Orientador: Francisco Antonio Menezes / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-07T09:14:46Z (GMT). No. of bitstreams: 1 Fontana_LuizAntonio_M.pdf: 833272 bytes, checksum: c80e60878c10acff4e3559bea3929d20 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho são apresentadas as expressões matemáticas necessárias para determinar o momento de inércia em função da curvatura para seções retangulares de concreto armado solicitadas a flexo-compressão reta. As expressões são determinadas através da integração analítica da curva tensão-deformação do concreto. Com base nestas expressões foi desenvolvido um programa de computador para calcular o momento de inércia em função da curvatura. O objetivo é obter o momento de inércia real da seção para ser utilizado na verificação das deformações. Para o programa é necessário conhecer: a geometria, a disposição das armaduras, as características dos materiais e as solicitações atuantes na seção. Na entrada de dados é possível controlar os coeficientes de ponderação dos materiais e das solicitações. Para o módulo de elasticidade, podem ser adotados os valores prescritos na NBR6118, ou outro valor que deve ser informado. A resistência à tração do concreto foi desprezada. Para validação dois modelos estruturais são analisados. A análise estrutural é feita de várias formas, sendo que uma delas é a análise considerando a não linearidade fisica (NLF) através da curvatura. Neste caso os elementos estruturais têm uma discretização maior, visando considerar a não linearidade ao longo do comprimento das peças. O objetivo é avaliar a possibilidade de implementar um processo de análise estrutural onde a consideração dos efeitos de segunda ordem seja relevante, que considere um. momento de inércia que aproxime o modelo matemático do modelo fisico real / Abstract: In this work, are presented the mathematic expressions necessary for determinate the moment of inertia in function of the curvature for rectangular cross-section the reinforced concrete submitted to mono-axial eccentricity. The expressions are determinate by the integration of analytic parabola rectangle stress strain diagram of concrete. Based in these expressions a computer system was developed to calculate the inertia of moment curvature. The objective is to get the moment of real inertia to be used in the verification of the deformations. It is necessary that the computer system know: geometry, the disposal of the bars, the characteristics of the materiaIs and operating requests in the section. When the database is imputed it is possible to have a control over the method of partial factors of materiaIs and solicitations. For the elasticity model may be adopt the NBR6118's values, or another value that must be informed. The resistance tension of concrete was rejected. To make the validation two structural models are analyzed. The structural analysis is made of severa! forms, one of them is the analysis considering no-linearity physical (NLP) through the curvature. In this case the structural elements have the biggest discretization, aiming to consider no-linearity along the length of the parts. The objective is to evaluate the possibility to implement a process of structural analysis where the effects of second order are relevant, that considers an inertia moment that can make the mathematical model dose to the real physical one / Mestrado / Estruturas / Mestre em Engenharia Civil

In this dissertation, we provide necessary conditions for an asymptotically stable equilibrium solution of a nonlinear ordinary differential equation be globally stable. An essential condition is a generalization of the criteria of Bendixson and Dulac for towdimensional differential equations which is used to ensure the absence of periodic orbits, we call this Bendixson criterion. We provide a new Bendixson criterion robust under C1 local perturbations, which together with the Global Stability Principle, ensure the global stability of an asymptotically stable equilibrium. We use this criterion in the study of asymptotic behavior of an epidemiological model called SEIRS / Nesta dissertação, forneceremos condições necessárias para que umasolução de equilíbrio assintoticamente estável de uma equação diferencial ordinária autônoma e não linear seja globalmente estável. Uma das condições essenciais consiste numa generalização dos critérios de Bendixson e Dulac para equações diferenciais bidimensionais que é usada para garantir a inexistência de órbitas periódicas, o qual denominamos critério de Bendixson. Forneceremos um novo critério de Bendixson robusto sobre uma C1 perturbação local, o qual juntamente como Princípio da EstabilidadeGlobal, garante a estabilidade global deum equilíbrio assintoticamente estável. Usaremos este critério no estudo do comportamento assintótico de um modelo epidemiológico intitulado SEIRS.

