## 3 Results and Discussion
### Seismic Dynamic Analyses of Unidirectional Eccentric Structures
#### 3.2.3 Response of Unidirectional Eccentric Structure under Bidirectional Mainshock
Compared with structures with different eccentricities, the symmetrical structure is most affected by the aftershock, and the maximum displacement under the aftershock is nearly 1.35 times of the mainshock displacement. If the structure eccentricity is larger, the effect of aftershock modulation amplitude is smaller. The IDRs of structures with eccentricities 0-30% under the bidirectional mainshock-aftershock sequences are shown in Figures 16b and 17b. Similarly, the IDR of the structure gradually increases with an increase in eccentricity, and the growth speed is rapid at high eccentricity. It is observed that the aftershock shows the most significant effect on the 0% eccentricity structure. When the aftershock amplitude is equal to the mainshock amplitude, the IDR of the aftershock is 1.3 times that of the mainshock. Figure 15: Response results of unidirectional eccentric structural models under bidirectional mainshock (case UBM): (**a**) Maximum displacements of top floor in Y direction; (**b**) residual displacements of top floor in Y direction; (**c**) relative torsional effects; (**d**) torsional angles. Figure 16: Seismic responses of structures under mainshock–aftershock sequences with different mainshock PGAs (case UBS): (**a**) Top floor maximum displacement with mainshock PGA at 0.15 g; (**b**) IDR with mainshock PGA at 0.15 g; (**c**) top floor maximum displacement with mainshock PGA at 0.25 g; (**d**) IDR with mainshock PGA at 0.25 g; (**e**) top floor maximum displacement with mainshock PGA at 0.32 g; (**f**) IDR with mainshock PGA at 0.32 g.  
Figure 17: Ratios of maximum displacement and IDR of structures under mainshock–aftershock sequences with different mainshock PGAs (case UBS): **(a)** Ratio of maximum displacement of aftershock to that of mainshock with mainshock PGA at 0.15 g; **(b)** ratio of IDR of aftershock to that of mainshock with mainshock PGA at 0.15 g; **(c)** ratio of maximum displacement of aftershock to that of mainshock with mainshock PGA at 0.25 g; **(d)** ratio of IDR of aftershock to that of mainshock with mainshock PGA at 0.25 g; **(e)** ratio of maximum displacement of aftershock to that of mainshock with mainshock PGA at 0.32 g; **(f)** ratio of IDR of aftershock to that of mainshock with mainshock PGA at 0.32 g.  
In the case of the mainshock, the PGA is 0.25 g, and the displacement growth speed slows down in the case of high eccentricity, as shown in Figure 16c. As illustrated in Figure 17c, despite the fact that the displacement of the structure with an eccentricity of 5% during the aftershock increased by 5% compared with that during the mainshock, the displacement of the other structures did not increase. It can be concluded that the aftershock shows a slight effect on eccentric structures with a life safety performance level. For the structural IDR, it can be seen in Figures 16d and 17d that the IDR of the aftershock cannot exceed that of the mainshock due to possible greater damage in mainshock loading. For the mainshock PGA of 0.32 g, the aftershock fails to show an increasing effect on the structural displacement or IDR for structures with all the different eccentricities. It can be seen from Figure 17e,f that the aftershock displacements of all structures did not exceed the mainshock displacements. This shows that the structure tends to be damaged after the first earthquake of a larger amplitude, and at this time, the aftershock response does not manage to exceed the mainshock. The reason could be that the structure's response to the bidirectional mainshock is already extremely large and its performance level at 0.32 g under the mainshock reaches collapse prevention. In the structure with high eccentricity (i.e., 30%), the IDR decreased, which showed that the structure had been damaged seriously or even collapsed. Therefore, the response of the aftershock can hardly exceed that of the mainshock.