En aquest treball s'ha desenvolupat un model per a l'anàlisi no lineal i evolutiva, en servei, de pòrtics plans de formigó armat o pretensat, aplicable també a estructures mixtes, que incorpora els principals fenòmens que intervenen en el seu comportament. El model es basa en una extensió de la formulació matricial per a l'anàlisi de barres (Formulació Matricial Generalitzada - FMG) aplicada a estructures reticulars planes. La contribució del formigó traccionat entre fissures (tension stiffening) es contempla mitjançant un model de fissuració distribuïda que modifica la lleii constitutiva del formigó en tracció. S'ha realitzat un estudi detallat de l'esmentat model tant en comportament instantani com diferit i es presenta una proposta par a la determinació dels coeficients que el defineixen a partir de les característiques seccionals. S'ha contemplat la construcció evolutiva tant a nivell seccional com estructural, la variació de les propietats dels materials amb el temps i la variació temporal de les accions. La generalitat de la proposta permet la incorporació del comportament diferit dels materials segons diferents formulacions i la inclusió futura de lleis constitutives no lineals per a l'acer o el formigó en compressió. El model s'ha mostrat capaç de reproduir de manera adequada els resultats obtinguts de procediments analítics, d'altres models i els d'assaigs disponibles en bases de proves de referència (benchmarks). També s'ha contrastat satisfactòriament amb els assaigs realitzats. En els exemples presentats es mostra l'aptitud per a l'anàlisi d'estructures amb un nombre relativament elevat de nusos i de barres i amb processos constructius diversos i es posa de manifest la possibilitat de realitzar estudis paramètrics per a analitzar la influència de diferents variables. La part experimental ha consistit en la construcció, instrumentació i assaig d'una biga contínua de formigó armat de dos trams amb càrregues puntuals aplicades al centre de cadascun d'ells. Poden distingir-se tres fases: càrrega fins a les condicions de servei, descàrrega i reforç, finalment, càrrega fins a la ruptura. El reforç consisteix en la incorporació de xapes metàl·liques adherides amb resines epoxídiques. La instrumentació instal·lada i els mesuraments manuals realitzats han permès seguir l'evolució de tensions, deformacions i desplaçaments. Els resultats mostrat un alt grau de concordança amb els que s'han obtingut amb el model numèric desenvolupat. / En el presente trabajo se ha desarrollado un modelo para el análisis no lineal y evolutivo, en servicio, de pórticos planos de hormigón armado o pretensado, también aplicable a estructuras mixtas, que incluye los principales fenómenos que intervienen en su comportamiento. El modelo se basa en una extensión de la formulación matricial para el análisis de barras (Formulación Matricial Generalizada - FMG) aplicada a estructuras reticulares planas. La contribución del hormigón traccionado entre fisuras (tension stiffening) se contempla mediante un modelo de fisuración distribuida que modifica la ley constitutiva del hormigón en tracción. Se ha realizado un estudio detallado de dicho modelo tanto en comportamiento instantáneo como diferido y se presenta una propuesta para la determinación de los coeficientes que lo definen a partir de las características seccionales. Se ha contemplado la construcción evolutiva tanto a nivel seccional como estructural, la variación de las propiedades de los materiales con el tiempo y la variación temporal de las acciones. La generalidad de la propuesta permite la incorporación del comportamiento diferido de los materiales según distintas formulaciones y la inclusión futura de leyes constitutivas no lineales para el acero o el hormigón en compresión. El modelo se ha mostrado capaz de reproducir de manera adecuada los resultados obtenidos de procedimientos analíticos, de otros modelos y los de ensayos disponibles en bases de pruebas de referencia (benchmarks). Asimismo se ha contrastado satisfactoriamente con los ensayos realizados. En los ejemplos presentados se muestra la aptitud para el análisis de estructuras con un número relativamente elevado de nudos y de barras y con procesos constructivos diversos y se pone de manifiesto la posibilidad de realizar estudios paramétricos para analizar la influencia de distintas variables. La parte experimental ha consistido en la construcción, instrumentación y ensayo de una viga continua de hormigón armado de dos vanos con cargas puntuales aplicadas en el centro de cada uno de ellos. Pueden distinguirse tres fases: carga hasta condiciones de servicio, descarga y refuerzo y, finalmente, carga hasta la rotura. El refuerzo consiste en la incorporación de chapas metálicas adheridas con resinas epoxídicas. La instrumentación instalada y las mediciones manuales realizadas han permitido seguir la evolución de tensiones, deformaciones y desplazamientos. Los resultados han tenido un alto grado de concordancia con los obtenidos mediante el modelo numérico desarrollado. / A model for the non-linear analysis under serviceability conditions of plane concrete frames (suitable for composite concrete - steel structures) taking into account segmental construction has been developed. The model is based in an extension of the classical matrix theory for the analysis of frames (Generalized Matrix Formulation - GMF). The contribution of the tensioned concrete between cracks (tension stiffening) is simulated by a modified constitutive law for concrete