La mayoría de las estructuras de hormigón armado se someten a solicitaciones combinadas de esfuerzos axiles, flexión, cortante y torsión. La fisuración del hormigón, plastificación de las armaduras y otros efectos no-lineales hacen que las secciones transversales de estos elementos presenten un comportamiento anisótropo que deriva en el acoplamiento de los esfuerzos normales y tangenciales. Es decir, esfuerzos normales o momentos flectores pueden producir deformaciones de corte y vice versa. Aunque en algunas ocaciones, esta interacción es considerada de forma simplificada en el dimensionamiento de estructuras, hasta el momento no se ha realizado un análisis profundo de los efectos acoplados en secciones de forma arbitraria bajo cargas 3D generales utilizando modelos de fibras.El objetivo principal de esta tesis es generalizar el análisis de secciones de hormigón armado mediante fibras, de forma que se pueda reproducir la res-puesta no-lineal acoplada frente a esfuerzos normales y tangenciales bajo solicitaciones tridimensionales generales. De igual forma, se pretende obtener, para los esfuerzos cortantes y torsión, la misma capacidad de representación de geometrías y combinación de materiales que ofrecen los modelos de fibras para esfuerzos de flexo-compresión.La primera problemática estriba en representar adecuadamente la cinemática de la sección transversal. Con la excepción de las deformaciones normales contenidas en el plano de la sección, no existe una teoría cinemática que a priori pueda dar la distribución del resto de deformaciones o tensiones en la sección, sin dejar de satisfacer las condiciones de equilibrio interno o continuidad entre las fibras que componen la misma.Por otra parte, para materiales anisótropos, como el hormigón fisurado, en general todos los esfuerzos internos pueden estar acoplados. Además, es preciso considerar la distorsión de la sección transversal para satisfacer el equilibrio entre fibras.El problema se aborda de forma general, considerando una sección de forma y materiales cualesquiera. Se parte del problema diferencial de equilibrio de un sólido con el que se ha podido deducir un sistema de equilibrio entre fibras (equilibrio a nivel sección). Se puede demostrar que éste es complementario al problema estándar de vigas. El sistema complementario permite recuperar información tridimensional que normalmente se pierde al resolver un problema de vigas.Posteriormente, se propone una solución interna del problema complementario, en la que el alabeo y la distorsión de la sección quedan expresados como una función de las deformaciones generalizadas de una viga: deformaciones axil y cortantes, curvaturas de flexión y torsión. No son necesarios grados de libertad adicionales a nivel estructura ni hipótesis a-priori sobre la forma de los campos de deformación o tensión interna.A partir de la formulación teórica, se desarrolla un modelo de elementos finitos plano de la sección transversal. El modelo está preparado para servir como respuesta constitutiva de cualquier tipo de elemento viga en sus puntos de integración. %Se evita así la necesidad de realizar un modelo de elementos sólidos de toda la barra para estudiar la respuesta frente a una combinación general de esfuerzos normales y tangenciales.Se implementan una serie de modelos constitutivos para distintos materiales. En particular, se implementa un modelo constitutivo triaxial para hormigón fisurado, considerando la anisotropía inducida por la fisuración e incluyendo la superficie de rotura según un criterio multiaxial.La formulación seccional es validada mediante varios casos de estudio teóricos y experimentales. La respuesta no-lineal acoplada bajo diversas combinaciones de esfuerzos normales y tangenciales es reproducida con precisión, lo cual queda patente tanto en las curvas esfuerzo-deformación obtenidas como en las matrices de rigidez seccionales.Finalmente, se recopilan las conclusiones derivadas de la presente investigación y seofren recomendaciones para futuros trabajos. / Most RC structures are subjected to combined normal and tangential forces, such as bending, axial load, shear and torsion. Concrete cracking, steel yielding and other material nonlinearities produce an anisotropic sectional response that results in a coupling between the effects of normal and shear forces, i.e. normal force or bending moments may produce shear strains and vice versa. Although this interaction is sometimes taken into account, in a simplified manner, in the design of RC structures, a deep analysis of the coupling effects of RC sections using fiber models has not yet been made for arbitrary shape sections under general 3D loading.The main objective of this thesis is to generalize the fiber-like sectional analysis of reinforced concrete elements, to make it capable of considering the coupled non-linear response under tangential and normal internal forces, from a general 3D loading.Similarly, it is desired to obtain, for torque and shear forces, the same capacity and versatility in reproducing complex geometry and materials combination that fiber-like sectional representations offers for bending and stretching.The first problematic lies in finding a proper representation of the section's kinematics under such general loading. Except for in-plane normal strains, there is no single kinematical theory capable of