In this paper, an approach is proposed to obtain fragility curves of reinforced concrete structures which can accumulate damage due to inelastic behavior when they are exposed to seismic load sequences in a given instant of time. The cumulative damage caused by earthquakes is quantified considering the maximum drift. This study is mainly focused on the stochastic uncertainty and variability of seismic occurrence, which are considered the main sources that can influence the performance of the structural system. The approach is validated with the help of a numerical study using a reinforced concrete continuous bridge considering the effect of cumulative damage given by seismic sequences for different time instants of 0, 50, 100, 150 and 200 years, after bridge construction. The bridge is located in the transition part of the soil in Mexico City. Different drift thresholds are studied to evaluate the probability of being exceeded. The proposed approach demonstrates the importance of considering the effect of cumulative damage under seismic sequences. In addition, it is assumed that it could be possible to design bridge structures that develop a certain pre-established drift threshold.

A multi-objective optimization approach in order to find the optimal cable overlap length in multi-span cable-stayed bridges with criss-cross cables is presented. The multi-objective optimization is solved by considering three objectives: 1) the cost of the cable system, 2) the displacement at the top of the pylon and 3) the alternate live load on the bridge. An unconventional criss-cross cable system configuration in which cables criss-cross at the center of intermediate spans is used for a bridge with five spans and four pylons. Taking into account both the cable overlap length and the different occurrences of alternate live load, the set of optimal solutions was obtained by the use of genetic algorithms. Results indicate that the optimal cable overlap length corresponds to three criss-crossing cables that corresponds to 0.28 times the length of the central span. Research on multi-span cable-stayed bridges with criss-cross cables allows the analysis of another solution for the problem of stabilizing the displacement of intermediate pylons in this kind of bridge.

An approach is proposed to evaluate the confidence factor implicit in structures over an interval of time, considering that the structural capacity and structural demand vary simultaneously over time. A new closed‐form mathematical expression of the confidence factor over a time interval is used, assuming that the structural capacity degradation is represented by a second degree polynomial function in the total interval. This formulation is made in accordance with the demand and capacity factor design format. Confidence factors at the ends of different time intervals are evaluated for an old ten‐story building. The confidence factors and their confidence levels, calculated under the assumption that the structural capacity degradation follows a linear function, and alternatively, a polynomial function, are compared. The maximum difference between confidence factors assuming both types of functions is 5% after 100 years of structure construction, which represents a small difference for the engineering practice.

An approach to evaluate the structural reliability taking into account the degradation of the structural capacity due to corrosion of reinforced concrete buildings at the end of a time interval is proposed. The structural reliability is expressed in terms of the confidence factor, within a Demand and Capacity Factor Design format (DCFD). A new closed-form mathematical expression that considers the non-linear structural capacity degradation due to corrosion by means of a second degree polynomial function is developed. The confidence factors are obtained under the assumption that the structural capacity degradation due to corrosion follows a linear and non-linear function over a time interval. The structural reliability is obtained for a three-story reinforced concrete building subjected to two sets of real seismic ground motions recorded in Acapulco Bay Mexico. Both, aleatory and epistemic uncertainties are taken into account into the analysis. A maximum difference of 3.5% between both functions after 83 years from the construction of the building was found.