44 resultados para bridge decks.


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The filling-withdrawal process of a long liquid bridge is analyzed using a one-dimensional linearized model for the dynamics of the liquid column. To carry out this study, a well-known standard operational method (Laplace transform) has been used, and time variation of both liquid velocity field and interface shape are obtained.

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In this article an experimental campaign aimed at validating a previously published simplified serviceability design method of the columns of long jointless structures is presented. The proposed method is also extended to include tension stiffening effects which proved to be significant in structures with small amount of reinforcement subjected to small axial loading. This extension allows significant improvement of predictions for this type of element. The campaign involved columns with different reinforcement and squashing load ratios, given that these parameters had been identified as crucial when designing columns subjected to imposed displacements. Experimental results are presented and discussed, with particular regard to cracking behaviour and structural stiffness. Considerations on tension stiffening effects are also made. Finally, the application of the method to typical bridge and building cases is presented, showing the feasibility of jointless construction, and the limits which should be respected.

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Since in 1940 the Tacoma Narrows Bridge was destroyed by the wind, aeroelastic instabilities have been recognized as one of the most challenging aspects of bridge design. They can produce long-term fatigue failure through vortex induced vibrations, or sudden collapse through self-excited flutter. These vibrations may also cause discomfort for the users and temporary closure of the bridge. Wind tunnel studies are a very helpful tool to understand these phenomena. By means of them, the critical wind speed at which vortex induced vibration and flutter appear can be precisely determined and the design of the bridge can be reconsidered in the early steps of the process. In this paper, an optimum design of the bridge section is sought. One of the most relevant parameters that influence the stability of a certain deck is the porosity of the barriers. Section model tests have been carried out to find whether an optimum value of the porosity of the barrier exists. This value or range of values must present neither vortex induced vibration nor flutter.

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Bridge building is a highly uncertain endeavour that entails considerable risk, as attested to by the succession of construction-related incidents and accidents recently reported in Spain and elsewhere. While efforts are being made to improve on-site safety, many issues are still outstanding, such as the establishment of reliability requirements for the ancillary systems used. The problems that must be dealt with in everyday practice, however, are more elementary and often attributable to human error. The overall organisation of the use of bridge construction equipment is in need of improvement. Close cooperation between the bridge engineers responsible for construction planning and ancillary element suppliers is imperative, for flawed interaction between building equipment and the bridge under construction may generate structural vulnerability. External quality assurance should likewise be mandatory

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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.