a-priori representing the correct distribution of the others strains or stresses satisfying, at the same time, inter-fiber equilibrium and continuity. On the other hand, for rather anisotropic materials, such as cracked concrete, all internal forces are, in general, coupled. It is also required that distortion is allowed for the section's kinematics in order to guarantee satisfaction of internal equilibrium.The problem is dealt in a general form considering arbitrary shaped sections and any material behaviour. Starting from the differential equilibrium of a solid, an inter-fiber equilibrium system (equilibrium at the sectional level) was deduced. This system, which is complementary to the standard equilibrium problem of a beam-column, allows to recuperate information of the three-dimensional problem that is generally lost when solving a beam problem.Further, a solution of the equilibrium at the sectional level is proposed in which the section's warping and distortion are posed as a function of the generalized beam-column strains (axial and shear strains, bending and torsion curvatures). No additional degrees of freedom are required at the structural level nor a-priori hypotheses on the distribution of the internal strains or stresses.After the theoretical formulation, a planar finite element model for cross-sectional analysis is developed. The model can be used as a constitutive law for general beam column elements at their integration points.A series of constitutive models have been implemented for several materials. In particular, a triaxial constitutive model for cracked concrete is implemented considering crackinduced anisotropy and a multiaxial failure criterion.The sectional formulation is validated by means of various theoretical and experimental case studies. Non-linear coupled response under normal and tangential internal forces is reproduced with accuracy, as can be seen both in the predicted internal force-strain curves and in the sectional stiffness matrixes.Finally, the conclusions drawn from the current research are summarized andrecomendations for future works are given.

<p>Today’s bridge design work in many cases demands a trustworthy dynamic analysis instead of using the traditional dynamic amplification factors. In this thesis a reliable 3D Bernoulli-Euler beam finite element model of the New Årsta Railway Bridge was prepared for thorough dynamic analysis using in situ bridge monitoring for correlation. The bridge is of the concrete box girder type with a heavily reinforced and prestressed bridge deck. The monitoring system was designed for long term monitoring with strain transducers embedded in the concrete and accelerometers mounted inside the edge beams and at the lower edge of the track slab.</p><p>The global finite element model used the exact bridge geometry but was simplified regarding prestressing cables and the two railway tracks. The prestressing cables and the tracks were consequently not included and an equivalent pure concrete model was identified.</p><p>A static macadam train load was eccentrically placed on one of the bridge’s two tracks. By using Vlasov’s torsional theory and thereby including constrained warping a realistic modulus of elasticity for the concrete without prestressing cables and stiffness contribution from the railway tracks was found. This was allowed by comparing measured strain from strain transducers with the linear elastic finite element model’s axial stresses. Mainly three monitoring bridge sections were used, each of which was modelled with plane strain finite elements subjected to sectional forces/moments from a static macadam train load and a separately calculated torsional curvature.</p><p>From the identified modulus of elasticity the global finite element model was updated for Poisson’s ratio and material density (mass) to correspond with natural frequencies from the performed signal analysis of accelerometer signals. The influence of warping on the natural frequencies of the global finite element model was assumed small and the bridge’s torsional behaviour was modelled to follow Saint-Venant’s torsional theory.</p><p>A first preliminary estimation of modal damping ratios was included. The results indicated that natural frequencies were in accordance between modelling and signal analysis results, especially concerning high energy modes. Estimated damping ratios for the first vibration modes far exceeded the lower limit value specified in bridge design codes and railway bridge dynamic analysis recommendations.</p>

Ocular torsion determination using search coils was a preferred method in a past few years. But advantages of the digital image processing techniques allows us to refuse search coils and use video-based techniques instead. The manufactures of the commercial video-based systems declare high accuracy of their product, but they don’t publish result analysis in public to improve it. We chose to use E. Greon’s (1997) suggested method with additional pattern matching using cross correlation. The landmarks of iris texture is used to track from frame to frame, so its important to enhance them. The researches helped to find out what is the most suitable iris processing and what are the optimal correlation parameters. The results showed, that a polar cross correlation can be applicable for ocular torsion measurement.

