Probabilistic analysis of shear capacity of reinforced concrete beams with a v/ d

The complexity in the shear behaviour of reinforced concrete (RC) beams increases with a decrease in the shear span to effective depth ratio (av/d) because of the increase in the contribution of concrete to the shear resistance of beams. Various models (e.g. numerical models and strut and tie models) for estimating the shear capacity of non-slender RC beams are proposed in the literature, with each having advantages and limitations. In this work, two simpler mechanics-based shear capacity models were considered, one for beams with 1≤av/d<2·5 and the other for beams with av/d<1. To quantify the modelling error associated with the considered shear capacity models, the predicted shear capacities were compared with experimental shear capacities of test beams included in a database created for this study. The randomness in shear capacity was quantified by performing probabilistic analyses of one set of nominally similar beams for each av/d range. Knowing the probability density function of the shear capacity and the mean and standard deviation of the shear capacity obtained using a first-order approximation, a characteristic shear capacity equation (Equation 5) is proposed for the design of beams with 1≤av/d<2·5 and av/d<1.