<p><b>In this dissertation we present the quantitative response of an epidemic of the so-called SIR-type, in a population consisting of a local component and a migrant component. Each component can be divided into three classes, the susceptible individuals, usually denoted by S, who are uninfected but may contract the disease, infected individuals (I) who are infected and can spread the disease to the susceptible individuals and the class (R) of recovered individuals. If a susceptible individual becomes infected, it moves into the infected class. An infected individual, at recovery, moves to the class R. Firstly we develop a model describing two interacting populations with vaccination. Assuming the vaccination rate in both groups or components are constant, we calculate a threshold parameter and we call it a vaccination reproductive number. This invariant determines whether the disease will die out or becomes endemic on the (in particular, local) population. Then we present the stability analysis of equilibrium points and the effect of vaccination. Our primary finding is that the behaviour of the disease free equilibrium depend on the vaccination rates of the combined population. We show that the disease free equilibrium is locally asymptotically stable if the vaccination reproductive number is less than one. Also our stability analysis show that the global stability of the disease free equilibrium depends on the basic reproduction number, not the vaccination reproductive number. If the vaccination reproductive number is greater than one, then the disease free equilibrium is unstable and there exists three endemic equilibrium points in our model. Two of these three endemic equilibria are so-called boundary equilibrium points, which means that the infection is only in one group of the population. The third one which we focus on is the general endemic point for the whole system. We derive a threshold condition that determines whether the endemic equilibria is locally asymptotically stable or not. Secondly, by assuming that the rate of vaccination in the migrant population is constant, we apply optimal control theory to find an optimal vaccination strategy in the local population. Our numerical simulation shows the effectiveness of the control strategy. This model is suitable for modeling the real life situation to control many communicable diseases. Models similar to the model used in the main contribution of our dissertation do exist in the literature. In fact, our model can be regarded as being in-between those of [Jia et al., Theoretical Population Biology 73 (2008) 437-448] and [Piccolo and Billings, Mathematical and Computer Modeling 42 (2005) 291-299]. Nevertheless our stability analysis is original, and furthermore we perform an optimal control study whereas the two cited papers do not. The essence of chapter 5 and 6 of this dissertation is being prepared for publication.</b></p>

The thesis is based on using dynamical systems theories and techniques to study the qualitative dynamics of herpes simplex virus type 2 (HSV-2), a sexually-transmitted disease of major public health significance. A deterministic model for the interaction of the virus with the immune system in the body of an infected individual (in vivo) is designed first of all. It is shown, using Lyapunov function and LaSalle's Invariance Principle, that the virus-free equilibrium of the model is globally-asymptotically stable whenever a certain biological threshold, known as the reproduction number, is less than unity. Furthermore, the model has at least one virus-present equilibrium when the threshold quantity exceeds unity. Using persistence theory, it is shown that the virus will always be present in vivo whenever the reproduction threshold exceeds unity. The analyses (theoretical and numerical) of this model show that a future HSV-2 vaccine that enhances cell-mediated immune response will be effective in curtailling HSV-2 burden in vivo. A new single-group model for the spread of HSV-2 in a homogenously-mixed sexually-active population is also designed. The disease-free equilibrium of the model is globally-asymptotically stable when its associated reproduction number is less than unity. The model has a unique endemic equilibrium, which is shown to be globally-stable for a special case, when the reproduction number exceeds unity. The model is extended to incorporate an imperfect vaccine with some therapeutic benefits. Using centre manifold theory, it is shown that the resulting vaccination model undergoes a vaccine-induced backward bifurcation (the epidemiological importance of the phenomenon of backward bifurcation is that the classical requirement of having the reproduction threshold less than unity is, although necessary, no longer sufficient for disease elimination. In such a case, disease elimination depends upon the initial sizes of the sub-populations of the model). Furthermore, it is shown that the use of such an imperfect vaccine could lead to a positive or detrimental population-level impact (depending on the sign of a certain threshold quantity). The model is extended to incorporate the effect of variability in HSV-2 susceptibility due to gender differences. The resulting two-group (sex-structured) model is shown to have essentially the same qualitative dynamics as the single-group model. Furthermore, it is shown that adding periodicity to the corresponding autonomous two-group model does not alter the dynamics of the autonomous two-group model (with respect to the elimination of the disease). The model is used to evaluate the impact of various anti-HSV control strategies. Finally, the two-group model is further extended to address the effect of risk structure (i.e., risk of acquiring or transmitting HSV-2). Unlike the two-group model described above, it is shown that the risk-structured model undergoes backward bifurcation under certain conditions (the backward bifurcation property can be removed if the susceptible population is not stratified according to the risk of acquiring infection). Thus, one of the main findings of this thesis is that risk structure can induce the phenomenon of backward bifurcation in the transmission dynamics of HSV-2 in a population.

