Acceleration Response Spectrum: Revisited for Higher Mode Effects

Abstract eng:
Acceleration response spectrum (ARS) is a tool that has conveniently been used in earthquake engineering in the last 75 years. One of the common uses of the response spectrum concept is the identification of higher mode contribution to the structural response. If the spectral acceleration (SA) corresponding to a higher mode (generally the second or third mode) is significantly larger than that of the first mode, the ground motion is accepted to induce higher mode response. However, in general, this interpretation is not necessarily correct because the structural response is usually inelastic and the ARS is obtained from linear elastic single degree of freedom (SDOF) response. ARS for constant base shear capacity coefficient has been developed to consider the inelastic response. However, such spectrum is not useful for higher mode effects identification since the SA for all the periods are bound by the base shear capacity coefficient and it is likely that the SA values corresponding to all the sought modes are the same. A modified ARS concept is introduced in this paper for a specific base shear coefficient at a desired period. In this modified ARS, a linear elastic SDOF system with a selected period (which generally corresponds to the first mode period) is analyzed with time history analysis. The time of the ground motion at which inelastic response initiates (i.e., the time when the restoring force first exceeds the base shear capacity) is determined from this analysis and the ground motion is redefined as the original ground motion truncated to this time defined by the initiation of inelastic response. Subsequently, the original ARS procedure is followed using the ground motion with truncated duration to obtain the modified ARS, namely the MARS. A theoretical background information is provided in the first part of the paper to explain why the proposed MARS is expected to produce a better indicator, compared to ARS, for the identification of ground motions leading to higher mode response. Subsequently, the outline for developing MARS is presented and the superiority of MARS in identifying the ground motions with higher mode effect is demonstrated using the results from nonlinear time history analyses conducted on a 35-story tall building.

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