Report - PEER - University of California, Berkeley

As an example, an idealized force-displacement relation (pushover curve) and theR-µ-T relation for the given pushover curve are shown in Fig.6.The coefficient of variation for ductility is strongly influenced by the dispersionof elastic displacement. It is higher for lower periods. As a rough estimate, a value ofabout 0.7 can be assumed for infilled frames with the fundamental period in the shortperiod range (Dolšek and Fajfar 2004a).Note that the idealized R-µ-T relation defined above is based on mean ductilityobtained by statistical analysis, in which the reduction factor R was fixed. It is shownin (Dolšek and Fajfar 2004a) that such an approach is conservative both for designand assessment. In the same paper it is shown that a more realistic R-µ-T relation canbe obtained if median is used as the central value instead of mean.Knowing the R-µ-T relation, the usual N2 procedure, as described in Chapter 2,can be employed. Note, however, that the performance point, defining the seismicdemand, is presented in the capacity-demand plot as the point where the horizontalline, at the acceleration S ay , intersects the appropriate inelastic spectrum, and not thepoint, where the capacity diagram intersects the demand spectrum.A similar extension of the N2 method can be made to any structural system,provided that an appropriate specific R-µ-T relation is available.5040302010Pushover curveIdealized, µs=1. 94,r=0. u 4700 0.2 0.4 0.6 0.8 1.0 1.2a) Top displacement / Height (%)Figure 6. Infilled frame: (a) force-displacement relation, (b) R-µ-T relation.5. INCREMENTAL N2 METHOD00 1 2 3 4 5b)T/T CThe incremental N2 (IN2) method (Dolšek and Fajfar 2004b, 2004c) is a relativelysimple non-linear method for determination of approximate IDA curves. An IDAcurve is determined with non-linear dynamic analyses (Vamvastsikos and Cornell2002), while each point of an IN2 curve (approximate IDA curve), which correspondsto a given seismic intensity, is determined with the N2 method.In order to determine an IN2 curve, first the ground motion intensity measure andthe demand measure have to be selected. The most appropriate pair of quantities is theR87654321µ s=1.94 r u=0.47T/T=3.D C 20µ=8µ=6µ=4µ=3µ=2µ=1.5365