Report - PEER - University of California, Berkeley

where R = the ratio of the strength required for elastic response and the yield strengthof an oscillator having an identical initial period, T. In general, the two relationshipsare seen to produce consistent results. However, the R-C 1 -T approach results insomewhat higher design strengths for intermediate period oscillators having relativelylarge ductility demands.2.4 Performance LimitsDiscrete performance objectives, consisting of the pairing of performance limits andhazard levels, may be considered. The performance limits are interpreted in termsrelevant to the response of the ESDOF system:• The peak displacement limit of the ESDOF system is equal to ∆ u /Γ 1 , where ∆ u =the roof drift limit.• The displacement ductility limit of the ESDOF system is equal to the systemductility limit.Note that peak dynamic interstory drifts can be related to peak roof drifts (e.g.,Ghoborah, 2004), and that simple analytical expressions can relate code limits onstory drift to roof drift limits.2.5 Required Strength DeterminationIf an estimate of the roof displacement at yield is available, then the required strengthcan be determined using the procedure described in this section. For other cases,Admissible Design Regions may be used to identify a continuum of yield points thatsatisfy one or more performance objectives (Aschheim and Black, 2000).Using standard approaches such as those described in ATC-40 (1996), the yielddisplacement of the ESDOF oscillator, ∆ y * , is given by∆*= ∆ / Γ(2)y y 1YPS are used to determine the required yield strength coefficient of the ESDOFoscillator, C y * , from which the base shear coefficient (at yield) of the MDOF system isdetermined asC = (3)*yC yα1The base shear strength (at yield) of the MDOF system is given by V y = C y W. Thefundamental period of the MDOF system matches that of the ESDOF system, givenby*∆yT = 2π , (4)*C gy486