L'objet de cette thèse est de démontrer une formule reliant les métriques de Ray-Singer hypoelliptique et de Milnor sur le déterminant de la cohomologie d'une variété riemannienne compacte par une déformation à la Witten du laplacien hypoelliptique en théorie de de Rham.

Os movimentos de massa de solo, geralmente, estão relacionados com a mobilização da resistência de uma ou várias superfícies de ruptura pré-existentes. Dessa maneira, o conhecimento da propriedade que rege esse comportamento (resistência ao cisalhamento residual) é de extrema importância no estudo da estabilidade de solos. Segundo Skempton (1985), resistência ao cisalhamento residual é a resistência mínima constante que o solo pode atingir, a baixas taxas de cisalhamento, após sofrer grandes deslocamentos. A determinação dos parâmetros de resistência ao cisalhamento residual pode ser realizada através de ensaios de cisalhamento por torção do tipo ring shear, adequado para estudar os mecanismos atuantes na ruptura, uma vez que permite a continuidade dos deslocamentos no solo. Nesse contexto, a pesquisa teve por objetivo desenvolver um equipamento de cisalhamento torsional baseado no ring shear descrito por Bishop et al. (1971) para avaliar o comportamento do solo a grandes deformações. O equipamento projetado foi validado, preliminarmente, segundo os resultados já publicados na literatura. / Landslides, generally, are related with the mobilization of shear strength of one or more preexisting rupture surfaces. Thus, knowledge of the property that governs this behavior (residual shear strength) has extreme importance in the stability soils study. According to Skempton (1985), residual shear strength is the minimum constant strength attained at low shear rates, at large displacements. The residual shear strength parameters can be accomplished through ring shear tests, suitable for studying the mechanisms in the rupture, since it provides continuity of displacements in the soil. In this context, the research aimed to develop a device based on ring shear described by Bishop et al. (1971) to evaluate the soil behavior in large deformations. The equipment designed was validated, preliminarily, according to the results already published in the literature.

Os movimentos de massa de solo, geralmente, estão relacionados com a mobilização da resistência de uma ou várias superfícies de ruptura pré-existentes. Dessa maneira, o conhecimento da propriedade que rege esse comportamento (resistência ao cisalhamento residual) é de extrema importância no estudo da estabilidade de solos. Segundo Skempton (1985), resistência ao cisalhamento residual é a resistência mínima constante que o solo pode atingir, a baixas taxas de cisalhamento, após sofrer grandes deslocamentos. A determinação dos parâmetros de resistência ao cisalhamento residual pode ser realizada através de ensaios de cisalhamento por torção do tipo ring shear, adequado para estudar os mecanismos atuantes na ruptura, uma vez que permite a continuidade dos deslocamentos no solo. Nesse contexto, a pesquisa teve por objetivo desenvolver um equipamento de cisalhamento torsional baseado no ring shear descrito por Bishop et al. (1971) para avaliar o comportamento do solo a grandes deformações. O equipamento projetado foi validado, preliminarmente, segundo os resultados já publicados na literatura. / Landslides, generally, are related with the mobilization of shear strength of one or more preexisting rupture surfaces. Thus, knowledge of the property that governs this behavior (residual shear strength) has extreme importance in the stability soils study. According to Skempton (1985), residual shear strength is the minimum constant strength attained at low shear rates, at large displacements. The residual shear strength parameters can be accomplished through ring shear tests, suitable for studying the mechanisms in the rupture, since it provides continuity of displacements in the soil. In this context, the research aimed to develop a device based on ring shear described by Bishop et al. (1971) to evaluate the soil behavior in large deformations. The equipment designed was validated, preliminarily, according to the results already published in the literature.