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El deterioro del hormigón por ciclos de hielo-deshielo en presencia de sales fundentes es causa frecuente de problemas en los puentes e infraestructuras existentes en los países europeos. Los daños producidos por los ciclos de hielo-deshielo en el hormigón pueden ser internos, fundamentalmente la fisuración y/o externos como el descascarillamiento (desgaste superficial). La España peninsular presenta unas características geográficas y climáticas particulares. El 18% de la superficie tiene una altura superior a 1000mts y, además, la altura media geográfica con respecto al nivel del mar es de 660mts (siendo el segundo país más montañoso de toda Europa).Esto hace que la Red de Carreteras del Estado se vea afectada, durante determinados periodos, por fenómenos meteorológicos adversos, en particular por nevadas y heladas, que pueden comprometer las condiciones de vialidad para la circulación de vehículos. Por este motivo la Dirección General de Carreteras realiza trabajos anualmente (campañas de vialidad invernal, de 6 meses de duración) para el mantenimiento de la vialidad de las carreteras cuando éstas se ven afectadas por estos fenómenos. Existen protocolos y planes operativos que permiten sistematizar estos trabajos de mantenimiento que, además, se han intensificado en los últimos 10 años, y que se fundamentan en el empleo de sales fundentes, principalmente NaCl, con la misión de que no haya placas de hielo, ni nieve, en las carreteras. En zonas de fuerte oscilación térmica, que con frecuencia en España se localizan en la zona central del Pirineo, parte de la cornisa Cantábrica y Sistema Central, se producen importantes deterioros en las estructuras y paramentos de hormigón producidos por los ciclos de hielo- deshielo. Pero además el uso de fundentes de vialidad invernal acelera en gran medida la evolución de estos daños. Los tableros de hormigón de puentes de carretera de unos 40-50 años de antigüedad carecen, en general, de un sistema de impermeabilización, y están formados frecuentemente por un firme de mezcla asfáltica, una emulsión adherente y el hormigón de la losa. En la presente tesis se realiza una investigación que pretende reproducir en laboratorio los procesos que tienen lugar en el hormigón de tableros de puentes existentes de carreteras, de unos 40-50 años de antigüedad, que están expuestos durante largos periodos a sales fundentes, con objeto de facilitar la vialidad invernal, y a cambios drásticos de temperatura (hielo y deshielo). Por ello se realizaron cuatro campañas de investigación, teniendo en cuenta que, si bien nos basamos en la norma europea UNE-CEN/TS 12390-9 “Ensayos de hormigón endurecido. Resistencia al hielo-deshielo. Pérdida de masa”, se fabricaron probetas no estandarizadas para este ensayo, pensado en realidad para determinar la afección de los ciclos únicamente a la pérdida de masa. Las dimensiones de las probetas en nuestro caso fueron 150x300 mm, 75 x 150mm (cilíndricas normalizadas para roturas a compresión según la norma UNE-EN 12390-3) y 286x76x76 (prismáticas normalizadas para estudiar cambio de volumen según la norma ASTM C157), lo cual nos permitió realizar sobre las mismas probetas más ensayos, según se presentan en la tesis y, sobre todo, poder comparar los resultados con probetas extraídas de dimensiones similares en puentes existentes. En la primera campaña, por aplicación de la citada norma, se realizaron ciclos de H/D, con y sin contacto con sales de deshielo (NaCl en disolución del 3% según establece dicha norma). El hormigón fabricado en laboratorio, tratando de simular el de losas de tableros de puentes antiguos, presentó una fc de 22,6 MPa y relación agua/cemento de 0,65. Las probetas de hormigón fabricadas se sometieron a ciclos agresivos de hielo/deshielo (H/D), empleando una temperatura máxima de +20ºC y una temperatura mínima de -20ºC al objeto de poder determinar la sensibilidad de este ensayo tanto al tipo de hormigón elaborado como al tipo de probeta fabricado (cilíndrica y prismática). Esta campaña tuvo una segunda fase para profundizar más en el comportamiento de las probetas sometidas a ciclos H/D en presencia de sales. En la segunda campaña, realizada sobre probetas de hormigón fabricadas en laboratorio iguales a las anteriores, la temperaturas mínima del ensayo se subió a -14ºC, lo que nos permitió analizar el proceso de deterioro con más detalle. (Realizando una serie de ensayos de caracterización no destructivos y otros destructivos, y validando su aplicación a la detección de los deterioros causados tras los ensayos acelerados de hielodeshielo. También mediante aplicación de técnicas de microscopía electrónica.) La tercera campaña, se realizó sobre probetas de hormigón de laboratorio similares a las anteriores, fc de 29,3Mpa y relación a/c de 0,65, en las que se aplicó en una cara un revestimiento asfáltico de 2-4cms, según fueran prismáticas y cilíndricas respectivamente, compuesto por una mezcla asfáltica real (AC16), sobre una imprimación bituminosa. (Para simular el nivel de impermeabilización que produce un firme sobre el tablero de un puente) La cuarta campaña, se desarrolló tras una cuidadosa selección de dos puentes de hormigón de 40-50 años de antigüedad, expuestos y sensibles a deterioros de hielodeshielo, y en carreteras con aportación de fundentes. Una vez esto se extrajeron testigos de hormigón de zonas sanas (nervios del tablero), para realizar en laboratorio los mismos ensayos acelerados de hielo-deshielo y de caracterización, de la segunda campaña, basados en la misma norma. De los resultados obtenidos se concluye que cuando se emplean sales fundentes se acelera de forma significativa el deterioro, aumentando tanto el contenido de agua en los poros como el gradiente generado (mecanismo de deterioro físico). Las sales de deshielo aceleran claramente la aparición del daño, que se incrementa incluso en un factor de 5 según se constata en esta investigación para los hormigones ensayados. Pero además se produce un gradiente de cloruros que se ha detectado tanto en los hormigones diseñados en laboratorio como en los extraídos de puentes existentes. En casi todos los casos han aparecido cambios en la microestructura de la pasta de cemento (mecanismo de deterioro químico), confirmándose la formación de un compuesto en el gel CSH de la pasta de cemento, del tipo Ca2SiO3Cl2, que posiblemente está contribuyendo a la alteración de la pasta y a la aceleración de los daños en presencia de sales fundentes. Existe un periodo entre la aparición de fisuración y la pérdida de masa. Las fisuras progresan rápidamente desde la interfase de los áridos más pequeños y angulosos, facilitando así el deterioro del hormigón. Se puede deducir así que el tipo de árido afecta al deterioro. En el caso de los testigos con recubrimiento asfáltico, parece haberse demostrado que la precipitación de sales genera tensiones en las zonas de hormigón cercanas al recubrimiento, que terminan por fisurar el material. Y se constata que el mecanimo de deterioro químico, probablemente tenga más repercusión que el físico, por cuanto el recubrimiento asfáltico es capaz de retener suficiente agua, como para que el gradiente de contenido de agua en el hormigón sea mucho menor que sin el recubrimiento. Se constató, sin embargo, la importancia del gradiente de cloruros en el hormigon. Por lo que se deduce que si bien el recubrimiento asfáltico es ciertamente protector frente a los ciclos H/D, su protección disminuye en presencia de sales; es decir, los cloruros acabarán afectando al hormigón del tablero del puente. Finalmente, entre los hormigones recientes y los antiguos extraídos de puentes reales, se observa que existen diferencias significativas en cuanto a la resistencia a los ciclos H/D entre ellos. Los hormigones más recientes resultan, a igualdad de propiedades, más resistentes tanto a ciclos de H/D en agua como en sales. Posiblemente el hecho de que los hormigones de los puentes hayan estado expuestos a condiciones de temperaturas extremas durante largos periodos de tiempo les ha sensibilizado. La tesis realizada, junto con nuevos contrastes que se realicen en el futuro, nos permitirá implementar una metodología basada en la extracción de testigos de tableros de puente reales para someterlos a ensayos de hielo-deshielo, basados en la norma europea UNECEN/ TS 12390-9 aunque con probetas no normalizadas para el mismo, y, a su vez, realizar sobre estas probetas otros ensayos de caracterización destructivos, que posibilitarán evaluar los daños ocasionados por este fenómeno y su evolución temporal, para actuar consecuentemente priorizando intervenciones de impermeabilización y reparación en el parque de puentes de la RCE. Incluso será posible la elaboración de mapas de riesgo, en función de las zonas de climatología más desfavorable y de los tratamientos de vialidad invernal que se lleven a cabo. Concrete damage by freeze-thaw cycles in the presence of melting salts frequently causes problems on bridges and infrastructures in European countries. Damage caused by freeze-thaw cycles in the concrete can be internal, essentially cracking and / or external as flaking (surface weathering due to environmental action). The peninsular Spain presents specific climatic and geographical characteristics. 