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.

The field of monitoring is one of rapid development. Advances in sensor technologies, in data communication paradigms and data processing algorithms all influence the possibilities of Structural Health Monitoring, damage detection, traffic monitoring and other implementations of monitoring systems. Bridges are a very critical part of a country’s infrastructure, they are expensive to build and maintain, and many uncertainties surround important factors determining the serviceability and deterioration of bridges. As such, bridges are good candidates for monitoring. Monitoring can extend the service life and avoid or postpone replacement, repair or strengthening work. Many bridges constitute a bottleneck in the transport network they serve with few or no alternative routes. The amount of resources saved, both to the owner and the users, by reducing the amount of non-operational time can easily justify the extra investment in monitoring. This thesis consists of an extended summary and three appended papers. The thesis presents advances in sensor technology, damage identification algorithms and Bridge Weigh-In-Motion techniques. Two case studies are carried out. In the first a bridge and traffic monitoring system is implemented in a highway suspension bridge to study the cause of unexpected wear in the bridge bearings. In the second a fully operational Bridge Weigh-In-Motion system is developed and deployed in a steel railway bridge. The gathered data was studied to obtain a characterization of the site specific traffic. / QC 20111122

Este trabalho apresenta o desenvolvimento de metodologia para avaliar a utilização do Sistema de Posicionamento Global (GPS) como ferramenta de pesquisa no estudo do comportamento dinâmico de obras viárias. Para ser caracterizado como um instrumento de medição, foi estudada a potencialidade de um método, que se fundamenta numa forma específica de coleta e processamento de dados GPS; análise dos resíduos resultantes do processamento da dupla diferença de fase e aplicação de análise espectral para filtragem de informações indesejáveis (multicaminhamento dos sinais GPS). A coleta envolve um oscilador eletro-mecânico, especialmente projetado, que permite calibrar as medidas de amplitude e freqüência das oscilações mensuráveis pela obra sob teste. Inúmeros experimentos foram realizados em ambientes de reflexões e difrações variáveis e com diversos tipos de receptores e antenas GPS. Alguns ensaios foram realizados utilizando, simultaneamente, equipamentos como transdutores de deslocamento, acelerômetros e estações totais. Comparando os resultados obtidos, mesmo com valores prescritos em normas e códigos, afirma-se que o GPS, sob o método de coleta de dados testado, é um instrumento confiável para detecção e caracterização do comportamento dinâmico de estruturas, apresentado confiabilidade para as medições realizadas, da ordem de décimos de milímetro. Quanto à detecção das freqüências, as mais baixas ficam comprometidas pela presença do multicaminhamento e as mais elevadas têm a detecção limitada pela máxima taxa de coleta dos receptores (Lei de Nyquist) / This work presents the development of a methodology to appraise the use of Global Positioning System (GPS) as a tool for researching of dynamic behavior of road transport structures. To be characterized as an instrument for measuring it was studied the potentiality of one method which includes a specific mode of GPS data collection; analyses of double difference phase residuals and application of spectral analyses and filtering for excluding undesirable information (multipath). The GPS data collected applies an electro-mechanical oscillator, specially built for that, which permits to calibrate the measures of frequency and amplitude of structure’s oscillations under dynamic load test. Several field tests were carried out in vicinities with high and low capacity of causing signal reflections and diffractions and with different types of GPS receivers and GPS antennas. A couple of fields were carried out using, at the same time, transducers of displacement, accelerometers and total stations. Comparing these results obtained even with values of codes, it is affirmed that GPS, under the data collection method tested, it is a trustworthy instrument for detection and characterization of dynamic behavior of structures, presenting reliability of measures ranging around tenths of millimeters. The very low frequencies are highly degraded by multipath and very high frequencies have its detection limited by the receiver data rate (Theorem’s Nyquist)