in tension. A detailed study of the model for both instantaneous and long - time behavior has been performed, and a proposal to determine the coefficients defining the uniaxial tensioned concrete constitutive relationship from sectional characteristics is presented. Segmental construction (sectional and structural), load history and temporal changing in material properties are considered in the model. The generality of the proposal allows simulating the materials time - dependent behavior using several formulations. In future development, non - linear constitutive laws for the steel and for the compressed concrete will be incorporated. The model has been able to adequately reproduce the results obtained from analytical procedures, other models and from experiments available in benchmarks. Likewise good agreement has been obtained with results from specific tests carried out for this work. An objective of the thesis was to develop a scaled - up model suitable to analyze structures with many elements and with diverse construction processes. The examples included show it as well as the possibility to make parametrical studies to analyze the influence of several variables. The experimental part of the work has consisted in the construction, instrumentation and testing of a two - span continuous reinforced concrete beam with concentrated loads at the center of each span. Three phases can be distinguished: loading until serviceability conditions, unloading and strengthening and, finally, loading until collapse. Strengthening consists in bonded steel plates using epoxy resins. The installed instrumentation and the manual measurements have allowed registering the variation of stresses, strains and displacements. The results have showed a good agreement with those obtained from the numerical model.

Fibrin is a biopolymer that assembles into a network during blood coagulation to become the structural scaffold of a blood clot. The precise mechanics of this network are crucial for a blood clot to properly stem the flow of blood at the site of vascular injury while still remaining pliable enough to avoid dislocation. A hallmark of fibrin's mechanical response is strain-stiffening: at small strains, its response is low and linear; while at high strains, its stiffness increases non-linearly with increasing strain. The physical origins of strain-stiffening have been studied for other biopolymer systems but have remained elusive for biopolymer networks composed of stiff filaments, such as fibrin. To understand the origins of this intriguing behavior, we directly observe and quantify the motion of all of the fibers in the fibrin networks as they undergo shear in 3D using confocal microscopy. We show that the strain-stiffening response of a clot is a result of the full network deformation rather than an intrinsic strain-stiffening response of the individual fibers. We observe a distinct transition from a linear, low-strain regime, where all fibers avoid any internal stretching, to a non-linear, high-strain regime, where an increasing number of fibers become stretched. This transition is characterized by a high degree of non-affine motion. Moreover, we are able to precisely calculate the non-linear stress-strain response of the network by using the strains on each fiber measured directly with confocal microscopy and by assuming the fibers behave like linearly elastic beams. This result confirms that it is the network deformation that causes the strain-stiffening behavior of fibrin clots. These data are consistent with predictions for low-connectivity networks with soft, bending, or floppy modes. Moreover, we show that the addition of small contractile cells, platelets, increases the low-strain stiffness of the network while the high-strain stiffness is independent of the presence of the platelets; this is also consistent with expectations for small contractile elements in a network with low connectivity. Our results elucidate the origins of strain-stiffening in fibrin networks as well as the mechanism underlying platelet-induced clot stiffening. / Physics

Doctor of Philosophy / Department of Civil Engineering / Hayder A. Rasheed / This study is conducted because of the lack of an existing theory to accurately predict the diagonal tension cracking in shallow reinforced concrete beams. A rational approach is followed to numerically derive the shear stress profile across the depth of the beam in cracked beams based on the smeared crack approach. Furthermore, the determined shear stress distribution coupled with the normal axial stress distribution are used to predict the principal stress variation across the depth and along the shear span using standard Mohr’s circle. Following a biaxial stress cracking criterion, the likely diagonal tension cracks along their orientation profile are predicted. Furthermore, this study is conducted to provide a mechanics-based understanding of the shear stress distribution in cracked reinforced concrete. This approach utilizes the transversal shear differential equation to evaluate the shear stress at any given depth by the variation of the axial stress distribution within an infinitesimal beam segment at that depth. In addition, this study presents a more accurate representation of the change in the strain profile parameters with respect to the sectional applied moment. Furthermore, the dowel action effect is derived to illustrate its significance on the shear stress distribution at various stages of loading.

