Thesis (Ph. D.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 151-157).

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-03-20Bitstream added on 2014-06-13T19:47:28Z : No. of bitstreams: 1 figueroalopez_rn_me_sjrp.pdf: 751046 bytes, checksum: 50788892bf3e9440cb207b1489c88d57 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho vamos estudar um modelo matemático que descreve as oscilações não lineares de uma ponte suspensa. Este modelo é dado por um sistema de equações diferenciais parciais que estão acopladas. Basicamente, estudaremos a existência e unicidade da solução fraca do sistema. Usaremos a teoria de operadores maximais monótonos para modelo linear e os semigrupos fortemente contínuos de contração para o modelo não linear. / In this work we study a mathematical model which describes the nonlinear oscillations of a bridge suspended. This model is given by a system of partial di®erential equations which are coupled. Basically, we study the existence and uniqueness of weak solution of the system. We use the theory of maximal monotone operators to model linear and strongly continuous semigroups of contraction for the nonlinear model.

Orientador: Germán Jesus Lozada Cruz / Banca: Alexandre Nolasco de Carvalho / Banca: Waldemar Donizete Bastos / Resumo: Neste trabalho vamos estudar um modelo matemático que descreve as oscilações não lineares de uma ponte suspensa. Este modelo é dado por um sistema de equações diferenciais parciais que estão acopladas. Basicamente, estudaremos a existência e unicidade da solução fraca do sistema. Usaremos a teoria de operadores maximais monótonos para modelo linear e os semigrupos fortemente contínuos de contração para o modelo não linear. / Abstract: In this work we study a mathematical model which describes the nonlinear oscillations of a bridge suspended. This model is given by a system of partial di®erential equations which are coupled. Basically, we study the existence and uniqueness of weak solution of the system. We use the theory of maximal monotone operators to model linear and strongly continuous semigroups of contraction for the nonlinear model. / Mestre

Uncertainty is ubiquitous in civil infrastructure systems and has a major impact on decision-making for structural safety and reliability, and for assessing and managing risk. This dissertation explores the field both from the theoretical-mathematical modeling point of view, as well as from the practical applications perspective. Two problems addressed in the dissertation: 1) how to quantify the randomness in material properties and 2) what’s the impact for the uncertainties in material properties on the response/safety of the civil structures. There are two distinct parts in the dissertation. Part I focuses on the strength evaluation of main cables for long span suspension bridges. A novel methodology is proposed to evaluate the ultimate strength of the main cables of suspension bridges using information obtained from site inspections and from tensile strength tests on selected wire samples extracted from the bridge’s main cables. A new model is proposed accounting for the spatial variation of individual wires’ strength along their length, an important physical attribute of corroded wires considered here for the first time. This model includes: (1) mapping the corrosion stage variation along one-panel-long wires that are visible during an inspection, (2) establishing probability distribution functions for the ultimate tensile strength of 18″ long wire segments in each corrosion stage group, (3) generating random realizations of the ultimate strength of all the wires in the cable’s cross section, accounting for their strength variation along the entire panel length, and (4) accounting for the effect of broken wires in the evaluation panel as well as in adjacent panels. A Monte Carlo simulation approach is finally proposed to generate random realizations of the ultimate overall strength of the cable, using an incremental loading procedure. The final outcome is the probability distribution of the ultimate strength of the entire cable. The methodology is demonstrated through the cable strength evaluation of the FDR Mid-Hudson Bridge and Bear Mountain Bridge in New York state, and compared with corresponding results obtained using the current guidelines of NCHRP Report 534. Part II is more theoretical in nature and focuses on estimating the stochastic response variability of structures with uncertain material properties modeled by stochastic fields. The concept of Variability Response Function (VRF) is applied in the dissertation to quantify the response variability (e.g., mean and variance) of statically indeterminate structures. Two types of response for statically indeterminate beams at a specific location x are studied: bending moment M(x) and displacement/deflection w(x). By solving the governing equations of the statically indeterminate structure, the responses along the length of the beam, M(x) and w(x), are expressed as a function of its (random) zero-moment location denoted by h. For bending moment M(x), combined with a second-order Taylor series expansion of the random zero-moment location h, novel Variability Response Function-based integral expressions for the variance of the response bending moment, Var[M(x)], are established. Extensive numerical examples are provided where the accuracy of the results obtained using the proposed formulation is validated using Monte Carlo simulations involving stochastic fields that follow truncated Gaussian and shifted lognormal probability distribution functions. These Monte Carlo simulation results indicate that the proposed Variability Response Functions are probability-distribution-independent. For deflection w(x), by introducing hinges at zero-moment location h, a statically indeterminate structure can be transformed into its equivalent statically determinate structure. An approximate close-form analytical expression of VRF is therefore built based on the transformed statically determinate structure with all (probabilistically) possible hinge locations. An ensemble average is taken to get the overall variability response function of the system, which can be replaced by the VRF with the hinge located at the same zero-moment point with the deterministic system without any randomness. This Variability Response Function can provide approximate estimates of the stochastic response variability with reasonable accuracy. Moreover, to get more accurate estimates of the statically indeterminate system, the results from the approximate variability response function can be further refined by introducing a correction term Dw. Finally, the corrected response variability of the original statically indeterminate structure can be obtained with almost perfect accuracy (compared to brute force Monte Carlo simulations). To sum up, the proposed VRFs of statically indeterminate beams, for both bending moment and deflection, have numerous desirable attributes including the capability to perform a full sensitivity analysis of the response variability with respect to the spectral characteristics of the random field modeling the uncertain material/system properties and establishing realizable upper bounds of the response variability.

