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.

Devido à fragilidade do concreto, o controle e combate da fissuração são de importância fundamental em estruturas de concreto armado. Uma maneira de melhorar as propriedades do concreto à tração é pelo emprego de fibras. A presente pesquisa é uma tentativa de fornecer diretrizes para o dimensionamento de estruturas de concreto armado com fibras, e armadura convencional sob condições de serviço. Apresenta-se inicialmente, um estudo do comportamento do material à tração. Um modelo probabilístico/micro-mecânico fundamentado na mecânica de fratura, e capaz de prever o comportamento pós-fissuração do compósito é apresentado. O modelo prevê a relação tensão-abertura de fissura do compósito levando em conta os seguintes micro-mecanismos: travejamento de agregado e fibras, a ruptura das fibras, os efeitos de: atrito local (snubbing effect), esmagamento da matriz, Cook-Gordon, e da pré-tração das fibras. Em nível estrutural, dois modelos macro-mecânicos são apresentados. O primeiro modelo tem premissa na teoria clássica de fissura, e o segundo na mecânica de dado. O primeiro modelo é ajustado para aplicação na previsão de espaçamento e aberturas de fissura em estruturas de concreto armado com fibras discretas e aleatoriamente dispostas. É demostrado que o modelo micro-mecânico pode alimentar perfeitamente o modelo macro-mecânico. Ensaios de tração com elementos de placas de argamassa com fibras armada com tela ou fios foram realizados. Os resultados teóricos previstos pelo modelo foram comparados com os obtidos do programa experimental, e mostram uma boa concordância, comprovando a validade do modelo apresentado. / Due to the brittleness of concrete, the control and prevention of cracking in reinforced concrete structures are of prime importance. One way of improving the tensile properties of concrete is by the addition of fibres. The present research is a trial to provide guidelines for the design of fibre reinforced concrete structures under service loads. First of all, a study of the tensile behaviour of the composite material is presented. A probabilistic/fracture mechanics based micromechanical model, capable of predicting the poscracking behaviour of the material is presented. The model predicts the tensile stress-crack width relationship, accounting for the following micromechanisms: fibre and aggregate bridging, fibre rupture, local snubbing, matrix spalling, the Cook-Gordon interface effect, and fibre prestressing. At the structural level, two macromechanical models are presented. One is founded on the classical theory of cracking, while the other, a shear lag model, is founded on the continuum damage mechanics. The first model is adjusted for application to the prevision of crack width and crack spacing in fibre reinforced concrete structures with short discrete and randomly dispersed fibres. It is shown that the micromechanical model fits very well in the macrostructural model. Tensile tests with mortar specimens reinforced with continuous steel wires or meshes and PVA or polypropylene fibres were carried out. The theoretical results predicted by the model were compared with results obtained from the experimental program, and show very good agreement, confirming the validity of the theoretical model.

Devido à fragilidade do concreto, o controle e combate da fissuração são de importância fundamental em estruturas de concreto armado. Uma maneira de melhorar as propriedades do concreto à tração é pelo emprego de fibras. A presente pesquisa é uma tentativa de fornecer diretrizes para o dimensionamento de estruturas de concreto armado com fibras, e armadura convencional sob condições de serviço. Apresenta-se inicialmente, um estudo do comportamento do material à tração. Um modelo probabilístico/micro-mecânico fundamentado na mecânica de fratura, e capaz de prever o comportamento pós-fissuração do compósito é apresentado. O modelo prevê a relação tensão-abertura de fissura do compósito levando em conta os seguintes micro-mecanismos: travejamento de agregado e fibras, a ruptura das fibras, os efeitos de: atrito local (snubbing effect), esmagamento da matriz, Cook-Gordon, e da pré-tração das fibras. Em nível estrutural, dois modelos macro-mecânicos são apresentados. O primeiro modelo tem premissa na teoria clássica de fissura, e o segundo na mecânica de dado. O primeiro modelo é ajustado para aplicação na previsão de espaçamento e aberturas de fissura em estruturas de concreto armado com fibras discretas e aleatoriamente dispostas. É demostrado que o modelo micro-mecânico pode alimentar perfeitamente o modelo macro-mecânico. Ensaios de tração com elementos de placas de argamassa com fibras armada com tela ou fios foram realizados. Os resultados teóricos previstos pelo modelo foram comparados com os obtidos do programa experimental, e mostram uma boa concordância, comprovando a validade do modelo apresentado. / Due to the brittleness of concrete, the control and prevention of