## 3 Results and Discussion
### Seismic Dynamic Analyses of Unidirectional Eccentric Structures
#### 3.2.3 Response of Unidirectional Eccentric Structure under Bidirectional Mainshock  
In this section, the seismic responses of the unidirectional eccentric structure under bidirectional mainshock-aftershock sequences (case UBM) are discussed. The influences of earthquake sequences and the eccentricity of structures on the structural seismic responses are discussed in this section. The difference is more significant in bidirectional earthquakes than in unidirectional earthquakes due to the coupled action of the translational mode and torsional mode, particularly in eccentric structures. The earthquake ground motions are loaded along two horizontal directions, i.e., the X and Y directions. According to the seismic design code of buildings [34], the ratio of PGA of ground motion loaded in the X direction to that in the Y direction is set as 1:0.85. \"CHICHI-CHY029-N\" and \"CHICHI-CHY029-E\" are used to name the ground motions in the X direction and the Y direction, respectively. The PGAs in the X direction and Y direction are 0.238 g and 0.185 g, respectively. In contrast to the displacement under bidirectional loading, as shown in Figure 15a, the Y direction displacement under unidirectional loading exhibits a similar upward trend with an increase in eccentricity. Additionally, when eccentricity is high, the growth rate slows. It is observed that the displacement of structural models with various eccentricities under bidirectional loading is larger than that under unidirectional loading, which shows that horizontal ground motion in the other direction (X direction) has an additional influence on the displacement in the Y direction. In Figure 15b, the residual displacements of structural models under unidirectional and bidirectional loadings are presented. It can be observed that the residual displacement increases in the overall trend with an improvement in eccentricity. But the residual displacement under biaxial loading is larger than that under unidirectional loading in small eccentricities, which demonstrates that the bidirectional horizontal ground motion has complex and adverse effects on the structural model. Figure 15c shows a comparison of the relative torsional effects on the structural model under unidirectional and bidirectional loadings. The relative torsional effects on the structural model almost increase linearly with an increase in eccentricity. Compared with the unidirectional loading, this parameter value of bidirectional loading is greater over the whole eccentricity range. Figure 15d illustrates the changing trend of torsional angles for structural models under unidirectional and bidirectional loadings. Although the torsional angle expresses the torsional behavior of a structure, it is still not a preferable index at several eccentricities. Both torsional angles seem to be the same. According to Figure 15a,c, with an increase in eccentricity, the torsional effect shows a trend of rising. In addition, the bidirectional loading causes more serious damage than unidirectional loading at each eccentricity. However, the torsional angle decreases at 30% eccentricity. Even at 5% eccentricity, the torsional angle of the bidirectional loading is smaller than that of the unidirectional loading. 2.4 Response of the Unidirectional Eccentric Structure under Bidirectional Mainshock-Aftershock Sequences  
The seismic responses of the unidirectional eccentric structure under bidirectional MSAS sequences (Case UBS) are explored. For the amplitude of the mainshock and aftershock, the mainshock PGAs are still 0.15 g, 0.25 g, and 0.32 g as determined above (Section 2.3), while the aftershock PGAs are still 0.6, 0.8, 0.9, and 1.0 times that of the mainshock. The amplitude of the ground motion loaded in the X direction is also 0.85 times that in the Y direction. When the mainshock PGA is 0.15 g, as shown in Figures 16a and 17a, the structural displacement will increase with an increase in eccentricity under the same aftershock intensity.