18% of the surface has a height greater than 1,000 m and the geographical average height from the sea level is 660 m (being the second most mountainous country in Europe). This makes the National Road Network affected during certain periods due to adverse weather, particularly snow and ice, which can compromise road conditions for vehicular traffic. For this reason the National Road Authority performs works annually (Winter Road Campaign, along 6 months) to maintain the viability of the roads when they are affected by these phenomena. There are protocols and operational plans that allow systematize these maintenance jobs, that also have intensified in the last 10 years, and which are based on the use of deicing salts, mainly NaCl, with the mission that no ice sheets, or snow appear on the roads. In areas of strong thermal cycling, which in Spain are located in the central area of the Pyrenees, part of the Cantabrian coast and Central System, significant deterioration take place in the structures and wall surfaces of concrete due to freeze-thaw. But also the use of deicing salts for winter maintenance greatly accelerated the development of such damages. The concrete decks for road bridges about 40-50 years old, lack generally a waterproofing system, and are often formed by a pavement of asphalt, an adhesive emulsion and concrete slab. In this thesis the research going on aims to reproduce in the laboratory the processes taking place in the concrete of an existing deck at road bridges, about 40-50 years old, they are exposed for long periods to icing salt, to be performed in order to facilitate winter maintenance, and drastic temperature changes (freezing and thawing). Therefore four campaigns of research were conducted, considering that while we rely on the European standard UNE-CEN/TS 12390-9 "Testing hardened concrete. Freezethaw resistance. Mass loss", nonstandard specimens were fabricated for this test, actually conceived to determine the affection of the cycles only to the mass loss. Dimensions of the samples were in our case 150x300 mm, 75 x 150mm (standard cylindrical specimens for compression fractures UNE-EN 12390-3) and 286x76x76 (standard prismatic specimens to study volume change ASTM C157), which allowed us to carry on same samples more trials, as presented in the thesis, and especially to compare the results with similar sized samples taken from real bridges. In the first campaign, by application of that European standard, freeze-thaw cycles, with and without contact with deicing salt (NaCl 3% solution in compliance with such standard) were performed. Concrete made in the laboratory, trying to simulate the old bridges, provided a compressive strength of 22.6 MPa and water/cement ratio of 0.65. In this activity, the concrete specimens produced were subjected to aggressive freeze/thaw using a maximum temperature of +20ºC and a minimum temperature of - 20°C in order to be able to determine the sensitivity of this test to the concrete and specimens fabricated. This campaign had a second phase to go deeper into the behavior of the specimens subjected to cycled freeze/thaw in the presence of salts. In the second campaign, conducted on similar concrete specimens manufactured in laboratory, temperatures of +20ºC and -14ºC were used in the tests, which allowed us to analyze the deterioration process in more detail (performing a series of non-destructive testing and other destructive characterization, validating its application to the detection of the damage caused after the accelerated freeze-thaw tests, and also by applying electron microscopy techniques). The third campaign was conducted on concrete specimens similar to the above manufactured in laboratory, both cylindrical and prismatic, which was applied on one side a 4 cm asphalt coating, consisting of a real asphalt mixture, on a bituminous primer (for simulate the level of waterproofing that produces a pavement on the bridge deck). The fourth campaign was developed after careful selection of two concrete bridges 40- 50 years old, exposed and sensitive to freeze-thaw damage, in roads with input of melting salts. Concrete cores were extracted from healthy areas, for the same accelerated laboratory freeze-thaw testing and characterization made for the second campaign, based on the same standard. From the results obtained it is concluded that when melting salts are employed deterioration accelerates significantly, thus increasing the water content in the pores, as the gradient. Besides, chloride gradient was detected both in the concrete designed in the laboratory and in the extracted in existing bridges. In all cases there have been changes in the microstructure of the cement paste, confirming the formation of a compound gel CSH of the cement paste, Ca2SiO3Cl2 type, which is possibly contributing to impair the cement paste and accelerating the damage in the presence of melting salts. The detailed study has demonstrated that the formation of new compounds can cause porosity at certain times of the cycles may decrease, paradoxically, as the new compound fills the pores, although this phenomenon does not stop the deterioration mechanism and impairments increase with the number of cycles. There is a period between the occurrence of cracking and mass loss. Cracks progress rapidly from the interface of the smallest and angular aggregate, thus facilitating the deterioration of concrete. It can be deduced so the aggregate type affects the deterioration. The presence of melting salts in the system clearly accelerates the onset of damage, which increases even by a factor of 5 as can be seen in this investigation for concrete tested. In the case of specimens with asphalt coating, it seems to have demonstrated that the precipitation of salts generate tensions in the areas close to the concrete coating that end up cracking the material. It follows that while the asphalt coating is certainly a protection against the freeze/thaw cycles, this protection decreases in the presence of salts; so the chlorides will finally affect the concrete bridge deck. Finally, among the recent concrete specimens and the old ones extracted from real bridges, it is observed that the mechanical strengths are very similar to each other, as well as the porosity values and the accumulation capacity after pore water saturation. However, there are significant differences in resistance to freeze/thaw cycles between them. More recent concrete are at equal properties more resistant both cycles freeze/thaw in water with or without salts. Possibly the fact that concrete bridges have been exposed to extreme temperatures for long periods of time has sensitized them. The study, along with new contrasts that occur in the future, allow us to implement a methodology based on the extraction of cores from the deck of real bridges for submission to freeze-thaw tests based on the European standard UNE-CEN/TS 12390-9 even with non-standard specimens for it, and in turn, performed on these samples other destructive characterization tests, which will enable to assess the damage caused by this phenomenon and its evolution, to act rightly prioritizing interventions improving the waterproofing and other repairs in the bridge stock of the National Road Network. It will even be possible to develop risk maps, depending on the worst weather areas and winter road treatments to be carried out.