Em epidemiologia matemática, muitos modelos de propagação de doenças infecciosas em populações têm sido analisados matematicamente e aplicados para doenças específicas. Neste trabalho um modelo de propagação de dengue é analisado considerando-se diferentes hipóteses sobre o tamanho da população humana. Mais precisamente, estamos interessados em verificar o impacto das variações populacionais a longo prazo no cálculo do parâmetro Ro e no equilíbrio endêmico. Vamos discutir algumas ideias que nortearam o processo de definição do parâmetro Ro a partir da construção do Operador de Próxima Geração. Através de um estudo qualitativo do modelo matemático, obtivemos que o equilíbrio livre de doença é globalmente assintoticamente estável se Ro é menor ou igual a 1 e instável se Ro>1. Para Ro>1, a estabilidade global do equilíbrio endêmico é provada usando um critério geral para estabilidade orbital de órbitas periódicas associadas a sistemas autônomos não lineares de altas ordens e resultados da teoria de sistemas competitivos para equações diferenciais ordinárias. Também foi desenvolvida uma análise de sensibilidade do Ro e do equilíbrio endêmico com relação aos parâmetros do modelo de propagação. Diversos cenários foram simulados a partir dos índices de sensibilidade obtidos nesta análise. Os resultados demonstram que, de forma geral, o parâmetro Ro e o equilíbrio endêmico apresentam considerável sensibilidade a taxa de picadas do vetor e a taxa de mortalidade do vetor. / In mathematical epidemiology many models of spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. In this work a dengue propagation model is analyzed considering different assumptions about the size of the human population. More precisely, we are interested to verify the impact of population long-term variations in the calculation of the parameter Ro and endemic equilibrium. We will discuss some ideas that guided the parameter setting process Ro from the construction of the Next Generation Operator. Through a qualitative study of the mathematical model, we found that the disease-free equilibrium is globally asymptotically stable if Ro is less or equal than 1 and unstable if Ro> 1. For Ro> 1 the global stability of the endemic equilibrium is proved using a general criterion for orbital stability of periodic orbits associated with nonlinear autonomous systems of higher orders and results of the theory of competitive systems for ordinary differential equations. Also a sensitivity analysis of the Ro and the endemic equilibrium with respect to the parameters of the propagation model was developed. Several scenarios were simulated from the sensitivity index obtained in this analysis. The results demonstrate that in general the parameter Ro and the endemic equilibrium are the most sensitive to the vector biting rate and the vector mortality rate.

The Diploma thesis deals with the assessment of global and local stability of the masonry gravity dam Pastviny, for two load conditions. The first part consists of a present state review describing selected masonry dams in the Czech Republic and abroad. Further on a conceptual and mathematical formulation of the seepage flow and strain-stress problem are stated. The case study is focused on the practical application of formulated problems on the Pastviny dam. Firstly the available data have been assembled and processed. Global and local safety of the dam was assessed for the selected most vulnerable profile of the dam body. In the final chapters 5, 6 and 7, the seepage flow, stress and strain have been calculated and graphically displayed. Finally global and local stability have been assessed and completed with final summary of the results and concluding remarks.