cracking in reinforced concrete structures are of prime importance. One way of improving the tensile properties of concrete is by the addition of fibres. The present research is a trial to provide guidelines for the design of fibre reinforced concrete structures under service loads. First of all, a study of the tensile behaviour of the composite material is presented. A probabilistic/fracture mechanics based micromechanical model, capable of predicting the poscracking behaviour of the material is presented. The model predicts the tensile stress-crack width relationship, accounting for the following micromechanisms: fibre and aggregate bridging, fibre rupture, local snubbing, matrix spalling, the Cook-Gordon interface effect, and fibre prestressing. At the structural level, two macromechanical models are presented. One is founded on the classical theory of cracking, while the other, a shear lag model, is founded on the continuum damage mechanics. The first model is adjusted for application to the prevision of crack width and crack spacing in fibre reinforced concrete structures with short discrete and randomly dispersed fibres. It is shown that the micromechanical model fits very well in the macrostructural model. Tensile tests with mortar specimens reinforced with continuous steel wires or meshes and PVA or polypropylene fibres were carried out. The theoretical results predicted by the model were compared with results obtained from the experimental program, and show very good agreement, confirming the validity of the theoretical model.

In the present work, the load-bearing behaviour of Textile Reinforced Concrete (TRC), which is a composite of a fine-grained concrete matrix and a reinforcement of high-performance fibres processed to textiles, exposed to uniaxial tensile loading was investigated based on numerical simulations. The investigations are focussed on reinforcement of multi-filament yarns of alkali-resistant glass. When embedded in concrete, these yarns are not entirely penetrated with cementitious matrix, which leads associated with the heterogeneity of the concrete and the yarns to a complex load-bearing and failure behaviour of the composite. The main objective of the work was the theoretical investigation of effects in the load-bearing behaviour of TRC, which cannot be explained solely by available experimental results. Therefore, a model was developed, which can describe the tensile behaviour of TRC in different experimental test setups with a unified approach. Neglecting effects resulting from Poisson’s effect, a one-dimensional model implemented within the framework of the Finite Element Method was established. Nevertheless, the model takes also transverse effects into account by a subdivision of the reinforcement yarns into so-called segments. The model incorporates two types of finite elements: bar and bond elements. In longitudinal direction, the bar elements are arranged in series to represent the load-bearing behaviour of matrix or reinforcement. In transverse direction these bar element chains are connected with bond elements. The model gains most of its complexity from non-linearities arising from the constitutive relations, e. g., limited tensile strength of concrete and reinforcement, tension softening of the concrete, waviness of the reinforcement and non-linear bond laws. Besides a deterministic description of the material behaviour, also a stochastic formulation based on a random field approach was introduced in the model. The model has a number of advantageous features, which are provided in this combination only in a few of the existing models concerning TRC. It provides stress distributions in the reinforcement and the concrete as well as properties of concrete crack development like crack spacing and crack widths, which are in some of the existing models input parameters and not a result of the simulations. Moreover, the successive failure of the reinforcement can be studied with the model. The model was applied to three types of tests, the filament pull-out test, the yarn pull-out test and tensile tests with multiple concrete cracking. The results of the simulations regarding the filament pull-out tests showed good correspondence with experimental data. Parametric studies were performed to investigate the influence of geometrical properties in these tests like embedding and free lengths of the filament as well as bond properties between filament and matrix. The presented results of simulations of yarn pull-out tests demonstrated the applicability of the model to this type of test. It has been shown that a relatively fine subdivision of the reinforcement is necessary to represent the successive failure of the reinforcement yarns appropriately. The presented results showed that the model can provide the distribution of failure positions in the reinforcement and the degradation development of yarns during loading. One of the main objectives of the work was to investigate effects concerning the tensile