Abutments influence in the dynamic response of bridges

A simplified analytical model of a short span bridge is proposed. The inertial interaction effects of pier foundations and abutments has been included in order to evaluate the response sensitivities to different soil-structure interaction variables. The modification of natural frequency and damping properties is shown for typical short span bridges of the integral deck-abutment type for longitudinal vibrations or general bridges for the transverse ones.

Simplified modelling of bridge abutments-soil interaction under seismic effects

A simplified model is proposed to show the importance that the dynamic soil-abutment interaction can have in the global behavior of bridges submitted to seismic loading. The modification of natural frequency and damping properties is shown in graphic form for typical short span bridges of the integral deck-abutment type for longitudinal vibrations or general ones for transverse vibrations.

Wheel-Rail Contact Forces in High-Speed Simply Supported Bridges at Resonance

The response of high-speed bridges at resonance, particularly under flexural vibrations, constitutes a subject of research for many scientists and engineers at the moment. The topic is of great interest because, as a matter of fact, such kind of behaviour is not unlikely to happen due to the elevated operating speeds of modern rains, which in many cases are equal to or even exceed 300 km/h ( [1,2]). The present paper addresses the subject of the evolution of the wheel-rail contact forces during resonance situations in simply supported bridges. Based on a dimensionless formulation of the equations of motion presented in [4], very similar to the one introduced by Klasztorny and Langer in [3], a parametric study is conducted and the contact forces in realistic situations analysed in detail. The effects of rail and wheel irregularities are not included in the model. The bridge is idealised as an Euler-Bernoulli beam, while the train is simulated by a system consisting of rigid bodies, springs and dampers. The situations such that a severe reduction of the contact force could take place are identified and compared with typical situations in actual bridges. To this end, the simply supported bridge is excited at resonace by means of a theoretical train consisting of 15 equidistant axles. The mechanical characteristics of all axles (unsprung mass, semi-sprung mass, and primary suspension system) are identical. This theoretical train permits the identification of the key parameters having an influence on the wheel-rail contact forces. In addition, a real case of a 17.5 m bridges traversed by the Eurostar train is analysed and checked against the theoretical results. The influence of three fundamental parameters is investigated in great detail: a) the ratio of the fundamental frequency of the bridge and natural frequency of the primary suspension of the vehicle; b) the ratio of the total mass of the bridge and the semi-sprung mass of the vehicle and c) the ratio between the length of the bridge and the characteristic distance between consecutive axles. The main conclusions derived from the investigation are: The wheel-rail contact forces undergo oscillations during the passage of the axles over the bridge. During resonance, these oscillations are more severe for the rear wheels than for the front ones. If denotes the span of a simply supported bridge, and the characteristic distance between consecutive groups of loads, the lower the value of , the greater the oscillations of the contact forces at resonance. For or greater, no likelihood of loss of wheel-rail contact has been detected. The ratio between the frequency of the primary suspension of the vehicle and the fundamental frequency of the bridge is denoted by (frequency ratio), and the ratio of the semi-sprung mass of the vehicle (mass of the bogie) and the total mass of the bridge is denoted by (mass ratio). For any given frequency ratio, the greater the mass ratio, the greater the oscillations of the contact forces at resonance. The oscillations of the contact forces at resonance, and therefore the likelihood of loss of wheel-rail contact, present a minimum for approximately between 0.5 and 1. For lower or higher values of the frequency ratio the oscillations of the contact forces increase. Neglecting the possible effects of torsional vibrations, the metal or composite bridges with a low linear mass have been found to be the ones where the contact forces may suffer the most severe oscillations. If single-track, simply supported, composite or metal bridges were used in high-speed lines, and damping ratios below 1% were expected, the minimum contact forces at resonance could drop to dangerous values. Nevertheless, this kind of structures is very unusual in modern high-speed railway lines.

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.

Estimating the modal parameters from multiple measurement setups using a joint state space model

Computing the modal parameters of structural systems often requires processing data from multiple non-simultaneously recorded setups of sensors. These setups share some sensors in common, the so-called reference sensors, which are fixed for all measurements, while the other sensors change their position from one setup to the next. One possibility is to process the setups separately resulting in different modal parameter estimates for each setup. Then, the reference sensors are used to merge or glue the different parts of the mode shapes to obtain global mode shapes, while the natural frequencies and damping ratios are usually averaged. In this paper we present a new state space model that processes all setups at once. The result is that the global mode shapes are obtained automatically, and only a value for the natural frequency and damping ratio of each mode is estimated. We also investigate the estimation of this model using maximum likelihood and the Expectation Maximization algorithm, and apply this technique to simulated and measured data corresponding to different structures.

