Table 12: Definition of damage states for bridge components (Choi et al., 2004) These are as follows:      Undamaged; Slightly damaged, but usable without repair or strengthening; Extensively damaged, but still repairable; No collapse, but so severely damaged that must be demolished; Collapse. Four limit states were defined to assess the bridge damage state including both qualitative and quantitative descriptions. Below the first limit state, no damage should take place and the expected response is of small displacement amplitude. This limit state is defined as the point that the first yielding of longitudinal reinforcing bars. Below the second limit state, bridge can experience minor structural damage and it is usable after the earthquake. Member flexural strengths may have been reached and limited ductility developed, provided that concrete spalling in plastic hinges does not occur and that residual crack widths remain sufficiently small. Cover concrete strain εc, is employed to identify this limit state. Below the third limit state, significant structural damage is expected. The bridge will be out of service after the earthquake unless significant repair is undertaken. However, repair and strengthening is feasible. Rupture of transverse reinforcement or buckling of longitudinal reinforcement should not occur and core concrete in plastic hinge regions should not need replacement. Below the final limit state extensive damage is expected, but the bridge should not have collapsed. Repair may be neither possible nor cost-effective. The structure will have to be demolished after the earthquake. Beyond this limit state, global collapse endangering life is expected since it corresponds to the inability of the structure to sustain gravity loads. A steel strain of 9% was assumed by Elnashai et al. (2004) to identify the final limit state. In the study of Choi et al. (2004), damage states of bridges were defined for column ductility demand, steel fixed and expansion bearing deformations, and elastomeric bearing deformations. The damage state definitions were based on the qualitative descriptions of the damage states as provided by HAZUS. The quantitative definitions of each damage states for the mentioned engineering demand parameters are presented in Table 12. The Bridge and Structural Engineer Engineering Demand Parameters Damage state Columns (µ) Steel Bearings (δ, mm) Expansion Bearings (δ, mm) Fixed Dowels (δ, mm) Expansion Dowels (δ, mm) Slight 1.0 < µ <2.0 1< δ <6 δ< 50 8<δ<100 δ <30 Moderate 2.0< µ <4.0 6< δ <20 50<δ <100 100 < δ < 150 30<δ<100 Extensive 4.0< µ <7.0 20< δ <40 100<δ<150 150<δ <255 100<δ <150 Complete 7.0< µ 40< δ 150<δ<255 255<δ 150<δ <255 Choi et al. (2004) mentioned that the damage states were quantified according to the recommendations from previous studies and experimental test results. The quantified damage states for the columns were described by the column curvature ductility and based on tests of non seismically designed columns, of which the lap-slices at the base were taken into account. The damage states for the bearings in the pre-stressed concrete girder bridges were based on fracture of the bearing and the displacement necessary for unseating. The problem of instability and unseating is a function of the size of the bearings and the width of the supports. The displacement at the complete damage limit state was assumed to be δ=255 mm by Choi et al. (2004), which accounts for the unseating of prestressed concrete girders. Nielson (2005) utilized bridge damage states described qualitatively by HAZUS. Engineering demand parameters of column curvature ductility, steel fixed and rocker bearing deformations, elastomeric fixed and expansion bearing deformations, and abutment displacements were employed for the quantification of damage states. Column curvature ductility values for each damage limit state were computed using the displacement ductility ratios specified by Hwang et al. (2001). In the CALTRANS (2006) approach, ordinary bridges are not allowed to collapse under the safety evaluation earthquake (SEE). The bent top displacement capacity to demand ratio is limited to ΔC/ΔD > 0.1 Based on the correlation of seismic response measures with damage levels, T. Yilmaz and A. Caner (2011) suggested displacement capacity-demand ratios of 1.1, 1.5 and 2.5, for significant, repairable and minimal Volume 45 Number 2 June 2015 85