The present study develops a more efficient method for the accurate modeling of nonlinear behavior of structural elements, being an essential ingredient in reliable assessment of collapse fragility curve, as an important issue in the performancebased earthquake engineering. To this end, beams and columns are often simulated by lumped plasticity models, consisting of one elastic element and two nonlinear spring elements at two ends to consider the effects of strength and stiffness degradation. Since introducing spring elements is obviously associated with the correct estimation of axial load ratio of each structural component during nonlinear dynamic analysis, the specific aim of this paper is to evaluate the effectiveness of any variation in the generated axial forces (axial efforts) in the elements on structural seismic response. For this purpose, fuzzy set theory has been utilized to assess the median of collapse fragility curves as fuzzy number by well-known α-cut approach. Then, herein, genetic algorithm has been employed to search for the maximum and minimum of this median in each membership degree α. Application of this methodology is illustrated through an example. It is shown that the primary advantage of the proposed assessment processes is to incorporate the influence of record to record variability, as aleatory uncertainty, and fuzziness in axial effort of the structural elements, as epistemic uncertainty, on the estimation of more realistic responses for structural systems with cyclic behavior and the evaluation of collapse performance of reinforced concrete buildings under seismic loads.