As crucial infrastructure systems remain in service up to and beyond their originally intended service lives, there has been a significant increase in efforts to quantify their current strength and remaining life span. Suspension bridges are of particular concern due to their impact on commerce, low repairability, and high replacement cost. As such, quantification of the performance of suspension bridge main cables at elevated temperatures is necessary for a holistic safety assessment. These cables are the primary load-carrying members, and are susceptible to vehicular fires near the midspan and anchorage where the cable sweeps low to the deck. Due to the dearth of empirical data regarding the thermomechanical properties of main cables, previous studies were forced to rely on thermomechanical properties derived for different materials, geometries, and scales. It is the chief goal of this dissertation to fill this void in high-temperature empirical data. First, the high temperature stress-strain behavior of the constituent ASTM A586 wires is examined. The coldworked wires are highly susceptible to recovery at elevated temperatures, which has the power to undo the primary strengthening mechanism. Large decreases in elastic modulus, yield stress, and ultimate stress are observed at elevated temperature. The high temperature stress-strain curves are fully parameterized, and a procedure for generating stress-strain curves at temperatures between 22°C and 724°C is provided. Next, the post-fire performance of the wire is quantified. Wires are heated to various temperatures up to 842°C and then allowed to cool before being tensile tested. The results of this testing show that a significant portion of the high-temperature strength-loss observed in the in-situ tests persists after cool-down. Exposure to elevated temperatures reduces strength and fundamentally alters the shape of the stress-strain curves of the heated and cooled wires. These post-fire stress-strain curves are fully parameterized, and a procedure for recreating them between 22°C and 842°C is provided. Next, the metallurgical underpinnings for the observed changes in mechanical behavior at and after high-temperature exposure are explored using neutron diffraction techniques. Two engineering beamline experiments generate peak-narrowing data that sheds light on the evolving dislocation density and crystallite size in this wire during and after heating. Results confirm that the decreases in wire strength that persist after cool-down are the product of recovery; temperatures in excess of 700°C decrease wire dislocation density to values similar to those of undeformed structural materials. Finally, the thermal conductivity of the main cable is addressed. The air voids and point contacts between the wires create a complex (and anisotropic) heat transfer situation within main cables. A one-to-one, 8200 kg mock-up of a panel of a suspension bridge main cable is constructed, instrumented, and heated. The data provided by the internal temperature sensors is used to tune the thermal conductivity of a representative finite element via a gradient descent algorithm. The resulting temperature-dependent thermal conductivity function allows the complex internal heat transfer of the main cable to be accurately approximated by a monolithic section with conductivity tuned to the measured behavior of a physical main cable. Cumulatively, the results of these studies shows that the thermomechanical properties of main cables are not well represented by previous approximations that are based on other materials and applications. The properties derived herein will facilitate more accurate performance estimates of suspension bridges subjected to fires than previously possible.