Measurements and Prediction of Pedestrian Walking Loads on an Aluminium Catwalk

During the last two decades the topic of human induced vibration has attracted a lot of attention among civil engineering practitioners and academics alike. Usually this type of problem may be encountered in pedestrian footbridges or floors of paperless offices. Slender designs are becoming increasingly popular, and as a consequence, the importance of paying attention to vibration serviceability also increases. This paper resumes the results obtained from measurements taken at different points of an aluminium catwalk which is 6 m in length by 0.6 m in width. Measurements were carried out when subjecting the structure to different actions:1)Static test: a steel cylinder of 35 kg was placed in the middle of the catwalk; 2)Dynamic test: this test consists of exciting the structure with singles impulses; 3)Dynamic test: people walking on the catwalk. Identification of the mechanical properties of the structure is an achievement of the paper. Indirect methods were used to estimate properties including the support stiffness, the beam bending stiffness, the mass of the structure (using Rayleigh method and iterative matrix method), the natural frequency (using the time domain and frequency domain analysis) and the damping ratio (by calculating the logarithmic decrement). Experimental results and numerical predictions for the response of an aluminium catwalk subjected to walking loads have been compared. The damping of this light weight structure depends on the amplitude of vibration which complicates the tuning of a structural model. In the light of the results obtained it seems that the used walking load model is not appropriate as the predicted transient vibration values (TTVs) are much higher than the measured ones.

Joint statistical analysis of multiple measurement setups for the estimation of vibrational modes

Computing the modal parameters of large structures in Operational Modal Analysis often requires to process data from multiple non simultaneously recorded setups of sensors. These setups share some sensors in common, the so-called reference sensors that are fixed for all the measurements, while the other sensors are moved from one setup to the next. One possibility is to process the setups separately what result in different modal parameter estimates for each setup. Then the reference sensors are used to merge or glue the different parts of the mode shapes to obtain global modes, while the natural frequencies and damping ratios are usually averaged. In this paper we present a state space model that can be used to process all setups at once so the global mode shapes are obtained automatically and subsequently only a value for the natural frequency and damping ratio of each mode is computed. We also present how this model can be estimated using maximum likelihood and the Expectation Maximization algorithm. We apply this technique to real data measured at a footbridge.

Influence of Strouhal number on pulsating methane–air coflow jet diffusion flames

Four periodically time-varying methane–air laminar coflow jet diffusion flames, each forced by pulsating the fuel jet's exit velocity Uj sinusoidally with a different modulation frequency wj and with a 50% amplitude variation, have been computed. Combustion of methane has been modeled by using a chemical mechanism with 15 species and 42 reactions, and the solution of the unsteady Navier–Stokes equations has been obtained numerically by using a modified vorticity-velocity formulation in the limit of low Mach number. The effect of wj on temperature and chemistry has been studied in detail. Three different regimes are found depending on the flame's Strouhal number S=awj/Uj, with a denoting the fuel jet radius. For small Strouhal number (S=0.1), the modulation introduces a perturbation that travels very far downstream, and certain variables oscillate at the frequency imposed by the fuel jet modulation. As the Strouhal number grows, the nondimensional frequency approaches the natural frequency of oscillation of the flickering flame (S≃0.2). A coupling with the pulsation frequency enhances the effect of the imposed modulation and a vigorous pinch-off is observed for S=0.25 and S=0.5. Larger values of S confine the oscillation to the jet's near-exit region, and the effects of the pulsation are reduced to small wiggles in the temperature and concentration values. Temperature and species mass fractions change appreciably near the jet centerline, where variations of over 2% for the temperature and 15% and 40% for the CO and OH mass fractions, respectively, are found. Transverse to the jet movement, however, the variations almost disappear at radial distances on the order of the fuel jet radius, indicating a fast damping of the oscillation in the spanwise direction.