As características arquitetônicas e o desempenho estrutural de pontes suspensas, estaiadas ou pênseis, têm determinado a sua crescente utilização em obras de arte destinadas a vencer grandes vãos. Essa utilização crescente que ocorreu no mundo nas últimas décadas se repete agora nos últimos anos no país. Várias dessas obras estão em execução e em projeto. Um dos aspectos relevantes na análise estrutural das pontes suspensas é o de seu comportamento quando submetidas à ação do vento. Apresenta-se o sistema computacional ANA-PSp desenvolvido especialmente para o estudo do movimento de tabuleiros de pontes suspensas sujeitas a esforços aeroelásticos e aerodinâmicos. Esse sistema computacional formado por um conjunto de subsistemas, é elaborado para a análise aeroelástica de pontes suspensas sob a ação de vento e permite análises paramétricas extensas dos fenômenos de drapejamento (flutter) e de martelamento (buffeting). A discretização da estrutura é efetuada pelo método dos elementos finitos e a redução dos graus de liberdade é realizada por superposição modal com modos selecionados que melhor descrevem os movimentos do tabuleiro. Utiliza-se modelo matemático reduzido para a análise multimodal no domínio do tempo e da freqüência. A velocidade crítica ou velocidade de drapejamento é determinada por procedimento de autovalores complexos com a obtenção de freqüências e taxas de amortecimentos modais para várias velocidades do vento. Adicionalmente, o fenômeno do drapejamento é estudado por séries temporais de respostas de coordenadas generalizadas e de deslocamentos selecionados e por análise espectral dessas séries temporais, que permitem a verificação das características de vibração do tabuleiro da ponte no domínio da freqüência. O estudo do fenômeno de martelamento considera esforços aeroelásticos determinísticos e esforços aerodinâmicos estocásticos e apresentam-se resultados em espectros de potência de deslocamentos e em desvios padrão de deslocamentos ao longo do tabuleiro. Para validar o sistema ANA-PSp, apresentam-se estudos de caso para a ponte estaiada da Normandia, para a ponte pênsil colapsada de Tacoma Narrows e para a ponte estaiada projetada, mas não executada, sobre o Rio Tietê e localizada na extremidade do complexo viário Jacu-Pêssego. / The architectonic characteristics and the structural performance of suspension bridges and cable-stayed bridges have determined their growing use on large span bridges. This growing usage, which has occurred world-wide during the last decades, is now being repeated in Brazil during the last few years. Several such bridges are presently either undergoing construction or being designed. One of the outstanding aspects in the structural analysis of suspension bridges is their behavior under wind action. This paper presents the computer system ANA-PSp, specially developed for studying the movement of suspended bridge decks under aeroelastic and aerodynamic forces. This computer system is formed by a group of subsystems and is created for aeroelastic analysis of suspended bridges under wind action. It allows extended parametric analyses of the flutter and the buffeting phenomena. Structural discretization is done by the finite element method and the reduction of degrees of freedom is obtained by modal superposition of the selected modes which best describe the deck movements. A reduced mathematical model is used for the multimodal analysis in the time and frequency domains. Critical velocity or flutter velocity is determined by a procedure of complex eigenvalues which obtains frequencies and damping ratios for different wind speeds. Additionally, the flutter phenomenon is studied by temporal series of answers to generalized coordinate responses and of selected displacements by spectral analysis of such temporal series, which allow us to verify the characteristics of the vibrations of the bridge deck in the frequency domain. The study of the buffeting phenomenon considers deterministic aeroelastic and stochastic aerodynamic forces. The paper presents results in displacement power spectra and in the standard deviation of displacements along the deck. In order to validate system ANA-PSp, case studies are presented for the cable-stayed Ponte de Normandie in Le Havre (France), for the collapsed suspension bridge on Tacoma Narrows and for the cable-stayed bridge, already designed but not built, on Tietê River, located at one end of the highway complex Jacu-Pêssego (São Paulo, SP, Brazil).