Les travaux effectués dans cette thèse portent sur l'étude du comportement des éléments en béton armé avec de l'acier inoxydable. Le comportement d'une barre d'acier seule n'est pas le même que celui d'une barre enrobée de béton. L'adhérence permet au béton situé entre les fissures de résister à des efforts de traction, réduisant ainsi le niveau moyen d'effort dans l'acier. La considération de cet effet a nécessité la mise en place d'une méthodologie expérimentale et numérique afin de déterminer les paramètres de transfert d'une partie des efforts de traction de l'acier vers le béton. Une nouvelle loi de comportement spécifique pour les barres en acier inoxydable a été développée. Cette loi est intégrée dans une approche de modélisation non linéaire du comportement d'éléments en béton armé selon une discrétisation par couches horizontales pour l'analyse en section et une discrétisation verticale pour l'analyse globale. Cette approche permet de déterminer les paramètres du modèle de raidissement en traction du béton. Ces paramètres sont identifiés grâce à la méthode inverse par comparaison entre les résultats expérimentaux et ceux issus du calcul numérique. La comparaison entre les résultats expérimentaux et la prédiction du modèle implémenté dans Abaqus démontre une très bonne concordance. Enfin, l'effet de l'acier inox sur les réponses structurales sous actions sismiques est présenté. Trois modèles sont conçus et analysés vis-à-vis de la capacité sismique en tenant compte de la ductilité structurale apportée par les armatures inox / This thesis focus on studying the behavior of composite concrete reinforced with inoxydable steel. The behavior of a bare steel bar is not the same as that of a bar embedded in concrete. The grip allows the concrete between cracks to resist tensile forces, thereby reducing the average level of stress in the reinforcement steel bars. The consideration of this effect required an experimental and numerical methodology to determine the parameters that describe the transfer of part of the tensile stress in steel bars to concrete. A new constitutive law has been specifically developed for the inoxydable steel bars. This law is integrated into a nonlinear modeling approach of reinforced concrete elements based on discretization in horizontal layers for the analysis section and a vertical discretization for the overall analysis. This approach is able to determine the tension stiffening parameters of the concrete. These parameters are identified using an inverse method by comparing experimental results and those from the numerical calculation. The comparison between experimental results and the prediction of the model implemented in Abaqus shows a very good correlation. Finally, the effect of inoxydable steel on structural responses under seismic actions is presented. Three models are designed and analyzed based on the seismic capacity taking into account the structural ductility of the inoxydable steel

Mit der vorliegenden Arbeit wurde ein Beitrag zur Klärung des Querkrafttragverhaltens von Wandscheiben im Mauerwerksbau geleistet. Die Untersuchungen umfassten hierbei analytische, numerische und versuchstechnische Betrachtungen. Als Grundlage für die Untersuchungen wurden FE-Elemente und FE Materialroutinen, die auf die Materialspezifik des Mauerwerks abgestimmt sind, entwickelt und in das Programmsystem ANSYS implementiert. Als wesentliche Eingangsgrößen sowohl für die analytischen als auch die numerischen Berechnungen werden diverse Materialparameter benötigt. Neben den üblichen Materialversuchen sind weiterführende Betrachtungen zu den „Kleinversuchen“ angestellt worden. Für einige Materialparameter waren numerische Rückrechnungen, wie z.B. für die Keilspaltversuche, erforderlich. Für ein breites Spektrum an Materialien, angefangen beim Ziegel über Mörtel bis zum Lehm, konnten wesentliche Werte ermittelt werden. Die vorhandenen analytischen Modelle der Schubfestigkeit wurden im Rahmen der vorgelegten Arbeit weiterentwickelt. Nach der Herleitung neuer