by C.M. Uang and A. Maarouf
September 1996, 167 pp.
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Abstract
Displacement amplification factor (DAF) for seismic design of multistory buildings has been
investigated. Expressed in terms of the seismic force reduction factor (FRF), which is better
known as the R, factor in Uniform Building Code (UBC) and R factor in NEHRP Recommended
Provisions, it was observed that the DAF/FRF ratios used in UBC and NEHRP are much smaller
than those used in the Mexican Code and Eurocode.
Four buildings (two steel and two reinforced concrete structures) which have been instrumented
by the California Division of Mines and Geology were studied to investigate if the DAF used
in UBC or NEHRP significantly underestimates maximum (inelastic) deformations. Building response
recorded during the 1989 Loma Prieta earthquake was used to calibrate mathematical models of
these buildings. Dynamic analyses were performed to investigate the relationship between the
DAF and FRF; an assemble of California historical earthquake records was used as input ground
motions. The effects of structural overstrength, types of collapse mechanism, stiffness
degradation, damping, fundamental period, and earthquake characteristics (impulse versus
"standard" type earthquakes, strong motion duration, earthquake predominant period) on the
DAF were investigated. The reliability of using a DAF as derived from either singledegreeof
freedom (SDOF) systems or shear building models (i.e., "stick" models) for practical design
was also studied.
The results have indicated that neither SDOF systems nor shear building models provides reliable
prediction of DAF for multistory buildings. It was found that the DAF/FRF ratio is practically
independent of the structure's fundamental period as long as it is longer than 0.3 of the
earthquake predominant period. The DAF/FRF ratio for estimating roof drift does not appear to
be affected by the type of failure mechanism and stiffness degradation. Nevertheless, this is
not true for estimating story drift; the DAF/FRF ratio can be significantly higher than 1.0 for
stiffness degrading systems with a soft story. Although the DAF required to estimate roof drift
is slightly less than FRF, the DAF for estimating story drift can be significantly higher than
FRF. For simplicity, it is recommended that a DAF which is equal to FRF be used for design purposes.
