Report - PEER - University of California, Berkeley

3. STUDY PARAMETERS AND ASSESSMENT ALGORITHMIn this paper, an assessment algorithm has been used to investigate the accuracy of theequivalent viscous damping approach (Kowalsky’s formulation of Jacobsen’sapproach [5]) as it’s been used in direct displacement-based seismic design (DDBD).Jacobsen’s approach was tested first for a sinusoidal earthquake to eliminate the mainassumption in his approach. Then it was tested for real earthquake records, and finallya comprehensive evaluation of the approach was carried out utilizing a large numberof earthquake records.3.1 Study ParametersIn this study, The Takeda hysteretic model [5] and Ring-Spring hysteretic model [6]were considered as shown in figure 4. An expression between displacement ductilityand hysteretic damping could be obtained by applying Jacobsen’s approach to bothmodels. The expression given by equations 6-8 is for the Takeda model, where µ isthe displacement ductility, α is the unloading stiffness and γ is the reloading stiffness.Two extreme cases were selected for the Takeda model: the smallest and largestloop possible by changing α and β values. For the Ring-Spring model only the largestpossible loop was considered and the equivalent viscous damping expression is notshown due to size limitations.ξ142= (6)πhyst R LAα −1[ − µ γ ]3 1R LA −(7)α −1= 1 − µ γ − [(rβµ/ γ )( 1 −1/µ ) + 1] 2 − β ( 1 −1/µ )4 42[(rβµ / γ )( 1 −1/µ ) ]2γ = rµ − r +1DpF(8)FβDpPreviousYieldKurK 0Fy+K0Dy-FyNo YieldK urK 0αDy=K 0( )DmDmDDmDy D0rsK0Krl0rK0K0F 0F -yD(a) Modified Takeda hysteretic model(b) Ring-Spring hysteretic modelFigure 4. Hysteretic models considered. (a) modified Takeda hysteretic model.(b) Ring-Spring hysteretic model.497