Assessment of epistemic uncertainties in the shear strength of slender reinforced concrete beams

• Selection of an appropriate model for shear capacity of reinforced concrete (RC) slender beams.
• Little effort has been dedicated to the modeling of the epistemic uncertainties associated to RC beams shear resistance.
• A filtered database is used in the non-linear regression analysis.
• The statistics of the model error associated with the proposed resistance expression are estimated.
• The proposed equation showed good correlation with respect to shear test results presented by Reineck et al.

Selection of an appropriate model for shear capacity of reinforced concrete (RC) slender beams poses a number of challenges. First, different models with different levels of conservatism have been proposed in an attempt to describe shear resistance. Second, according to Reineck et al. (2014), code provisions for shear capacity of RC beams with shear reinforcement have been primarily derived from test data with respect to the required amount of shear reinforcement and the calculation of maximum shear capacity. Third, current models have been developed based on databases presenting two major drawbacks: (i) most data points are crowded in the small size range, and (ii) the means of the subsidiary influencing parameters are very different within different intervals of beam size (or beam depth). In this study, a filtered database is used in such a way to circumvent the drawbacks mentioned above. A random variable “model error”, i.e. ratio experimental to predicted shear strength, is associated to each of the shear models analyzed in this work (NBR 6118, ACI 318, EUROCODE 2, and CSA A.23.3). It was observed that in some cases, most notably for the effective depth, a trend exists for a decrease in the “model error” as the effective depth increases. Considering the limitations of the four analyzed models, a nonlinear regression model was proposed. The database presented by Reineck et al. (2014) was used in the assessment of the effectiveness and accuracy of the proposed regression model. No trend was found associated to the most significant variables in the shear strength prediction, i.e. a uniform level of conservatism is attained throughout the range of these variables. The regression model proposed herein and the attendant statistics of the model error (mean, coefficient of variation and type of distribution) can be easily used in a reliability analysis procedure to assess safety levels implicit in different design procedures.