Glass Fibre-Reinforced Polymer (GFRP) bars offer a feasible alternative in locations where steel is not the suitable reinforcement; namely locations that are sensitive to corrosion. In this study 60 specimens, 52 GFRP reinforced and 8 steel reinforced, were constructed and tested under direct tension in order to investigate the tension stiffening and cracking behaviour. The effects of different variables such as the bar type, the bar diameter, the reinforcement ratio and the concrete strength on tension stiffening and crack spacing were studied. The current code provisions for tension stiffening, namely ACI-440 and CEB-FIP were evaluated against the obtained test data. It was determined that the current code provisions significantly overestimate tension stiffening in GFRP reinforced specimens. A new tension stiffening model was, therefore, developed that provides better simulation of the test data. The CEB-FIP 1978 model for crack spacing was also modified for GFRP reinforced members.

Glass Fibre-Reinforced Polymer (GFRP) bars offer a feasible alternative in locations where steel is not the suitable reinforcement; namely locations that are sensitive to corrosion. In this study 60 specimens, 52 GFRP reinforced and 8 steel reinforced, were constructed and tested under direct tension in order to investigate the tension stiffening and cracking behaviour. The effects of different variables such as the bar type, the bar diameter, the reinforcement ratio and the concrete strength on tension stiffening and crack spacing were studied. The current code provisions for tension stiffening, namely ACI-440 and CEB-FIP were evaluated against the obtained test data. It was determined that the current code provisions significantly overestimate tension stiffening in GFRP reinforced specimens. A new tension stiffening model was, therefore, developed that provides better simulation of the test data. The CEB-FIP 1978 model for crack spacing was also modified for GFRP reinforced members.

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.

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

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.

Dėl sąveikos su armatūros strypais iš esmės pakinta tempiamojo betono fizikinis įtempių ir deformacijų būvis, todėl taikyti vientiso tempiamojo betono įtempių ir deformacijų diagramas negalima. Armuotojo betono atveju šios diagramos yra pakeičiamos vadinamosiomis tempiamojo sustandėjimo įtempių ir deformacijų diagramomis, tačiau iki šiol nėra priimta bendro metodo, kaip jas reikėtų apskaičiuoti. Baigiamojo magistro darbo tikslas – pasiūlyti tempiamojo betono įtempių ir deformacijų fizikinį modelį. Baigiamajame darbe atlikta kritinė literatūros šaltinių betono tempiamojo sustandėjimo tematika analizė. Atlikti tempiamųjų gelžbetoninių elementų eksperimentiniai ir skaitiniai tyrimai. Literatūros šaltiniuose aptiktų eksperimentinių tyrimų rezultatai palyginti su atliktais eksperimentiniais ir skaitiniais tyrimais. Pagal atrinktus duomenis išvestas tempiamojo betono įtempių ir deformacijų fizikinis modelis bei atlikta jo statistinė analizė. Baigiamąjį magistro darbą sudaro įvadas, trys skyriai, išvados bei literatūros sąrašas. Darbo apimtis – 64 puslapiai. Tekste pateikta 50 formulių, 41 paveikslas ir 10 lentelių. Rašant darbą remtasi 30 literatūros šaltinių. / Interaction between concrete and reinforcement changes the way tensile concrete behaves thus the stress–strain relationship for solid tensile concrete cannot be applied anymore. In the case of reinforced concrete, these graphs are changed with so–called tension stiffening diagrams but until now there has been no confirmed method that would allow us to determine it. The aim of the master thesis is to propose a physical model for stress–strain relationship of tensile concrete. In the master thesis a close analysis of a number of scientific articles about tension stiffening has been done. Experimental and numerical research for tensile reinforced concrete members has been performed. The data found in scientific articles has been compared with the data of experimental and numerical research. Based on the results of experimental research a physical model for stress–strain relationship of tensile concrete has been proposed, also a statistical accuracy analysis of the model has been performed. The master thesis consists of introduction, three chapters, conclusions and references. Total number of pages is 64. Thesis includes 50 equations, 41 figures and 10 tables. Paper refers to 30 scientific source materials.

The Aveston Copper and Kelly (ACK) Method has been routinely used in estimating the efficiency of the bond between the textile and cementitious matrix. This method however has a limited applicability due to the simplifying assumptions such as perfect bond. A numerical model for simulation of tensile behavior of reinforced cement-based composites is presented to capture the inefficiency of the bond mechanisms. In this approach the role of interface properties which are instrumental in the simulation of the tensile response is investigated. The model simulates the tension stiffening effect of cracked matrix, and evolution of crack spacing in tensile members. Independent experimental results obtained from literature are used to verify the model and develop composite tensile stress strain response using alkali resistant (AR) glass textile reinforced concrete. The composite stress strain response is then used with a bilinear representation of the composite obtained from the tensile stiffening model. The closed form and simplified equations for representation of flexural response are obtained and used for both back-calculation and also design. A method based on the average moment-curvature relationship in the structural design and analysis of one way and two way flexural elements using yield line analysis approaches is proposed. This comprehensive approach directly shows the interrelation of fundamental materials characterization techniques with simplified design equations for further utilization of textile reinforced concrete materials.