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CSMIP 96-02

"Evaluation of Displacement Amplification Factor for Seismic Design Provisions"

by C.-M. Uang and A. Maarouf

September 1996, 167 pp.

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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 single-degree-of- 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.