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Title Modelling of Reinforced Concrete at Elevated Temperatures
Author Carstensen, Josephine Voigt (Section for Building Design, Department of Civil Engineering, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Supervisor Jomaas, Grunde (Section for Building Design, Department of Civil Engineering, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Pankaj, Pankaj (School of Engineering, The University of Edinburgh)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2011
Abstract Previous disasters have elucidated that accurate and realistic modelling of concrete behaviour at elevated temperatures is fundamental for the safe design of, for example, nuclear and structures exposed to fire. However, when the same model is evaluated with different mesh sizes, the existing models for the behaviour of concrete at elevated temperatures are subject to problems with convergence of results in the Finite Element (FE) analysis. These problems arise as a result of the problem of localization of deformations associated with the post-peak response of concrete. This current research focuses on the modelling of the uniaxial behaviours of reinforced concrete at elevated temperatures and in particular on the key issues associated with the post-peak behaviour. It is generally recognized that in order to obtain mesh independent results of models of reinforced concrete in FE-analysis at ambient conditions, a fracture energy based material model must be adopted. In tension, such models are widely used and in most FE-codes, for example ABAQUS, it is possible to define the tensile post-peak behaviour in three ways; either through an element size dependent stress-strain relation, through a stress-displacement formulation or by giving the tensile fracture energy and letting ABAQUS define the behaviour. However, if reinforced concrete is to be considered, the tensile definition must account for the tension stiffening effect that gradually shifts the load-bearing capacity from the concrete to the reinforcement as the cracking progresses. This issue can be tackled by defining an element size dependent interaction stress contribution that is combined with the concrete contribution for the definition of the post-peak behaviour. In compression the fracture energy based behaviour models are less used and the compressive fracture energy is, for example, not discussed in any current codes and it is generally examined by very few. To apply a fracture energy based compressive model in a FE-analysis, an element size dependent stress-strain formulation must be used. In this current research, the existing models for the ambient condition have been extended to elevated temperatures, largely by applying the material properties at a given elevated temperature to the current formulation. Therefore, the existing models have been evaluated prior to the extension and it has been found necessary to express limits for their application. It is well established that a limit on the maximum element size exists. However, herein it has been found that restrictions on the minimum element size and, if modelling the tension stiffening through the definition of an interaction stress contribution, on the minimum level of reinforcement admissible also apply. As experimental data is currently not available on the evolution of the compressive and the tensile fracture energy with temperature, the fracture energies inherent in the existing elevated temperature models have been examined. It has been found that the tensile fracture energy inherent in the currently available model follows the decay function for material strength. The compressive fracture energy has been based on the models by four current compressive models where two considers solely the instantaneous stress-related strain and two includes the effects of the LITS. It has been established that the current compressive elevated temperature models does not agree on the post-peak behaviour and that the LITS does not seem to have an effect on the post-peak response. The limits of application are extended to elevated temperatures by expressing a validity range for the element sizes and a minimum reinforcement ratio. It has been found that up to about 500!C, the maximum element size is typically governed by the tensile properties after which the compressive parameters are governing. Once the compressive model becomes governing, it only provides meaningful results within a very limited range of mesh-sizes. This range should be considered the new validity domain of the model. This novel model for the uniaxial behaviours of reinforced concrete at elevated temperatures can readily be applied for FE analysis, for example in ABAQUS, and, if the modelling is performed within the limits of application, it is possible to get mesh independent results of the analyses with different mesh configurations.
Pages 98
Fulltext
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Admin Creation date: 2012-01-16    Update date: 2012-01-16    Source: dtu    ID: 317169    Original MXD