A Strength Amplification Factor to Counterbalance P–∆ Effects in Steel Moment Resisting Frames

The importance of P–Δ effects is generally modest in the elastic range of behaviour. However, it becomes significant when the structure experiences large plastic deformations. Seismic codes indicate that P–Δ effects may be counterbalanced through an increase in the lateral strength required by a first order analysis. The expressions suggested in codes for this amplification factor are simplistic and often criticized by researchers. Hence, the paper proposes a formulation of the strength amplification factor, which is alternative to those of seismic codes. This formulation is a generalization of the one derived in the past by the authors based on the numerical response of SDOF systems. To validate the proposed formulation, steel moment resisting frames characterized by different sensitivity to P–Δ effects are considered. Each structure is designed taking into account P–Δ effects in keeping with provisions of seismic codes or according to the proposed strength amplification factor. To comment on the effectiveness of the proposal, the nonlinear seismic response of these structures is determined by nonlinear static analysis. The increase in size of the cross-sections required to counterbalance P–Δ effects is also determined to compare the costs of structures designed according to the proposed and existing formulations.