamente y a efectos de estudiar el problema dentro de un marco geotécnico real, se ha seleccionado una zona española de actuación, siendo ésta Andalucía, en la que se ha utilizado de manera muy importante la técnica de micropilotes sobre todo en problemas de estabilidad de terraplenes a media ladera. A partir de ahí, se ha realizado un estudio de las propiedades geotécnicas de los materiales (principalmente suelos y rocas muy blandas) que están presentes en esta zona geográfica, estudio que ha sido principalmente bibliográfico o a partir de la experiencia en la zona del Director de esta tesis. Del análisis realizado se han establecido ordenes de magnitud de los parámetros geotécnicos, principalmente la cohesión y el ángulo de rozamiento interno (además del módulo de deformación aparente o de un módulo de reacción lateral equivalente) para los diversos terrenos andaluces. Con el objeto de conocer el efecto de la ejecución de un micropilote en el terreno (volumen medio real del micropilote, una vez ejecutado; efecto de la presión aplicada en las propiedades del suelo circundante, etc.) se ha realizado una encuesta entre diversas empresas españolas especializadas en la técnica de los micropilotes, a efectos de controlar los volúmenes de inyección y las presiones aplicadas, en función de la deformabilidad del terreno circundante a dichos micropilotes, con lo que se ha logrado definir una rigidez a flexión equivalente de los mismos y la definición y características de una corona de terreno “mejorado” lograda mediante la introducción de la lechada y el efecto de la presión alrededor del micropilote. Con las premisas anteriores y a partir de los parámetros geotécnicos determinados para los terrenos andaluces, se ha procedido a estudiar la estabilidad de terraplenes apoyados sobre taludes a media ladera, mediante el uso de elementos finitos con el Código Plaxis 2D. En el capítulo 5. “Simulación del comportamiento de micropilotes estabilizando terraplenes”, se han desarrollado diversas simulaciones. Para empezar se simplificó el problema simulando casos similares a algunos reales en los que se conocía que los terraplenes habían llegado hasta su situación límite (de los que se disponía información de movimientos medidos con inclinómetros), a partir de ahí se inició la simulación de la inestabilidad para establecer el valor de los parámetros de resistencia al corte del terreno (mediante un análisis retrospectivo – back-análisis) comprobando a su vez que estos valores eran similares a los deducidos del estudio bibliográfico. Seguidamente se han introducido los micropilotes en el borde de la carretera y se ha analizado el comportamiento de éstos y del talud del terraplén (una vez construidos los micropilotes), con el objeto de establecer las bases para su diseño. De este modo y adoptando los distintos parámetros geotécnicos establecidos para los terrenos andaluces, se simularon tres casos reales (en Granada, Málaga y Ceuta), comparando los resultados de dichas simulaciones numéricas con los resultados de medidas reales de campo (desplazamientos del terreno, medidos con inclinómetros), obteniéndose una reproducción bastante acorde a los movimientos registrados. Con las primeras simulaciones se concluye que al instalar los micropilotes la zona más insegura de la ladera es la de aguas abajo. La superficie de rotura ya no afecta a la calzada que protegen los micropilotes. De ahí que se deduzca que esta solución sea válida y se haya aplicado masivamente en Andalucía. En esas condiciones, podría decirse que no se está simulando adecuadamente el trabajo de flexión de los micropilotes (en la superficie de rotura, ya que no les corta), aunque se utilicen elementos viga. Por esta razón se ha realizado otra simulación, basada en las siguientes hipótesis: − Se desprecia totalmente la masa potencialmente deslizante, es decir, la que está por delante de la fila exterior de micros. − La estratigrafía del terreno es similar a la considerada en las primeras simulaciones. − La barrera de micropilotes está constituida por dos elementos inclinados (uno hacia dentro del terraplén y otro hacia fuera), con inclinación 1(H):3(V). − Se puede introducir la rigidez del encepado. − Los micros están separados 0,556 m ó 1,00 m dentro de la misma alineación. − El empotramiento de los micropilotes en el sustrato resistente puede ser entre 1,5 y 7,0 m. Al “anular” el terreno que está por delante de los micropilotes, a lo largo del talud, estos elementos empiezan claramente a trabajar, pudiendo deducirse los esfuerzos de cortante y de flexión que puedan actuar sobre ellos (cota superior pero prácticamente muy cerca de la solución real). En esta nueva modelación se ha considerado tanto la rigidez equivalente (coeficiente ϴ) como la corona de terreno tratado concéntrico al micropilote. De acuerdo a esto último, y gracias a la comparación de estas modelaciones con valores reales de movimientos en laderas instrumentadas con problemas de estabilidad, se ha verificado