O escopo do trabalho é estudar o problema da torção uniforme em barras de seção maciça e resolvê-lo analiticamente para obter o momento de inércia à torção da seção transversal e os deslocamentos ao longo de toda a barra. Este trabalho foi desenvolvido no contexto da Teoria da Elasticidade, utilizando o método semi-inverso para determinar as equações de Saint-Venant para a torção uniforme. As seções em forma de elipse e triângulo eqüilátero foram resolvidas utilizando a função de tensão de Prandtl, a função empenamento e a sua conjugada harmônica. A seção retangular foi resolvida utilizando as funções empenamento e de Prandtl desenvolvidas em séries infinitas. Foi desenvolvida uma formulação matricial utilizando o Método de Galerkin para resolver problemas que não possuem solução fechada. / The main purpose of this essay is to present the issue of the uniform torsion in solid section bars and to solve it analytically to achieve the moment of inertia to the torsion of the transversal section and the displacements throughout the whole bar. This essay was developed in the Elasticity Theory context, using the semi-inverse method to determine the Saint-Venant equations to the uniform torsion. The sections in ellipse and equilateral triangle were solved using the Prandtl stress function, the warping function and its harmonic conjugate. The rectangular section was solved using the warping and the Prandtl functions developed in infinite series. A formulation based on matrixes was developed using the Galerkin method to solve problems that do not have closed solution.

A verificação da estabilidade lateral de vigas pré-moldadas merece maior atenção em vigas longas e delgadas, especialmente durante as fases transitórias, como o içamento e o transporte, e também quando se leva em conta a deformabilidade das ligações temporárias. Apresenta-se nesta tese, um estado da arte sobre o problema da instabilidade lateral em vigas pré-moldadas, a fim de situar este trabalho no contexto técnico atual, bem como estudos anteriores relacionados à torção pura e quando associada a outras solicitações. Alguns modelos numéricos foram implementados computacionalmente a fim de simular o comportamento não-linear físico de vigas de concreto armado e protendido sob ação conjunta de torção, flexão bi-lateral e força axial. O modelo adequado a situações onde a torção é predominante sobre a flexão baseia-se na analogia ao comportamento de treliça espacial e na extensão da teoria dos campos diagonais comprimidos. Os resultados numéricos obtidos foram satisfatoriamente comparados aos experimentais disponíveis na literatura técnica. Nos casos onde a flexão é predominate, utilizou-se um modelo numérico que permite calcular a rigidez à torção após a fissuração por flexão da viga, sendo este o recomendado para as análises das fases transitórias de içamento por cabos. Duas vigas longas e esbeltas de concreto armado, sob tombamento lateral gradual e ação única do peso-próprio, foram moldadas e ensaiadas no laboratório. Os resultados experimentais obtidos serviram para validar o modelo numérico. No ensaio, a utilização de estações totais para medidas de deslocamentos mostrou ser uma boa alternativa, comparando-se bem aos resultados numéricos calculados. As medidas experimentais das deformações no concreto e nas armaduras concordaram satisfatoriamente com as respostas numéricas. Na aplicação à elementos estruturais com protensão, o comportamento numérico obtido para uma viga protendida de ponte de seção I, sob tombamento lateral gradual, comparou-se satisfatoriamente com a resposta experimental. Enfim, a medida da segurança do içamento de uma viga protendida de ponte e de uma tesoura protendida de cobertura foi calculada numericamente, considerando apoios deformáveis à torção. Os resultados numéricos mostram a importância de se escolher adequadamente o comprimento dos balanços, bem como a inclinação dos cabos de suspensão, garantindo a estabilidade da viga / The lateral stability of long and slender precast concrete beams requires great attention. In particular, it is important to ensure the stability of these members during transitory phases like tilting and transport, and also when the deformability of temporary supports is taken into account. The state of the art of the problem of lateral stability in precast concrete beams is presented in order to place this work in the current technical context. Previous studies of the problem of pure torsion and combined loading are reviewed. Numerical models considering the physical non-linear behavior of reinforced and prestressed concrete beams subjected to combined torsion, bi-axial bending and axial loads were implemented. The appropriate model when torsion dominates over bending is based on the space truss model and an extension of the diagonal compression field theory. The numerical results obtained compared satisfactorily