Ao contrário da catenária, o estudo da parábola é encontrado com freqüência nos livros didáticos de matemática. Dois livros didáticos foram analisados para esta pesquisa: o livro de Olavo Freire de 1894, que associa o formato do cabo pênsil ao de uma parábola, e o livro da década de 1970 de Osvaldo Sangiorgi, que relaciona à figura de um balanço a forma de uma parábola. Notamos que esses livros didáticos com oitenta anos de diferença usam a corda suspensa para representar a forma parabólica. Como o formato de um cabo suspenso pelas extremidades sob a ação do seu próprio peso é representado pela catenária, sentimo-nos motivados a pesquisar sobre as curvas e entender por quais delas, afinal, o cabo da ponte pênsil é mais bem representado. Visto que essa dúvida surgiu a partir de livros didáticos, discorremos sobre a função do livro de matemática, na sala de aula, como indicadores do ensino da matemática, de um determinado local, dentro de determinado contexto histórico-político. No decorrer da história da matemática, houve confusão entre essas duas curvas, a qual motivou o estudo da catenária a partir do século XVII. Essa fase da história é conhecida como época das curvas, e em 1600, por Huygens, que se iniciaram seus estudos. Examinamos as curvas catenária e parábola no âmbito da educação e da história da matemática, bem como suas propriedades e aplicações práticas no âmbito da engenharia de pontes pênseis e na arquitetura. Amparamo-nos em leituras específicas de construção e história de algumas pontes pênseis e chegamos a visitar a Ponte Estaiada em São Paulo ainda em edificação, para entendermos como os engenheiros utilizam as propriedades das curvas catenária e parábola em sua construção. Os resultados revelaram que, surpreendentemente, o exemplo adotado no livro de Olavo Freire para representar uma parábola não levou em consideração o que acontece na prática da engenharia das pontes pênseis, e o ressurgimento do exemplo do balanço no livro de Osvaldo Sangiorgi, pareceu reforçar a tese de que havia, sim, certa confusão entre as duas curvas. Utilizando o software gráfico Winplot, construímos as curvas catenária e parábola e pudemos visualizar as diferenças ou similaridades entre elas. Finalizando, comprovamos algebricamente a aproximação entre as curvas catenária e parábola e a definição de parábola no ponto de vista da engenharia. / Unlike the catenary, the study of the parabola is often found in textbooks of Mathematics. Two textbooks were analyzed for this research: the book of Olavo Freire, 1894, which combines the format of the cable suspended to a parabola, and the book of the decade of 1970 of Osvaldo Sangiorgi, which relates to the figure of a stock as a parabola. Note that these textbooks with eighty years of difference used the rope suspended to represent the parabolic shape. As the format of a cable suspended by the extremities under the action of its own weight is the catenary, we felt motivated to search on the curves and understand how, after all, the cable of the suspension bridge is best represented. Since this question came from textbooks, we studied the basis of the book of Mathematics in the classroom, as indicators of teaching Mathematics in a given location, within a certain historical and political context. Throughout the history of Mathematics, there was confusion between these two curves, which led the study of catenary from the seventeenth century. This phase of history is known as the curves season, and in 1600, by Huygens, who started their studies. We have audited the catenary curves and parabola in education and the history of Mathematics, and its properties and practical applications in the Engineering of suspension bridges and architecture. Supported us in specific readings of history and construction of some suspension bridges and even payed a visit to the bridge Estaiada in Sao Paulo which is still under construction, to understand how the engineers use the properties of the catenary curves and parabola in its construction. The results showed that, surprisingly, the example used in the book of Olavo Freire to represent a parabola did not bring into account what happens in the practice of Engineering of the suspension bridges, and the resurgence of the example of the balance sheet in the book of Osvaldo Sangiorgi seemed to strengthen the argument that there was some confusion between the two curves. Using the software chart Winplot, the catenary and parabola curves were built and we could visualize the differences or similarities between them. At last, using algebra we proved the rapprochement between the catenary curves and definition of parabola in terms of Engineering.