Due to the emergence of new materials and advanced engineering technology, slender footbridges are increasingly becoming popular to satisfy the modern transportation needs and the aesthetical requirements of society. These structures however are always &quotlively" with low stiffness, low mass, low damping and low natural frequencies. As a consequence, they are prone to vibration induced by human activities and can suffer severe vibration serviceability problems, particularly in the lateral direction. This phenomenon has been evidenced by the excessive lateral vibration of many footbridges worldwide such as the Millennium Bridge in London and the T-Bridge in Japan. Unfortunately, present bridge design codes worldwide do not provide sufficient guidelines and information to address such vibrations problems and to ensure safety and serviceability due to the lack of knowledge on the dynamic performance of such slender vibration sensitive bridge structures. A conceptual study has been carried out to comprehensively investigate the dynamic characteristics of slender suspension footbridges under human-induced dynamic loads and a footbridge model in full size with pre-tensioned reverse profiled cables in the vertical and horizontal planes has been proposed for this purpose. A similar physical suspension bridge model was designed and constructed in the laboratory, and experimental testings have been carried out to calibrate the computer simulations. The synchronous excitation induced by walking has been modelled as crowd walking dynamic loads which consist of dynamic vertical force, dynamic lateral force and static vertical force. The dynamic behaviour under synchronous excitation is simulated by resonant vibration at the pacing rate which coincides with a natural frequency of the footbridge structure. Two structural analysis software packages, Microstran and SAP2000 have been employed in the extensive numerical analysis. Research results show that the structural stiffness and vibration properties of suspension footbridges with pre-tensioned reverse profiled cables can be adjusted by choosing different structural parameters such as cable sag, cable section and pretensions in the reverse profiled cables. Slender suspension footbridges always have four main kinds of vibration modes: lateral, torsional, vertical and longitudinal modes. The lateral and torsional modes are often combined together and become two kinds of coupled modes: coupled lateral-torsional modes and coupled torsionallateral modes. Such kind of slender footbridges also have different dynamic performance in the lateral and vertical directions, and damping has only a small effect on the lateral vibration but significant effect on the vertical one. The fundamental coupled lateral-torsional mode and vertical mode are easily excited when crowd walking dynamic loads are distributed on full bridge deck. When the crowd walking dynamic loads are distributed eccentrically on half width of the deck, the fundamental coupled torsional-lateral mode can be excited and large lateral deflection can be induced. Higher order vertical modes and coupled lateral-torsional modes can also be excited by groups of walking pedestrians under certain conditions. It is found that the coupling coefficient introduced in this thesis to describe the coupling of a coupled mode, is an important factor which has significant effect on the lateral dynamic performance of slender suspension footbridges. The coupling coefficient, however, is influenced by many structural parameters such as cable configuration, cable section, cable sag, bridge span and pre-tensions, etc. In general, a large dynamic amplification factor is expected when the fundamental mode of a footbridge structure is the coupled lateral-torsional mode with a small coupling coefficient. The research findings of this thesis are useful in understanding the complex dynamic behaviour of slender and vibration sensitive suspension footbridges under humaninduced dynamic loads. They are also helpful in developing design guidance and techniques to improve the dynamic performance of such slender vibration sensitive footbridges and similar structures and hence to ensure their safety and serviceability.

As características arquitetônicas e o desempenho estrutural de pontes suspensas, estaiadas ou pênseis, têm determinado a sua crescente utilização em obras de arte destinadas a vencer grandes vãos. Essa utilização crescente que ocorreu no mundo nas últimas décadas se repete agora nos últimos anos no país. Várias dessas obras estão em execução e em projeto. Um dos aspectos relevantes na análise estrutural das pontes suspensas é o de seu comportamento quando submetidas à ação do vento. Apresenta-se o sistema computacional ANA-PSp desenvolvido especialmente para o estudo do movimento de tabuleiros de pontes suspensas sujeitas a esforços aeroelásticos e aerodinâmicos. Esse sistema computacional formado por um conjunto de subsistemas, é elaborado para a análise aeroelástica de pontes suspensas sob a ação de vento e permite análises paramétricas extensas dos fenômenos de drapejamento (flutter) e de martelamento (buffeting). A discretização da estrutura é efetuada pelo método dos elementos finitos e a redução dos graus de liberdade é realizada por superposição modal com modos selecionados que melhor descrevem os movimentos do tabuleiro. Utiliza-se modelo matemático reduzido para a análise multimodal no domínio do tempo e da freqüência. A velocidade crítica ou velocidade de drapejamento é determinada por procedimento de autovalores complexos com a obtenção de freqüências e taxas de amortecimentos modais para várias velocidades do vento. Adicionalmente, o fenômeno do drapejamento é estudado por séries temporais de respostas de coordenadas generalizadas e de deslocamentos selecionados e por análise espectral dessas séries temporais, que permitem a verificação das características de vibração do tabuleiro da ponte no domínio da freqüência. O estudo do fenômeno de martelamento considera esforços aeroelásticos determinísticos e esforços aerodinâmicos estocásticos e apresentam-se resultados em espectros de potência de deslocamentos e em desvios padrão de deslocamentos ao longo do tabuleiro. Para validar o sistema ANA-PSp, apresentam-se estudos de caso para a ponte estaiada da Normandia, para a ponte pênsil colapsada de Tacoma Narrows e para a ponte estaiada projetada, mas não executada, sobre o Rio Tietê e localizada na extremidade do complexo viário Jacu-Pêssego. / The architectonic characteristics and the structural performance of suspension bridges and cable-stayed bridges have determined their growing use on large span bridges. This growing usage, which has occurred world-wide during the last decades, is now being repeated in Brazil during the last few years. Several such bridges are presently either undergoing construction or being designed. One of the outstanding aspects in the structural analysis of suspension bridges is their behavior under wind action. This paper presents the computer system ANA-PSp, specially developed for studying the movement of suspended bridge decks under aeroelastic and aerodynamic forces. This computer system is formed by a group of subsystems and is created for aeroelastic analysis of suspended bridges under wind action. It allows extended parametric analyses of the flutter and the buffeting phenomena. Structural discretization is done by the finite element method and the reduction of degrees of freedom is obtained by modal superposition of the selected modes which best describe the deck movements. A reduced mathematical model is used for the multimodal analysis in the time and frequency domains. Critical velocity or flutter velocity is determined by a procedure of complex eigenvalues which obtains frequencies and damping ratios for different wind speeds. Additionally, the flutter phenomenon is studied by temporal series of answers to generalized coordinate responses and of selected displacements by spectral analysis of such temporal series, which allow us to verify the characteristics of the vibrations of the bridge deck in the frequency domain. The study of the buffeting phenomenon considers deterministic aeroelastic and stochastic aerodynamic forces. The paper presents results in displacement power spectra and in the standard deviation of displacements along the deck. In order to validate system ANA-PSp, case studies are presented for the cable-stayed Ponte de Normandie in Le Havre (France), for the collapsed suspension bridge on Tacoma Narrows and for the cable-stayed bridge, already designed but not built, on Tietê River, located at one end of the highway complex Jacu-Pêssego (São Paulo, SP, Brazil).

