On the Reliability of Serviceability Calculations for Flexural Cracked Reinforced Concrete Beams

Under in-service conditions, beams and slabs in reinforced concrete structures are almost always cracked, as the tensile strength of the concrete is low. Due to the irreversible reduction in overall stiffness resulting from cracking and the residual deflection after unloading, the structural response is load path dependent. In this paper, an existing average moment of inertia model and Monte Carlo simulation (MCS) are adopted to take into account the effect of historical cracking damage on the reliability of serviceability calculations for reinforced concrete (RC) members. The suitability of the average moment of inertia model for reliability analysis is verified by considering experimental tests on a total of eleven reinforced concrete beams. The errors associated with both the effective and average moment of inertia predicted by the model are calibrated using the experimental data. By using the proposed approach to account for the various sources of uncertainty in reinforced concrete beams, the quantitative loss in the short-term and long-term serviceability reliability of a cracked reinforced concrete beam was calculated. The results confirm that the effect of historical cracking damage on short-term serviceability reliability should be taken into account when the deflection induced by historical loading is larger than the deflection limitation. Light historical damage has no influence on the short-term serviceability reliability, although it affects the probability density distribution of the deflection. However, in the long-term serviceability reliability analysis, even when the historical damage is light, the long-term serviceability reliability index is decreased as the cracking damage to the stiffness affects the time-dependent deflection. Additionally, the later a damaging load is applied to a reinforced concrete beam, the less is the influence of cracking damage on the long-term serviceability reliability.