que existe una similitud bastante importante entre los valores teóricos obtenidos y los medidos en campo, en relación al comportamiento de los micropilotes ejecutados en terraplenes a media ladera. Finalmente para completar el análisis de los micropilotes trabajando a flexión, se ha estudiado el caso de micropilotes dispuestos verticalmente, trabajando como pantallas discontinuas provistas de anclajes, aplicado a un caso real en la ciudad de Granada, en la obra “Hospital de Nuestra Señora de la Salud”. Para su análisis se utilizó el código numérico CYPE, basado en que la reacción del terreno se simula con muelles de rigidez Kh o “módulo de balasto” horizontal, introduciendo en la modelación como variables: a) Las diferentes medidas obtenidas en campo; b) El espesor de terreno cuaternario, que por lo que se pudo determinar, era variable, c) La rigidez y tensión inicial de los anclajes. d) La rigidez del terreno a través de valores relativos de Kh, recopilados en el estudio de los suelos de Andalucía, concretamente en la zona de Granada. Dicha pantalla se instrumentó con 4 inclinómetros (introducidos en los tubos de armadura de cuatro micropilotes), a efectos de controlar los desplazamientos horizontales del muro de contención durante las excavaciones pertinentes, a efectos de comprobar la seguridad del conjunto. A partir del modelo de cálculo desarrollado, se ha comprobado que el valor de Kh pierde importancia debido al gran número de niveles de anclajes, en lo concerniente a las deformaciones horizontales de la pantalla. Por otro lado, los momentos flectores son bastante sensibles a la distancia entre anclajes, al valor de la tensión inicial de los mismos y al valor de Kh. Dicho modelo también ha permitido reproducir de manera fiable los valores de desplazamientos medidos en campo y deducir los parámetros de deformabilidad del terreno, Kh, con valores del orden de la mitad de los medidos en el Metro Ligero de Granada, pero visiblemente superiores a los deducibles de ábacos que permiten obtener Kh para suelos granulares con poca cohesión (gravas y cuaternario superior de Sevilla) como es el caso del ábaco de Arozamena, debido, a nuestro juicio, a la cementación de los materiales presentes en Granada. En definitiva, de las anteriores deducciones se podría pensar en la optimización del diseño de los micropilotes en las obras que se prevean ejecutar en Granada, con similares características al caso de la pantalla vertical arriostrada mediante varios niveles de anclajes y en las que los materiales de emplazamiento tengan un comportamiento geotécnico similar a los estudiados, con el consiguiente ahorro económico. Con todo ello, se considera que se ha hecho una importante aportación para el diseño de futuras obras de micropilotes, trabajando a flexión y cortante, en obras de estabilización de laderas o de excavaciones. Using micropiles in civil engineering has transformed the techniques of stabilization of embankments on the natural or artificial slopes, because although the piles may be the cheapest option, the use of micropiles can reach inaccessible places with lower cost of earthworks, carrying out small work platforms. Machinery used is smaller, lightweight and versatile, including the possibility of manufacturing mortars or cement grouts over distances of several tens of meters of the element to build. However, making a review of the technical documentation available in the engineering field, it was found that systems designed in some cases (micropiles in embankments on the natural slopes, micropiles in vertical cut-off walls, micropiles like "umbrella" in tunnels, etc.) were quite poor or underdeveloped. Premise that concludes the builder has gone ahead (as usually happen in geotechnical engineering) of calculation or theoretical analysis. In the same way it was determined that most of the micropiles are used in underpinning works or as a new foundation solution in conditions of difficult access, in which case the design of micropiles is defined by axial, compressive or tensile loads, considered in regulations as the " Handbook for the design and execution of micropiles in road construction" of the Ministry of Development. The micropiles used to stabilize embankments on the slopes and micropiles act as retaining walls, where they work under shear stress and bending moment, there are not neither reliable systems analysis nor the problem of soil-micropile interaction are properly introduced. Moreover, in many cases, the geotechnical parameters used do not have a proper technical and theoretical basis for what designs may be excessively safe, or the opposite, in most cases. One of the main objectives of this research is to study the behavior of micro piles which are subjected to bending moment and shear stress, as well as other important objectives described in the pertinent section of this thesis. It should be noted that this study has not included the case of quasi-horizontal micropiles working bending moment (as the "umbrella" in tunnels), because it is considered they have a different behavior and calculation, which is outside the scope of this research. It has gone in depth in the study of using micropiles on slopes, presenting real cases of works made, statistics, problems of design and implementation, simplified calculation methods and theoretical modeling in each case, carried out by using FEM (Finite Element Method) Code Plaxis 2D. To accomplish the objectives of this research, It has been started with the development of the "state of the art" which stipulate types, applications, characteristics and calculation of micropiles that are commonly used. In order to study the problem in a real geotechnical field, it has been selected a Spanish zone of action, this being Andalusia, in which it has been used in a very important way, the technique of micropiles especially in embankments stability on natural slopes. From there, it has made a study of the geotechnical properties of the materials (mainly very soft soils and rocks) that are found in this geographical area, which has been mainly a bibliographic study or from the experience in the area of the Director of this thesis. It has been set orders of magnitude of the geotechnical parameters from analyzing made, especially the cohesion and angle of internal friction (also apparent deformation module or a side reaction module equivalent) for various typical Andalusian ground. In order to determine the effect of the implementation of a micropile on the ground (real average volume of micropile once carried out, effect of the pressure applied on the properties of the surrounding soil, etc.) it has conducted a survey among various skilled companies in the technique of micropiles, in order to control injection volumes and pressures applied, depending on the deformability of surrounding terrain such micropiles, whereby it has been possible to define a bending stiffness and the definition and characteristics of a crown land "improved" achieved by introducing the slurry and the effect of the pressure around the micropile. With the previous premises and from the geotechnical parameters determined for the Andalusian terrain, we proceeded to study the stability of embankments resting on batters on the slope, using FEM Code Plaxis 2D. In the fifth chapter "Simulation of the behavior of micropiles stabilizing embankments", there were several different numerical simulations. To begin the problem was simplified simulating similar to some real in which it was known that the embankments had reached their limit situation (for which information of movements measured with inclinometers were available), from there the simulation of instability is initiated to set the value of the shear strength parameters of the ground (by a retrospective analysis or back-analysis) checking these values were similar to those deduced from the bibliographical study Then micropiles have been introduced along the roadside and its behavior was analyzed as well as the slope of embankment (once micropiles were built ), in order to establish the basis for its design. In this way and taking the different geotechnical parameters for the Andalusian terrain, three real cases (in Granada, Malaga and Ceuta) were simulated by comparing the results of these numerical simulations with the results of real field measurements (ground displacements measured with inclinometers), getting quite consistent information according to registered movements. After the first simulations it has been concluded that after installing the micropiles the most insecure area of the natural slope is the downstream. The failure surface no longer affects the road that protects micropiles. Hence it is inferred that this solution is acceptable and it has been massively applied in Andalusia. Under these conditions, one could say that it is not working properly simulating the bending moment of micropiles (on the failure surface, and that does not cut them), although beam elements are used. Therefore another simulation was performed based on the following hypotheses: − The potentially sliding mass is totally neglected, that is, which is ahead of the outer row of micropiles. − Stratigraphy field is similar to the one considered in the first simulations. − Micropiles barrier is constituted by two inclined elements (one inward and one fill out) with inclination 1 (H): 3 (V). − You can enter the stiffness of the pile cap. − The microlies lines are separated 0.556 m or 1.00 m in the same alignment. − The embedding of the micropiles in the tough substrate can be between 1.5 and 7.0 m. To "annul" the ground that is in front of the micro piles, along the slope, these elements clearly start working, efforts can be inferred shear stress and bending moment which may affect them (upper bound but pretty close to the real) solution. In this new modeling it has been considered both equivalent stiffness coefficient (θ) as the treated soil crown concentric to the