Fragility assessment requires characterization of a component or system's performance through a performance function/limit-state equation. The exceedance of limit-state is representative of failure or damage state. For the purposes of evaluating piping fragility, characterizing the behavior of T-joints through an appropriate performance function is critical, as failures in piping are generally localized at the location of T-joints, elbows, and nozzles. Past studies have utilized a monotonic rotation-based performance function. However, the existing criteria does not account for the effect of cyclic behavior. As observed during prior experimental studies, the T-joint behavior under cyclic loading is different from that under monotonic loading, and therefore, it is important to include the effects of cyclic behavior while characterizing a performance function. Moreover, the monotonic rotation-based performance function could not replicate all the leakage locations observed during experimental studies on a full-scale two-story piping system. Therefore, it is important to develop a new limit-state for accurate piping fragility assessment. This paper presents the development of a new limit state which considers the cyclic behavior of a T-joint and quantifies the number of cycles to failure.