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

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

Wind tunnel analysis on the influence of cantilever parapets on the wind loads on curved roofs

Different methods to reduce the high suction caused by conical vortices have been reported in the literature: vertical parapets, either solids or porous, placed at the roof edges being the most analysed configuration. Another method for alleviating the high suction peaks due to conical vortices is to round the roof edges. Very recently, the use of some non-standard parapet configurations, like cantilever parapets, has been suggested. In this paper, its efficiency to reduce suction loads on curved roofs is experimentally checked by testing the pressure distribution on the curved roof of a low-rise building model in a wind tunnel. Very high suction loads have been measured on this model, the magnitude of these high suction loads being significantly decreased when cantilever...

An integrated approach to conceptual design of arch bridges with curved deck

El concepto de funicularidad se puede extender a estructuras lineales espaciales como, por ejemplo, los puentes arco con tablero curvo. Estas estructuras, especialmente pasarelas peatonales, son consecuencia de la necesidad de encajar trazados exigentes y de dar respuesta a nuevas demandas arquitectónicas. En las estructuras curvas el diseño conceptual juega un papel absolutamente esencial. Siempre ha sido así, pero en el caso presente, cabe resaltar que una errónea elección de la geometría conlleva una serie de problemas que se irán acumulando a lo largo del proceso de proyecto, de la construcción y de la vida de la estructura. En este trabajo se presenta SOFIA (Shaping Optimal Form with an Interactive Approach), una herramienta capaz de, conocida la geometría del tablero, de buscar automáticamente la forma del arco antifunicular correspondiente. El planteamiento seguido es conceptualmente el mismo que el utilizado en la búsqueda de formas óptimas en estructuras en dos dimensiones: el arco antifunicular es el que representa, para unas cargas dadas, el lugar geométrico de los puntos con momento flector nulo. La herramienta ha sido desarrollada en un entorno integrado, interactivo y paramético. Su implementación está ilustrada y unos ejemplos de análisis paramétricos están desarrollados. La posición transversal relativa entre tablero y arco ha sido investigada para obtener la configuración del puente estructuralmente más eficiente. Las pasarelas curvas se han convertido en un problema de ingeniería más común de lo habitual en el contexto de los desarrollos urbanos cuando el cliente está buscando un fuerte componente estético: un diseño conceptual adecuado permite obtener una estructura eficiente y elegante. Spatial arch bridges represent an innovative answer to demands on functionality, structural optimization and aesthetics for curved decks, popular in urban contexts. This thesis presents SOFIA (Shaping Optimal Form with an Interactive Approach), a methodology for conceptual designing of antifunicular spatial arch bridges with curved deck in a parametric, interactive and integrated environment. The approach and its implementation are in-depth described and detailed examples of parametric analyses are illustrated. The optimal deck-arch relative transversal position has been investigated for obtaining the most cost-effective bridge. Curved footbridges have become a more common engineering problem in the context of urban developments when the client is looking for a strong aesthetics component: an appropriate conceptual design allows to obtain an efficient and elegant structure.

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.

Nonlinear models for lateral dynamics of railway vehicles on bridges subject to wind action

The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require threedimensional coupled vehicle-bridge models, wheree consideration of wheel to rail contact is a key aspect. Furthermore, an adequate evaluation of safety of rail traffic requires nonlinear models. A nonlinear coupled model is proposed here for vehicle-structure vertical and lateral dynamics. Vehicles are considered as fully three-dimensional multibody systems including gyroscopic terms and large rotation effects. The bridge structure is modeled by means of finite elements which may be of beam, shell or continuum type and may include geometric or material nonlinearities. The track geometry includes distributed track alignment irregularities. Both subsystems (bridge and vehicles) are described with coordinates in absolute reference frames, as opposed to alternative approaches which describe the multibody system with coordinates relative to the base bridge motion. The wheelrail contact employed is a semi-Hertzian model based on realistic wheel-rail profiles. It allows a detailed geometrical description of the contact patch under each wheel including multiple-point contact, flange contact and uplift. Normal and tangential stresses in each contact are integrated at each time-step to obtain the resultant contact forces. The models have been implemented within an existing finite element analysis software with multibody capabilities, Abaqus (Simulia Ltd., 2010). Further details of the model are presented in Antolín et al. (2012). Representative applications are presented for railway vehicles under lateral wind action on laterally compliant viaducts, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle.

