Simplified estimation of reliability in structures subjected to seismic loads using the demand-capacity ratio format

In this paper, closed-form expressions to calculate both the mean annual failure rate and the confidence factor are proposed. Reliability indicators are estimated assuming a normalization between capacity and demand called \(I_{DC}\)_. Simplified closed-form expressions are obtained in accordance with the probability seismic demand analysis used in SAC/FEMA. Uncertainties associated to mechanical, geometrical, and epistemic properties are taken into account, as well as uncertainties related to the occurrence of earthquakes. A comparison of both the mean annual failure rate and the confidence factor with \(I_{DC}\) and the expressions proposed by Cornell and collaborators is performed. The numerical approach for the mean annual failure rate is obtained to verify the approximation of the closed-form solutions. Reliability indicators are obtained using six continuous reinforced concrete bridges designed to comply with three drift thresholds (0.002, 0.003 and 0.004). The bridge systems are situated in transition soil of Mexico City. Maximum differences of 4.1% and 10.6% are obtained between the proposed expression and the numerical solution for the mean annual rate of failure, estimated for two limit states: serviceability and collapse. The confidence factor presents differences of 5.2% between the present study and the original formulation.