Report - PEER - University of California, Berkeley

The values of the displacement modification coefficients have been proposedfirst in the NEHRP Guidelines for Seismic Rehabilitation (Federal EmergencyManagement Agency, 1997) for different building framings systems and performancelevels. The first coefficient C 1 is the spectral ratio of maximum inelastic to elasticdisplacements where the inelastic system exhibits negligible deterioration in stiffnessand strength. Such an ideal inelastic performance may be displayed by new buildingsdesigned and detailed to satisfy the requirements of modern seismic design codes.This coefficient is later studied extensively by Miranda (2000) for ground motionsrecorded on different soil conditions, and for several ductility factors. The secondcoefficient C 2 is the spectral ratio of the maximum inelastic displacements ofdeteriorating and non-deteriorating (elasto-plastic) systems. Existing structures thatdo not conform with modern code requirements usually exhibit significantdeterioration under strong seismic excitation, therefore their maximum displacementresponses are controlled more with the C 2 coefficient rather than the C 1 coefficient.Song and Pincheira (2000) and Gupta and Kunnath (1998) studied the influence ofdifferent hysteresis parameters on C 2 . One problem that arises in their evaluation ofC 2 is that the hysteresis models developed for representing the deteriorating systemsdepend on too many parameters, most of which are difficult to calibrate withexperimental data. Miranda et al. (2002) evaluated the C 2 coefficient proposed inFEMA356 (Federal Emergency Management Agency, 2000) by employing a stiffnessdegrading model for representing the deteriorating systems. This is a limitedevaluation however since stiffness degrading model is only suitable for a Type 2Structure described in FEMA where C 2 is equal to unity.An energy-based model is developed in this study that accounts for both thestiffness and strength deterioration (Sucuoğlu and Erberik, 2004). The model has beencalibrated by using the results of experimental studies on concrete members subjectedto constant and variable amplitude cyclic displacements. Then the C 2 coefficient isevaluated for different levels of deterioration under ground motions classified withrespect to the site conditions.ENERGY-BASED DETERIORATION IN STRUCTURAL SYSTEMSStructural systems can be classified into two groups according to the behavior theyexhibit when they are subjected to cyclic loading in the inelastic response range: (a)Non-deteriorating systems, (b) Deteriorating systems. Non-deteriorating systemsexhibit no or very little strength loss under cyclic loading. Systems with stiffnessdeterioration are also included in this group. Such structures display stable hysteresisloops with constant energy dissipation in each constant-amplitude cycle. Howeverdeteriorating systems cannot maintain stable energy dissipation under cyclic loadingand dissipated energy reduces with increasing number of cycles. Therefore cyclicenergy dissipation capacity can be employed as a convenient measure indifferentiating between non-deteriorating and deteriorating systems.422