Probabilistic indicator to classify the failure mode of reinforced-concrete columns

In order to reconcile the large dispersion in classifying the failure mode of reinforced-concrete (RC) columns, a probabilistic indicator was developed by comparing the flexural strength with the shear strength. Specifically, a simplified truss-and-arch model was first built to develop the flexural strength model and shear strength model of RC columns to derive an explicit expression for the probabilistic indicator. The five unknown model parameters in the explicit expression were then carefully defined as random variables to represent the prevailing uncertainties with prior distribution ranges from 0 to 1·0. An experimental database was constructed to estimate the posterior cumulative distribution of the five unknown model parameters by comparing the measured strengths. Moreover, by defining unity as the threshold value of the probabilistic density function of the probabilistic indicator, the probability categorising the damage of RC columns into a specific failure mode was determined for each specimen. Finally, as a by-product of developing the probabilistic indicator, a closed-form expression of a probabilistic model in terms of a mean prediction model and a standard deviation prediction model was developed for engineers to estimate the required minimum transverse reinforcement ratio of RC columns.