A new type of cantilever beam gyroscope is introduced, modeled, and analyzed. The main structure includes a cantilever beam and a rigid body attached to the free end of the beam. The model accounts for the eccentricity, that is the offset of the center of mass of the rigid body relative to the beam's free end. The first and second moments of mass and the rotary inertia appear in the equations of motion and boundary conditions. The common mechanism of electrostatic actuation of microgyroscopes is used with the difference of computing the force at the center of mass resulting in the electrostatic force and moment in the boundary conditions. By using the extended Hamilton's principle, the method of assumed modes, and Lagrange's differential equations, the equations of motion, boundary conditions, and the discretized model are developed. The generalized model simplifies to other beam gyroscope models by setting the required parameters to zero. Considering the DC and AC components of the actuating and sensing methods, the response is resolved into the static and dynamic components. The static configuration is studied for an increasing DC voltage. For the uncoupled system of equations, the explicit equation relating the DC load and the static configuration is computed and solved for the static configuration of the beam-rigid body in each direction. Including the rotation rate, the stationary analysis is performed, the stationary pull-in voltage is identified, and it is shown that the angular rotation rate does not affect the static configuration. The modal frequencies of the beam-rigid body gyroscope are studied and the instability region due to the rotation rate is computed. It is shown that the gyroscope can operate in the frequency modulation mode and the amplitude modulation mode. To operate the beam-rigid body gyroscope in the frequency modulation mode, the closed-form relation of the observed modal frequency split and the input rotation rate is computed. The calibration curves are generated for a variety of DC loads. It is shown that the scale factor improves by matching the zero rotation rate natural frequencies. The method of multiple scales is used to study the reduced-order nonlinear dynamics of the oscillations around the static equilibrium. The modulation equations, the ``slow'' system, are derived and solved for the steady-state solutions. The computational shooting method is employed to evaluate the results of the perturbation method. The frequency response and force response plots are generated. For combinations of parameters resulting in a single-valued response, the two methods are in excellent agreement. The synchronization of the response occurs in the sense direction for initially mismatched natural frequencies. The global stability of the system is studied by drawing phase-plane diagrams and long-time integration of response trajectories. The separatrices are computed, the jump phenomena is numerically shown, and the dynamic pull-in of the response is demonstrated. The fold bifurcation points are identified and it is shown that the response jumps to the higher/lower branch beyond the bifurcation points in forward/backward sweep of the amplitude and the excitation frequency of AC voltage. The mechanical-thermal (thermomechanical) noise effect on the sense response is characterized by using a linear approximation of the system and the nonlinear "slow" system obtained by using the method of multiple scales. To perform linear analysis, the negligible effect of Coriolis force on the drive amplitude is discarded. The second-order drive resonator is solved for the drive amplitude and phase. Finding the sense response due to the thermal noise force and the Coriolis force and equating them computes the mechanical-thermal noise equivalent rotation rate in terms of system parameters and mode shapes. The noise force is included in the third-order equation of the perturbation and equation to account for that in the reduced-order nonlinear response. The numerical results of linear and reduced-order nonlinear thermal noise analyses agree. It is shown that higher quality factor, higher AC voltage, and operating at lower DC points result in better resolution of the microsensor.

