Report - PEER - University of California, Berkeley

spectral acceleration and the top (roof) displacement, which allow also thevisualization of the procedure (Fig.7a). Other relevant quantities, like maximum storydrift, rotation at the column and beam end, shear force in a structural element and in ajoint, and story acceleration, can be employed as secondary demand measures. Theyare related to roof displacement and can be uniquely determined if roof displacementis known. The secondary demand measures can be used, together with the maindemand measure, for performance assessment at different performance levels.Roof displacement and other relevant demand measures for a chosen series ofspectral accelerations are determined by the N2 method. The shape of the IN2 curvedepends on the inelastic spectra applied in the N2 method, which are based on therelation between strength reduction factor, ductility and period (the R-µ-T relation). Ifa simple R-µ-T relation, based on equal displacement rule in the medium- and longperiodrange, is used, the IN2 curve is linear for structures with period higher than T C .A more complex R-µ-T relation is used for infilled RC frames (Eqs. 1 to 6). In thiscase IN2 curve is four-linear (Fig.7). Note that a bilinear relation is used alreadybefore yielding. Considering the piecewise linearity of the IN2 curve, only a fewpoints have to determined in order to obtain the complete IN2 curve.Usually the inelastic spectra, used in the N2 method, represent mean spectra andconsequently the IN2 curve represents a mean curve. More specifically, the R-µ-Trelation for infilled frames (Eqs. 1 to 6), represents an idealization of the R-µ-Trelation, calculated for mean ductility given the reduction factor.The determination of a point on the IN2 curve is visualised in Fig.7a. The point isdefined with the pair: elastic spectral acceleration (1.07g), corresponding to theequivalent elastic period T, on the Y-axis, and the corresponding inelasticdisplacement demand (6.59cm) on the X-axis. By repeating the procedure for manylevels of elastic spectral acceleration, the complete IN2 curve can be obtained aspresented in Fig.7b.S (g)a1.21.070.90.6T=0.29 sElastic spectrumIN2 curveInelastic spectrum =0.49IN20.30.5IDACapacity diagram2.25 cm 6.59 cm000 2 4 6 8 10 0 5 10 15 20a) S (cm)b) Top displacement (cm)dµ 6.5S (g)a1.5Figure 7. Infilled frame: (a) capacity diagram, demand spectra and IN2 curve(for SDOF system), (b) mean ± σ IDA and IN2 curve.21ea σM n-MeanMean+σ366