Report - PEER - University of California, Berkeley

normalized dispalcemets10.750.50.250IAChopraAydinoğlu - CQCAydinoğlu - sum0 50 100 150 200stationFigure 4. Normalized displacements of V213 (multi-mode and IA methods).2.2 Multimode ProceduresRealizing the limited applicability of the single mode methods, several researchershave developed methods taking into account the influence of higher modes. Howeverthey were predominantly tested for building structures. For example, Chopra’smethod (Chopra 2002) is a push-over based procedure, where the structure is pushedusing displacements shapes of all important modes, determined by the elastic multimodalanalysis. The results are then combined using SRSS rule. However, such anapproach may not be applicable for irregular (i.e., torsionally flexible) viaducts (seeFig. 4), since the method does not take into account that the shape of the modes aswell as their contribution to the total response are changing during the response.Aydinoğlu (2004) takes into account variations of modes and variation of theirimportance during the response. Properties of a structure are changing according tothe formation of the plastic hinges. The CQC rule is used to combine importantmodes. However, in the case of the viaduct V213 such an approach still overestimatesthe displacements on the stiff side of the viaduct (Fig. 4). It seems that this is due tothe CQC combination rule, where the sign of the quantities is lost (neglected). If, inthis particular case, contributions of different modes are simply summed, the resultsare much closer to the results of the inelastic time-history analysis. By definition anymulti-mode spectral method depends on combination rules. Furthermore, nocombination rule can be fully theoretically justified. Therefore, the research related toinelastic spectral multimode procedures is still a long way to go. The importance andinfluence of different combination rules was recognized and studied by Reinhorn andhis associates (DeRue 1998) who analyzed the viaduct very similar to the V213.2.3 Irregularity IndexKawashima (2004) reports that in the questionnaire survey 46% of the 100 Japanesecivil engineers answered that “they want to use dynamic response analysis for bridgesto which push-over analysis provides poor application”. But which are those bridges?V213 viaduct is one such example. Single mode methods do not work for this viaduct.Some multi mode methods may improve results, but the outcome is uncertain and296