P-delta ( PΔ) effects can worsen the seismic performance of building and bridge structures and potentially lead to dynamic instability and collapse. An accurate characterization of PΔ effects is therefore imperative, for both design and assessment of structures. Adopting an earthquake database composed of 7032 ground motions, this article uses the results of a large statistical analysis of amplifications of the displacement demand due to PΔ effects for bilinear single-degree-of-freedom systems to investigate and improve practice-oriented methods to account for PΔ effects. A large range of fundamental periods, ductility levels, and effective heights are investigated, and limits for dynamic instability and negligible PΔ effects are examined in terms of both elastic and inelastic stability coefficients. It is seen that systems with the same stability coefficient present increased PΔ induced displacement amplification with reducing fundamental period and increasing ductility level. New expressions for estimation of the median values of the PΔ displacement amplification ratio are proposed that take into account the combined effect of stability coefficient, ductility level, and fundamental period with improved transition close to dynamic instability. Results of the numerical analyses indicate that the new expressions provide improved accuracy over existing approaches without undue complexity.
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