micropile. According to the latter, and by comparing these values with real modeling movements on field slopes instrumented with stability problems, it was verified that there is quite a significant similarity between the obtained theoretical values and the measured field in relation to the behavior of micropiles executed in embankments along the natural slope. Finally to complete the analysis of micropiles working in bending conditions, we have studied the case of micropiles arranged vertically, working as discontinued cut-off walls including anchors, applied to a real case in the city of Granada, in the play "Hospital of Our Lady of the Health ". CYPE numeric code, based on the reaction of the ground is simulated spring stiffness Kh or "subgrade" horizontal, introduced in modeling was used as variables for analysis: a) The different measurements obtained in field; b) The thickness of quaternary ground, so that could be determined, was variable, c) The stiffness and the prestress of the anchors. d) The stiffness of the ground through relative values of Kh, collected in the study of soils in Andalusia, particularly in the area of Granada. (previously study of the Andalusia soils) This cut-off wall was implemented with 4 inclinometers (introduced in armor tubes four micropiles) in order to control the horizontal displacements of the retaining wall during the relevant excavations, in order to ensure the safety of the whole. From the developed model calculation, it was found that the value of Kh becomes less important because a large number of anchors levels, with regard to the horizontal deformation of the cut-off wall. On the other hand, the bending moments are quite sensitive to the distance between anchors, the initial voltage value thereof and the value of Kh. This model has also been reproduced reliably displacement values measured in the field and deduce parameters terrain deformability, Kh, with values around half the measured Light Rail in Granada, but visibly higher than deductible of abacuses which can obtain Kh for granular soils with low cohesion (upper Quaternary gravels and Sevilla) such as Abacus Arozamena, because, in our view, to cementing materials in Granada. In short, previous deductions you might think on optimizing the design of micropiles in the works that are expected to perform in Granada, with similar characteristics to the case of the vertical cut-off wall braced through several levels of anchors and in which materials location have a geotechnical behavior similar to those studied, with the consequent economic savings. With all this, it is considered that a significant contribution have been made for the design of future works of micropiles, bending moment and shear stress working in slope stabilization works or excavations.

Contribución del tablero y de la subestructura frente al pandeo global de pilas esbeltas de hormigón armado : determinación simplificada de una "coacción equivalente"

Las pilas de los puentes son elementos habitualmente verticales que, generalmente, se encuentran sometidos a un estado de flexión compuesta. Su altura significativa en muchas ocasiones y la gran resistencia de los materiales constituyentes de estos elementos – hormigón y acero – hace que se encuentren pilas de cierta esbeltez en la que los problemas de inestabilidad asociados al cálculo en segundo orden debido a la no linealidad geométrica deben ser considerados. Además, la mayoría de las pilas de nuestros puentes y viaductos están hechas de hormigón armado por lo que se debe considerar la fisuración del hormigón en las zonas en que esté traccionado. Es decir, el estudio del pandeo de pilas esbeltas de puentes requiere también la consideración de un cálculo en segundo orden mecánico, y no solo geométrico. Por otra parte, una pila de un viaducto no es un elemento que pueda considerarse como aislado; al contrario, su conexión con el tablero hace que aparezca una interacción entre la propia pila y aquél que, en cierta medida, supone una cierta coacción al movimiento de la propia cabeza de pila. Esto hace que el estudio de la inestabilidad de una pila esbelta de un puente no puede ser resuelto con la “teoría del pandeo de la pieza aislada”. Se plantea, entonces, la cuestión de intentar definir un procedimiento que permita abordar el problema complicado del pandeo de pilas esbeltas de puentes pero empleando herramientas de cálculo no tan complejas como las que resuelven “el pandeo global de una estructura multibarra, teniendo en cuenta todas las no linealidades, incluidas las de las coacciones”. Es decir, se trata de encontrar un procedimiento, que resulta ser iterativo, que resuelva el problema planteado de forma aproximada, pero suficientemente ajustada al resultado real, pero empleando programas “convencionales” de cálculo que sean capaces de : - por una parte, en la estructura completa: o calcular en régimen elástico lineal una estructura plana o espacial multibarra compleja; - por otra, en un modelo de una