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A low-cost vibration monitoring system has been developed and installed on an urban steel- plated stress-ribbon footbridge. The system continuously measures: the acceleration (using 18 triaxial MEMS accelerometers distributed along the structure), the ambient temperature and the wind velocity and direction. Automated output-only modal parameter estimation based on the Stochastic Subspace Identification (SSI) is carried out in order to extract the modal parameters, i.e., the natural frequencies, damping ratios and modal shapes. Thus, this paper analyzes the time evolution of the modal parameters over a whole-year data monitoring. Firstly, for similar environmental/operational factors, the uncertainties associated to the time window size used are studied and quantified. Secondly, a methodology to track the vibration modes has been established since several of them with closely-spaced natural frequencies are identified. Thirdly, the modal parameters have been correlated against external factors. It has been shown that this stress-ribbon structure is highly sensitive to temperature variation (frequency changes of more than 20%) with strongly seasonal and daily trends

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The San Pedro Bridge has six spans and is 750 m (2460 ft) long, 88 m (290 ft) high, 12 m (39 ft) wide, and curved with a radius of 700 m (2300 ft). It was built in 1993 using the cantilever method. Its super - structure is a prestressed concrete box girder with main spans of 150 m (490 ft). In 2008 and 2009, the width of the platform was enlarged to 23 m (75 ft) using five movable sets of scaffolding. The bridge remained open to traffic during construction. The original platform was widened 6 m (20 ft) on each side by connecting a new lightweight concrete cantilever to the original upper slab. These cantilevers were supported by steelstruts. The tie into the upper slab was made with new transverse post-tensioned tendons. The original superstructure was strengthened to resist the additional dead load of the expansion and live loads of the extra traffic. An additional new central web and a composite concrete-steel section were constructed and connected to the concrete box and central web using vertical high-strength post-tensioning bars. Also, external post-tensioning cables were implemented. It was also necessary to strengthen the connection of the original concrete box section to the piers. Detailed calculations were performed to evaluate the load distribution transmitted to the piers by the webs and by the original inclined concrete walls of the box girder. Finally, a detailed second-order-analysis of the complete structure was made to guarantee the resistance of the piers compared with actual loads