Fenómenos de galope en piezas prismáticas con sección en H

El objetivo de esta Tesis es el estudio sistemático del fenómeno aeroelástico de galope de una viga prismática con sección transversal en H. En particular, se pretende analizar la influencia de determinados parámetros geométricos que definen la geometría de la sección y el efecto del ángulo de ataque de la corriente sobre la estabilidad del fenómeno de oscilación. El interés en el estudio de esta forma de la sección transversal de una viga se basa en el hecho de que, con cierta frecuencia, se sigue utilizando, por su buen comportamiento estructural, en construcciones civiles como tableros y tirantes de puentes de gran longitud, señalizaciones, luminarias y, en general, en grandes estructuras metálicas. Los parámetros geométricos seleccionados para su estudio son tres: el espesor de las dos alas verticales, su porosidad y el espesor de sendas ranuras en la zona de unión entre el alma y las alas de la sección. Inicialmente se han realizado ensayos estáticos en un túnel aerodinámico con objeto de obtener las cargas aerodinámicas y poder aplicar el criterio casi-estático de Glauert - Den Hartog. En estos ensayos, se han medido tanto las fuerzas de sustentación y resistencia aerodinámicas como las distribuciones de presiones en la superficie de la zona central de la sección. Posteriormente, se han realizado ensayos de visualización de flujo, utilizando un túnel de humos, para poder comprender mejor el comportamiento físico del aire alrededor del cuerpo. El estudio estático se ha completado realizando ensayos con PIV, que permiten realizar una medida precisa de la velocidad del campo fluido. Por último, se han realizado ensayos dinámicos en otro túnel aerodinámico con objeto de contrastar la aplicabilidad del criterio casi-estático, la velocidad de inicio de galope y la amplitud de las oscilaciones producidas. Los resultados muestran que el espesor de las alas verticales, aunque modifica apreciablemente la magnitud de las cargas aerodinámicas, no afecta sustancialmente a la estabilidad a galope, mientras que su porosidad sí ejerce un control efectivo que permite reducir este fenómeno e incluso evitarlo, en determinados casos. En todas las situaciones el criterio de Glauert-Glauert - Den Hartog ha resultado ser aplicable y, en ocasiones, más restrictivo que los resultados obtenidos en ensayos dinámicos. La presencia de una ranura en la zona de unión entre el alma y las dos alas, o su combinación con la porosidad en las alas, reduce la intensidad de galope, incrementando la velocidad crítica de su inicio, pero no logra hacer que desaparezca, como se justificará en el desarrollo del trabajo. ABSTRACT Galloping is a type of aeroelastic instability characterized by a large amplitude oscillation at the natural frequency of the structure, producing normal motion to wind. It usually occurs in slender bodies lightly damped at sufficiently high speeds. In this thesis an experimental study has been developed on the galloping instability of a beam with H cross section, which is inscribed in a rectangle with a slender 1: 2. A systematic study has been carried out of the influence of three different geometric parameters on galloping, in the range of 0 to 90° angle of attack of the incoming stream. These parameters are the thickness of the flanges of the section, the porosity of the flanges, the thickness of two slots along the span, in the area between the flange and the central core of the section, and the combination effect of the last two parameters. First of all, static tests have been performed in a wind tunnel to determine the lift and drag forces by using a balance and then the quasi-static stability criterion due to Glauert-Den Hartog has been determined. Later, to better understand and verify the results previously obtained, it has also been tested the pressure distribution on the surface of the model, flow visualization in a second, smoke, wind tunnel, and Particle Image Velocimetry (PIV) study of the flow around the section, in a third tunnel. Finally, dynamic tests have been performed, on a fourth wind tunnel, for determining the amplitude and frequency of the oscillations in each case. The results have been collected in stability diagrams for each geometric parameter studied. These results show that the more critical angles of attack of the stream for galloping behavior are close to 0 and 90º. It has been found that the thickness of the flanges, although changes the galloping behavior on the section, does not reduce it substantially. However, the porosity in the flanges has been proved to be an efficient control mechanism on galloping, and even above 40% porosity, it disappears. The thickness of the slot studied and its combination with the porosity in the flanges in some cases reduces the aerodynamic forces appreciably but fail to prevent galloping at all angles of attack.