The thesis is based on using dynamical systems theories and techniques to study the qualitative dynamics of herpes simplex virus type 2 (HSV-2), a sexually-transmitted disease of major public health significance. A deterministic model for the interaction of the virus with the immune system in the body of an infected individual (in vivo) is designed first of all. It is shown, using Lyapunov function and LaSalle's Invariance Principle, that the virus-free equilibrium of the model is globally-asymptotically stable whenever a certain biological threshold, known as the reproduction number, is less than unity. Furthermore, the model has at least one virus-present equilibrium when the threshold quantity exceeds unity. Using persistence theory, it is shown that the virus will always be present in vivo whenever the reproduction threshold exceeds unity. The analyses (theoretical and numerical) of this model show that a future HSV-2 vaccine that enhances cell-mediated immune response will be effective in curtailling HSV-2 burden in vivo. A new single-group model for the spread of HSV-2 in a homogenously-mixed sexually-active population is also designed. The disease-free equilibrium of the model is globally-asymptotically stable when its associated reproduction number is less than unity. The model has a unique endemic equilibrium, which is shown to be globally-stable for a special case, when the reproduction number exceeds unity. The model is extended to incorporate an imperfect vaccine with some therapeutic benefits. Using centre manifold theory, it is shown that the resulting vaccination model undergoes a vaccine-induced backward bifurcation (the epidemiological importance of the phenomenon of backward bifurcation is that the classical requirement of having the reproduction threshold less than unity is, although necessary, no longer sufficient for disease elimination. In such a case, disease elimination depends upon the initial sizes of the sub-populations of the model). Furthermore, it is shown that the use of such an imperfect vaccine could lead to a positive or detrimental population-level impact (depending on the sign of a certain threshold quantity). The model is extended to incorporate the effect of variability in HSV-2 susceptibility due to gender differences. The resulting two-group (sex-structured) model is shown to have essentially the same qualitative dynamics as the single-group model. Furthermore, it is shown that adding periodicity to the corresponding autonomous two-group model does not alter the dynamics of the autonomous two-group model (with respect to the elimination of the disease). The model is used to evaluate the impact of various anti-HSV control strategies. Finally, the two-group model is further extended to address the effect of risk structure (i.e., risk of acquiring or transmitting HSV-2). Unlike the two-group model described above, it is shown that the risk-structured model undergoes backward bifurcation under certain conditions (the backward bifurcation property can be removed if the susceptible population is not stratified according to the risk of acquiring infection). Thus, one of the main findings of this thesis is that risk structure can induce the phenomenon of backward bifurcation in the transmission dynamics of HSV-2 in a population.

>Magister Scientiae - MSc / In this dissertation we present the quantitative response of an epidemic of the so-called SIR-type, in a population consisting of a local component and a migrant component. Each component can be divided into three classes, the susceptible individuals, usually denoted by S, who are uninfected but may contract the disease, infected individuals (I) who are infected and can spread the disease to the susceptible individuals and the class (R) of recovered individuals. If a susceptible individual becomes infected, it moves into the infected class. An infected individual, at recovery, moves to the class R. Firstly we develop a model describing two interacting populations with vaccination. Assuming the vaccination rate in both groups or components are constant, we calculate a threshold parameter and we call it a vaccination reproductive number. This invariant determines whether the disease will die out or becomes endemic on the (in particular, local) population. Then we present the stability analysis of equilibrium points and the effect of vaccination. Our primary finding is that the behaviour of the disease free equilibrium depend on the vaccination rates of the combined population. We show that the disease free equilibrium is locally asymptotically stable if the vaccination reproductive number is less than one. Also our stability analysis show that the global stability of the disease free equilibrium depends on the basic reproduction number, not the vaccination reproductive number. If the vaccination reproductive number is greater than one, then the disease free equilibrium is unstable and there exists three endemic equilibrium points in our model. Two of these three endemic equilibria are so-called boundary equilibrium points, which means that the infection is only in one group of the population. The third one which we focus on is the general endemic point for the whole system. We