Effectiveness of Design Procedures in Counteracting Second Order Effects in Steel Moment Resisting Frames

The seismic response of structures is always influenced by second order (P–Δ) effects. The importance of these effects becomes significant when the structure experiences large plastic deformations. Seismic codes indicate that P–Δ effects may be counteracted by means of an increase of the lateral strength required by a first order analysis, but the expressions of the Strength Amplification Factor (SAF) given in codes are often criticized by researchers. This paper proposes and validates a formulation of the SAF for Moment Resisting Frames (MRFs), which is a generalization of that derived in the past by some of the authors based on the response of SDOF systems. To this end, in a first stage of the research a set of steel MRFs is designed and analyzed neglecting P–Δ effects. The seismic response is determined by nonlinear static and incremental dynamic analyses and the mean annual frequency of exceedance of the Significant Damage (SD) and Near Collapse (NC) limit states is computed. In a second stage, each structure is re-designed and analyzed considering P–Δ effects. P–Δ effects are counteracted in design according to provisions of European, American and Canadian seismic codes or according to other formulations proposed in literature, such as that proposed by Bernal and that proposed by the authors. The accuracy of the design provisions accounting for P–Δ effects is determined by comparing the response of the structures designed in the first and in the second stages.