Joints are the most critical elements in a steel framed structure. In most design guides or codes, the joints are assumed to a have higher fire resistance than the connected structural members because of the lower temperatures in the joints. However, in severe fire conditions, a connected beam's temperature may be higher than its limiting temperature and the beam may develop catenary action when the beam’s axial shortening from large deflections becomes greater than the beam’s thermal expansion. This beam catenary action force could fracture the joints, increasing the risk of progressive collapse. This research focuses on the interaction between joints and the connected steel beams and columns in steel framed structures in fire, including how the behaviour of a joint-beam assembly may be efficiently analyzed and how the joints may be constructed to achieve high degrees of catenary action. Three methods of simulating the joint behaviour in fire have been developed and implemented in the commercial finite element software ABAQUS. In the first modelling method, all structural members, including the connections, were simulated using detailed solid elements to enable detailed behaviour of the structure to be faithfully represented. In the second method, the columns were represented by conventional line (beam) elements, the joints were represented using springs (Connector Elements) based on the component based method, and the beam was modelled using solid elements. In the third method, the joints were modelled using springs as in the second method and the beam and columns were simulated using line (beam) elements. As expected, the detailed simulation method was extremely time-consuming, but was able to produce detailed and accurate results. The simulation results from the second and third methods contained some inaccuracies, but depending on the simulation objective, their simulation results may be acceptable. In particular, the third simulation method was very efficient, suitable for simulating complete frame structures under very large deflections in fire. The first method (detailed finite element method) was then used to investigate how to change the joint details to increase the survivability of restrained steel beams and beam-column assemblies at high temperatures since it enables detailed behaviour of the structure to be faithfully represented. It is found that by improving joint deformation capacity, in particular, using extended endplate connection with fire resistant bolts, very high temperatures can be resisted. The frame robustness in fire was investigated using the third simulation method to save computation time. The simulation structure was three-bay by three-floor and different scenarios of fire location, fire spread and initial structural damage were considered. The simulation results show that once failure of a column occurs, progressive collapse of the structure could be easily triggered and it would be rather futile to only enhance the joint capacity. Therefore, in addition to the measures of improving joint capacities (both rotation and strength), design of the affected columns should include consideration of the additional catenary forces from the connected beams and the increased effective lengths. Furthermore, the lateral bracing system should be ensured to provide the structure with lateral restraint.

This thesis presents the stability analysis of an Electric Road System (ERS), which is often abbreviated as eHighway, used for the electrification of the hybrid vehicle. The overall system modelling of the ERS, starting from the sub-station to the critical part of the Scania hybrid truck is performed in the MATLAB Simulink environment. The ERS consists of an overhead catenary line (OCL), where vehicles are electrified by using a pantograph mounted over the vehicle. The stability analysis of the power supply of the overhead line is done by taking into account several aspects of the system. The simulation results are validated with the real test track measurements and the deviations are shown. The frequency response of the system is considered to measure the stability margin. The resonance conditions are clarified and essential variable choke is proposed to damp them out. Also the harmonic components injected from the vehicle side, that are in the closer range of the resonance, are figured out and filtered. When multiple vehicles are electrified from the same catenary line, then there are interferences in between the vehicles. These disturbances both to the vehicles and the overhead power supply system are presented in the time domain. Finally, the results are shown to demonstrate the effectiveness of the variable choke to increase the stability margin in the overhead supply system. In the frequency domain results, it has shown that the resonance is shifted out of the system operating frequency. In the time domain results, it has shown that the high amplitude of the current and voltage signals are sufficiently damped out by variable choke implementation.