Este trabalho aborda um tipo de passarela que está ganhando bastante notoriedade internacionalmente. Inúmeras obras vêm sendo construídas em diversos países, embora no Brasil ainda seja quase desconhecida. Basicamente, a estrutura é composta por cabos livremente suspensos, sobre os quais se apóia o tabuleiro formado por elementos pré-moldados de concreto. A protensão é utilizada como forma de enrijecer o conjunto. Dentre suas principais características, estão a rapidez e a facilidade de execução, a estética bastante agradável e o custo competitivo. Inicialmente, apresenta-se uma conceituação básica e um estado da arte. Em seguida, é estudado o comportamento estrutural da passarela. Alguns tópicos relativos à análise dinâmica e às fundações são brevemente comentados. Finalizando a dissertação, é feita uma aplicação numérica, enfatizando os aspectos que a diferenciam das estruturas convencionais / This work treats a kind of pedestrian bridge that is standing out internationally. Several structures have been built in different countries, although they are almost unknown in Brazil. Basically, the deck is formed by precast concrete elements over free suspended cables. Prestressing is applied behind the abutments to provide rigidity to the structure. Quick and easy to assemble, aesthetically beautiful and the competitive cost are some of their main features. First, the basic concepts and a state of art are presented. Then, the structural behavior is studied. Some questions related to dynamic analysis and foundations are briefly commented. Ending the dissertation, an example is done, with emphasis to the aspects that make the stress-ribbon a non-conventional structure

Estudos sobre a instabilidade aeroelástica em estruturas de pontes suspensas têm adquirido relevante destaque no âmbito das pesquisas em engenharia do vento nos últimos anos, haja vista que as definições resultantes dessa análise apresentam informações essenciais ao projeto, cálculo e concepção desse tipo de estrutura. Considerando que os escoamentos ao redor de pontes suspensas apresentam características turbulentas, o conhecimento acerca desse fenômeno torna-se fundamental para a análise da interação vento-ponte, estabelecendo a turbulência como uma importante e complexa vertente dentro dessa pesquisa. Nesse contexto, o presente trabalho visa contribuir com o tema através da análise numérica da ação do vento na seção transversal do tabuleiro de pontes suspensas, verificando seu comportamento quando estiverem submetidas à ação dos esforços provenientes do vento na interação de um escoamento turbulento com o tabuleiro da ponte. No trabalho foi investigada a atuação dos esforços aerodinâmicos na estrutura da ponte, ensejando na obtenção dos coeficientes aerodinâmicos de arrasto, sustentação e momento. Também foi analisado o comportamento do tabuleiro para o surgimento das vibrações induzidas por vórtices, permitindo o cálculo da frequência de desprendimento de vórtices e determinação do número de Strouhal. No que tange aos esforços aeroelásticos para o estudo específico do drapejamento (flutter), foram avaliadas as amplitudes de deslocamentos torcionais para o cálculo e obtenção da velocidade crítica do vento que acarreta o fenômeno do flutter. Juntamente com as análises aerodinâmicas e aeroelásticas da seção transversal da ponte, diferentes modelos de turbulência foram aplicados nas simulações para se estabelecer uma análise comparativa entre os escoamentos. As simulações computacionais desenvolvidas e apresentadas neste trabalho foram realizadas com auxílio de um programa de CFD (Computational Fluid Dynamics). Os modelos de ponte utilizados no trabalho foram o da ponte suspensa Great Belt East, localizada na Dinamarca e da ponte estaiada Sunshine Skyway, localizada nos Estados Unidos. Para validação da técnica computacional, os resultados das simulações foram comparados com dados numéricos e experimentais disponíveis na literatura. / Researches about aeroelastic instability in long span suspension bridges have been consistently the focus in wind engineering field in recent years, therefore the definitions from that study present essential information to design and construction of this type of road structure. Considering that fluid flows around bridges show some turbulent features, the knowledge about turbulence become critical for this wind-bridge interaction analysis, establishing the turbulence modeling study as an important and complex part within that research. According to this context, the meaning of this research was to contribute with numerical analysis of wind effects on a suspension bridge deck, verifying its behavior when this model is subjected to the action of wind loads from a turbulent fluid flow. The bridge aerodynamic behaviour was investigated and aerodynamic coefficients of drag, lift and moment were calculated. Flow induced vibrations were also analyzed for the bridge deck model, allowing it to obtain the vortex shedding frequency and Strouhal number. With regard to aeroelasticity and focusing on flutter study, the amplitudes of torsional displacements were evaluated as well as the analysis of critical wind velocity that causes flutter instabilities. Along with aerodynamic and aeroelastic analysis of the bridge deck cross sectional, fluid flow features were studied and compared applying several turbulence models to simulations. The numerical approach developed and shown in this work was performed by CFD (Computational Fluid Dynamics) software. The bridge deck models used at this dissertation were the Great Belt East suspension bridge, located in Denmark and the Sunshine Skyway cable stayed bridge, located in USA. In order to validate the computational technique, simulation results from this research were compared with numerical and experimental test data available in papers and literature.