Influence of soil stiffness on the dynamic response of an offshore wind turbine

La industria de la energía eólica marina ha crecido de forma significativa durante los últimos 15 años, y se espera que siga creciendo durante los siguientes. La construcción de torres en aguas cada vez más profundas y el aumento en potencia y tamaño de las turbinas han creado la necesidad de diseñar estructuras de soporte cada vez más fiables y optimizadas, lo que requiere un profundo conocimiento de su comportamiento. Este trabajo se centra en la respuesta dinámica de una turbina marina con cimentación tipo monopilote y sobre la que actúa la fuerza del viento. Se han realizado cálculos con distintas propiedades del suelo para cubrir un rango de rigideces que va desde una arena muy suelta a una muy densa. De este modo se ha analizado la influencia que tiene la rigidez del suelo en el comportamiento de la estructura. Se han llevado a cabo análisis estáticos y dinámicos en un modelo de elementos finitos implementado en Abaqus. El desplazamiento en la cabeza de la torre y la tensión en su base se han obtenido en función de la rigidez del suelo, y con ellos se ha calculado la amplificación dinámica producida cuando la frecuencia natural del sistema suelo‐cimentación torre se aproxima a la frecuencia de la carga. Dos diferentes enfoques a la hora de modelizar el suelo se han comparado: uno utilizando elementos continuos y otro utilizando muelles elásticos no lineales. Por último, un análisis de fiabilidad se ha llevado a cabo con un modelo analítico para calcular la probabilidad de resonancia del sistema, en el que se han considerado las propiedades de rigidez del suelo como variables aleatorias. Offshore wind energy industry has experienced a significant growth over the past 15 years, and it is expected to continue its growth in the coming years. The expansion to increasingly deep waters and the rise in power and size of the turbines have led to a need for more reliable and optimized support designs, which requires an extensive knowledge of the behaviour of these structures. This work focuses on the dynamic response of an offshore wind turbine founded on a monopile and subjected to wind loading. Different soil properties have been considered in order to cover the range of stiffness from a very loose to a very dense sand. In this way, the influence of stiffness on the structure behaviour has been assessed. Static and dynamic analyses have been carried out by means of a finite element model implemented in Abaqus. Head displacement and stress at the tower base have been obtained as functions of soil stiffness, and they have been used to calculate the dynamic amplification that is produced when the natural frequency of the system soil‐foundation‐tower approaches the load frequency. Two different approaches of soil modelling have been compared: soil modelled as a continuum and soil simulated with non linear elastic springs. Finally, a reliability analysis to assess the probability of resonance has been performed with an analytical model, in which soil stiffness properties are considered as stochastic variables.

State space models for multi-setup operational modal analysis

Operational Modal Analysis consists on estimate the modal parameters of a structure (natural frequencies, damping ratios and modal vectors) from output-only vibration measurements. The modal vectors can be only estimated where a sensor is placed, so when the number of available sensors is lower than the number of tested points, it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors): some sensors stay at the same position from setup to setup, and the other sensors change the position until all the tested points are covered. The permanent sensors are then used to merge the mode shape estimated at each setup (or partial modal vectors) into global modal vectors. Traditionally, the partial modal vectors are estimated independently setup by setup, and the global modal vectors are obtained in a postprocess phase. In this work we present two state space models that can be used to process all the recorded setups at the same time, and we also present how these models can be estimated using the maximum likelihood method. The result is that the global mode shape of each mode is obtained automatically, and subsequently, a single value for the natural frequency and damping ratio of the mode is computed. Finally, both models are compared using real measured data.