Afin de réduire les émissions de gaz à effet de serre et le coût du transport maritime, l'utilisation des cerfs-volants comme système de propulsion auxiliaire des navires est prometteuse. Pour estimer les performances et l’opérabilité d’un navire tracté par cerf-volant, une modélisation dynamique du système est alors mise en oeuvre. Une modélisation analytique de cerf-volant est utilisée. Ce modèle néglige la masse du cerf-volant et suppose que les lignes sont droites et indéformables. Ces hypothèses conduisent à un modèle cinématique dépendant du coefficient de portance et de la finesse aérodynamique. Une évolution linéaire des coefficients aérodynamiques en fonction de la courbure de la trajectoire de vol est proposée. Par ailleurs, en développant un modèle quasi analytique de ligne, il est montré qu’à partir de 2 m.s-1 de vent relatif que l’hypothèse de ligne droite est raisonnable. En se basant sur un modèle de ligne, un critère analytique de vitesse de vent minimum permettant un vol quasi-statique est présenté. Dans le but de résoudre l’ensemble des termes d’interaction entre le cerf-volant et le navire, un modèle linéarisé de tenue à la mer temporelle est développé. Le produit de convolution de la réponse impulsionnelle du navire est calculé avec des systèmes d’états. Cependant comme celle-ci représente mal les mouvements horizontaux des navires, le modèle développé est alors couplé à un modèle de manoeuvrabilité. Pour étudier les interactions entre le cerf-volant et le navire un couplage monolithique et un couplage dissocié sont comparés. Le couplage dissocié néglige l’influence des mouvements du navire sur le vol du cerf-volant. En cas de mer calme, les résultats obtenus par les deux types de couplage sont très proches. En cas de houle régulière les mouvements du navire sont principalement causés par la houle. Le couplage monolithique montre qu’un réseau de sous-harmoniques basse fréquence apparait alors dans le spectre d’excitation du navire. La fréquence fondamentale des sous-harmoniques est donnée par la différence entre la fréquence de vague et la fréquence de l’harmonique la plus proche de l’excitation du kite. Quand cette différence est suffisamment petite, un phénomène d’accrochage apparait. Ce phénomène est bénéfique pour le cerf-volant et le navire quand le décalage des harmoniques d'excitation correspond à une augmentation. Par ailleurs, une étude de la stabilité de route montre qu'il est nécessaire de contrôler activement le safran. / In order to reduce greenhouse gas emissions and shipping costs, the use of kites as an auxiliary propulsion device for ships is promising. In order to estimate the performance and the operability of a kite-towed vessel, a dynamic modeling of the system is implemented. A classical kite modeling is used. This model neglects the mass of the kite and assumes straight and inelastic tethers. These assumptions lead to a kinematic model depending on the lift coefficient and the aerodynamic lift to drag ration angle. A linear evolution of these aerodynamic coefficients as a function of the curvature of the flight path is proposed. In addition, by developing a quasi-analytical line model, it is shown that from 2 m.s-1 of relative wind the straight tether assumption is reasonable. Based on the tether model, an analytical criterion assessing the minimum wind speed to enable a quasi-static kite flight is developed. To solve all the interaction terms between the kite and the ship, a time domain seakeeping model based on the linearized ship equation of motion assuming a potential flow is developed. The convolution product of the impulse response of the ship is computed with state-space systems. However, since horizontal ship motions are not well represented by such theories, a coupling with a maneuvering model is presented.Comparisons to experimental data tests show good agreements. To study the interactions between the kite and the ship, a monolithic coupling and a dissociated coupling are compared. The dissociated coupling neglects the influence of ship motions on the kite flight. In a calm water case, results obtained by the two types of coupling are very close. In regular waves, ship motions are dominated by the wave influence. Thus, with the monolithic coupling, a network of low frequency subharmonic appears in the kite excitation spectrum. The fundamental frequency of the subharmonic is given by the difference between the wave frequency and the frequency of the nearest kite excitation harmonic. When this difference is small enough, a lock-in phenomenon appears. This phenomenon is a benefit for the kite and the ship when the shift of the excitation harmonics corresponds to an increase. Furthermore, a course keeping stability study shows that the rudder needs to be actively controlled.

Railways are a main element of a sustainable transport policy in several countries as they are considered a safe, efficient and green mode of transportation. Owing to these advantages, there is a cumulative request for the railway industry to increase the performance, the capacity and the availability in addition to safely transport goods and people at higher speeds. To meet the demand, large adjustment of the infrastructure and improvement of maintenance process are required.  Inspection activities are essential in establishing the required maintenance, and it is periodically required to reduce unexpected failures and to prevent dangerous consequences.  Maintenance of railway catenary systems is a critical task for warranting the safety of electrical railway operation.Usually, the catenary inspection is performed manually by trained personnel. However, as in all human-based inspections characterized by slowness and lack of objectivity, might have a number of crucial disadvantages and potentially lead to dangerous consequences. With the rapid progress of artificial intelligence, it is appropriate for computer vision detection approaches to replace the traditional manual methods during inspections.  In this thesis, a strategy for monitoring the health of catenary wires is developed, which include the various steps needed to detect anomalies in this component. Moreover, a solution for detecting different types of wires in the railway catenary system was implemented, in which a deep learning framework is developed by combining the Convolutional Neural Network (CNN) and the Region Proposal Network (RPN).

This thesis confronts the possibility of an architecture which limits and reveals, freedom for a way to live, for the activities of man which are vital to a good life. An architecture which is investigated and projected through making. Architecture Separates and makes Distinct, while finding meaningful connection. The work of drawing here attempts to project an architecture which is vital to man, by providing a connection to the activities of Man, in which the spirit of their beginning is recaptured and renewed through a reimagining of the Institutions of Man. Where a sense of Wonder is imperative, and the sense of the eternal in architecture is cultivated. One where a renewal is possible and sense of the cosmos is more evident. On the Threshold of 'Where the desire to express meets the possible' (Kahn) using architectural form. Awareness What is the form? Beginning with the room / Master of Architecture

