Report - PEER - University of California, Berkeley

of the bilinear model with the energy dissipated by one cycle of sinusoidal responseof a spring-dashpot-mass system at resonance, with spring constant K eff yields:2ξhyst = R LA(2)πR LAA=A12( µ −1)(1− r)=µ (1 + rµ− r)In Eq.(3), A 1 is the area of the nonlinear hysteretic loop, A 2 is the area of the rigidperfectly plastic loop that passes through the maximum displacement, and µ is thedisplacement ductility.F(3)A 2A 1K 0rK 0DyK effD tDFigure 1. Jacobsen’s equivalent damping approach.2. BACKGROUND OF DIRECT DISPLACEMENT-BASED DESIGNAs discussed earlier, the fundamental goal of the direct displacement-based design isto obtain a structure which will reach a predefined target displacement when thestructure is subjected to an earthquake consistent with the design level event. DDBDis a response spectrum-based design procedure in which the substitute structuremethodology, developed by Gulkan and Sozen [2] and expanded to multi-degree-offreedom structure by Shibata and Sozen [3], is utilized to model an inelastic systemwith equivalent elastic properties as shown in figure 1.After general parameters such as column height and mass being established, thefollowing steps could be followed to obtain the design forces:1. Obtain a target displacement (D t ): In the case of a single column bridge, thetarget displacement can be obtained from the drift ratio or strain criterion thatdefines the desired level of performance of the column.2. Estimate level of equivalent viscous damping (ξ eq ): Using the chosen targetdisplacement and an estimated yield displacement based on the column sectionand yield curvature, the ductility level is calculated in accordance with Eq.(4).The ductility versus hysteretic damping relationship is obtained utilizingJacobsen’s approach with a convenient assumed hysteretic model. An additional0%-5% viscous damping could be added to obtain the level of equivalent viscousdamping. An example of the ductility versus equivalent damping relation is495