<div>The growing need to improve the power density of compact thermal systems necessitates developing new techniques to modulate the convective heat transfer efficiently. In the present research, acoustic streaming is evaluated as a potential technology to achieve this objective. Numerical simulations using the linearized and fully non-linear Navier-Stokes equations are employed to characterize the physics underlying this process. The linearized Navier-Stokes equations accurately replicate the low-frequency flow unsteadiness, which is used to find the optimal control parameters. Local and global stability analysis tools were developed to identify the modes with a global and positive heat transfer effect.</div><div><br></div><div>High-fidelity numerical simulations are performed to evaluate the effect of the excitation at selected frequencies, directed by the linear stability analysis, on the heat and momentum transport in the flow. Results indicate that, under favorable conditions, superimposing an acoustic wave, traveling along with the flow, can <i>resonate</i> within the domain and lead to a significant heat transfer enhancement with minimal skin friction losses. Two main flow configurations are considered; at the fixed Reynolds number Re_b=3000, in the supersonic case, 10.1% heat transfer enhancement is achieved by an 8.4% skin friction increase; however, in the subsonic case, 10% enhancement in heat transfer only caused a 5.3% increase to the skin friction. The deviation between these two quantities suggests a violation of the Reynolds analogy. This study is extended to include a larger Reynolds number, namely Re_b=6000 at M_b=0.75 and a similar response is observed. The effect of excitation amplitude and frequency on the resonance, limit-cycle oscillations, heat transfer, and skin friction are also investigated here.</div><div><br></div><div>Applying acoustic waves normal to the flow in the spanwise direction disrupts the near-wall turbulent structures that are primarily responsible for heat and momentum transport near the solid boundary. Direct numerical simulations were employed to investigate this technique in a supersonic channel flow at M_b=1.5 and Re_b=3000. The external excitation is applied through a periodic body force in the spanwise direction, mimicking loudspeakers placed on both walls that are operating with a 180^o phase shift. By keeping the product of forcing amplitude A_f and pulsation period (<i>T</i>) constant, spanwise velocity perturbations are generated with a similar amplitude at different frequencies. Under this condition, spanwise pulsations at <i>T</i>=20 and <i>T</i>=10 show up to 8% reduction in Nusselt number as well as the skin friction coefficient. Excitation at higher or lower frequencies fails to achieve such high level of modulations in heat and momentum transport processes near the walls.<br> <br>In configurations involving a spatially-developing boundary layer, a computational setup that includes laminar, transitional, and turbulent regions inside the domain is considered and the impact of acoustic excitation on this flow configuration has been characterized. Large-eddy simulations with dynamic Smagorinsky sub-grid scale modeling has been implemented, due to the excessive computational cost of DNS calculations at high-Reynolds numbers. The optimal excitation frequency that resembles the mode chosen for the fully-developed case has been identified via global stability analysis. Fully non-linear simulations of the spatially-developing boundary layer subjected to the excitation at this frequency reveal an interaction between the <i>pulsations</i> and the perturbations originated from the tripping which creates a re-laminarization zone traveling downstream. Such technique can locally enhance or reduce the heat transfer along the walls.<br></div>

Au cours des dernières décennies, la théorie de la stabilité a été intensivement utilisée pour caractériser le comportement instationnaire d'écoulements. Cela a donné naissance à un grand nombre d'approches, mais malheureusement chacune d'entre elles semble présenter ses propres limitations. De plus, leurs conditions de validité sont encore très mal connues, ce qui soulève la question de la fiabilité de ce genre de méthodes dans un cas général.Cette problématique est traitée dans cette thèse en s'intéressant dans un premier temps aux approches classiques de stabilité, qui étudient l'évolution de petites perturbations autour d'une solution stationnaire -- un champ de base -- des équations de Navier-Stokes. Pour cela, le phénomène du screech -- un bruit tonal que peuvent causer les jets sous-détendus -- est étudié d'un point de vue de la stabilité linéaire. Les résultats obtenus montrent que la dynamique non-linéaire du phénomène est correctement prédite par