derive a threshold condition that determines whether the endemic equilibria is locally asymptotically stable or not. Secondly, by assuming that the rate of vaccination in the migrant population is constant, we apply optimal control theory to find an optimal vaccination strategy in the local population. Our numerical simulation shows the effectiveness of the control strategy. This model is suitable for modeling the real life situation to control many communicable diseases. Models similar to the model used in the main contribution of our dissertation do exist in the literature. In fact, our model can be regarded as being in-between those of [Jia et al., Theoretical Population Biology 73 (2008) 437-448] and [Piccolo and Billings, Mathematical and Computer Modeling 42 (2005) 291-299]. Nevertheless our stability analysis is original, and furthermore we perform an optimal control study whereas the two cited papers do not. The essence of chapter 5 and 6 of this dissertation is being prepared for publication. / South Africa

Made available in DSpace on 2016-06-02T20:09:07Z (GMT). No. of bitstreams: 1 DissACJJ.pdf: 4431196 bytes, checksum: 0cd979c0d63cf2d4e62f5e4290affb0c (MD5) Previous issue date: 2007-08-30 / This research comprehends a study of the analysis procedures of the global stability in precast concrete structures, considering the effect of the semi-rigid connections. A Look over in the standards and directives of the precast structures project was necessary specifically on the procedures of global stability verification, recommended by the NBR 6118. Besides, it was looked to identify particular situations where the analysis of the precast concrete structures differentiates of the analysis of the structures cast in place. Such discussion is relevant at the moment of the publication of the new NBR 9062, where the effect of the behavior of the beam-to-column connections must be considered in the analysis of the global stability. In the carried through studies, the frame action proportionate by the bending moment resistant beam-to-column connections is a efficient method of bracing of the structure since that the interdependence of some factors is analyzed as the number of the floors, the stiffness and the cracking of columns and the beams and the fixity factor &#945;R. Finally, examples of numerical application are presented with intention to guide the designer of precast concrete structures in the analysis of structures with semi-rigid connections. / Esta pesquisa compreende o estudo dos procedimentos de análise da estabilidade global em estruturas pré-moldadas considerando o efeito das ligações semi-rígidas. Foi realizada uma revisão dos critérios e diretrizes de projeto em estruturas pré-moldadas necessárias no procedimento de verificação da estabilidade global recomendada pela NBR 6118. Além disto, procurou-se identificar situações particulares em que a análise das estruturas pré-moldadas se diferencia da análise das estruturas moldadas no local. Tal discussão é relevante no momento da publicação da nova NBR-9062, onde o efeito do comportamento das ligações viga-pilar deve ser considerado na análise da estabilidade global. Nos estudos realizados, o efeito de pórtico proporcionado pelas ligações viga-pilar resistentes à flexão mostrou-se um método de contraventamento adequado desde que seja analisada a interdependência de vários fatores como o número de pavimentos, a rigidez e a fissuração de pilares e vigas e o fator de restrição à rotação &#945;R. Finalmente, são apresentados exemplos de aplicação numérica com o intuito de orientar o projetista de estruturas pré-moldadas na análise de estruturas com ligações semi-rígidas.

Made available in DSpace on 2016-06-02T20:09:21Z (GMT). No. of bitstreams: 1 6140.pdf: 6135586 bytes, checksum: ace614f1a8541a55cfb3a642af660b84 (MD5) Previous issue date: 2014-02-10 / A widely used solution in multiple pavement's edifications to absorb lateral action of the wind and promote structure stability, is to create an element of large rigidity, usually at stairs and elevators areas, denominated central core or bracing core. This structural element is formed by the junction of pillars walls and normally has a C format, what implies having the shear center is not coincidente with the gravity center of the section. It is assumed that always when the resulting of the action does not cross the section s shear center, will occur a tortion of the central core and the building. In order to verify this hipothesis inicially four models were proposed. The first with the shear center coinciding to the ground plan center. The second with the nucleus positioned in a region generally sugested in architectural projects, in other words, aligned to the central porticos, in this case with the CG very close to the center of the ground plan. The third example consists in turning the nucleus totally eccentric. At the fourth example the eccentric nucleus has its rigidity increased. Four aspects are analysed: 1) The structure must be capable of resisting the efforts introduced by the action of the wind; 2) The structure must be rigid enough to satisfy the limits of deformation for the actions in Estado Limite de Serviço; 3) The reinforcement