material behaviour of TRC, which could not be explained, hitherto, based solely on experimental results. Hence, a large number of parametric studies was performed concerning tensile tests with multiple concrete cracking, which reflect the tensile behaviour of TRC as occurring in practice. The results of the simulations showed that the model is able to reproduce the typical tripartite stress-strain response of TRC consisting of the uncracked state, the state of multiple matrix cracking and the post-cracking state as known from experimental investigations. The best agreement between simulated and experimental results was achieved considering scatter in the material properties of concrete as well as concrete tension softening and reinforcement waviness. / Die vorliegende Arbeit beschäftigt sich mit Untersuchungen zum einaxialen Zugtragverhalten von Textilbeton. Textilbeton ist ein Verbundwerkstoff bestehend aus einer Matrix aus Feinbeton und einer Bewehrung aus Multifilamentgarnen aus Hochleistungsfasern, welche zu textilen Strukturen verarbeitet sind. Die Untersuchungen konzentrieren sich auf Bewehrungen aus alkali-resistentem Glas. Das Tragverhalten des Verbundwerkstoffs ist komplex, was aus der Heterogenität der Matrix und der Garne sowie der unvollständigen Durchdringung der Garne mit Matrix resultiert. Das Hauptziel der Arbeit ist die theoretische Untersuchung von Effekten und Mechanismen innerhalb des Lastabtragverhaltens von Textilbeton, welche nicht vollständig anhand verfügbarer experimenteller Ergebnisse erklärt werden können. Das entsprechende Modell zur Beschreibung des Zugtragverhaltens von Textilbeton soll verschiedene experimentelle Versuchstypen mit einem einheitlichen Modell abbilden können. Unter Vernachlässigung von Querdehneffekten wurde ein eindimensionales Modell entwickelt und im Rahmen der Finite-Elemente-Methode numerisch implementiert. Es werden jedoch auch Lastabtragmechanismen in Querrichtung durch eine Unterteilung der Bewehrungsgarne in sogenannte Segmente berücksichtigt. Das Modell enthält zwei Typen von finiten Elementen: Stabelemente und Verbundelemente. In Längsrichtung werden Stabelemente kettenförmig angeordnet, um das Tragverhalten von Matrix und Bewehrung abzubilden. In Querrichtung sind die Stabelementketten mit Verbundelementen gekoppelt. Das Modell erhält seine Komplexität hauptsächlich aus Nichtlinearitäten in der Materialbeschreibung, z.B. durch begrenzte Zugfestigkeiten von Matrix und Bewehrung, Zugentfestigung der Matrix, Welligkeit der Bewehrung und nichtlineare Verbundgesetze. Neben einer deterministischen Beschreibung des Materialverhaltens beinhaltet das Modell auch eine stochastische Beschreibung auf Grundlage eines Zufallsfeldansatzes. Mit dem Modell können Spannungsverteilungen im Verbundwerkstoff und Eigenschaften der Betonrissentwicklung, z.B. in Form von Rissbreiten und Rissabständen untersucht werden, was in dieser Kombination nur mit wenigen der existierenden Modelle für Textilbeton möglich ist. In vielen der vorhandenen Modelle sind diese Eigenschaften Eingangsgrößen für die Berechnungen und keine Ergebnisse. Darüber hinaus kann anhand des Modells auch das sukzessive Versagen der Bewehrungsgarne studiert werden. Das Modell wurde auf drei verschiedene Versuchstypen angewendet: den Filamentauszugversuch, den Garnauszugversuch und Dehnkörperversuche. Die Berechnungsergebnisse zu den Filamentauszugversuchen zeigten eine gute Übereinstimmung mit experimentellen Resultaten. Zudem wurden Parameterstudien durchgeführt, um Einflüsse aus Geometrieeigenschaften wie der eingebetteten und freien Filamentlänge sowie Materialeigenschaften wie dem Verbund zwischen Matrix und Filament zu untersuchen. Die Berechnungsergebnisse zum Garnauszugversuch demonstrierten die Anwendbarkeit des Modells auf diesen Versuchstyp. Es wurde gezeigt, dass für eine realitätsnahe Abbildung des Versagensverhaltens der Bewehrungsgarne eine relativ feine Auflösung der Bewehrung notwendig ist. Die Berechnungen lieferten die Verteilung von Versagenspositionen in der Bewehrung und die Entwicklung der Degradation der Garne im Belastungsverlauf. Ein Hauptziel der Arbeit war die Untersuchung von Effekten im Zugtragverhalten von Textilbeton, die bisher nicht durch experimentelle Untersuchungen erklärt werden konnten. Daher wurde eine Vielzahl von Parameterstudien zu Dehnkörpern mit mehrfacher Matrixrissbildung, welche das Zugtragverhalten von Textilbeton ähnlich praktischen Anwendungen abbilden, durchgeführt. Die Berechnungsergebnisse zeigten, dass der experimentell beobachtete dreigeteilte Verlauf der Spannungs-Dehnungs-Beziehung von Textilbeton bestehend aus dem ungerissenen Zustand, dem Zustand der Matrixrissbildung und dem Zustand der abgeschlossenen Rissbildung vom Modell wiedergegeben wird. Die beste Übereinstimmung zwischen berechneten und experimentellen Ergebnissen ergab sich unter Einbeziehung von Streuungen in den Materialeigenschaften der Matrix, der Zugentfestigung der Matrix und der Welligkeit der Bewehrung.