O estudo do fenômeno de vibrações induzidas pela emissão de vórtices, ou VIV, em risers é um tópico de grande relevância para a engenharia oceânica. Nos últimos anos, diversos resultados vêm sendo apresentados, numéricos e/ou experimentais, buscando o entendimento dos fundamentos deste fenômeno de interação fluido-estrutural, no entanto, sem um entendimento conclusivo e abrangente. Neste contexto, risers também estão sujeitos à ação de correntezas oceânicas e, consequentemente, ao fenômeno de VIV. Neste sentido, o presente estudo traz resultados de uma abordagem experimental para o entendimento do fenômeno de VIV em risers lançados em catenária, configuração que representa grande parte das geometrias adotadas em lançamentos atuais. No entanto, a realização de experimentos com risers em tanque de provas pressupõe a utilização de modelos reduzidos, o que, por si só, representa um grande desafio de pesquisa. Para tanto, desenvolveu-se uma metodologia para a modelagem de risers em escala reduzida, com foco na similaridade entre parâmetros importantes que garantam um comportamento dinâmico equivalente àquele em escala real. Foram, então, realizados experimentos de VIV com catenárias concebidas e construídas com base nesta metodologia, posteriormente ensaiadas em tanque de reboque. Para análise dos resultados, foram utilizadas técnicas como a decomposição modal, que possibilitou a comparação desses com alguns resultados da literatura, mostrando que o fenômeno de VIV na catenária se processa de maneira bastante semelhante ao identificado nos cilindros flexíveis. Além disso, a extensa base de dados experimentais apresentada e discutida nesta tese contribui para futura validação de diversos modelos matemáticos e códigos numéricos de predição do VIV em catenárias, descrevendo com detalhes inúmeros comportamentos imersos neste problema importante de engenharia. / The study of Vortex-induced vibrations in risers is a topic of great relevance in the context of ocean engineering. In recent years, several numerical and experimental results have been presented, addressing the understanding of the fundamentals of this fluid-structure interaction phenomenon, however without a conclusive and comprehensive understanding. In this context, risers are exposed to the action of ocean currents and consequently to the phenomenon of VIV. In this sense, the present study provides results of an experimental approach to understanding the VIV phenomenon on risers launched in catenary configuration, which represents much of the geometries adopted today. However, performing risers experiments in towing-tanks presupposes the use of small-scale models, which represents a major research challenge. Therefore, a methodology for modeling reduced scale risers was developed. The focus of this methodology was on the similarity between certain important parameters that guarantee an equivalent full-scale dynamic behavior. VIV experiments were then performed in the towing tank, with the designed and constructed catenary, based on this methodology. Techniques such as modal decomposition were used for the analysis of the results. This allows the comparison of the results with classical literature paradigms showing that VIV response in the catenary is close to results obtained with flexible cylinders. Furthermore, the large experimental database presented and discussed in the study may contribute to future validation of several mathematical models and numerical codes of VIV prediction in catenary risers, describing in detail several immersed behaviors in this important engineering problem.

O estudo do fenômeno de vibrações induzidas pela emissão de vórtices, ou VIV, em risers é um tópico de grande relevância para a engenharia oceânica. Nos últimos anos, diversos resultados vêm sendo apresentados, numéricos e/ou experimentais, buscando o entendimento dos fundamentos deste fenômeno de interação fluido-estrutural, no entanto, sem um entendimento conclusivo e abrangente. Neste contexto, risers também estão sujeitos à ação de correntezas oceânicas e, consequentemente, ao fenômeno de VIV. Neste sentido, o presente estudo traz resultados de uma abordagem experimental para o entendimento do fenômeno de VIV em risers lançados em catenária, configuração que representa grande parte das geometrias adotadas em lançamentos atuais. No entanto, a realização de experimentos com risers em tanque de provas pressupõe a utilização de modelos reduzidos, o que, por si só, representa um grande desafio de pesquisa. Para tanto, desenvolveu-se uma metodologia para a modelagem de risers em escala reduzida, com foco na similaridade entre parâmetros importantes que garantam um comportamento dinâmico equivalente àquele em escala real. Foram, então, realizados experimentos de VIV com catenárias concebidas e construídas com base nesta metodologia, posteriormente ensaiadas em tanque de reboque. Para análise dos resultados, foram utilizadas técnicas como a decomposição modal, que possibilitou a comparação desses com alguns resultados da literatura, mostrando que o fenômeno de VIV na catenária se processa de maneira bastante semelhante ao identificado nos cilindros flexíveis. Além disso, a extensa base de dados experimentais apresentada e discutida nesta tese contribui para futura validação de diversos modelos matemáticos e códigos numéricos de predição do VIV em catenárias, descrevendo com detalhes inúmeros comportamentos imersos neste problema importante de engenharia. / The study of Vortex-induced vibrations in risers is a topic of great relevance in the context of ocean engineering. In recent years, several numerical and experimental results have been presented, addressing the understanding of the fundamentals of this fluid-structure interaction phenomenon, however without a conclusive and comprehensive understanding. In this context, risers are exposed to the action of ocean currents and consequently to the phenomenon of VIV. In this sense, the present study provides results of an experimental approach to understanding the VIV phenomenon on risers launched in catenary configuration, which represents much of the geometries adopted today. However, performing risers experiments in towing-tanks presupposes the use of small-scale models, which represents a major research challenge. Therefore, a methodology for modeling reduced scale risers was developed. The focus of this methodology was on the similarity between certain important parameters that guarantee an equivalent full-scale dynamic behavior. VIV experiments were then performed in the towing tank, with the designed and constructed catenary, based on this methodology. Techniques such as modal decomposition were used for the analysis of the results. This allows the comparison of the results with classical literature paradigms showing that VIV response in the catenary is close to results obtained with flexible cylinders. Furthermore, the large experimental database presented and discussed in the study may contribute to future validation of several mathematical models and numerical codes of VIV prediction in catenary risers, describing in detail several immersed behaviors in this important engineering problem.