Flood frequency analysis by a bivariate model based on copulas

La adecuada estimación de avenidas de diseño asociadas a altos periodos de retorno es necesaria para el diseño y gestión de estructuras hidráulicas como presas. En la práctica, la estimación de estos cuantiles se realiza normalmente a través de análisis de frecuencia univariados, basados en su mayoría en el estudio de caudales punta. Sin embargo, la naturaleza de las avenidas es multivariada, siendo esencial tener en cuenta características representativas de las avenidas, tales como caudal punta, volumen y duración del hidrograma, con el fin de llevar a cabo un análisis apropiado; especialmente cuando el caudal de entrada se transforma en un caudal de salida diferente durante el proceso de laminación en un embalse o llanura de inundación. Los análisis de frecuencia de avenidas multivariados han sido tradicionalmente llevados a cabo mediante el uso de distribuciones bivariadas estándar con el fin de modelar variables correlacionadas. Sin embargo, su uso conlleva limitaciones como la necesidad de usar el mismo tipo de distribuciones marginales para todas las variables y la existencia de una relación de dependencia lineal entre ellas. Recientemente, el uso de cópulas se ha extendido en hidrología debido a sus beneficios en relación al contexto multivariado, permitiendo superar los inconvenientes de las técnicas tradicionales. Una copula es una función que representa la estructura de dependencia de las variables de estudio, y permite obtener la distribución de frecuencia multivariada de dichas variables mediante sus distribuciones marginales, sin importar el tipo de distribución marginal utilizada. La estimación de periodos de retorno multivariados, y por lo tanto, de cuantiles multivariados, también se facilita debido a la manera en la que las cópulas están formuladas. La presente tesis doctoral busca proporcionar metodologías que mejoren las técnicas tradicionales usadas por profesionales para estimar cuantiles de avenida más adecuados para el diseño y la gestión de presas, así como para la evaluación del riesgo de avenida, mediante análisis de frecuencia de avenidas bivariados basados en cópulas. Las variables consideradas para ello son el caudal punta y el volumen del hidrograma. Con el objetivo de llevar a cabo un estudio completo, la presente investigación abarca: (i) el análisis de frecuencia de avenidas local bivariado centrado en examinar y comparar los periodos de retorno teóricos basados en la probabilidad natural de ocurrencia de una avenida, con el periodo de retorno asociado al riesgo de sobrevertido de la presa bajo análisis, con el fin de proporcionar cuantiles en una estación de aforo determinada; (ii) la extensión del enfoque local al regional, proporcionando un procedimiento completo para llevar a cabo un análisis de frecuencia de avenidas regional bivariado para proporcionar cuantiles en estaciones sin aforar o para mejorar la estimación de dichos cuantiles en estaciones aforadas; (iii) el uso de cópulas para investigar tendencias bivariadas en avenidas debido al aumento de los niveles de urbanización en una cuenca; y (iv) la extensión de series de avenida observadas mediante la combinación de los beneficios de un modelo basado en cópulas y de un modelo hidrometeorológico. Accurate design flood estimates associated with high return periods are necessary to design and manage hydraulic structures such as dams. In practice, the estimate of such quantiles is usually done via univariate flood frequency analyses, mostly based on the study of peak flows. Nevertheless, the nature of floods is multivariate, being essential to consider representative flood characteristics, such as flood peak, hydrograph volume and hydrograph duration to carry out an appropriate analysis; especially when the inflow peak is transformed into a different outflow peak during the routing process in a reservoir or floodplain. Multivariate flood frequency analyses have been traditionally performed by using standard bivariate distributions to model correlated variables, yet they entail some shortcomings such as the need of using the same kind of marginal distribution for all variables and the assumption of a linear dependence relation between them. Recently, the use of copulas has been extended in hydrology because of their benefits regarding dealing with the multivariate context, as they overcome the drawbacks of the traditional approach. A copula is a function that represents the dependence structure of the studied variables, and allows obtaining the multivariate frequency distribution of them by using their marginal distributions, regardless of the kind of marginal distributions considered. The estimate of multivariate return periods, and therefore multivariate quantiles, is also facilitated by the way in which copulas are formulated. The present doctoral thesis seeks to provide methodologies that improve traditional techniques used by practitioners, in order to estimate more appropriate flood quantiles for dam design, dam management and flood risk assessment, through bivariate flood frequency analyses based on the copula approach. The flood variables considered for that goal are peak flow and hydrograph volume. In order to accomplish a complete study, the present research addresses: (i) a bivariate local flood frequency analysis focused on examining and comparing theoretical return periods based on the natural probability of occurrence of a flood, with the return period associated with the risk of dam overtopping, to estimate quantiles at a given gauged site; (ii) the extension of the local to the regional approach, supplying a complete procedure for performing a bivariate regional flood frequency analysis to either estimate quantiles at ungauged sites or improve at-site estimates at gauged sites; (iii) the use of copulas to investigate bivariate flood trends due to increasing urbanisation levels in a catchment; and (iv) the extension of observed flood series by combining the benefits of a copula-based model and a hydro-meteorological model.