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

This paper discusses the application of the Structural Performance factor (SP) within a Direct Displacement-Based Design framework (Direct-DBD). As stated within the New Zealand loadings standard, NZS1170.5:2004 [1], the SP factor is a base shear multiplier (reduction factor) for ductile structures, i.e. as the design ductility increases, the SP factor reduces. The SP 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 SP factor also recognizes the less dependable seismic performance of non-ductile structures, by permitting less of a reduction (a larger SP factor) for non-ductile structures. Within a traditional force-based design framework the SP 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 SP is applied to the seismic demand, the design base shear is effectively multiplied by (SP)2 (i.e. a two-fold reduction). This paper presents a “DBD-corrected” SP factor to be applied to the design response spectrum in Direct-DBD in order to achieve the intent of the SP factor as it applies to force-based design. The proposed DBD-corrected SP factor is attractive in that it is identical to the SP relationship applied to the elastic site hazard spectrum C(T) for numerical integration time history method of analysis within NZS 1170.5:2004 [1], SP,DDBD = (1+SP)/2.