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El presente trabajo de investigación se ocupa del estudio de las vibraciones verticales inducidas por vórtices (VIV) en aquellos puentes que, por sus características geométricas y propiedades dinámicas, muestran cierta sensibilidad este tipo de fenómeno aeroelástico. El objeto principal es el análisis del mecanismo de interacción viento-estructura sobre secciones no fuseladas de geometría simple, con objeto de realizar una adecuada caracterización del problema y poder abordar posteriormente el análisis de otras secciones de geometría más compleja, representativas de los principales elementos estructurales de los puentes, como arcos, tableros, torres y pilas. Este aspecto es fundamental durante la fase de diseño del puente, donde deberán tenerse en cuenta también una serie de detalles que pueden influir significativamente su sensibilidad ante problemas aerodinámicos, como la morfología y dimensiones principales de la sección transversal del tablero, la disposición de barreras de seguridad y barreras cortaviento, o las riostras que unen diferentes elementos estructurales. La configuración de dos elementos en tándem o la construcción de un puente en las inmediaciones de otro existente son otros aspectos a considerar respecto a la sensibilidad frente a efectos aeroelásticos. El estudio se ha llevado a cabo principalmente mediante la implementación de simulaciones numéricas que reproducen la interacción entre la corriente de aire y secciones representativas de modelos estructurales, a partir de un código CFD basado en el método de las partículas de vórtices (VPM), siguiendo por tanto un esquema Lagrangiano. Los resultados han sido validados con datos experimentales existentes, valores procedentes de ensayos en túnel de viento y registros reales a partir de diferentes casos de estudio: Alconétar (2006), Niterói (1980), Trans- Tokyo Bay (1995) y Volgogrado (2010). Finalmente, se propone un modelo semi-empírico para la estimación del rango de velocidades críticas y amplitudes de oscilación basado en la utilización de las derivadas de flameo de Scanlan, y la densidad espectral de las fuerzas aerodinámicas en el dominio de la frecuencia. The present research work concerns the study of vertical vortex-induced vibrations (VIV) in bridges which show certain sensitivity to this type of aeroelastic phenomenon. It focuses on the analysis of the wind-structure interaction mechanism on bluff sections, with the objective of making a good characterisation of the problem and subsequently addressing the analysis of sections with a complex geometry, which are representative of the bridge structural elements, such as arches, decks, towers and piers. This issue is of relative importance during the bridge design phase, since minor details of the aforementioned elements can significantly influence its sensitivity to aerodynamic problems. The shape and main dimensions of the deck cross section, the addition of safety barriers and windshields, the presence of braces to enhance the structure mechanical properties, the utilisation of cross sections in tandem arrangement, or the erection of a new bridge in the vicinity of another existing one are some of the aspects to be considered regarding the sensitivity to the aeroelastic effects. The study has been carried out mainly through the implementation of numerical simulations that reproduces the interaction between the airflow and the representative cross section of a structural bridge model, by the use of a CFD code based on the vortex particle method (VPM), thus following a Lagrangian scheme. The results have been validated with existing experimental data, values from wind tunnel tests and full scale observations from the different case studies: Alconétar (2006), Niterói (1980), Trans-Tokyo Bay (1995) and Volgograd (2010). Finally, a new semi-empirical model is proposed for the estimation of the critical wind velocity ranges and oscillation amplitudes based on the use of the Scanlan’s flutter derivatives and the power spectral density of aerodynamic force time history in the frequency domain.