sola barra aislada: o considerar las no linealidades geométricas y mecánicas a nivel tensodeformacional, o considerar la no linealidad producida por la fisuración del hormigón, o considerar una coacción “elástica” en el extremo de la pieza. El objeto de este trabajo es precisamente la definición de ese procedimiento iterativo aproximado, la justificación de su validez, mediante su aplicación a diversos casos paramétricos, y la presentación de sus condicionantes y limitaciones. Además, para conseguir estos objetivos se han elaborado unos ábacos de nueva creación que permiten estimar la reducción de rigidez que supone la fisuración del hormigón en secciones huecas monocajón de hormigón armado. También se han creado unos novedosos diagramas de interacción axil-flector válidos para este tipo de secciones en flexión biaxial. Por último, hay que reseñar que otro de los objetivos de este trabajo – que, además, le da título - era cuantificar el valor de la coacción que existe en la cabeza de una pila debido a que el tablero transmite las cargas de una pila al resto de los integrantes de la subestructura y ésta, por tanto, colabora a reducir los movimientos de la cabeza de pila en cuestión. Es decir, la cabeza de una pila no está exenta lo cual mejora su comportamiento frente al pandeo. El régimen de trabajo de esta coacción es claramente no lineal, ya que la rigidez de las pilas depende de su grado de fisuración. Además, también influye cómo las afecta la no linealidad geométrica que, para la misma carga, aumenta la flexión de segundo orden de cada pila. En este documento se define cuánto vale esta coacción, cómo hay que calcularla y se comprueba su ajuste a los resultados obtenidos en el l modelo no lineal completo. The piers of the bridges are vertical elements where axial loads and bending moments are to be considered. They are often high and also the strength of the materials they are made of (concrete and steel) is also high. This means that slender piers are very common and, so, the instabilities produced by the second order effects due to the geometrical non linear effects are to be considered. In addition to this, the piers are usually made of reinforced concrete and, so, the effects of the cracking of the concrete should also be evaluated. That is, the analysis of the instabilities of te piers of a bridge should consider both the mechanical and the geometrical non linearities. Additionally, the pier of a bridge is not a single element, but just the opposite; the connection of the pier to the deck of the bridge means that the movements of the top of the pier are reduced compared to the situation of having a free end at the top of the pier. The connection between the pier and the deck is the reason why the instability of the pier cannot be analysed using “the buckling of a compressed single element method”. So, the question of defining an approximate method for analysing the buckling of the slender piers of a bridge but using a software less complex than what it is needed for analysing the “ global buckling of a multibeam structure considering all t”, is arisen. Then, the goal should be trying to find a procedure for analysing the said complex problem of the buckling of the slender piers of a bridge using a simplified method. This method could be an iterative (step by step) procedure, being accurate enough, using “normal” software having the following capabilities: - Related to the calculation of the global structure o Ability for calculating a multibesam strucutre using elastic analysis. - Related to the calculation of a single beam strcuture:: o Ability for taking into account the geometrical and mechanical () non linearities o Ability for taking into account the cracking of the concrete. o Ability for using partial stiff constraints (elastic springs) at the end of the elements One of the objectives of this document is just defining this simplified methodology, justifying the accuracy of the proposed procedure by using it on some different bridges and presenting the exclusions and limitations of the propose method. In addition to this, some new charts have been created for calculating the reduction of the stiffness of hollow cross sections made of reinforced concrete. Also, new charts for calculating the reinforcing of hollow cross sections under biaxial bending moments are also included in the document. Finally, it is to be said that another aim of the document – as it is stated on the title on the document – is defining the value of the constraint on the top of the pier because of the connection of the pier to the deck .. and to the other piers. That is, the top of the pier is not a free end of a beam and so the buckling resistance of the pier is significantly improved. This constraint is a non-elastic constraint because the stiffness of each pier depends on the level of cracking. Additionally, the geometrical non linearity is to be considered as there is an amplification of the bending moments due to the increasing of the movements of the top of the pier. This document is defining how this constraints is to be calculated; also the accuracy of the calculations is evaluated comparing the final results with the results of the complete non linear calculations