Gleichungen galt es, diese für die Anwendung zu vereinfachen. Es sind auch numerische Modelle erläutert, die einen minimierten Wandausschnitt darstellen und mit denen eine direkte Berechnung der Schubfestigkeit möglich ist. Neben der Schubfestigkeit des Mauerwerks haben auch die Wandgeometrie und die Einbindung der Wand in das Gebäude Einfluss auf die maßgebende Querkrafttragfähigkeit. Zu deren Berücksichtigung werden wiederum Ingenieurmodelle benötigt, deren Komponenten hier eingehender betrachtet wurden. Als Grundlage dienten weitere Versuche basierend auf dem Modell der Aussteifungswand im Gebäude. Sowohl aus den analytisch gewonnenen Gleichungen als auch aus den an den Versuchen kalibrierten Gleichungen sind Lösungen für die Normung entwickelt worden. Diese beinhalten neben Gleichungen für das genaue Verfahren auch stark vereinfachte Bemessungslösungen mit tabellarisch aufbereiteten Mindestquerschnitten für die Aussteifungswände.

A deterministic approach based on a modal expansion and modal receptance method has been developed to evaluate the airborne sound insulation of aircraft panels with stringer and ring frame attachments. Furthermore, this method was extended to predict the noise radiation of stiffening panel subjected to TBL excitation. This approach integrates with the fast and accurate methods in evaluating the modal excitation terms and modal radiation efficiency. Based on these advantages, the effects of the curvature, overpressure, stringers, ring frames, hydrodynamic coincidence, composite structures and structural dissipation on the acoustical properties of a typical aircraft panel are able to be investigated efficiently. Theoretic predictions were compared with laboratory measurements conducted on both model structures and aircraft panels. It was found that a small curvature may result in significant deterioration of the sound transmission loss at frequencies of interest. Unlike a flat uniform panel, the theoretical prediction for curved panels from the infinite model can not provide good agreement with the measurement close to and well below the ring frequency. However, in this frequency range, the finite model has been proved to be applicable For the large curved airplane panels studied here, it was found that the ring frames have little influence on sound transmission loss in the frequency range of interest. However the stringers may have considerable influence on sound transmission loss. The stringer improves this for a curved panel around the ring frequency, but it may result in a potential deterioration of the sound transmission loss above the ring frequency. In this study it is evident that the sound transmission loss of the composite skin attached with composite stringers is lower than that of the metallic panel attached with metallic stringers. At frequencies higher than the corresponding ring frequency of the curved panel, both experiment and theoretical prediction reveal that the overpressure at the concave side tends to reduce the sound transmission loss at the rate of about 0.5dB /10000 Pa. While at lower frequencies, say well below the ring frequency, the overpressure may increase or reduce sound transmission loss of a finite panel, depending on the shift of the resonant frequencies resulting from the overpressure. For TBL excitation, numerical investigation reveals that the panel with the ring frames behaves more like a sub-panel between two frames. Below 500Hz, the ring frames slightly enhance the sound radiation while dramatically increasing it around 1.3kHz. The TBL forcing field excites the same vibration lever for the panel with and without ring frame attachments, but the modes excited for the panel with ring frames radiate more sound. Unlike the ring frames, the stringers increase sound radiation below 1kHz. Above 1kHz, the sub-panels between two bays respond independently and the stringer effects is therefore not obvious. / <p>QC 20100908</p>

