Closure to “Observations on the Reliability of Alternative Multiple-Mode Pushover Analysis Methods” by T. Tjhin, M. Aschheim, and E. Hernández-Montes
Publication: Journal of Structural Engineering
Volume 134, Issue 9
The authors in no way wish to diminish the discusser’s contribution to the development of the MPA procedure. Much of the discussion focused on this procedure, although the technical note was concerned only with two alternative procedures, in which energy-based pushover curves are used to identify modal contributions.
The discusser acknowledges that the MPA procedure can cause reversals in the higher-mode pushover curves obtained for some buildings. Because inelastic response dissipates energy (rather than creating energy), it is not appropriate to represent the building using an equivalent SDOF system whose force-displacement response contains such a reversal. To do so would imply a violation of the first law of thermodynamics.
The energy-based pushover method was developed directly from, and as an extension to, the MPA procedure. Use of the energy-based displacement as an index for the pushover curve avoids outright reversals as well as disproportionate increases in displacement that are observed when the roof displacement is used as an index for the capacity curve (Hernández-Montes et al. 2004). The postyield stiffness obtained with this approach appears to improve the accuracy of peak roof displacement estimates (Tjhin et al., 2005). However, further improvements in pushover methods may be possible. For example, Kalkan and Kunnath (2006) developed an adaptive pushover procedure using the energy-based approach and report that this approach led to more stable and smoother capacity curves.
Having eliminated the problem of reversals, the authors were able to address in the technical note the errors in combining “modal” responses for systems responding nonlinearly. Differences in results obtained using the two alternative methods indicate that at least some higher-“mode” responses were nonlinear when computed using the energy-based approach. The results demonstrate that the computed value of peak story shear, overturning moment, and in some cases, interstory drift, was influenced more by the method of analysis than by the particular ground motion record used in the nonlinear dynamic analyses. This indicates that the assumptions embedded in these alternative methods were more consequential than the randomness associated with particular ground motion waveforms, where the records are scaled to achieve a uniform peak roof drift. This important observation led to the development of an analysis procedure known as the “scaled NDP” (Aschheim et al., 2007). The scaled NDP does not involve modal combinations and thus avoids potential problems and limitations that stem from combining modal responses for systems responding nonlinearly.
Relatively simple methods are most useful for preliminary design, where member sizes have yet to be established. A very elegant approach for estimating the maximum interstory drift over the height of the building at this stage is described by Miranda (1999) and Miranda and Rayes (2002). Once preliminary member sizes have been established, detailed evaluation presents a trade-off between the accuracy of the results and the effort required of the analyst. We agree with the discusser that in some cases the conditions under which simplified analysis procedures may be used with confidence require further clarification, as there is little point in generating results of uncertain accuracy.
References
Aschheim, M., Tjhin, T., Hamburger, R., Comartin, C., and Inel, M. (2007). “The scaled nonlinear dynamic procedure.” Eng. Struct., 29(7), 1422–1441.
Kalkan, E., and Kunnath, S. K. (2006). “Adaptive modal combination procedure for nonlinear static analysis of building structures.” J. Struct. Eng., 132(11), 1721–1731.
Miranda, E. (1999). “Approximate seismic lateral deformation demands in multistory buildings.” J. Struct. Eng., 125(4), 417–425.
Miranda, E., and Reyes, C. J. (2002). “Approximate lateral drift demands in multistory buildings with nonuniform stiffness.” J. Struct. Eng., 128(7), 840–849.
Henández-Montes, E., Kwon, O.-S., and Aschheim, M. (2004). “An energy-based formulation for first-and multiple-mode nonlinear static (Pushover) analyses.” J. Earthquake Eng., 8(1), 69–88.
Tjhin, T., Aschherm, M., and Henández-Montes, E. (2005). “Estimates of peak roof displacement using ‘equivalent’ single degree of freedom systems.” J. Struct. Eng., 131(3), 517–522.
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© 2008 ASCE.
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Published online: Sep 1, 2008
Published in print: Sep 2008
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