ratio must not exceed to the limits specified in standard; 4) The verifications concerning global stability must be attended. The study shows that the position of the nucleus at the ground plan and slenderness directly influences in the occurence or not of tortion of the building as a whole. Although the wind falls on the nucleus core shear center, being asymmetrical the rigidity of the building in plan, a tortion will occur. May also be concluded that the core bracing does not support the effort proveniente of wind action by itself, before, the other pillars also contribute. / Uma solução bastante usada em edificações de múltiplos pavimentos para absorver a ação lateral do vento, e prover a estrutura de estabilidade, é criar um elemento de grande rigidez, em geral na região de escadas e elevadores, denominado núcleo central ou núcleo de contraventamento. Este elemento estrutural é formado pela junção de pilares paredes e normalmente tem seção em formato C, o que implica ter o centro de cisalhamento não coincidente com o centro de gravidade da seção. Supõe-se que sempre que a resultante da ação não passar pelo centro de cisalhamento da seção, ocorrerá torção do núcleo central e do prédio. Para verificação desta hipótese foram propostos inicialmente quatro modelos. O primeiro com o centro de cisalhamento coincidindo com o centro da planta. O segundo com núcleo posicionado em região mais comumente sugerido em projetos arquitetônicos, ou seja, alinhado aos pórticos centrais, e neste caso com o CG muito próximo ao centro da planta. O terceiro exemplo consiste em tornar o núcleo totalmente excêntrico. No quarto exemplo o núcleo excêntrico tem rigidez aumentada. Quatro aspectos são verificados: 1) A estrutura deve ser capaz de resistir aos esforços introduzidos pela ação do vento; 2) A estrutura deve ter rigidez suficiente para satisfazer os limites de deformação para as ações em Estado Limite de Serviço; 3) A taxa de armadura não deve exceder aos limites especificados em norma; 4) Devem ser atendidas às verificações quanto à estabilidade global. O estudo mostrou que a posição do núcleo em planta e a esbeltez influencia diretamente na ocorrência ou não de torção do prédio com um todo. Ainda que o vento incida no centro de cisalhamento do núcleo, estando assimétrica a rigidez do prédio em planta, ocorrerá torção. Pode-se concluir também que o núcleo de contraventamento não trata sozinho o esforço proveniente da ação do vento, antes os demais pilares também contribuem.

Cette thèse vise à mettre en évidence les limites du contrôle passif en utilisant des éléments de rugosité miniaturisés. La topologie des écoulements induite par la présence d’une rugosité cylindrique et des générateurs de tourbillons miniaturisés a été étudiée pour analyser la dynamique pour des temps court et long. Différentes bifurcations supercritiques ont été examinées au moyen d’une analyse de stabilité globale. La bifurcation souscritique est déclenchée par des mécanismes de croissance transitoire de l'énergie ou par la réceptivité de modes globaux stables. Des structures deforçage optimal 3D sont extraites pour comprendre la distribution spatiale liée à la fréquence de résonance du système. La simulation numérique directe perturbée révèle le rôle central du mode global le moins stable dans les instationnarités non-linéaires observées. Une analyse détaillée des structures tourbillonnaires montre qu’elles sont principalement liées aux mécanismes linéaires sous-jacents. La principale caractéristique globale du mode propre est liée à la présence d’une zone de séparation en aval de la rugosité cylindrique. En utilisant des générateurs de tourbillon miniaturisés, cette zone de séparation est fortement diminuée et aucun mode global isolé est alors présent. La dynamique de l’écoulement se révèle être conduit non seulement par le nombre de Reynolds de rugosité et par son rapport d'aspect géométrique, mais aussi par le rapport entre la hauteur de la rugosité et l’epaisseur de couche limite. / This thesis aims at highlighting the limits of passive control by usingminiaturized roughness elements. The flow topology induced by the presence ofcylindrical roughness and miniaturized vertex generators has been studied to uncover asymptotic and short time dynamics. Supercritical bifurcations has been investigated by means of global stability analysis. Subcritical bifurcation are induced by transient growth of the energy or receptivity of stable global modes. 3D optimal forcing structures are extracted to figure out the spatial distribution linked to the resonant pulsation. Perturbed direct numerical simulation reveals the pivotal role of the less steady global mode in the non-linear unsteadiness. A detailed analysis of the flowstructures is provided and linked to the involved linear mechanisms. Global feature of the eigenmode are linked to the presence of the separation zone behind the cylindrical roughness. By using miniaturized vortex generators the separation zone is suppressed and no isolated global modes are present. The flow dynamics turns out to be driven not only by roughness Reynolds number and geometrical aspect ratio but also by the ratio between the roughness height and the boundary layer thickens.

