Report - PEER - University of California, Berkeley

some procedures are (contrary to the opinion of their authors) quite complicated forthe use in design.An attempt was made (Isaković et al. 2003) to provide designers with a simpletool (a single number called irregularity index) to identify those bridges to bepreferably analyzed by inelastic time history analysis rather than by the standardsingle mode N2 procedure. The concept of the proposed irregularity index ispresented in Figure 5. It is based on the comparison of the displacement shapesobtained in the two iterations of the push-over in the N2 method (it could be used inthe elastic range to determine the applicability of the Rayleigh’s method, too). If theareas bounded by these displacements lines are very different, the displacements arechanging during the response, and the inelastic time-history analysis is recommended.If not, the designer may proceed with further steps of the N2 procedure.What is “very different” is still quite arbitrarily defined, but in general the indexbelow 5 % defines conservatively the viaduct, which can be analyzed by push-overprocedure (defined as regular viaduct). Some examples of regular and irregularbridges and corresponding irregularity indices are presented in Table 1.Forces1 st iterationNormalised displacementsIndexF i,02 nd iterationφ i,0∆xx i∑ φi, 0 − φi,1 ∆xicompared toFi, 1 = f ( φi,0 )φ i,1∑ φi , 0 ∆x iFigure 5. Definition of the irregularity index.Table 1. Irregularity index for several types of viaducts (PGA = 0.35g)Example of viaductV123 PV213 PV121 PV232 PV213 RDifference betweenSDOF and MDOF - D[%]Irregularity indexIRI [%]7.4 6.97.9 ("weak" reinforc.)14.4 ("strong" reinforc.)4.4 (PGA = 0.7 g)7.3 ("weak" reinforcement)19.6 ("strong" reinforcement)1.7 (PGA = 0.7g)7.2 9.30.4 0.445.5 17.4P — viaducts with pinned supports at the abutments; R — viaducts with rollersupports at the abutments; weak reinforcement — based on seismic forces intransverse direction; strong reinforcement — based on seismic forces in bothdirections297