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The lower stability limit for axisymmetric floating zones at rest between equal coaxial disks has been experimentally verified for several disk-separation/disk-diameter ratios by using the neutral buoyancy technique. Results show a close agre ment with theory in the case of bridge disruption and a wide scatter in the case of bridge etachment.

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Besides space laboratories for in-orbit experimentation, Earth based facilities for laboratory experimentation are of paramount importance for the enhancement on liquid bridge knowledge. In spite of the constraints imposed by simulated microgravity (which force to work either with very small size liquid bridges or by using the Plateau tank technique, amongst other techniques), the availability and accessibility of Earth facilities can circumvent in many cases the drawbacks associated with simulated microgravity conditions. To support theoretical and in orbit experimental studies on liquid bridges under reduced gravity conditions, several ground facilities were developed at IDR. In the following these ground facilities are briefly described, and main results obtained by using them are cited.

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Underbridge: relocalización del Gujari Bazaar bajo el Ellis Bridge, Ahmedabad, India

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The wavelet transform and Lipschitz exponent perform well in detecting signal singularity.With the bridge crack damage modeled as rotational springs based on fracture mechanics, the deflection time history of the beam under the moving load is determined with a numerical method. The continuous wavelet transformation (CWT) is applied to the deflection of the beam to identify the location of the damage, and the Lipschitz exponent is used to evaluate the damage degree. The influence of different damage degrees,multiple damage, different sensor locations, load velocity and load magnitude are studied.Besides, the feasibility of this method is verified by a model experiment.

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Although the primary objective on designing a structure is to support the external loads, the achievement of an optimal layout that reduces all costs associated with the structure is an aspect of increasing interest. The problem of finding the optimal layout for bridgelike structures subjected to a uniform load is considered. The problem is formulated following a theory on economy of frame structures, using the stress volume as the objective function and including the selection of appropriate values for statically indeterminate reactions. It is solved in a function space of finite dimension instead of using a general variational approach, obtaining near-optimal solutions. The results obtained with this profitable strategy are very close to the best layouts known to date, with differences of less than 2% for the stress volume, but with a simpler layout that can be recognized in some real bridges. This strategy could be a guide to preliminary design of bridges subject to a wide class of costs.