A verificação ao cisalhamento de vigas de concreto armado é realizada, geralmente, assumindo sua independência do comportamento à flexão. Dentre os mecanismos que influenciam na resistência à força cortante, a força cortante transmitida pelo banzo comprimido da viga e o engrenamento de agregados são os mais abordados em pesquisas nos ultimos anos. Ambos dependem do nível de tensões normais atuante na seção do elemento. Sendo assim, o comportamento ao cisalhamento fica evidentemente dependente do comportamento à flexão e de como o concreto se comporta à tração e à compressão. Para melhor entender este comportamento, este trabalho compreendeu duas frentes de análise: experimental e numérica. Ensaios de tirantes foram realizados no intuito de avaliar o enrijecimento à tração do concreto com fibras. Além disso, ensaios de flexão em três pontos em prismas de 15cm x 15cm x 50 cm foram feitos para avaliar o comportamento pós-pico à tração do concreto. Ensaios de compressão em cilindros de concreto 10×20cm foram realizados de maneira a apontar estimativas para a energia de fratura à compressão e o comportamento pós-pico do concreto com diferentes taxas volumétricas de fibras. Seguindo os resultados experimentais, simulações numéricas dos ensaios de flexão em três pontos e dos ensaios de compressão foram desenvolvidas com o intuito de melhorar o entendimento dos ensaios realizados. Estes estudos aperfeiçoaram primordialmente os conhecimentos do comportamento do concreto à tração e compressão pós-fissuração. Foram ensaiadas nove vigas de concreto armado variando volume de fibras e a relação entre a distância da carga até o apoio mais próximo e a altura útil da viga ( a / d). Os resultados destes ensaios mostram que a resistência à força cortante aumenta com a taxa volumétrica de fibras e que o esquema estático adotado interfere pouco na resistência. Além disso, os resultados do estudo de caracterização do comportamento pós-pico do concreto foi aplicado na simulação numérica da viga. Os resultados numéricos apontam diferenças na rigidez global quando comparados com os resultados experimentais. / The shear strength verification of reinforced concrete beams is generally performed assuming their independence from the flexural behavior. Among the mechanisms that influence the shear strength, the shear force transmitted by the concrete compressed zone of the beam and the aggregate interlock are the most studied in the last years. Both depend on the level of normal stresses acting on the element section. Therefore, the shear behavior is obviously dependent on the flexural behavior and how the concrete behaves in tension and compression. For a better understanding, this work comprised two fronts of analysis: experimental and numerical. Tension ties tests were performed in order to evaluate the tension stiffening of concrete with fibers. In addition, three-point bending tests on 15cm x 15cm x 50cm prisms were made to evaluate the post-peak tension behavior of the concrete, or tension softening. Compression tests on 10 × 20cm concrete cylinders were carried out in order to estimate the compression fracture energy and the post-peak behavior of concrete with different volumetric fiber rates. Following the experimental results, numerical simulations of the three-point bending tests and the compression tests were developed with the aim of improving the understanding of the tests performed. These studies have the aim of improving the understanding of the three-point bending and compression tests performed. Nine reinforced concrete beams were tested, varying the volume of fibers and the relation between the distance of the load to the closest support and the useful height of the beam (a/d). The results of these tests show that shear strength increases with the volumetric rate of fibers and that the static scheme adopted does not interfere in resistance. In addition, the results of the post-peak concrete characterization study of the concrete were applied in the numerical simulation of the beam. Numerical results show differences in overall stiffness when compared with experimental results.