På den svenska järnvägen används två olika återledningssystem på kontaktledningen, autotransformatorsystem och boostertransformatorsystem. De flesta sträckor i Sverige har idag boostertransformatorsystem. I takt med utvecklingen av järnvägen så ställs det andra krav på banorna, till exempel införandet av höghastighetståg. Problemformuleringen blev således frågan om vilket system som föredras vid upprustning eller nybyggnad av järnvägen. Beräkningar på överföringsförmåga beroende på spänningshållningen i systemen samt en modell för en livscykelkostnadsanalys gav svaren på hur skillnaden ser ut i dessa system från ett tekniskt och ekonomiskt perspektiv. Resultaten visar att båda systemen fungerar på den svenska järnvägen. Beroende på hur trafiken, banutformningen samt kostnaderna för ett enskilt system ser ut kan båda systemen användas. Resultatet visar också att vid låg trafiktäthet har AT-systemet större energiförluster än ett BT-system. Vid hög trafiktäthet har ett BT-system större energiförluster än ett AT-system. Resultaten visar också att autotransformator-systemet har en bättre överföringsförmåga av effekt men är dyrt. Boostertransformatorsystemet å andra sidan har en sämre överföringsförmåga av effekt men är billigare. / On the Swedish railway, two different return systems are used on the overhead line, autotransformer systems and booster transformer systems. Most routes in Sweden today have booster transformer systems. In step with the development of the railway, other requirements are placed on the lines, for example the introduction of high-speed trains. The problem formulation thus became the question of which system is preferred for upgrading or new construction of the railway. Calculations of transmission capacity depending on the voltage control in the systems and a model for a life cycle cost analysis gave the answers to what the difference looks like in these systems from a technical and economic perspective. The results show that both systems work on the Swedish railway. Depending on the traffic, track design and costs of an individual system, both systems can be used. The results also show that at low traffic density, the AT system has greater energy losses than a BT system. At high traffic density, a BT system has greater energy losses than an AT system. The results show that the autotransformer system has a better transmission capacity of power but is expensive. The booster transformer system, on the other hand, has a poorer transmission capacity of power but is cheaper.

Der Vortrag beschreibt, wie sich mittels Kettenlinien als Kerbgeometrie der Spannungskonzentrationsfaktor an Querschnittsübergängen auf nahezu 1 reduzieren lässt. Mittels globaler Sensitivitätsstudien in der p-FEM-Software Creo Simulate wird mithilfe eines in Creo Parametric parametrisierten CAD-Modells der Kettenlinie in Parameterdarstellung ein normiertes Kerbzahldiagramm erstellt. Dieses erlaubt die Dimensionierung einer Kerbe, d.h. die Festlegung ihrer exakten Geometrie und der damit verbundenen Kerbzahl αk ohne die weitere Verwendung eines FEM-Programmes. / The presentation describes how to reduce the stress concentration factor at cross section transitions to nearly 1 by using a catenary curve as notch geometry (catenary fillet). With help of global sensitivity studies performed in the p-FEM-code Creo Simulate, a normalized stress concentration factor diagram is drawn. Therefore, a CAD-model of the catenary curve in parametric representation was developed. The diagram created allows to dimension the notch, that means to determine its exact geometry and stress concentration factor Kt, without further usage of a FEM code.