Structures with cumulative damage

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.