The breaking of axisymmetric slender liquid bridges

Liquids held by surface tension forces can bridge the gap between two solid bodies placed not too far apart from each other. The equilibrium conditions and stability criteria for static, cylindrical liquid bridges are well known. However, the behaviour of an unstable liquid bridge, regarding both its transition toward breaking and the resulting configuration, is a matter for discussion. The dynamical problem of axisymmetric rupture of a long liquid bridge anchored at two equal coaxial disks is treated in this paper through the adoption of one-dimensional theories which are widely used in capillary jet problems

The influence of axial microgravity on the breakage of axisymmetric slender liquid bridges

The dynamics of inviscid, axisymmetric liquid bridges permits a simplified treatment if the bridge is long enough. Under such condition the evolution of the liquid zone is satisfactorily explained through a non-linear one-dimensional model. In the case of breaking, the one-dimensional model fails when the neck radius of the liquid column is close to zero; however, the model allows the calculation of the time variation of the liquid-bridge interface as well as of the fluid velocity field and, because the last part of the evolution is not needed, the overall results such as the breaking time and the volume of each of the two drops resulting after breakage can be calculated. In this paper numerical results concerning the behavior of clinical liquid bridges subjected to a small axial gravitational field are presented.

Stability of slender, axisymmetric liquid bridges between unequal disks

The stability of slender, axisymmetric liquid bridges held by surface tension forces between two coaxial, parallel solid disks having different radii is studied by using standard perturbation techniques. The results obtained show that the behaviour of such configurations becomes similar to that of liquid bridges between equal disks when subject to small axial gravity forces.

One-dimensional self-similar solution of the dynamics of axisymmetric slender liquid bridges

In this paper the dynamics of axisymmetric, slender, viscous liquid bridges having volume close to the cylindrical one, and subjected to a small gravitational field parallel to the axis of the liquid bridge, is considered within the context of one-dimensional theories. Although the dynamics of liquid bridges has been treated through a numerical analysis in the inviscid case, numerical methods become inappropriate to study configurations close to the static stability limit because the evolution time, and thence the computing time, increases excessively. To avoid this difficulty, the problem of the evolution of these liquid bridges has been attacked through a nonlinear analysis based on the singular perturbation method and, whenever possible, the results obtained are compared with the numerical ones.

The dynamics of axisymmetric slender liquid bridges between unequal disks

n this paper the influence of an axial microgravity on the dynamic stability of axisymmetric slender liquid bridges between unequal disks is numerically studied by using a one-dimensional theory. The breaking of such liquid configurations is analyzed and the dependence of some overall characteristics of the breaking process on the value of axial microgravity, the geometry and the volume of the liquid bridge, as well as stability limits are obtained.

Experiments with liquid bridges in simulated microgravity

A feature of stability diagrams of liquid bridges between unequal disks subjected to small axial gravity forces is that, for each separation of disks, there is a value of microgravity for which an absolute minimum volume limit is reached. The dependence of such microgravity values on the liquid bridge geometry has been experimentally checked by using the neutral buoyancy technique, experimental results being in complete agreement with theoretical ones. Analytical background assuring the experimental procedure used is presented, and a second order analytical expression for the equilirium interface is also calculated.

Numerical and experimental study of the dynamics of axisymmetric slender liquid bridges

A one-dimensional inviscid slice model has been used to study numerically the influence of axial microgravity on the breaking of liquid bridges having a volume close to that of gravitationless minimum volume stability limit. Equilibrium shapes and stability limits have been obtained as well as the dependence of the volume of the two drops formed after breaking on both the length and the volume of the liquid bridge. The breaking process has also been studied experimentally. Good agreement has been found between theory and experiment for neutrally buoyant systems

Axisymmetric long liquid bridges in a time-dependent microgravity field

This paper deals with the dynamics of liquid bridges when subjected to an oscillatory microgravity field. The analysis has been performed by using a one-dimensional slice model, already used in liquid bridge problems, which allows to calculate not only the resonance frequencies of a wide range of such fluid configurations but also the dependence of the dynamic response of the liquid bridge on the frequency on the imposed perturbations. Theoretical results are compared with experimental ones obtained aboard Spacelab-Dl, the agreement between theoretical and experimental results being satisfactory

Axisymmetric long liquid bridges stability and resonances

In this paper mathematical expressions for minimum-volume stability limits and resonance frequencies of axisymmetric long liquid bridges are presented. These expressions are valid for a wide range of liquid bridge configurations, accounting for ef-fects like unequal disks and axial microgravity in the case of minimum-volume stability limits,and unequal disks, axial microgravity,non-zero viscosity and liquid bridge volume different from the cylindrical one in the case of resonance frequencies.

The Future of the Technologies of Shell and spatial Structures. Bridges

The objective of this lecture is try to predict the future of this important type of spatial structures. In this way the activities of the different IASS Technical Working Groups can be stimulated and coordinated in order to play a more relevant role in this future. To grasp a possible evolution of bridges it is convenient a reflection on the bridge history and on their present situation, particularly in relation to the different existing achievements.