une analyse linéaire de stabilité du champ de base. Une confrontation avec d'autres analyses similaires montre qu'un tel résultat n'est pas toujours observé. Cependant, lorsque les oscillations auto-entretenues d'un écoulement sont provoquées par un bouclage acoustique, comme c'est le cas entre autres pour le screech, l'écoulement de cavité ou encore les jets impactants, alors les non-linéarités ont une faible influence sur le phénomène de sélection de fréquence. Cela explique la capacité d'une analyse linéaire à caractériser ces écoulements, même dans le régime non-linéaire.Une autre approche, consistant à étudier la stabilité linéaire du champ moyen, a montré de bons résultats dans certaines configurations qui ne peuvent être correctement étudiées par une analyse linéaire du champ de base. Cela est justifié dans cette thèse en mettant en évidence le rôle que joue la résolvante autour du champ moyen dans la dynamique d'un écoulement. Il est montré que lorsque cet opérateur présente une forte séparation de valeurs singulières, ce qui correspond à l'existence d'un mécanisme d'instabilité fort, alors les modes de Fourier de l'écoulement sont proportionnels aux modes de résolvante dominants. Ce résultat fournit des conditions mathématiques et physiques pour l'utilisation et le sens de diverses méthodes d'analyse du champ moyen, telles qu'une analyse d'équations de stabilité parabolisées (Parabolised Stability Equations). De plus, cela permet de mettre en place un modèle de prédiction du spectre fréquentiel en tout point d'un écoulement, à partir d'une ou de quelques mesures ponctuelles et du champ moyen. L'ensemble de ces résultats est illustré et validé sur un cas de marche descendante turbulente. Enfin, cela est exploité dans un cadre expérimental, afin de reconstruire le comportement instationnaire d'un jet rond transitionnel, à partir de la seule connaissance du champ moyen et d'une mesure ponctuelle. L'étude montre que, sous certaines précautions expérimentales, la reconstruction est très précise et robuste. / Linear stability theory has been intensively used over the past decades for the characterization of unsteady flow behaviors. While the existing approaches are numerous, none has the ability to address any general flow. Moreover, clear validity conditions for these techniques are often missing, and this raises the question of their general reliability.In this thesis, this question is addressed by first considering the classical stability approach, which focuses on the evolution of small disturbances about a steady solution -- a base flow -- of the Navier-Stokes equations.To this end, the screech phenomenon -- a tonal noise that is sometimes generated by underexpanded jets -- is studied from alinear stability point of view. The results reveal that the nonlinear dynamics of this phenomenon is well-predicted by a linear base flow stability analysis. A confrontation with other similar analyses from the literature shows that such a satisfactory result is not always observed. However, when a self-sustained oscillating flow is driven by an acoustic feedback loop, as it is the case for the screech phenomenon, cavity flows and impinging jets for instance, then the nonlinearities have a weak impact on the frequency selection process, explaining the ability of a linear analysis to characterize the flow, even in the nonlinear regime.Another alternative approach, based on a linearization about the mean flow, is known to be successful in some cases where a base flow analysis fails. This observation from the literature is explained in this thesis by outlining the role of the resolvent operator, arising from a linearization about the mean flow, in the dynamics of a flow. The main finding is that if this operator displays a clear separation of singular values, which relates to the existence of one strong convective instability mechanism, then the Fourier modes areproportional to the first resolvent modes. This result provides mathematical and physical conditions for the use and meaning of several mean flow stability techniques, such as a parabolised stability equations analysis of a mean flow.Moreover, it leads to a predictive model for the frequency spectrum of a flow field at any arbitrary location, from the sole knowledge of the mean flow and the frequency spectrum at one or more points. All these findings are illustrated and validated in the case of a turbulent backward facing step flow. Finally, these results are exploited in an experimental context, for the reconstruction of the unsteady behavior of a transitional round jet, from the sole knowledge of the mean flow and one point-wise measurement. The study shows that, after following a few experimental precautions, detailed in the manuscript, the reconstruction is very accurate and robust.

