Implementation of the structural performance factor (Sp) within a displacement-based design framework

Abstract

This paper discusses the application of the Structural Performance factor (S_P) within a Direct Displacement-Based Design framework (Direct-DBD). As stated within the New Zealand loadings standard, NZS1170.5:2004 [1], the S_P factor is a base shear multiplier (reduction factor) for ductile structures, i.e. as the design ductility increases, the S_P factor reduces. The S_P factor is intended to acknowledge the better-than-expected structural behaviour of ductile systems (both strength, and ductility capacity) by accounting for attributes of response that designers are unable to reliably estimate. The S_P factor also recognizes the less dependable seismic performance of non-ductile structures, by permitting less of a reduction (a larger S_P factor) for non-ductile structures. Within a traditional force-based design framework the S_P factor can be applied to either the design response spectrum (a seismic hazard/demand multiplier), or as a base shear multiplier at the end of design (structural capacity multiplier) – either of these two approaches will yield an identical design in terms of the required design base shear and computed ULS displacement/drift demands. However, these two approaches yield very different outcomes within a Direct-DBD framework – in particular, if S_P is applied to the seismic demand, the design base shear is effectively multiplied by (S_P)² (i.e. a two-fold reduction). This paper presents a “DBD-corrected” S_P factor to be applied to the design response spectrum in Direct-DBD in order to achieve the intent of the S_P factor as it applies to force-based design. The proposed DBD-corrected S_P factor is attractive in that it is identical to the S_P relationship applied to the elastic site hazard spectrum C(T) for numerical integration time history method of analysis within NZS 1170.5:2004 [1], S_P,DDBD = (1+S_P)/2.