Shear capacity distribution of reinforced concrete beams: An information theoretic entropy approach

Using the concept of information theoretic entropy, the probability density function (pdf) of shear capacity of the reinforced concrete beam with stirrup reinforcement is determined. Entropy, expressed in terms of Shannon functional, is maximized subjected to the statistical moment and normalization constraints of pdf of shear capacity. The statistical moments of shear capacity distribution are obtained using second-order approximation of shear capacity equation. The pdf so determined has strong statistical mechanics interpretation of maximum entropy principle. Also, a procedure for goodness-of-fit test has been proposed, for the given data, using the information theoretic entropy as a measure of goodness-of-fit. In the present investigation, beams of three different ranges of shear span to effective depth ratios are considered. The mechanics-based shear capacity equations, presented earlier by authors along with associated modelling errors, are used for estimating the statistical moments of shear capacity distribution. The computationally efficient approach of determination of maximum entropy distribution presented in this article can be viewed as an alternate to the process of determination of pdf using brute force Monte Carlo simulation approach.