Este trabalho aborda um tipo de passarela que está ganhando bastante notoriedade internacionalmente. Inúmeras obras vêm sendo construídas em diversos países, embora no Brasil ainda seja quase desconhecida. Basicamente, a estrutura é composta por cabos livremente suspensos, sobre os quais se apóia o tabuleiro formado por elementos pré-moldados de concreto. A protensão é utilizada como forma de enrijecer o conjunto. Dentre suas principais características, estão a rapidez e a facilidade de execução, a estética bastante agradável e o custo competitivo. Inicialmente, apresenta-se uma conceituação básica e um estado da arte. Em seguida, é estudado o comportamento estrutural da passarela. Alguns tópicos relativos à análise dinâmica e às fundações são brevemente comentados. Finalizando a dissertação, é feita uma aplicação numérica, enfatizando os aspectos que a diferenciam das estruturas convencionais / This work treats a kind of pedestrian bridge that is standing out internationally. Several structures have been built in different countries, although they are almost unknown in Brazil. Basically, the deck is formed by precast concrete elements over free suspended cables. Prestressing is applied behind the abutments to provide rigidity to the structure. Quick and easy to assemble, aesthetically beautiful and the competitive cost are some of their main features. First, the basic concepts and a state of art are presented. Then, the structural behavior is studied. Some questions related to dynamic analysis and foundations are briefly commented. Ending the dissertation, an example is done, with emphasis to the aspects that make the stress-ribbon a non-conventional structure

Estudos sobre a instabilidade aeroelástica em estruturas de pontes suspensas têm adquirido relevante destaque no âmbito das pesquisas em engenharia do vento nos últimos anos, haja vista que as definições resultantes dessa análise apresentam informações essenciais ao projeto, cálculo e concepção desse tipo de estrutura. Considerando que os escoamentos ao redor de pontes suspensas apresentam características turbulentas, o conhecimento acerca desse fenômeno torna-se fundamental para a análise da interação vento-ponte, estabelecendo a turbulência como uma importante e complexa vertente dentro dessa pesquisa. Nesse contexto, o presente trabalho visa contribuir com o tema através da análise numérica da ação do vento na seção transversal do tabuleiro de pontes suspensas, verificando seu comportamento quando estiverem submetidas à ação dos esforços provenientes do vento na interação de um escoamento turbulento com o tabuleiro da ponte. No trabalho foi investigada a atuação dos esforços aerodinâmicos na estrutura da ponte, ensejando na obtenção dos coeficientes aerodinâmicos de arrasto, sustentação e momento. Também foi analisado o comportamento do tabuleiro para o surgimento das vibrações induzidas por vórtices, permitindo o cálculo da frequência de desprendimento de vórtices e determinação do número de Strouhal. No que tange aos esforços aeroelásticos para o estudo específico do drapejamento (flutter), foram avaliadas as amplitudes de deslocamentos torcionais para o cálculo e obtenção da velocidade crítica do vento que acarreta o fenômeno do flutter. Juntamente com as análises aerodinâmicas e aeroelásticas da seção transversal da ponte, diferentes modelos de turbulência foram aplicados nas simulações para se estabelecer uma análise comparativa entre os escoamentos. As simulações computacionais desenvolvidas e apresentadas neste trabalho foram realizadas com auxílio de um programa de CFD (Computational Fluid Dynamics). Os modelos de ponte utilizados no trabalho foram o da ponte suspensa Great Belt East, localizada na Dinamarca e da ponte estaiada Sunshine Skyway, localizada nos Estados Unidos. Para validação da técnica computacional, os resultados das simulações foram comparados com dados numéricos e experimentais disponíveis na literatura. / Researches about aeroelastic instability in long span suspension bridges have been consistently the focus in wind engineering field in recent years, therefore the definitions from that study present essential information to design and construction of this type of road structure. Considering that fluid flows around bridges show some turbulent features, the knowledge about turbulence become critical for this wind-bridge interaction analysis, establishing the turbulence modeling study as an important and complex part within that research. According to this context, the meaning of this research was to contribute with numerical analysis of wind effects on a suspension bridge deck, verifying its behavior when this model is subjected to the action of wind loads from a turbulent fluid flow. The bridge aerodynamic behaviour was investigated and aerodynamic coefficients of drag, lift and moment were calculated. Flow induced vibrations were also analyzed for the bridge deck model, allowing it to obtain the vortex shedding frequency and Strouhal number. With regard to aeroelasticity and focusing on flutter study, the amplitudes of torsional displacements were evaluated as well as the analysis of critical wind velocity that causes flutter instabilities. Along with aerodynamic and aeroelastic analysis of the bridge deck cross sectional, fluid flow features were studied and compared applying several turbulence models to simulations. The numerical approach developed and shown in this work was performed by CFD (Computational Fluid Dynamics) software. The bridge deck models used at this dissertation were the Great Belt East suspension bridge, located in Denmark and the Sunshine Skyway cable stayed bridge, located in USA. In order to validate the computational technique, simulation results from this research were compared with numerical and experimental test data available in papers and literature.

