Report - PEER - University of California, Berkeley

shown in figure 2; for instance, a ductility of 2.1 and the Takeda smallest loophysteretic model yield a 10% hysteretic damping.µ ∆ =D t /D y (4)Equivalent Hysteretic Damping40%35%30%25%20%15%10%5%0%Takeda SmallTakeda LargeRing-Spring Large0 1 2 3 4 5 6 7 8Displacement Ductility (µ ∆ )Figure 2. Hysteretic damping versus ductility for modified Takeda and Ring-Spring models.3. Determine effective period of the structure (T eff ): utilizing the targetdisplacement, level of equivalent viscous damping and elastic response spectrafor the chosen seismic demand, the equivalent period of the structure could bedetermined as shown in figure 3. For a design displacement of 0.375m and 10%level of damping, the equivalent period is estimated to be 2.1 seconds.4. Evaluate effective stiffness (K eff ) and design base shear (V B ): using theequivalent period and the structure mass, the equivalent stiffness could be easilycalculated as given by Eq.(5). Compute the base shear by multiplying theequivalent stiffness by the target design displacement (D t ).Keff2 M= 4π(5)T2eff5. Design the structure: and check for the assumed or estimated yielddisplacement, if it changes significantly, repeat the previous steps untilconvergence is achieved.Spectral Displacement (m)1.501.251.000.750.500.255.0%10.0%15.0%20.0%Design DisplacementEquivalent VisousDampingEquivalent Period0.000.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Period (sec)Figure 3. Obtaining effective period for direct displacement-based design.496