Dans les océans profonds linéairement stratifiés, la déstabilisation des ondes de gravité internes est importante car elle contribue probablement au mélange turbulent et à la circulation thermohaline.À l'aide de simulations numériques directes, nous créons un faisceau d'onde interne progressive. Cette situation est équivalente à une onde produite par l'oscillation de la marée sur une topographie sous-marine. Nous retrouvons les résultats expérimentaux obtenus par cite{Bourget13} : le faisceau se déstabilise en un mode petite échelle. Nous regardons l'effet d'un écoulement horizontal moyen sur cette instabilité en prenant soin d'abaisser la fréquence de forçage afin de compenser l'effet doppler et de conserver localement la même onde. Un cas limite apparaît lorsque le forçage devient stationnaire, ce qui équivaut à une onde de sillage issue d'un écoulement constant au dessus d'une topographie.Les écoulements à petite vitesse voient une instabilité petite échelle similaire au cas marée alors que les écoulement intermédiaires restent stables. Les écoulements plus rapides (jusqu'au cas sillage) voient, par contre, une instabilité bien plus grande échelle que celle dans le cas marée. Cette sélection d'échelle est robuste aux variations du nombre de Froude, de Reynolds, de la taille du faisceau ou de l'angle de l'onde.Nous montrons que ces instabilités peuvent être décrites comme des triades résonantes et que les différentes échelles correspondent à différentes branches triadiques. Nous confirmons la présence de cas stables pour des vitesses intermédiaires en calculant les modes propres comme des modes de Floquet à l'aide d'un algorithme d'Arnoldi--Krylov, et en montrant qu'ils sont associés à des taux de croissance négatifs.Le cas sillage est instable et nous le stabilisons par une méthode deselective frequency damping cite{Akervik06} afin d'obtenir un écoulement de base stationnaire autour duquel nous calculons les perturbations optimales qui maximisent l'énergie totale à différents horizons temporels. Pour des horizons courts, la perturbation optimale est petite échelle alors que pour des horizons longs, elle est grande échelle et converge vers la solution non-linéaire obtenue précédemment. Les horizons courts voient une instabilité triadique petite échelle advectée par l'écoulement et les horizons longs développent une instabilité d'une branche triadique grande échelle capable de se maintenir dans le faisceau malgré l'écoulement.Nous interprétons cette sélection de mode par le biais de la théorie des instabilités absolue ou convective. Dans le cas de l'onde de sillage l'instabilité grande échelle est absolue alors que la petite échelle est convective (et domine la croissance transitoire puisque son taux de croissance local est supérieur). Les rôles s'inversent dans le cas marée et l'instabilité petit échelle devient absolue alors que la grande échelle est convective. Nous confirmons cette hypothèse en calculant la réponse impulsionnelle d'une onde plane monochromatique dans un domaine 2Dpériodique. L'évolution spatio-temporelle d'une perturbation localisée en temps et en espace montre la formation de trois paquets d'onde, chacun étant associé à une branche triadique que nous identifions par une extension de la théorie triadique prenant en compte un désaccordage cite{McEwan77} et permettant de calculer la vitesse de groupe des sommets des paquets. En calculant ensuite le taux de croissance absolu le long de rayons à x/t et z/t constant, nous validons notre hypothèse. / Internal gravity waves that exist in a continuously stratified fluid are particularly important in the ocean. They transport energy and are thought to generate turbulent mixing, which contribute to the deep ocean circulation.We generate an internal wave beam that propagates in a continuously stratified fluid with direct numerical simulations. This situation is equivalent to a tidal wave, where the tidal flow oscillates over a topography and generates a wave. Experimental results obtained by cite{Bourget13} are recovered, ie. the beam destabilizes into a small scale mode. We consider the effect of an horizontal mean flow on the instability and lower the forcing frequency in order to compensate for the doppler effect and to keep locally the same wave. A limit case appears when the forcing becomes stationary. This case is equivalent to a lee wave appearing when a stratified fluid flows over a topography.For small mean flow, small scale instabilities develop as in the tidal case. The beam then stabilizes at intermediate mean flows and destabilizes again for increasing flow speed. At this second threshold, down to the lee wave case, the instability is of much larger scale than for the tidal case. Varying the Reynolds number, the Froude number, the wave angle or the beam size doesn't affect the instability scale selection : a small scale instability in the tidal regime, and large scale instability in the lee regime.We show that the instability mechanism may be interpreted using the