## 3 Results and Discussion
### Seismic Dynamic Analyses of Bidirectional Eccentric Structures  
#### 3.3.1 Response of Bidirectional Eccentric Structure under Bidirectional Mainshock  
In this section, the seismic analyses of bidirectional eccentric structures under bidirectional mainshock (case BBM) are studied. The earthquake ground motions used in the case are the same as the aforementioned earthquake records, i.e., the \"CHCHCHI-CHY029-N\" and \"CHCHCHI-CHY029-E\" earthquake records. The eccentric structural models used in the case are bidirectional eccentric models which are developed by a unidirectional eccentric structure. Both of them have the same eccentricity. The mass center of the bidirectional eccentric structure is adjusted along the x-axial and y-axial directions at the same time. The seismic responses of unidirectional and bidirectional eccentric structures with different eccentricities are compared. As shown in Figure 18, the overall trend of the bidirectional eccentric structure increases with the improvement in eccentricity. The increasing trend is more obvious in the Y direction than that in the X direction. Comparing unidirectional eccentric structure and bidirectional eccentric structure, after loading the same bidirectional earthquakes, the displacement trend of unidirectional eccentric structure is positively correlated with the eccentricity, probably a linear relationship, while the bidirectional eccentric structure is more complex. Moreover, the torsional angles of the unidirectional eccentric structure and the bidirectional eccentric structure are presented in Figure 19. It can be seen that both torsional angles climb upward with an increase in eccentricity. This indicates that the torsional effect of the bidirectional eccentric structure is slightly larger than that of the unidirectional eccentric structure. 3.2 Response of the Bidirectional Eccentric Structure under Bidirectional Mainshock-Aftershock Sequences  
The seismic responses of the bidirectional eccentric structure under bidirectional mainshock-aftershock sequences (case BBS) are further examined through a dynamic analysis. The maximum displacement responses of the structures are presented in Figure 20a,c,e. To investigate the influence of aftershock, the ratios of the maximum displacement under the MSAS sequences to the displacement under the mainshock are also compared, which are shown in Figure 21a,c,e. It can be demonstrated that structures with small eccentricities are more sensitive to aftershocks, and the maximum impact of aftershocks on displacement can reach 1.5 times that of the mainshock (at the mainshock PGA 0.15 g). But, for high PGAs of the mainshock (i.e., 0.25 g and 0.32 g), aftershocks have little impact on the structural displacement. Only for symmetrical structures and structures with small eccentricities, such as 5% eccentric structures, could aftershocks increase the displacement response, but the increase effect is less than 5%. As illustrated in Figure 20b,d,f, with an improvement in eccentricity, the IDR increases obviously and uniformly at eccentricities of 0-15%, increases slowly at eccentricities of 1-25%, and decreases at the stage of 25-30%. The influence of aftershocks on IDR is only reflected in the structures with an eccentricity of 0% and 5%, which is similar to the maximum displacement response. Figure 21b,d,f also show that when the mainshock PGA is 0.15 g, the aftershock IDR can reach up to 1.4 times that of the mainshock. However, the aftershock IDR is about 1.06 times the mainshock IDR in the case of a mainshock PGA of 0.25 g, and equal to zero time in the case of a mainshock PGA of 0.32 g.  
Figure 19: Comparison of the torsional angles between the unidirectional eccentric structure and the bidirectional eccentric structure. Figure 18: Comparison of top floor displacement of unidirectional eccentric structure and bidirectional eccentric structure with different eccentricities: (**a**) Top floor displacement in the Y direction; (**b**) top floor displacement in the X direction.