Funicularity and equilibrium for high-performance conceptual structural design

Las estructuras que trabajan por forma se caracterizan por la íntima e indisociable relación entre geometría y comportamiento estructural. Por consiguiente, la elección de una apropiada geometría es el paso previo indispensable en el diseño conceptual de dichas estructuras. En esa tarea, la selección de las posibles geometrías antifuniculares para las distribuciones de cargas permanentes más habituales son más bien limitadas y, muchas veces, son criterios no estructurales (adaptabilidad funcional, estética, proceso constructivo, etc.) los que no permiten la utilización de dichas geometrías que garantizarían el máximo aprovechamiento del material. En este contexto, esta tesis estudia la posibilidad de obtener una estructura sin momentos flectores incluso si la geometría no es antifunicular para sus cargas permanentes. En efecto, esta tesis presenta un procedimiento, basado en la estática gráfica, que demuestra cómo un conjunto de cargas adicionales, introducidas a través de un sistema de pretensado exterior con elementos post-tesos, puede eliminar los momentos flectores debidos a cargas permanentes en cualquier geometría plana. Esto se traduce en una estructura antifunicular que proporciona respuestas innovadoras a demandas conjuntas de versatilidad arquitectónica y optimización del material. Dicha metodología gráfica ha sido implementada en un software distribuido libremente (EXOEQUILIBRIUM), donde el análisis estructural y la variación geométrica están incluidos en el mismo entorno interactivo y paramétrico. La utilización de estas herramientas permite más versatilidad en la búsqueda de nuevas formas eficientes, lo cual tiene gran importancia en el diseño conceptual de estructuras, liberando al ingeniero de la limitación del propio cálculo y de la incomprensión del comportamiento estructural, facilitando extraordinariamente el hecho creativo a la luz de una metodología de este estilo. Esta tesis incluye la aplicación de estos procedimientos a estructuras de cualquier geometría y distribución inicial de cargas, así como el estudio de diferentes posibles criterios de diseño para optimizar la posición del sistema de post-tesado. Además, la metodología ha sido empleada en el proyecto de maquetas a escala reducida y en la construcción de un pabellón hecho enteramente de cartón, lo que ha permitido obtener una validación física del procedimiento desarrollado. En definitiva, esta tesis expande de manera relevante el rango de posibles geometrías antifuniculares y abre enormes posibilidades para el diseño de estructuras que combinan eficiencia estructural y flexibilidad arquitectónica.Curved structures are characterized by the critical relationship between their geometry and structural behaviour, and selecting an appropriate shape in the conceptual design of such structures is important for achieving materialefficiency. However, the set of bending-free geometries are limited and, often, non-structural design criteria (e.g., usability, architectural needs, aesthetics) prohibit the selection of purely funicular or antifunicular shapes. In response to this issue, this thesis studies the possibility of achieving an axial-only behaviour even if the geometry departs from the ideally bending-free shape. This dissertation presents a new design approach, based on graphic statics that shows how bending moments in a two-dimensional geometry can be eliminated by adding forces through an external post-tensioning system. This results in bending-free structures that provide innovative answers to combined demands on versatility and material optimization. The graphical procedure has been implemented in a free-downloadable design-driven software (EXOEQUILIBRIUM) where structural performance evaluations and geometric variation are embedded within an interactive and parametric working environment. This provides greater versatility in finding new efficient structural configurations during the first design stages, bridging the gap between architectural shaping and structural analysis. The thesis includes the application of the developed graphical procedure to shapes with random curvature and distribution of loads. Furthermore, the effect of different design criteria on the internal force distribution has been analyzed. Finally, the construction of reduced- and large-scale models provides further physical validation of the method and insights about the structural behaviour of these structures. In summary, this work strongly expands the range of possible forms that exhibit a bending-free behaviour and, de facto, opens up new possibilities for designs that combine high-performing solutions with architectural freedom.