with the experimental ones available in the technical literature. In bending dominated cases, a numerical model that evaluates the torsional stiffness in a cracked state due to bending is recommended for the analyses of temporary phases such as tilting. Two slender reinforced concrete beam models were built and tested under controlled gradual tilting conditions and self-weight action. These experimental results were used to validate the numerical model. Experimental results obtained using total stations for measuring displacements showed to be a good alternative, comparing well with those provided by the numerical model. The experimental measures of deformations in concrete and steel agreed well with the numerical calculations. Good agreement between numerical and experimental results was obtained for a prestressed concrete I-beam gradually tilted. Finally, a numerical analysis considering the flexibility of the supports of a prestressed concrete I-beam and a prestressed concrete truss with variable cross-section was carried out. The numerical results showed the importance of choosing the appropriate overhang length as well as the inclination of the suspension cables, in order to ensure the stability of the beam

Os movimentos de massa de solo, geralmente, estão relacionados com a mobilização da resistência de uma ou várias superfícies de ruptura pré-existentes. Dessa maneira, o conhecimento da propriedade que rege esse comportamento (resistência ao cisalhamento residual) é de extrema importância no estudo da estabilidade de solos. Segundo Skempton (1985), resistência ao cisalhamento residual é a resistência mínima constante que o solo pode atingir, a baixas taxas de cisalhamento, após sofrer grandes deslocamentos. A determinação dos parâmetros de resistência ao cisalhamento residual pode ser realizada através de ensaios de cisalhamento por torção do tipo ring shear, adequado para estudar os mecanismos atuantes na ruptura, uma vez que permite a continuidade dos deslocamentos no solo. Nesse contexto, a pesquisa teve por objetivo desenvolver um equipamento de cisalhamento torsional baseado no ring shear descrito por Bishop et al. (1971) para avaliar o comportamento do solo a grandes deformações. O equipamento projetado foi validado, preliminarmente, segundo os resultados já publicados na literatura. / Landslides, generally, are related with the mobilization of shear strength of one or more preexisting rupture surfaces. Thus, knowledge of the property that governs this behavior (residual shear strength) has extreme importance in the stability soils study. According to Skempton (1985), residual shear strength is the minimum constant strength attained at low shear rates, at large displacements. The residual shear strength parameters can be accomplished through ring shear tests, suitable for studying the mechanisms in the rupture, since it provides continuity of displacements in the soil. In this context, the research aimed to develop a device based on ring shear described by Bishop et al. (1971) to evaluate the soil behavior in large deformations. The equipment designed was validated, preliminarily, according to the results already published in the literature.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-19T18:27:28Z No. of bitstreams: 1 santiagomilerquispemamani.pdf: 952447 bytes, checksum: 6008ae3816024f866eea3c17d560372d (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T12:39:21Z (GMT) No. of bitstreams: 1 santiagomilerquispemamani.pdf: 952447 bytes, checksum: 6008ae3816024f866eea3c17d560372d (MD5) / Made available in DSpace on 2017-02-07T12:39:21Z (GMT). No. of bitstreams: 1 santiagomilerquispemamani.pdf: 952447 bytes, checksum: 6008ae3816024f866eea3c17d560372d (MD5) Previous issue date: 2016-04-25 / O objetivo deste trabalho é apresentar o resultado dado por Bass em [4], que determina uma condição no domínio de integridade R para que todo módulo finitamente gerado e livre de torção seja escrito como soma direta de módulos de posto 1. Mostramos que uma condição necessária é que todo ideal em R seja gerado por dois elementos, ou seja, que esses domínios sejam quase domínios de Dedekind. Em seguida, aplicamos o resultado na descrição de módulos livres de torção e de posto finito sobre os anéis de coordenadas de curvas singulares, cujas singularidades são nós ou cúspides. / The aim of this paper is to present the result given by Bass in [4], which determines a condition on the integral domain R so that every finitely generated torsion free module is written as a direct sum of modules of rank 1. We show that a necessary condition is that all ideal in R is generated by two elements, in other words, that these domains are almost Dedekind domains. Then, we apply the result in the description of torsion free modules of finite rank over the coordinate rings of singular curves, whose singularities are nodal or cuspidal.