# Seismic Vulnerability Assessment of Hybrid Mold Transformer Based on Dynamic Analyses
## 3 Analytical Model Development of Hybrid Mold Transformer and its Validation  
### Analytical Model Development  
In this study, the analytical model was established by means of the MIDAS GEN commercial structural analysis program [25]. Figure 2 presents the analytical model of the mold transformer in detail. The analytical model was constructed to describe the major characteristics of the prototype specimen in terms of geometrical, mechanical, and dynamic properties. The configurations of the mold transformer (Figure 2a) can be divided into two major components of a frame system (Figure 2b) and coils (Figure 2c). The frame system consists of the top beams, bottom beams, bed beams, and steel core. Tables 2 and 3 report the mechanical properties of the mold transformer's components and the dynamic parameters of the mold transformer model, respectively. The steel core was modeled as beam elements using thin box-shaped cross-sections with dimensions of 240 mm \(\times\) 200 mm. As shown in Figure 2e, in order to consider the mass distribution of the frame, the total steel core mass of 2.37 tons (according to the manufacturer's specifications) was divided into 11 distributed masses; the distributed masses at the centers of the vertical components (points B, E, and H) are twice of those at the ends (points A, C, D, F, G, and K). In addition, as shown in Figure 2d, the bed and bottom beams were modeled as beam elements with U-shaped sections. The masses of the bed and bottom beams were evaluated considering the mass density of steel material (7850 kg/m\({}^{3}\)) and the volumes of the beams, and those beams were connected together. The top beams were modeled in a similar manner to those of the bed and bottom beams. As shown in Figure 2d,e, the steel core model was connected to the bottom beam model at points L, M, and N via pairs of linear springs. Based on the shaking table test results, the bolts connecting the bottom beams and bed beams were recognized as the main weak point of the prototype specimen. In the analytical model, such bolts were modeled as systems consisting of linear springs with stiffness \(k_{i}\) and viscous dampers with the damping coefficient \(c_{i}\), where \(I=x\)-, \(y\)-, and \(z\)-directions, as shown in Figure 2d. The stiffness \(k_{\text{i}}\) and damping \(c_{i}\) were calculated based on the effective stiffness and damping ratio of the prototype specimen obtained from the shaking table test results (see Table 3). It is assumed that the damping behavior of the whole mold transformer was concentrated at the location of the bolts. The anchor bolts (M16) connecting the mold transformer and the concrete slab were modeled as linear springs with a fixed boundary condition by using the actual material stiffness of the M16 anchor bolts. In addition, the coils were cast in epoxy with an average elastic modulus of 100,000 N/mm\({}^{2}\) and yield strength of 110 MPa, according to the specifications of the manufacturer. In the analytical model, three coils were modeled as the system of beam elements and connected to the core by the linear springs at points A-K, as shown in Figure 2f. In order to consider the distribution of coil mass, the total mass of each coil of 0.42 ton (according to the manufacturer's specifications) was divided into 12 distributed masses at the top, middle, and bottom locations of each coil. The distributed masses at the middle are twice those at the top and bottom, as shown in Figure 2f. Each coil has a height and width of 1200 mm and 610 mm, respectively.