triadic instability. Scale selection corresponds to different branches of triadic resonance. We confirm the presence of a stability region for intermediate value of the mean advection velocity by computing the linear eigenmode as Floquet mode with an Arnoldi-Krylov technique and show that the leading eigenmode has a negative growth rate.In the lee wave, case the flow is unstable and a selective frequency damping method cite{Akervik06} is used to compute a steady base flow. We then implement a linear direct-adjoint method to compute the optimal perturbations that maximizes the total energy at different time horizons. At short time horizon, the optimal perturbation is small scale while at large time the perturbation switches to a large scale solution and converges to the large scale mode observed through the nonlinear simulations. Short time transients correspond to the small scale triadic instability advected by the flow whereas the long time large scale instability corresponds to large scale branch of the triadic instability that is able to sustain the flow.We propose an interpretation of the selection of these different instabilities in term of absolute and convective instability. In the case of the lee wave, the large scale instability is absolute whereas the small scale instability is convective (and dominates the short time transient growth because it has a larger local growth rate). When the mean flow is varied, the properties of small scale and large scale instabilities exchange: in the tidal case the short scale instability is absolute and the large scale convective. This conjecture is confirmed by computing the impulse response around a plane monochromatic internal gravity wave in an extended two dimensional periodic domain. The spatio temporal evolution of a perturbation localized in space and time points out the formation of three different wave packets corresponding to different branches of triadic instability. Using the triadic theory with finite detuning cite{McEwan77},we derive the group velocity at the maximum growth rate of the three different branches of triadic instability and find a good agreement with the velocity of the three wave paquet maxima in the impulse response. Analyzing the impulse response along rays, i.e. at x/t and z/tconstant, we compute the absolute growth rate along all possible rays and validate our conjecture.

Nos últimos anos a presença da informática auxiliando os projetos de estruturas de edifícios em concreto armado com múltiplos pavimentos tem atingido grandes proporções. Particularmente em relação à análise das respostas da estrutura frente a solicitações impostas, essa presença possibilita a consideração de modelos estruturais teóricos muito consistentes. Por outro lado, tradicionalmente existem modelos chamados de simplificados que também retratam as respostas da estrutura, porém normalmente com menor grau de aproximação em relação ao comportamento real. Nesse sentido, são apresentadas modelagens de estruturas convencionais de edifícios compreendidas pelos dois aspectos citados, sendo analisados esforços solicitantes e deslocamentos em vigas e pilares frente a ações verticais e horizontais (análise elástico-linear). Notadamente, há uma grande preocupação com o estudo da evolução dos esforços solicitantes nesses elementos ao longo da altura do edifício. Também são abordados os esforços de 2ª ordem global, que aparecem quando atuam simultaneamente as ações verticais e horizontais. Com o intuito de exemplificar e comparar resultados, diferentes modelos estruturais são utilizados na análise do projeto de um edifício em concreto armado com múltiplos pavimentos, construído na cidade de São Carlos-SP, devendo-se destacar a modelagem tridimensional. / In the last years the computation presence auxiliaring the designs of reinforced concrete structures of multistorey buildings has reached great proportions. Particularly concerning the analysis of structural answers due to imputed solicitations, this presence makes possible the consideration of theoretical structural models very consistents. In the other side, traditionally there are models called simplifieds that also describe the structural answers, however normally with less approximation degree concerning the real behavior. In this way, modellings of conventional building structures comprehended by the two cited aspects are presented, being analysed efforts and displacements in beams and columns due to vertical and horizontal loads (elastic-linear analysis). Notably, there is a great preoccupation with the study of the efforts evolution in these elements along the building height. Also are discussed the global 2nd. arder efforts, that appear when the vertical and horizontal loads act simultaneously. In order to exemplify and to compare results, different structural models are utilized in the analysis of the design of a reinforced concrete multistorey building, constructed in São Carlos city, São Paulo state, having to detach the tridimensional modelling.

