Analytical probabilistic model for shear strength prediction of reinforced concrete beams without shear reinforcement: Fid-Bau Portal

Analytical probabilistic model for shear strength prediction of reinforced concrete beams without shear reinforcement

Ning, Chao-Lie / Li, Bing

To account for the prevailing uncertainty in shear strength prediction of reinforced concrete beams without shear reinforcement, an analytical probabilistic model in terms of a mean prediction model and a standard deviation prediction model was developed. Specifically, a function form giving the probabilistic representation was first derived with the well-known relationship between the shear forces and the rate of change of bending moments along the beam to reflect the combination of beam action and arch action. Then, two unknown model parameters involved in the developed function form are defined carefully with clear physical meanings as two basic random variables to represent the prevailing uncertainty. After that, the prior distribution ranges of the two unknown model parameters were updated with a constructed experimental database and the generalized likelihood uncertainty estimation method. Moreover, to facilitate the application in engineering practice, the closed-form expression of the developed probabilistic model was derived with the stochastic analysis method to provide a prediction band of shear strength in terms of the mean plus or minus several times standard deviation for each specimen. Performance evaluation demonstrates its advantage, where the measured data and the shear strength predicted by the deterministic models were covered and performed as a quantile of the normal probability density function. Therefore, based on the developed analytical probabilistic model, not only can the reinforced concrete beams without shear reinforcement be designed in confidence but also the prediction accuracy of those deterministic shear strength models can be evaluated in probability for each specimen.