# Seismic Vulnerability Assessment of Hybrid Mold Transformer Based on Dynamic Analyses
## 4 Dynamic Analyses and Development of Seismic Fragility Curves
### Identifications of Damage States and Limit States  
From the shaking table test results, three weak points of the mold transformer were adopted as critical damage states, as shown in Figure 15. The first damage states (DS1) correspond to the failure of the spacers, the second damage states (DS2) correspond to the excessive coil movement in Y-direction, and the third damage states (DS3) correspond to the loosening of linked bolts between the bottom and bed beams. According to the recommendation specified in ASCE 41-17 Standard [42], the target performance levels used to evaluate the seismic vulnerability of the nonstructural elements for buildings can be selected among Operational (OP), Position Retention (PR), and Life Safety (LS). Specifically, the OP performance level involves the functional nonstructural equipment required for normal use regardless of minor damage; the PR performance level involves nonstructural equipment, which is secured in place and might be able to function if necessary service is available; and the LS performance level involves nonstructural equipment that can sustain significant damage but not become dislodged and fall in a manner that could cause death or serious injury to occupants or people. In order to evaluate the seismic performance of the mold transformer, the target performance levels were selected based on the correlation with critical damage states, as shown in Figure 16. Specifically, damage in spacers (DS1) can lead to slippage of the HV and LV coils away from the original positions and the interaction between them, which involve the OP and PR performance levels; and excessive movement in the Y-direction (DS2) can cause interaction with the adjacent equipment and breaking of the electrical wires, which involve the OP and PR performance levels; and the degree of loosening at the bottom bolts (DS3) can affect the functional operation or lead to the collapse of the entire transformer and threaten human life, which involve the OP, PR, and LS performance levels.  
When correlating the performance levels and damage states, the values of the limit states were defined for each target performance level corresponding to the damage states. The parameters by which the limit states were evaluated were partly based on the observation from shaking table test results [27] and partly based on judgment. Specifically, for the DS1, the peak response acceleration at the coils (PRA) in the Y-direction is strongly related to the spacer damage due to the fact that the  
Figure 14: Magnitude versus peak ground acceleration (PGA) of selected ground motions.  
Figure 13: Magnitude versus closet ruptured distance of selected ground motions.  
lowest effective stiffness is in this direction. Accordingly, for the DS1, the values of the limit states corresponding to the OP and PR performance levels were respectively determined to be 0.22 g, which corresponds to the time when the cracks were initially formed, and 0.69 g, which corresponds to the time when the spacers were failed, as observed during shaking table tests. For the DS2, the maximum displacement in the Y-direction at the top beams is strongly related to the excessive movement of the transformer. Accordingly, the values of the limit states corresponding to the OP and PR performance levels were determined to be 50 mm and 75 mm, respectively, based on the provisions as well as the recommendations of the Korea Research Institute [43]. For the DS3, the maximum displacement in the Z-direction at the bottom beam is strongly related to the degree of loosening of the link bolted between the bottom beam and bed beam; and the values of the limit states corresponding to the OP, PR, and LS performance levels were determined to be 2.2 mm, 6.6 mm, and 12.45 mm, respectively, based on the experiment test results [27]. The summary of the value of the limit state corresponding to each damage state is presented in Table 6.