Report - PEER - University of California, Berkeley

Relative Height20118160.8140.6 12100.4 860.2 4200.0 0.2 0.4 0.6 0.8 1.0AmplitudeM oment FramesDual (St raight Line)Slender Shear WallsFigure 1. Deflectedshapes used fordetermining values ofΓ 1 and α 1 in Table 1.Figure 2. The stability of the yield displacement withchanges in lateral strength. The capacity curves wereobtained for two four-story moment-resistant steelframes in which beam and column depths remainedconstant and section weights were varied.the fundamental period of vibration is recognized to be affected by the lateral strength(e.g., Priestley, 2000) and the number of stories. Because the yield displacement isrelatively stable, it is a more robust parameter to use for preliminary design.The displacement of the roof at yield may be estimated based on experience,simple formulae, or a previous nonlinear static analysis. For example, the yielddisplacement of steel moment-resistant frames often is 1 to 1.2% of the height of theframe. Estimates of the yield displacement of other systems are available; forexample, Pinho (2004) provides estimates of the yield displacement of reinforcedconcrete moment resistant frames.2.3 Inelastic Response SpectraEstimates of the inelastic response of the “equivalent” SDOF (ESDOF) systems arerequired. The graphic depiction of inelastic demands and the underlying relationshipsused to estimate these demands, given the elastic ordinates, are discussed below.The expected peak displacement response of inelastic systems can be estimatedon the basis of elastic response spectra using equivalent linearization anddisplacement modification approaches. Equivalent linearization (e.g., the CapacitySpectrum Method) estimates the peak response on the basis of a linear elastic systemhaving increased damping and reduced stiffness. Displacement modificationconsiders the strength reduction (R) factor and period (T) to estimate the peakdisplacement in relation to the response of an elastic system having the same period483