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The present study addresses the probabilistic seismic capacity evaluation of the existing non-ductile reinforced concrete structures that are vulnerable to shear, and thus axial, failures of their columns. The probability of structural collapse at a target lateral displacement imposed by seismic hazard is estimated by reliability analysis. For this purpose, the prevalent nonlinear static procedure is extended with finite element reliability analysis. The global structural model is enhanced by incorporating probabilistic capacity and post-failure response models of individual columns. The challenges in the detection of collapse and the potential problems and remedies in the reliability analysis due to 'gradient discontinuities' are presented. In particular, 'smoothing' of the post-failure response models is implemented to represent realistic member behaviour and to avoid non-convergence in the reliability analysis. Finally, parameter importance measures are employed to identify the parameters with the highest contribution to the uncertainty in the structural performance.

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