Report - PEER - University of California, Berkeley

The results for all 100 earthquake records were averaged and plotted as afunction of equivalent damping against oscillator periods as shown in figures 8 and 9.The coefficient of variation of the average values, which represents the scatter of thedata around its average, is also shown in the same figures.On average, the hysteretic models which predict less damping have better results,which suggest that all over Jacobsen’s approach overestimates damping andconsequently underestimates actual displacements. It worth mentioning that byaveraging the results, the effect of earthquake characteristics has been eliminatedsince the ratios are about the same for all oscillators. The coefficients of variation arebounded between 10% and 30% except for short periods, which is fairly goodconsidering the large number of earthquakes considered.Average D TH \ D Design1.41.21.00.80.64.0% 6.0%0.48.0% 10.0%0.212.0% 14.0%0.00.0 1.0 2.0 3.0 4.0 5.0Effective Period (sec)(a) Average D TH /D Design for Takeda small loopCoefficient of Variation100%90%80%70%60%50%40%30%20%10%0%4.0% 6.0%8.0% 10.0%12.0% 14.0%0.0 1.0 2.0 3.0 4.0 5.0Effective Period (sec)(b) CoV for Takeda small loopFigure 8. Average time-history to design displacement ratios for Ring-Springhysteretic model and 100 earthquake records.5. CONCLUSIONSSince the major assumption in Jacobsen’s approach is a sinusoidal response, theapproach was tested with a sinusoidal earthquake; the results indicated, as expected,that the approach works very well, however, it overestimates the displacements forperiods less than the sine wave fundamental period. In some cases the approachunderestimates the displacements not only due to overestimating damping but alsodue to the shift in the hysteretic loops because the oscillator starts vibrating around anew equilibrium position. A wider scatter is clearly noticed for real earthquakerecords, which varies based on the earthquake characteristics, oscillator fundamentalperiod and level of ductility.The results for 100 earthquake records indicate that Jacobsen’s approach, onaverage, overestimates damping and consequently underestimates the actualdisplacements which suggest that a reduction factor is needed. As a part of futurework, a reduction factors will be obtained based on hysteretic model and level ofductility.503