SUMMARYDeveloped herein is an improved pushover analysis procedure based on structural dynamics theory, which retains the conceptual simplicity and computational attractiveness of current procedures with invariant force distribution. In this modal pushover analysis (MPA), the seismic demand due to individual terms in the modal expansion of the e ective earthquake forces is determined by a pushover analysis using the inertia force distribution for each mode. Combining these 'modal' demands due to the ÿrst two or three terms of the expansion provides an estimate of the total seismic demand on inelastic systems. When applied to elastic systems, the MPA procedure is shown to be equivalent to standard response spectrum analysis (RSA). When the peak inelastic response of a 9-storey steel building determined by the approximate MPA procedure is compared with rigorous non-linear response history analysis, it is demonstrated that MPA estimates the response of buildings responding well into the inelastic range to a similar degree of accuracy as RSA in estimating peak response of elastic systems. Thus, the MPA procedure is accurate enough for practical application in building evaluation and design.
SUMMARYBased on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric-plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the e ective earthquake forces is determined by non-linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each oor level. These 'modal' demands due to the ÿrst few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems. When applied to elastic systems, the MPA procedure is equivalent to standard response spectrum analysis (RSA). The MPA estimates of seismic demand for torsionally-sti and torsionally-exible unsymmetric systems are shown to be similarly accurate as they are for the symmetric building; however, the results deteriorate for a torsionally-similarly-sti unsymmetric-plan system and the ground motion considered because (a) elastic modes are strongly coupled, and (b) roof displacement is underestimated by the CQC modal combination rule (which would also limit accuracy of RSA for linearly elastic systems).
Most seismic codes specify empirical fonnulas to estimate the fundamental vibration period of buildings. Evaluated first in this paper are the fonnulas specified in present U.S. codes using the available data on the fundamental period of buildings "measured" from their motions recorded during eight California earth quakes, starting with the 1971 San Fernando earthquake and ending with the 1994 Northridge earthquake. It is shown that, although the code fonnulas provide periods that are generally shorter than measured periods, these fonnulas can be improved to provide better correlation with the measured data. Subsequently, improved fonnulas for estimating the fundamental periods of reinforced concrete (RC) and steel moment-resisting frame buildings are developed by regression analysis of the measured period data. Also recommended are factors to limit the period calculated by a rational analysis, such as Rayleigh's method.
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