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American Association of State Highway and Transportation Officials (ASHTO) specifications have prescribed lateral load distribution factors to calculate the bending moments and shear forces for the design of highway bridges for civilian highway traffic. The maximum bending moments and shear forces caused by a wheel line load (or the entire vehicle) placed on the girders are multiplied by the distribution factors to calculate the design forces to include the effect of the load distribution laterally to the girders by the bridge deck. However, the use of these AASHTO distribution factors may not provide accurate estimate of the maximum forces for military vehicles, which usually have significantly different loading pattern than those of the civilian vehicles. Therefore, this study was conducted to develop new formulas for the lateral load distribution factors for military vehicles. The study considered six different types of military vehicles, three wheeled vehicles and the other three tracked vehicles. The bridge database used for developing AASHTO distribution factors formulas was also used in this study. The focus of this study was to develop the distribution factors formulas for three different types of bridges: steel girder bridges, pre-stressed concrete bridges, and concrete T-beam bridges. The bridges in each category were analyzed for the six types of military vehicles by the harmonic decomposition approach to calculate the distribution factor. This thesis provides a total of 52 new formulas for different types of vehicles, different types of bridges, bending moment and shear force values, interior and exterior girders, and for single and multiple lane loading cases. The distribution factors calculated with the formulas were compared with those calculated by direct analyses of the bridges to evaluate the accuracy of the proposed formulas. Comparisons were also made between the values calculated by the new formulas, post-LRFD formulas prescribed in 1996 AASHTO Standard Specification, and simple pre-LRFD formulas that were prescribed by AASHTO before 1994. / Master of Science

Résumé Nous présentons en premier lieu dans ce travail les principales notions de la théorie de l'Analyse Limite (AL) — ou théorie des charges limites — en mécanique. Puis nous proposons une méthode de point intérieur destinée à résoudre des problèmes de programmation convexe posés par la méthode statique de l'AL, en vue d'obtenir des bornes inférieures de la charge limite (ou de ruine) d'un système mécanique. Les principales caractéristiques de cette méthode de point intérieur sont exposées en détail, et particulièrement son itération type. En second lieu, nous exposons l'application de cet algorithme sur un problème concret d'analyse limite, sur une large gamme de tailles numériques, et nous comparons pour validation les résultats obtenus avec ceux déjà existants ainsi qu'avec ceux calculés à partir de versions linéarisées du problème statique. Nous analysons également les résultats obtenus pour des problèmes classiques avec matériaux de Gurson, pour lesquels la linéarisation ou la programmation conique ne s'applique pas. La deuxième partie de cet ouvrage a trait à la méthode cinématique de l'analyse limite, qui, elle, s'occupe de fournir des bornes supérieures des charges limites. En premier lieu, nous traitons de l'équivalence entre la méthode cinématique classique et la méthode cinématique mixe, en partant d'une l'approche variationnelle fournie précédemment par Radenkovic et Nguyen. Ensuite, prenant en compte les exigences particulières aux formulations numériques, nous présentons une méthode mixte originale, parfaitement cinématique, utilisant aussi bien des champs de vitesses linéaires que quadratiques, continus ou discontinus. Son modus operandi pratique est tiré de l'analyse des conditions d'optimalité de Karush, Kuhn et Tucker, fournissant par là un exemple significatif d'interaction fructueuse entre la mécanique et la programmation mathématique. La méthode est testée sur des problèmes classiques avec les critères de plasticité de von Mises/Tresca et Gurson. Ces test démontrent l'efficacité remarquable de cette méthode mixte — qui par ailleurs n'utilise que le critère de plasticité comme information sur le matériau — et sa robustesse, laquelle s'avère même supérieure à celle de codes commerciaux récents de programmation conique. Enfin, nous présentons une approche de décomposition, elle aussi originale, des problèmes de bornes supérieures en analyse limite. Cette approche est basée à la fois sur la méthode cinématique mixte et l'algorithme de point intérieur précédents, et elle est conçue pour utiliser jusqu'à des champs de vitesse quadratiques discontinus. Détaillée dans le cas de la déformation plane, cette approche apparaît très rapidement convergente, ainsi que nous le vérifions sur le problème du barreau comprimé de von Mises/Tresca dans le cas de champs de vitesse linéaires continus. Puis elle est appliquée, dans le cas de champs quadratiques discontinus, au problème classique de la stabilité du talus vertical de Tresca, avec des résultats particulièrement remarquables puisqu'ils améliorent nettement les solutions cinématiques connues jusqu'à présent dans la littérature sur le sujet. Cette caractéristique de forte convergence qualifie particulièrement cette méthode de décomposition comme algorithme de base pour une parallélisation directe— ou récursive — de l'approche par éléments finis de l'analyse limite. Abstract Firstly, the main notions of the theory of Limit analysis (LA) in Mechanics —or collapse load theory – is presented. Then is proposed an Interior Point method to solve convex programming problems raised by the static method of LA, in order to obtain lower bounds to the collapse (or limit) load of a mechanical system. We explain the main features of this Interior Point method, describing in particular its typical iteration. Secondly, we show and analyze the results of its application to a practical Limit Analysis problem, for a wide range of sizes, and we compare them for validation with existing results and with those of linearized versions of the static problem. Classical problems are also analyzed for Gurson materials to which linearization or conic programming does not apply. The second part of this work focuses on the kinematical method of Limit Analysis, aiming this time to provide upper bounds on collapse loads. In a first step, we detail the equivalence between the classical an general mixed approaches, starting from an earlier variational approach of Radenkovic and Nguyen. In a second step, keeping in mind numerical formulation requirements, an original purely kinematical mixed method—using linear or quadratic, continuous or discontinuous velocity fields as virtual variables—is proposed. Its practical modus operandi is deduced from the Karush-Kuhn-Tucker optimality conditions, providing an example of crossfertilization between mechanics and mathematical programming. The method is tested on classical problems for von Mises/tresca and Gurson plasticity criteria. Using only the yield criterion as material data, it appears very efficient and robust, even more reliable than recent conic commercial codes. Furthermore, both static and kinematic present approaches give rise to the first solutions of problem for homogeneous Gurson materials. Finally, an original decomposition approach of the upper bound method of limit analysis is proposed. It is based on both previous kinematical approach and interior point solver, using up to discontinuous quadratic velocity. Detailed in plane strain, this method appears very rapidly convergent, as verified in the von Mises/Tresca compressed bar problem in the linear continuous velocity case. Then the method is applied, using discontinuous quadratic velocity fields, to the classical problem of the stability of a Tresca vertical cut, with very significant results as they notably improved the kinematical solutions of the literature. Moreover its strong convergence qualifies this decomposition scheme as a suitable algorithm for a direct—or recursive—parallelization of the LA finite element approach.

