Report - PEER - University of California, Berkeley

linear methods, restricted to symmetric structures, which can be modelled by a planarstructural model. In this paper, the extensions of the N2 method are summarized.A pushover based non-linear analysis of plan-asymmetric buildings, whichexperience torsional rotations, proved to be a difficult problem. As a preliminarysolution, it is proposed to determine the global displacement demand in eachhorizontal direction by a uni-directional pushover analysis of a 3D structural model,and to estimate the torsional influence from the results of elastic modal analysis of thesame model. This proposal is based on results of limited parametric studies, whichsuggest that the torsional effects decrease with increasing intensity of ground motionand with related increase of plastic deformations. Consequently, torsionalamplification determined by elastic analysis may represent a conservative estimate.The N2 method employs inelastic spectra for the determination of seismicdemand. Inelastic spectra are determined from the elastic demand spectra by usingstrength reduction factors. In the basic variant of the N2 method, simple R-µ-Trelationships are used, based on equal displacement rule in medium- and long-periodrange of the spectrum. This assumption, although valid for many structural systems, isnot appropriate for RC frames infilled with masonry, which are characterised by astrong stiffness and strength degradation after infill fails. Specific R-µ-T relationshipshave been developed for this type of structural systems. The example demonstrateshow any R-µ-T relationship can be employed in the N2 method.The result of an Incremental dynamic analysis (IDA) is an IDA curve, whichrepresents the relation between a structural response parameter versus the intensitylevel of ground motion, and the corresponding variability. IDA requires a largenumber of inelastic time-history analyses of MDOF structural systems and is thustime consuming. An estimate of the IDA curve can be obtained by a series of N2analyses, called IN2 (Incremental N2) analysis. An IN2 curve, which is the result ofIN2 analysis, can be combined with generic variability for different structuralsystems, determined by parametric studies.2. SUMMARY OF THE N2 METHOD — BASIC VARIANTThe N2 method (N comes from Nonlinear analysis and 2 comes from 2 mathematicalmodels) was developed at the University of Ljubljana in mid-eighties. Theformulation of the method in the AD format enables the visual interpretation of theprocedure and of the relations between the basic quantities controlling the seismicresponse. For details about the basic version of the N2 method, limited to planarstructural models, see e.g., (Fajfar and Gašperšič 1996 and Fajfar 2000).In the N2 method, first the pushover analysis of the MDOF model is performed.Pushover curve is then transformed to the capacity diagram. The seismic demand forthe equivalent SDOF system with a period T can be determined as follows: Elasticdemand in terms of acceleration S ae and displacement S de is determined from theelastic spectrum. The inelastic acceleration demand S a is equal to the yieldacceleration S ay , which represents the acceleration capacity of the inelastic system.358