Reliability assessments of concrete structures using non-linear finite element analyses
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Reliability assessment of slender concrete columns using Non-linear finite element analysis (NLFEA) is studied in this thesis. Several reliability methods in combination with NLFEA are applied and discussed to assess the consistency of the Eurocode design calculations in regard to reliability. The Eurocode applies the safety format of Partial safety factor (PSF) which assumes a linear Limit state function (LSF). Using NLFEA may result in a non-linear limit state, hence violating the assumption of the PSF method. Still, the Eurocode recommends using the PSF format on non-linear problems when NLFEA are conducted. Current research on concrete structures involves formulating new safety formats that are applicable to NLFEA and non-linear LSFs. This thesis further adapts the current research to the problem of slender columns subject to large second order effects. The reliability is assessed by a response surface method in combination with first and second order reliability methods. Both NLFEA and an analytic approach was used in the probabilistic design. The Monte Carlo method was applied as well to determine the accuracy of the methods. Five random variables were introduced, namely the concrete compressive strength, the reinforcement yield strength, the concrete stiffness, the eccentricity of the load and the load itself. The material and geometric uncertainty have been implemented, while some considerations were made towards the modelling uncertainty. Safety factors applicable to several case configurations were also sought by assessing different concrete grades and column slenderness. Suggestions for improvements in a future version of Eurocode 2 is given. For slender columns, it may seem advantageous to propose a new set of safety factors that are calibrated to consider second order effects. In general, safety factors associated to second order effects should be increased, and safety factors associated to the cross-sectional resistance may be decreased or set to one.