Stochastic Analysis of Effective Moment of Inertia of Cracked In-Service Reinforced Concrete Beams

For cracked reinforced concrete structures in working service life, calculation of the stiffness of the cracked reinforced concrete beam is important for the serviceability design of reinforced concrete structures. However, owing to the uncertainty and nonlinearity of concrete, it is difficult to precisely predict the effective moment of inertia of cracked concrete beams. In this study, the dimensionless equation for the effective moment of inertia recommended in specification GB50010-2010 for in-service reinforced concrete beams was derived, and a Monte Carlo method was employed to analyse its stochastic properties. The dimensionless effective moment of inertia was calculated using both a stochastic analysis with random variables and a deterministic analysis with mean values of the parameters. The results indicate that the mean values obtained with the stochastic analysis are not in agreement with those calculated with the deterministic analysis owing to the cracking nonlinearity of concrete. In addition, through regression of the stochastic analysis results, mean values of the effective moment of inertia are estimated at the 95% confidence interval. Finally, a sensitivity coefficient reflecting the correlation between each random variable and the effective moment of inertia was calculated using a partial correlation coefficient. The results demonstrate that the tensile strength of concrete is the most sensitive variable, while the compressive strength of concrete has nearly no effect on the effective moment of inertia.