Report - PEER - University of California, Berkeley

for a response governed by the fundamental mode only, those problems can be easilyovercome by using an adaptive procedure, in which instantaneous seismic loads andthe corresponding deformed shape amplitudes are always compatible at eachincremental step of a piecewise linear analysis, because both are expressed in termsof instantaneous mode shapes. In such an analysis procedure, plotting theconventional pushover curve is completely avoided and the capacity diagram of themodal SDOF system, which may include P-delta effects, can be developed directly forthe seismic demand estimation (Aydinoglu 2003, 2004).It should be stressed that even if the above-described adaptive procedure can beconsidered to provide the right answer to the single-mode pushover analysis, the mainproblem remains unresolved: Such an analysis can be reliably applied to only twodimensionalresponse of low-rise building structures regular in plan, where theseismic response can be assumed essentially governed by the fundamental mode.Hence it follows that improved procedures are required for high-rise and/or planirregularbuildings and irregular bridges to account for higher-mode effects in apractical, but at the same time a rational manner. As a matter of fact significant effortshave been devoted in recent years to achieve this objective (Gupta and Kunnath 2000,Antoniou et al 2002, Chopra and Goel 2002). In this respect, Incremental ResponseSpectrum Analysis (IRSA) procedure has been introduced recently (Aydinoglu 2003).It is further extended to include P-delta effects (Aydinoglu 2004) and elaborated inthis paper as an improved pushover procedure intended for use in routine engineeringpractice.2. PRACTICAL IMPLEMENTATION OF INCREMENTAL RESPONSESPECTRUM ANALYSIS (IRSA) PROCEDUREIncremental Response Spectrum Analysis (IRSA) procedure is essentially based on apiecewise linear Response Spectrum Analysis (RSA) procedure applied at eachincremental step of a pushover analysis (Aydinoglu 2003).Adopting lumped plasticity approach, i.e., using plastic hinges to characterize thenonlinear behavior of structural members, any incremental pushover step (i) isdefined in IRSA as representing a piecewise linear response increment in between theformation of two consecutive plastic hinges at discrete response points (i–1) and (i)during the so-called pushover-history process.Applying modal expansion at the (i)’th piecewise linear pushover step, theincrement of the displacement vector in the n’th mode, ∆u∆u(i) (i) (i) (i)n n xn n(i)n, can be expressed as= Φ Γ ∆d(1)(i)(i)where ∆ d nrepresents modal displacement increment, Φndenotes instantaneous(i)mode shape vector and Γxnrefers to instantaneous participation factor for a groundmotion in a given x direction. The eigenvalue analysis is governed by( K − K ) Φ = (ω ) MΦ (2)(i) (i) (i) (i) 2 (i)G n n n347