A non-linear analysis of lying a floating pipeline on the seabed

In this article, a model for the determination of displacements, deformations and tensions of a submarine pipeline during the construction is presented. The process is carried out from an initial floating situation to the final laying position on the seabed. The existence of currents and small waves are also considered. Firstly, this technique, usually applied to polyethylene pipelines, is described in this paper as well as some real world examples, as well as the variables that can be modified to control the behavior of the structure. A detailed description of the actions in this process is considered, specially the ones related to marine environment, as Archimedes force, current and sea waves. The behavior of the pipeline is modeled with a non linear elasto dynamic model where geometric non linearities are taken into account. A 3-D beam model, without cross section deformation effects, is developed. Special care is taken in the numerical analysis, developed within an updated lagrangian formulation framework, with the sea bed contact, the follower forces due to the external water pressures and the dynamic actions. Finally, some subroutines are implemented into ANSYS to simulate the two dimensional case, where the whole construction process is achieved. With this software, a sensibility analysis of the bending moments, axial forces and stresses obtained with different values of the control variables in order to optimize the construction steps. These control variables are, the axial load in the pipe, the inundated inner length and the distance of the control barge from the coast.

Bending continuous structures with SMAs: a novel robotic fish design

In this paper, we describe our research on bio-inspired locomotion systems using deformable structures and smart materials, concretely shape memory alloys (SMAs). These types of materials allow us to explore the possibility of building motor-less and gear-less robots. A swimming underwater fish-like robot has been developed whose movements are generated using SMAs. These actuators are suitable for bending the continuous backbone of the fish, which in turn causes a change in the curvature of the body. This type of structural arrangement is inspired by fish red muscles, which are mainly recruited during steady swimming for the bending of a flexible but nearly incompressible structure such as the fishbone. This paper reviews the design process of these bio-inspired structures, from the motivations and physiological inspiration to the mechatronics design, control and simulations, leading to actual experimental trials and results. The focus of this work is to present the mechanisms by which standard swimming patterns can be reproduced with the proposed design. Moreover, the performance of the SMA-based actuators’ control in terms of actuation speed and position accuracy is also addressed.

A computer program for the analysis of the dynamic bending-torsion coupling in bridges using a mini-computer

The analysis of modes and natural frequencies is of primary interest in the computation of the response of bridges. In this article the transfer matrix method is applied to this problem to provide a computer code to calculate the natural frequencies and modes of bridge-like structures. The Fortran computer code is suitable for running on small computers and results are presented for a railway bridge.

The analysis of the basketball coach speech during the moments of game and pause in relation to the performance in competition

In the area of the professional competition, the coach is a fundamental part in the management of a team and more concretely in the game planning. During the competition, the management of the times of pause and times out as well as the conduct of the coach during the same ones is an aspect to analyze in the sports performance. It is for this that it becomes necessary to know some of the behaviors that turn out to be more frequent by the coach and that are more related to a positive performance of his players. For it there has been realized a study of 7 cases of expert coaches in those that his verbal behavior has observed during 4 games. It has focused on the content of the information only to verbal level, on his meaning. The information that have been obtained in the study shows a major quantity of information elaborated during the pauses of the games and a major tactical content with regard to the moments of game. On the other hand, a relation exists between a major number of questions and a minor number of psychological instructions when the score is adverse, whereas in case of victory, a direct relation does not exist with any category. The rest of categories of the speech do not meet influenced directly for the result, for what it is not possible to consider a direct and immediate relation between the coach verbal behavior during the pauses and the result of the game, except in punctual moments.