In the present work, the load-bearing behaviour of Textile Reinforced Concrete (TRC), which is a composite of a fine-grained concrete matrix and a reinforcement of high-performance fibres processed to textiles, exposed to uniaxial tensile loading was investigated based on numerical simulations. The investigations are focussed on reinforcement of multi-filament yarns of alkali-resistant glass. When embedded in concrete, these yarns are not entirely penetrated with cementitious matrix, which leads associated with the heterogeneity of the concrete and the yarns to a complex load-bearing and failure behaviour of the composite. The main objective of the work was the theoretical investigation of effects in the load-bearing behaviour of TRC, which cannot be explained solely by available experimental results. Therefore, a model was developed, which can describe the tensile behaviour of TRC in different experimental test setups with a unified approach. Neglecting effects resulting from Poisson’s effect, a one-dimensional model implemented within the framework of the Finite Element Method was established. Nevertheless, the model takes also transverse effects into account by a subdivision of the reinforcement yarns into so-called segments. The model incorporates two types of finite elements: bar and bond elements. In longitudinal direction, the bar elements are arranged in series to represent the load-bearing behaviour of matrix or reinforcement. In transverse direction these bar element chains are connected with bond elements. The model gains most of its complexity from non-linearities arising from the constitutive relations, e. g., limited tensile strength of concrete and reinforcement, tension softening of the concrete, waviness of the reinforcement and non-linear bond laws. Besides a deterministic description of the material behaviour, also a stochastic formulation based on a random field approach was introduced in the model. The model has a number of advantageous features, which are provided in this combination only in a few of the existing models concerning TRC. It provides stress distributions in the reinforcement and the concrete as well as properties of concrete crack development like crack spacing and crack widths, which are in some of the existing models input parameters and not a result of the simulations. Moreover, the successive failure of the reinforcement can be studied with the model. The model was applied to three types of tests, the filament pull-out test, the yarn pull-out test and tensile tests with multiple concrete cracking. The results of the simulations regarding the filament pull-out tests showed good correspondence with experimental data. Parametric studies were performed to investigate the influence of geometrical properties in these tests like embedding and free lengths of the filament as well as bond properties between filament and matrix. The presented results of simulations of yarn pull-out tests demonstrated the applicability of the model to this type of test. It has been shown that a relatively fine subdivision of the reinforcement is necessary to represent the successive failure of the reinforcement yarns appropriately. The presented results showed that the model can provide the distribution of failure positions in the reinforcement and the degradation development of yarns during loading. One of the main objectives of the work was to investigate effects concerning the tensile material behaviour of TRC, which could not be explained, hitherto, based solely on experimental results. Hence, a large number of parametric studies was performed concerning tensile tests with multiple concrete cracking, which reflect the tensile behaviour of TRC as occurring in practice. The results of the simulations showed that the model is able to reproduce the typical tripartite stress-strain response of TRC consisting of the uncracked state, the state of multiple matrix cracking and the post-cracking state as known from experimental investigations. The best agreement between simulated and experimental results was achieved considering scatter in the material properties of concrete as well as concrete tension softening and reinforcement waviness. / Die vorliegende