Aspects of design of reinforced concrete structures using nonlinear finite element analyses
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Non-linear finite element analyses (NLFEA) of reinforced concrete structures have gained much attention in the structural engineering community during the last decade, and the practising engineer is now equipped with an advanced tool that can be used in the design process. The three main objectives of the present work has been i) to develop a solution strategy for NLFEA applicable during design of large reinforced concrete structures, ii) to quantify the modelling uncertainty obtained with the solution strategy, and iii) to quantify the variability of the compressive strength of concrete. These are central ingredients in the semi-probabilistic safety formats for NLFEA introduced in the literature. A solution strategy comprises all the choices that need to be made in order to perform a NLFEA, and the modelling uncertainty indicates how well the analysis outcomes compare to the real physical behaviour. A three dimensional material model for concrete was adapted and implemented in a finite element software. The material model required only one material parameter, the uniaxial compressive strength. The complete solution strategy is discussed in detail in the appended papers. A refinement of the solution strategy is only justified if the resulting modelling uncertainty is reduced, if necessary knowledge about the basic variables can be obtained, and if in the end it can be shown to produce results that provide a better basis for decision making. The modelling uncertainty was quantified by comparing NLFEA predictions to experimental outcomes, resulting in a bias of 1.10 and a coefficient of variation of 0.11. All the uncertainties that are not explicitly considered in the NLFEA will implicitly contribute to the estimated modelling uncertainty, and a pure modelling uncertainty is thus not straightforward to obtain. This is unfortunate, since the modelling uncertainty will carry a large part of the uncertainties in the problem. However, it can be useful, since the analyst later does not need to consider the uncertainties that were not considered during quantification of the modelling uncertainty. A hierarchical model for the variability of material properties was formulated for the study of the compressive strength of ready-mixed concrete. By combining Bayesian inference and maximum likelihood estimators, the contributions from the different hierarchical levels were quantified. The method was demonstrated on more than 14000 compressive strength recordings from the Norwegian market. The results indicate that the designer should specify strength classes that better utilize the strength potential of the durability class. A closer collaboration between the designer, contractor and the producer is expected to result in improved concrete specifications. In addition to summarizing the main findings of the work, this thesis contains a part describing the background and the context of the work.