Incremental Response Spectrum Analysis

Abstract. The so-called Nonlinear Static Procedure (NSP) based on pushover analysis has been developed
in the last decade as a practical engineering tool to estimate the inelastic response quantities
in the framework of performance-based seismic evaluation of structures. However NSP suffers from
a major drawback in that it is restricted with a single-mode response and therefore the procedure can
be reliably applied only to the two-dimensional response of low-rise, regular buildings. Recognizing
the continuously intensifying use of the pushover-based NSP in the engineering practice, the present
paper attempts to develop a new pushover analysis procedure to cater for the multi-mode response
in a practical and theoretically consistent manner. The proposed Incremental Response Spectrum
Analysis (IRSA) procedure is based on the approximate development of the so-called modal capacity
diagrams, which are defined as the backbone curves of the modal hysteresis loops. Modal capacity
diagrams are used for the estimation of instantaneous modal inelastic spectral displacements in a
piecewise linear process called pushover-history analysis. It is illustrated through an example analysis
that the proposed IRSA procedure can estimate with a reasonable accuracy the peak inelastic
response quantities of interest, such as story drift ratios and plastic hinge rotations as well as the
story shears and overturning moments. A practical version of the procedure is also developed which
is based on the code-specified smooth response spectrum and the well-known equal displacement
rule.