Reliability analysis to resolve difficulty in choosing from alternative deflection models of RC beams

The probability of failure in reliability analysis depends on the integration of the joint probability density function (PDF) of uncertain variables at the violation regions of limit state functions corresponding to these variables. There might exist uncertainty in choosing computational models of resultants, which includes uncertain variables, and are incorporated in the limit state function. This uncertainty is not random, but can be considered as an epistemic uncertainty, since this uncertainty represents ambiguity in choosing from among alternative computational models; such an uncertainty is known as “non-specificity”.In this study, non-specificity of computational models is implemented in reliability analysis for determining the deflections of reinforced concrete (RC) beams. A methodology to quantify this non-specificity is presented using possibility theory. Three deflection computational models, which accounts for the rigidity of concrete under tension using an effective moment of inertia, are selected. A limit state for a deflection limit is formulated for each deflection model and the probability of exceeding the deflection limits is calculated for each. Using possibility distributions, the three probabilities of exceeding a deflection limit are integrated and a new set of probabilities of exceeding a deflection limit are determined, where each probability is associated with a new metric that describes model non-specificity called the degree of confirmation. A case study illustrating the new reliability analysis to compute the non-specificity of a computational model is presented.

► A framework to consider the ‘non-specificity’ of RC deflection models in reliability analysis is presented.
► Proposed framework was demonstrated through a case study of the reliability analysis for the deflection of a RC beam.
► It was shown that the probabilities of exceeding a deflection limit are estimated with respect to a ‘degree of confirmation’.