Este trabalho apresenta o desenvolvimento de metodologia para avaliar a utilização do Sistema de Posicionamento Global (GPS) como ferramenta de pesquisa no estudo do comportamento dinâmico de obras viárias. Para ser caracterizado como um instrumento de medição, foi estudada a potencialidade de um método, que se fundamenta numa forma específica de coleta e processamento de dados GPS; análise dos resíduos resultantes do processamento da dupla diferença de fase e aplicação de análise espectral para filtragem de informações indesejáveis (multicaminhamento dos sinais GPS). A coleta envolve um oscilador eletro-mecânico, especialmente projetado, que permite calibrar as medidas de amplitude e freqüência das oscilações mensuráveis pela obra sob teste. Inúmeros experimentos foram realizados em ambientes de reflexões e difrações variáveis e com diversos tipos de receptores e antenas GPS. Alguns ensaios foram realizados utilizando, simultaneamente, equipamentos como transdutores de deslocamento, acelerômetros e estações totais. Comparando os resultados obtidos, mesmo com valores prescritos em normas e códigos, afirma-se que o GPS, sob o método de coleta de dados testado, é um instrumento confiável para detecção e caracterização do comportamento dinâmico de estruturas, apresentado confiabilidade para as medições realizadas, da ordem de décimos de milímetro. Quanto à detecção das freqüências, as mais baixas ficam comprometidas pela presença do multicaminhamento e as mais elevadas têm a detecção limitada pela máxima taxa de coleta dos receptores (Lei de Nyquist) / This work presents the development of a methodology to appraise the use of Global Positioning System (GPS) as a tool for researching of dynamic behavior of road transport structures. To be characterized as an instrument for measuring it was studied the potentiality of one method which includes a specific mode of GPS data collection; analyses of double difference phase residuals and application of spectral analyses and filtering for excluding undesirable information (multipath). The GPS data collected applies an electro-mechanical oscillator, specially built for that, which permits to calibrate the measures of frequency and amplitude of structure’s oscillations under dynamic load test. Several field tests were carried out in vicinities with high and low capacity of causing signal reflections and diffractions and with different types of GPS receivers and GPS antennas. A couple of fields were carried out using, at the same time, transducers of displacement, accelerometers and total stations. Comparing these results obtained even with values of codes, it is affirmed that GPS, under the data collection method tested, it is a trustworthy instrument for detection and characterization of dynamic behavior of structures, presenting reliability of measures ranging around tenths of millimeters. The very low frequencies are highly degraded by multipath and very high frequencies have its detection limited by the receiver data rate (Theorem’s Nyquist)

The subject of this diploma thesis is design a cable-supported pedestrian bridge. Three different variants of the solution were created for the design. For detailed processing, variant no.2 was chosen - a suspended bridge with a pylon in the middle of the span. The main task is the static design of the supporting structure. The model for the lengthways is created in ANSYS. The SCIA engineer was used to solve crosswise. The assessment and dimensioning was done according to the limit state principles and valid standards.

The topic of this thesis is a design of stress ribbon bridge across the deep valley. The construction of the footbridge contains stress ribbon bridge with external cables and final prestressing tendons. The bridge deck is in a parabolic arc and the suspension cables are in two bend down parabolic arcs. The construction is reproduced for evaluation of longitudinal direction in the Ansys 14.0 programme and for transversal direction in the Scia Engineer 15.1 programme. The model was solved in several phases, nonlinerally. The pier was reproduced in the Scia Engineer 15.1 programme for local effect of action. The construction was evaluated for dynamic action. The construction is assessed according to the actual EN standards.