O presente trabalho é uma contribuição para o esclarecimento e a quantificação das influências na deformabilidade e na capacidade portante de elementos unidimensionais de concreto armado em solicitação plana, decorrentes da não-linearidade física dos materiais concreto e aço, bem como da fissuração e do enrijecimento da armadura tracionada, também na sua fase plástica. Para aplicações práticas determinam-se a rigidez à flexão e a capacidade de rotação plástica dos elementos estruturais, o que permite limitar com mais precisão e coerência a demanda de rotação plástica obtida na análise. De início, descrevem-se os comportamentos não-lineares do concreto e do aço, aplicando-se conceitos da Mecânica da Fratura, bem como a atuação conjunta destes materiais, sob os aspectos de aderência e de fissuração. O núcleo deste trabalho concentra-se na obtenção do diagrama momento-curvatura e dos seus pontos principais, e na subseqüente determinação da capacidade de rotação plástica dos mencionados elementos. Consideram-se as seções geradas a partir da seção duplo T assimétrico, com várias camadas de armadura, sujeitas à flexão composta normal. Com dados deste diagrama e através do modelo da viga equivalente simétrica, posteriormente estendido à viga equivalente assimétrica e às vigas contínuas de pórticos planos, determina-se a capacidade de rotação plástica, considerando-se nesta suas múltiplas influências. Por fim, comparam-se os resultados teóricos e experimentais da capacidade de rotação plástica, e resumem-se as principais conclusões encontradas e os pontos que exigem subseqüente desenvolvimento. / The present study is a contribution to the enlightenment and evaluation of the influences on deformability and load carrying capacity of one-dimensional elements of reinforced concrete subject to in-plane loading, arisen from the constitutive non-linearity of concrete and steel, as well as from the concrete cracking and the tension stiffening of the reinforcement, prior and after yielding. For practical applications, the flexural rigidity and the plastic rotation capacity of structural elements are determined, which makes it possible to limit, more precisely and coherently, the plastic rotation demand coming from the analysis. Firstly, the non-linear behaviors of concrete and steel are described, applying concepts of Fracture Mechanics, and then the joint action of both materials concerning bond and cracking is studied. The core of this study lies on obtaining the bending moment-curvature diagram, specially its main points, and on the subsequent determination of the plastic rotation capacity of the aforementioned elements. The cross-sections generated from an asymmetric double T cross-section are considered, with several layers of reinforcement, acted upon simple or combined bending about one principal axis. With data based on this diagram and through the model of equivalent symmetric beam, later extended to equivalent asymmetric beam and to continuous beams of plane frames, the plastic rotation capacity is determined, considering its multiple influences. Finally, theoretical and experimental results of plastic rotation capacity are compared, and the main conclusions and points in need of subsequent development are summarized.

It is well known that crack spacings and widths can be reduced with the addition of steel fibres to a concrete mix. However, test data for the tensile behaviour of steel fibre reinforced concrete members containing conventional steel reinforcement (R/FRC members) are scarce relative to those of reinforced concrete (RC) specimens and fibre reinforced concrete (FRC) specimens without reinforcing bars. In this research program, uniaxial tension tests were conducted on 12 RC and 48 R/FRC specimens in order to observe cracking and tension stiffening behaviour. The parameters under observation were fibre volumetric content, fibre length and aspect ratio, conventional reinforcement ratio and steel reinforcing bar diameter. ‘Dog-bone’ tension tests and bending tests were also performed in order to determine tensile material properties. It was discovered that currently available crack spacing formulae significantly overestimate the average stabilized crack spacing for R/FRC; therefore, an improved crack spacing model was developed and proposed.

It is well known that crack spacings and widths can be reduced with the addition of steel fibres to a concrete mix. However, test data for the tensile behaviour of steel fibre reinforced concrete members containing conventional steel reinforcement (R/FRC members) are scarce relative to those of reinforced concrete (RC) specimens and fibre reinforced concrete (FRC) specimens without reinforcing bars. In this research program, uniaxial tension tests were conducted on 12 RC and 48 R/FRC specimens in order to observe cracking and tension stiffening behaviour. The parameters under observation were fibre volumetric content, fibre length and aspect ratio, conventional reinforcement ratio and steel reinforcing bar diameter. ‘Dog-bone’ tension tests and bending tests were also performed in order to determine tensile material properties. It was discovered that currently available crack spacing formulae significantly overestimate the average stabilized crack spacing for R/FRC; therefore, an improved crack spacing model was developed and proposed.