r - The Hong Kong Polytechnic University

CONCLUSIONS
Performance-based design and assessment requires reasonable estimates to be made of the distribution (both
median and dispersion) of nonlinear structural responses. Studies were performed with the goals of establishing
an optimal ground motion scaling procedure for uni-directional response-history analysis and providing a
technical basis for future work on selecting and scaling pairs of ground motions for bi-directional response
analysis. Three ground-motion scaling methods were evaluated using nonlinear single-degree of freedom
models with yield strengths ranging from 0.06W to infinity and periods ranging from 0.01 to 4 seconds. Two
sets of 25 pairs of ground motions were used in the study: one set of near-fault motions and the other set of
far-field motions. Only the results for the near-fault motions are presented in this paper.
The key conclusions of the studies are summarized below. These conclusions are limited to
first-mode-dominated buildings with minor to moderate inelastic deformation and typical base-isolated
structures. For structures in which multiple modes contribute significantly to the drift and acceleration response
due to earthquake shaking (e.g., tall buildings), alternate procedures may be required.
1. Method 1 (geomean scaling) preserves the irregular spectral shapes of recorded ground motion and some
dispersion in the spectral demand. The shape of the median spectrum for a bin of ground motions scaled
by this method depends solely on the pre-scaled shape of the median spectrum for the bin. If a wide range
of periods must be addressed for analysis, and multiple magnitude-distance pairs dominate the target
spectrum at different periods across the range of interest, it will be difficult to select a bin of ground
motions whose median spectrum closely matches the target spectrum. For such a circumstance, multiple
bins of ground motions should be considered at different periods of interest. This conclusion applies to all
amplitude-scaling methods.
2. Method 2, spectrum-matching scaling, underestimates the median benchmark displacement demand (from
the results of Method 1) in highly nonlinear SDOF systems and cannot capture the dispersion in the
structural response because the scatter in the spectral ordinates is eliminated by the matching process.
Earthquake ground motions that are spectrally matched to target median spectrum should not be used to
characterize a distribution of seismic responses resulting from a distribution of spectral demand because
the median displacement response will be underestimated for highly nonlinear systems and the dispersion
in the displacement response will be underestimated by a wide margin for all systems, regardless of
whether the response is linear or nonlinear.
3. Method 3, Sa( T 1)
scaling, provides unbiased estimates of median benchmark responses of nonlinear
systems and produces dispersions of the same order as or greater than those of Method 1 for nonlinear
systems with ductility greater than 3 because the first mode period does not necessarily dictate the
response of such systems. However, the method cannot capture (and was not intended to capture) the
benchmark dispersion in response of elastic and near-elastic systems.
ACKNOWLEDGEMENTS
This research is supported by the department of Civil Engineering, National Taiwan University and a grant
(Code# ’09 R&D A01) from Cutting-edge Urban Development Program funded by Ministry of Land, Transport
and Maritime Affairs of Korean government.
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