A busca por estruturas mais esbeltas, economicamente viáveis e esteticamente atraentes impulsionou a evolução e inovação no ramo de pontes. A protensão, tanto interna quanto externa, tem sido usada em larga escala e devido à sua eficiência, diversas técnicas foram desenvolvidas e utilizadas, como os estais. A ponte extradorso é uma estrutura que mantém características das pontes de viga reta construídas por balanços sucessivos, assim como de pontes estaiadas. A ponte com protensão no extradorso é uma estrutura recente e inovadora, que ainda é pouco utilizada no Brasil. O conceito desenvolvido em 1988 foi construído pela primeira vez em 1994 no Japão. Por serem estruturas com extensos vãos e que podem sofrer vibração excessiva, quando submetidas a carregamentos dinâmicos de grande intensidade, como os carregamentos móveis, é importante analisar o comportamento destas. A dinâmica das estruturas engloba a determinação das frequências naturais e dos modos de vibração naturais da estrutura, assim como os possíveis deslocamentos, esforços internos, velocidade e acelerações. Os modelos computacionais, usando o princípio do método dos elementos finitos, quando devidamente utilizados, podem representar valores muito próximos à realidade da estrutura em serviço. Este trabalho tem a intenção de analisar o comportamento dinâmico da ponte situada na TO-010, entre Miracema e Lajeado, inaugurada em 2011, quando submetida a diferentes carregamentos móveis e com diferentes velocidades, comparando-os com a análise estática. / Searching for more slender structures, economically viable and aesthetically appealing drove and innovation in the bridges. Prestressing, both internal and external, has been used on a large scale due to its efficiency; several techniques have been developed and used, as the stays. The extradosed bridge is a structure that retains characteristics of straight girder bridges built by successive balances, as well as cable-stayed bridge. Prestressing extradosed is an innovative new structure, which is not widely used in Brazil. The concept developed in 1988 was first constructed in 1994 in Japan. Because they are structures with long spans and can suffer excessive vibration when subjected to dynamic loading of high intensity such as live loads, it is important to analyze their behavior. The dynamic of structures includes determining the frequency and mode of natural vibration of the structure, as well as the possible displacements and internal forces. Computer models, using the principle of the finite element method, when properly calibrated, can represent values close to the reality of the structure in service. This paper intends to analyze the dynamic behavior of the bridge located in the TO-010, between Miracema and Lajeado, inaugurated in 2011, when subjected to different moving load, and moving at different speed, comparing them with the static analysis. / 5000