[pt] O Brasil possui um Sistema Interligado Nacional (SIN) que se baseia na geração de energia elétrica por meio de usinas hidrelétricas, térmicas, solares fotovoltaicas e eólicas. O planejamento e operação deste sistema é efetuado com base em previsões efetuadas em curto, médio e longo prazo a fim de evitar imprevistos que possam afetar o suprimento da demanda de energia elétrica em território nacional. Uma das informações consideradas fundamentais em cada uma das etapas do planejamento da operação é a carga, ou seja, a demanda por energia elétrica. Quando trabalhada em curto prazo, esta é importante para a programação diária da operação, garantindo um cenário ótimo para uso dos recursos disponíveis e, em cenário mais atual, determinação do Preço de Liquidação das Diferenças a cada hora. Quando trabalhada em médio prazo, esta funciona como base para manutenções de redes e negociações de contrato. Já em longo prazo, a previsão é importante para fornecer informações usadas como base para estratégias de expansão do Sistema. Normalmente a previsão em longo prazo é trabalhada de maneira a escalonar a curva histórica anual, mas as constantes alterações no hábito de consumo da população e a inserção de novas fontes ocasionam relevantes alterações no perfil da curva de carga diária em longo prazo, tornando necessário o planejamento não somente da expansão do sistema, mas também a forma com que este poderá ser programado. Assim, com o objetivo de propor uma ferramenta de suporte ao mercado brasileiro de energia, este trabalho propõe uma Metodologia para Geração de Cenários de Carga de Longo Prazo. O método proposto propõe uma abordagem bottom-up para previsão anual da demanda utilizando premissas de trabalhos acadêmicos recentes, propõe um método de geração de perfis específicos para suprir a escassez de dados horários detalhados no Brasil e propõe a utilização da Abordagem de Decomposição Parcial a fim de transformar as previsões anuais de demanda em curvas de carga horária. Finalizando a aplicação da Metodologia para Geração de Cenários de Longo Prazo, diferentes resultados gerados são utilizados para aplicação de simulação por Monte Carlo, sendo os intervalos de confianças gerados com base na resposta, possíveis cenários de comportamento da carga no futuro, transformando um método de previsão previamente determinístico em um previsor de cenários. Com o objetivo de demonstrar resultados da método, a Metodologia é aplicada para geração de cenários de longo prazo para a região sudeste brasileira até 2020 com base na curva histórica de 2016, apesar de ser capaz de gerar previsões para horizontes maiores, demonstrando verdadeiro potencial para se adaptar a possíveis alterações na curva de carga. / [en] Brazil has a National Interconnected System which produces and transmits electrical energy through a hydro-thermo-wind system. The planning and operation of this system is based on short, medium and long term on forecasts in order to avoid unforeseen that may affect the electricity supply in national territory. The short-term forecast is important for daily schedule of operation, certifying the resource use optimal scenario and, in a current scenario, the determination of Settlement Price for Differences at each hour. The medium-term forecast is used as a basis for network maintenance and contract negotiations. The long-term forecast is important to provide information used as basis for system expansion strategies. Usually, the long-term forecast is made staggering the annual load curve, however, the constant changes on people electrical consumption habits and insertion of new electrical generation sources cause relevant changes in daily load curve profile over the long term, making necessary not only the expansion planning, but also the way it can be programmed on long-term horizon. Thus, in order to propose a support tool to the Brazilian energy market, this work presents a Scenarios Generation Methodology. Such procedure proposes bottom-up approach as an annual demand projection provider, using assumptions of recent academic works, proposes a specific profile generation method as a way to overcome the lack of specific hourly data in Brazil. Not only that, the method also proposes Partial Decomposition Approach to adapt annual electricity demand into hourly load curves. Concluding the Scenarios Generation Methodology, future scenarios are developed by Monte Carlo simulation applied over different obtained results and confidence intervals calculated based on response are possible values of load behavior in the future, thus turning a deterministic forecasting method into a scenarios generation methodology. In order to demonstrate the Methodology application, it is used to generate long-term scenarios for the southeast Brazilian region by 2020 based on historical load curve from 2016, although it is capable of generating forecasts for larger horizons, proving true potential to adapt to possible changes on load curve.