Arbeit beschäftigt sich mit Untersuchungen zum einaxialen Zugtragverhalten von Textilbeton. Textilbeton ist ein Verbundwerkstoff bestehend aus einer Matrix aus Feinbeton und einer Bewehrung aus Multifilamentgarnen aus Hochleistungsfasern, welche zu textilen Strukturen verarbeitet sind. Die Untersuchungen konzentrieren sich auf Bewehrungen aus alkali-resistentem Glas. Das Tragverhalten des Verbundwerkstoffs ist komplex, was aus der Heterogenität der Matrix und der Garne sowie der unvollständigen Durchdringung der Garne mit Matrix resultiert. Das Hauptziel der Arbeit ist die theoretische Untersuchung von Effekten und Mechanismen innerhalb des Lastabtragverhaltens von Textilbeton, welche nicht vollständig anhand verfügbarer experimenteller Ergebnisse erklärt werden können. Das entsprechende Modell zur Beschreibung des Zugtragverhaltens von Textilbeton soll verschiedene experimentelle Versuchstypen mit einem einheitlichen Modell abbilden können. Unter Vernachlässigung von Querdehneffekten wurde ein eindimensionales Modell entwickelt und im Rahmen der Finite-Elemente-Methode numerisch implementiert. Es werden jedoch auch Lastabtragmechanismen in Querrichtung durch eine Unterteilung der Bewehrungsgarne in sogenannte Segmente berücksichtigt. Das Modell enthält zwei Typen von finiten Elementen: Stabelemente und Verbundelemente. In Längsrichtung werden Stabelemente kettenförmig angeordnet, um das Tragverhalten von Matrix und Bewehrung abzubilden. In Querrichtung sind die Stabelementketten mit Verbundelementen gekoppelt. Das Modell erhält seine Komplexität hauptsächlich aus Nichtlinearitäten in der Materialbeschreibung, z.B. durch begrenzte Zugfestigkeiten von Matrix und Bewehrung, Zugentfestigung der Matrix, Welligkeit der Bewehrung und nichtlineare Verbundgesetze. Neben einer deterministischen Beschreibung des Materialverhaltens beinhaltet das Modell auch eine stochastische Beschreibung auf Grundlage eines Zufallsfeldansatzes. Mit dem Modell können Spannungsverteilungen im Verbundwerkstoff und Eigenschaften der Betonrissentwicklung, z.B. in Form von Rissbreiten und Rissabständen untersucht werden, was in dieser Kombination nur mit wenigen der existierenden Modelle für Textilbeton möglich ist. In vielen der vorhandenen Modelle sind diese Eigenschaften Eingangsgrößen für die Berechnungen und keine Ergebnisse. Darüber hinaus kann anhand des Modells auch das sukzessive Versagen der Bewehrungsgarne studiert werden. Das Modell wurde auf drei verschiedene Versuchstypen angewendet: den Filamentauszugversuch, den Garnauszugversuch und Dehnkörperversuche. Die Berechnungsergebnisse zu den Filamentauszugversuchen zeigten eine gute Übereinstimmung mit experimentellen Resultaten. Zudem wurden Parameterstudien durchgeführt, um Einflüsse aus Geometrieeigenschaften wie der eingebetteten und freien Filamentlänge sowie Materialeigenschaften wie dem Verbund zwischen Matrix und Filament zu untersuchen. Die Berechnungsergebnisse zum Garnauszugversuch demonstrierten die Anwendbarkeit des Modells auf diesen Versuchstyp. Es wurde gezeigt, dass für eine realitätsnahe Abbildung des Versagensverhaltens der Bewehrungsgarne eine relativ feine Auflösung der Bewehrung notwendig ist. Die Berechnungen lieferten die Verteilung von Versagenspositionen in der Bewehrung und die Entwicklung der Degradation der Garne im Belastungsverlauf. Ein Hauptziel der Arbeit war die Untersuchung von Effekten im Zugtragverhalten von Textilbeton, die bisher nicht durch experimentelle Untersuchungen erklärt werden konnten. Daher wurde eine Vielzahl von Parameterstudien zu Dehnkörpern mit mehrfacher Matrixrissbildung, welche das Zugtragverhalten von Textilbeton ähnlich praktischen Anwendungen abbilden, durchgeführt. Die Berechnungsergebnisse zeigten, dass der experimentell beobachtete dreigeteilte Verlauf der Spannungs-Dehnungs-Beziehung von Textilbeton bestehend aus dem ungerissenen Zustand, dem Zustand der Matrixrissbildung und dem Zustand der abgeschlossenen Rissbildung vom Modell wiedergegeben wird. Die beste Übereinstimmung zwischen berechneten und experimentellen Ergebnissen ergab sich unter Einbeziehung von Streuungen in den Materialeigenschaften der Matrix, der Zugentfestigung der Matrix und der Welligkeit der Bewehrung.