Reloading/Unloading Stiffness And Serviceability Reliability Of In-serviced Cracked Reinforced Concrete Beams

Reinforced concrete members are widely used in civil engineering.Under in-serviced conditions,or suffering from the accidental loads(impacting loads,unexpected overloads,etc.),due to the low tensile strength of the concrete,reinforced concrete members are usually cracked.After unloading,due to the irreversible reduction in the overall stiffness resulting from cracking and the steel-concrete bond damage,the deflection of structure increase,and the serviceability reliability decrease.In this paper,a method to evaluate the serviceability reliability of in-serviced cracked reinforced concrete beams is proposed,considering the effect of cracking damage.A total of eleven beams are tested and reported in this paper.According to the measured crack distribution and the experimental load-deflection response,the average moment of inertia of the tested beam was assessed.The suitability of the average moment of inertia model for reliability analysis is verified by considering the results of the four reinforced concrete beams with the same parameters.The errors associated with both the effective and average moment of inertia are calibrated by using the experimental data.In this paper,a method combines existing average moment of inertia model and Monte Carlo simulation(MCS)are proposed including the various sources of uncertainty in reinforced concrete beams,to take into account the effect of historical cracking damage on the reliability of serviceability calculations for reinforced concrete(RC)members.The quantitative loss in the short-term and long-term serviceability reliability of a cracked reinforced concrete beam was calculated.The results show when the deflection caused by historical loading may be larger than the deflection limitation,it is necessary to take into account the effect of historical cracking damage on short-term serviceability reliability.Lightly historical damage affects the short-term serviceability reliability,although it has no influence on the probability density distribution of the deflection.However,in long-term serviceability reliability analysis,even if the historical damage is light,the long-term serviceability reliability index would be decreased,as the cracking could damage the stiffness and affect the time-dependent creep and shrinkage deformation.In addition,the later the reinforced concrete beam is subjected to the damage load,the less influence of the cracking damage can be found on the long-term serviceability reliability.