La maladie de Newcastle (MN) grève lourdement les productions aviaires malgaches, essentielles à l'alimentation et à l'économie familiales. La MN est une dominante pathologique en l'absence de vaccination généralisée. L'objectif de cette thèse est la modélisation, la validation et l'analyse mathématique de modèles de transmission du virus de la MN (VMN) dans les systèmes avicoles villageois en général et à Madagascar en particulier. Nous proposons de nouveaux modèles basés sur les connaissances actuelles de l'histoire naturelle de la transmission du VMN. Ainsi, nous présentons deux modèles mathématiques à compartiments de la transmission du VMN dans une population de poules : un premier modèle avec transmission environnementale et un deuxième modèle où la vaccination contre la maladie est prise en compte. Nous présentons une analyse complète de la stabilité de ces modèles à l'aide des techniques de Lyapunov suivant la valeur du taux de reproduction de base R0. Le travail s'est appuyé sur des enquêtes de terrain pour comprendre les pratiques de vaccination actuelles à Madagascar. / Newcastle disease (ND) severely harms Malagasy bird productions, mainly uses to food and family economy. ND is a pathological dominant without general vaccination. The objective of this thesis is modelling the transmission of ND virus (NDV) in smallholder chicken farms in general and, Madagascar in particular. We propose new models based on the state of art and the epidemiology currently known from the transmission of the NDV. Thus, we present two models of the transmission of NDV: a first model with environmental transmission and a second model in which imperfect vaccination of chickens is considered. We present a thorough analysis of the stability of the models using the Lyapunov techniques and obtain the basic reproduction ratio R0. This work is based on field surveys to understand the current vaccination practices in Madagascar.

Nos últimos anos a presença da informática auxiliando os projetos de estruturas de edifícios em concreto armado com múltiplos pavimentos tem atingido grandes proporções. Particularmente em relação à análise das respostas da estrutura frente a solicitações impostas, essa presença possibilita a consideração de modelos estruturais teóricos muito consistentes. Por outro lado, tradicionalmente existem modelos chamados de simplificados que também retratam as respostas da estrutura, porém normalmente com menor grau de aproximação em relação ao comportamento real. Nesse sentido, são apresentadas modelagens de estruturas convencionais de edifícios compreendidas pelos dois aspectos citados, sendo analisados esforços solicitantes e deslocamentos em vigas e pilares frente a ações verticais e horizontais (análise elástico-linear). Notadamente, há uma grande preocupação com o estudo da evolução dos esforços solicitantes nesses elementos ao longo da altura do edifício. Também são abordados os esforços de 2ª ordem global, que aparecem quando atuam simultaneamente as ações verticais e horizontais. Com o intuito de exemplificar e comparar resultados, diferentes modelos estruturais são utilizados na análise do projeto de um edifício em concreto armado com múltiplos pavimentos, construído na cidade de São Carlos-SP, devendo-se destacar a modelagem tridimensional. / In the last years the computation presence auxiliaring the designs of reinforced concrete structures of multistorey buildings has reached great proportions. Particularly concerning the analysis of structural answers due to imputed solicitations, this presence makes possible the consideration of theoretical structural models very consistents. In the other side, traditionally there are models called simplifieds that also describe the structural answers, however normally with less approximation degree concerning the real behavior. In this way, modellings of conventional building structures comprehended by the two cited aspects are presented, being analysed efforts and displacements in beams and columns due to vertical and horizontal loads (elastic-linear analysis). Notably, there is a great preoccupation with the study of the efforts evolution in these elements along the building height. Also are discussed the global 2nd. arder efforts, that appear when the vertical and horizontal loads act simultaneously. In order to exemplify and to compare results, different structural models are utilized in the analysis of the design of a reinforced concrete multistorey building, constructed in São Carlos city, São Paulo state, having to detach the tridimensional modelling.