No presente trabalho são avaliados os principais parâmetros de projeto na análise da estabilidade global de estruturas em concreto pré-moldado de múltiplos pavimentos, considerando a não-linearidade física (NLF), não-linearidade geométrica (NLG) e ligações semi-rígidas. Os sistemas estruturais analisados são constituídos por pórticos com ligação viga-pilar semi-rígida e pilares engastados na fundação. As ligações viga-pilar têm sua tipologia definida por chumbadores retos e capa de concreto moldado in loco com armadura de continuidade. A NLF é avaliada segundo a construção dos diagramas M x N x 1/r, onde foi considerado de forma consistente o efeito da força normal, da armadura passiva, da armadura ativa e a reologia do concreto. São propostas funções e definidos coeficientes redutores de rigidez que foram comparados com valores apontados em expressões normativas que contemplam de forma aproximada a NLF. A NLG é avaliada com o auxílio do programa ANSYS e na forma aproximada segundo o coeficiente z e o método da carga lateral fictícia (P-). Apresentam-se modelos analíticos de caracterização de rigidez e resistência de ligações viga-pilar ao momento fletor negativo e positivo. Na análise numérica é feito um estudo de caso completo de uma estrutura típica de múltiplos pavimentos em concreto pré-moldado com o auxílio do programa ANSYS, avaliando-se diferentes formas de consideração da NLF e da NLG. É analisada a distribuição de esforços na estrutura frente às combinações de ações utilizadas e os modelos de comportamento das ligações, para algumas variações de geometria e carregamento. Dentre as conclusões, pode ser citado que os coeficientes redutores obtidos segundo o diagrama M x N x 1/r divergem das indicações normativas para consideração simplificada de NLF. Quanto à consideração simplificada de análise NLG, o coeficiente z apresentou resultados melhores na previsão dos esforços de segunda ordem em relação aos obtidos por 0,95.z. / In this research it was evaluated the main design parameters in the analysis of global stability of multi-storey precast concrete framed structures considering the physical nonlinearity (PNL), geometric nonlinearity (GNL) and semi-rigid connections behavior. The structural systems considered are those consisting of frames with beam-to-column semi-rigid connection and columns inset in the foundation. The beam-to-column connections are defined by two dowels and cast-in-place concrete cap with longitudinal reinforced bars. The PNL is evaluated according the M x N x 1/r diagrams, where are considered the effect of normal force, the reinforcing steel, prestressing steel and creep. Functions are proposed and reducing stiffness coefficients are defined, with were compared with codes that include the approximated PNL. The GNL is evaluated according to ANSYS software by no approximate analisys and its approximate according to the coefficient z and (P-) method. This research presents an analytical model characterization of stiffness and strength of beam-to-column connections to the negative and positive bending moment. In the numerical analysis is made a full case study of a typical multi-storey precast concrete framed structure with the aid of the ANSYS software, evaluating different forms of consideration of the PNL and the GNL. It analysed the bending moment distribution according the combinations of actions used and the behavioral models of connections, for some variations at geometry and loading. The reduction coefficients of flexural rigidity obtained according the M x N x 1/r diagrams differ from normative indications for simplified account of PNL. In GNL simplified analysis, the coefficient z showed better results in predicting the second-order effects with respect to those obtained by the coefficient 0,95. z.

