Report - PEER - University of California, Berkeley

The relations apply to SDOF systems. However, they can be used also for a largeclass of MDOF systems, which can be adequately represented by equivalent SDOFsystems. The combination with the nonlinear pushover analysis substantiallyincreases the accuracy of the procedure compared to the traditional ductility factormethod.3. EXTENSION TO PLAN—ASYMMETRIC BUILDINGSThe original N2 method is, like other simplified non-linear methods, restricted to 2Danalysis. In order to extend the applicability of the method to plan-asymmetricbuildings, which require a 3D structural model, a procedure based on pushoveranalysis of a 3D building model was proposed in (Fajfar 2002) and implemented in(Fajfar et al. 2002). The test results have indicated that some improvements of the N2method for asymmetric structures are still needed, therefore the research on inelasticstructural response of asymmetric structures has been continued. Based on severalextensive parametric studies reported in (Fajfar et al. 2004) we concluded that (a) theamplification of displacements determined by the elastic analysis can be used as arough estimate also in the inelastic range and (b) any favourable torsional effect onthe stiff side of torsionally stiff buildings, which may arise from elastic analysis, maydisappear in the inelastic range. Based on these results, the following procedure isproposed, which represents a combination of non-linear static and linear dynamicanalysis. It can be applied both for torsionally stiff and torsionally flexible buildings.Two independent analyses in two horizontal directions are performed. For eachdirection, first a pushover analysis of a 3D structural model is made. The transverseelements should be included in the model. Lateral loads are applied in mass centres.Based on the obtained base shear – top displacement relationship, an equivalentSDOF system is determined. Top displacement corresponds to the mass centre. Thetransformation from the MDOF to the SDOF system and vice versa is the same as inthe case of a 2D model. The procedure for determining the target displacement of theequivalent SDOF system is also the same as in the case of 2D analysis. Seismicdemands (deformation quantities: displacements, storey drifts, rotations andductilities, and quantities related to accelerations, which may be relevant for brittleelements and contents of the building) are determined by pushing the structure to thetarget displacement for each of two horizontal directions separately.In the next step of analysis, a usual elastic modal analysis employing the samemathematical model as in pushover analysis and the same demand spectra as fordetermination of target displacement is performed for both directions of loading.Demand quantities obtained for two directions of loading are combined by the SRSSrule. The resulting seismic demand in terms of displacements at different locations atthe top of the building is used for the determination of correction factors to be appliedto the results of pushover analyses. A single correction factor is determined for eachvertical plane of load-bearing elements (e.g., a structural wall or a plane frame) and itdepends on the position of the plane in the plan. The correction factors are aimed to361