O presente trabalho tem como objetivo desenvolver processos analíticos e programas computacionais para avaliação da estabilidade global e pré-dimensionamento de pórticos planos em concreto pré-moldado com base na garantia da estabilidade global. Em relação à avaliação da estabilidade global, são propostas duas expressões. A primeira está relacionada à expressão do limite do parâmetro de estabilidade aplicada a pórticos planos em concreto pré-moldado. A segunda expressão tem o objetivo determinar o deslocamento horizontal de topo de pórticos planos em concreto pré-moldado de um pavimento. A expressão do limite alternativo do parâmetro de estabilidade é deduzida a partir dos valores obtidos da relação entre o deslocamento horizontal médio e de topo de 1320 pórticos. A expressão é função do fator de restrição da ligação, contemplando, dessa forma, os efeitos causados pela semirrígidez das ligações no comportamento da estabilidade global desse sistema estrutural. A equação de determinação do deslocamento horizontal de topo de pórticos planos em concreto pré-moldado de um pavimento é deduzida com base no método dos deslocamentos. Em relação ao pré-dimensionamento de pórticos planos em concreto pré-moldado, são propostos processos analíticos para o pré-dimensionamento dos pilares de pórticos de um pavimento com ligação semirrígida e de pórticos de múltiplos pavimentos com ligações rígidas e articuladas. Os processos analíticos são constituídos pela expressão da rigidez equivalente de estabilidade de pórticos, desenvolvida através das equações do parâmetro de estabilidade e do seu limite alternativo. O trabalho ainda apresenta o Programa de Avaliação da Estabilidade Global e Pré-dimensionamento de Pórticos Planos em Concreto Pré-moldado, denominado PRE-MOLDIM. O programa é constituído por quatro módulos. O primeiro módulo realiza a avaliação da estabilidade global e verificação da deslocabilidade lateral de pórticos planos em concreto pré-moldado. O segundo módulo tem o objetivo de definir as dimensões mínimas dos pilares em função da garantia da estabilidade global e do deslocamento lateral admissível. O terceiro módulo define o valor da rigidez das ligações necessário para que sejam atendidos os quesitos de estabilidade global e deslocamento lateral admissível. O quarto módulo realiza o dimensionamento da armadura de continuidade de uma típica ligação viga-pilar em concreto pré-moldado. O dimensionamento da armadura de continuidade é realizado em função da garantia da estabilidade global e do deslocamento lateral admissível de pórticos planos em concreto pré-moldado. A aplicação dos processos analíticos e programas computacionais em exemplos comprovaram, de forma satisfatória, o desempenho de suas funções. Os valores obtidos pela expressão alternativa do limite do parâmetro de estabilidade são compatíveis com o limite do coeficiente \'gama\'z. Os valores do deslocamento de topo de pórticos de um pavimento com ligações semirrígidas, obtidos pelo processo analítico, são próximos dos valores obtidos pela simulação numérica. Os pilares pré-dimensionados pelos processos analíticos conseguem garantir de forma satisfatória estabilidade global dos pórticos planos em concreto pré-moldado. / The present work aims to develop analytical processes and computer programs for the evaluation of global stability and preliminary design of plane frames in precast concrete based on ensuring global stability. Regarding the evaluation of global stability, two analytical expressions are proposed. The first is related to the expression of the limit of the stability parameter applied to plane frames in precast concrete. The second expression has the objective to determine the horizontal displacement of the top of plane frames in precast concrete for a floor. The expression of the alternative stability limit of the parameter is deduced from the values obtained from the relationship between the average and the top horizontal displacement of 1320 frames. The expression is a function of the limiting factor of the connection, thus contemplating the effects caused by the semi-rigidity of the connection on the global stability behavior of this structural system. The equation for determining the horizontal displacement of the top of plane frames in precast concrete pavement is obtained based on the displacement method. Regarding the preliminary design of plane frames in precast concrete, analytical procedures are proposed for the preliminary design of column of an one store frame with semi-rigid connection and a multiple store frames with rigid and articulated connections. The analytical processes are constituted by the expression of equivalent stiffness of frame stability, developed through the equations of the stability parameter and its alternative limit. The work also presents the Program of Global Stability Evaluation and Preliminary Design of Plane Frames in Precast Concrete, called PRE-MOLDIM. The program consists of four modules. The first module performs the evaluation of global stability and verification of lateral plane frames displaceability in precast concrete. The second module aims to set minimum dimensions for the pillars due to guarantee the global stability and check the allowable lateral displacement. The third module defines the value of the connections stiffness so the matter of global stability and allowable lateral displacement are satisfied. The fourth module performs the design of continuity armor of a typical beam-column connection in precast concrete. The design armour continuity is made on the basis of ensuring the global stability and lateral displacement allowable plane frames in precast concrete. The application of analytical processes and computer programs in examples proved satisfactorily, the performance of its functions. The values obtained by the alternative expression of the limit of stability parameter are compatible with the limit of the coefficient \'gama\'z. The offset values top venting a pavement with semi-rigid connections, obtained by the analytical process, are close to the values obtained by numerical simulation. The preliminary designed pillars by analytical processes can ensure a satisfactory global stability of the plane frames in precast concrete.