## 3 Results and Discussion
### Seismic Dynamic Analyses of Unidirectional Eccentric Structures
#### 3.2.1 Response of the Unidirectional Eccentric Structure under Unidirectional Mainshock
The torsional angle steadily increases with increasing eccentricity and increases approximately linearly when the eccentricity is between 0% and 15%. The growth rate decreases when the eccentricity is in the range of 15-25%, but the slope is negative after surpassing an eccentricity of 25%. It clearly presents  
Figure 8: Maximum displacements of structural models in: (**a**) the Y direction; (**b**) the X direction. Figure 7: Acceleration time history of the CHICHI-CHY029-N mainshock record. the process that the structure follows from the elastic stage to the plastic stage and its finally destruction with the rise in eccentricity. Figure 11 shows the moving trend of relative torsional effect with a change in eccentricity. The relative torsional effect \(\gamma\) is defined as the ratio of the displacement at the radius of rotation from the rigid center to the translational displacement of the floor. It reflects the ratio of the torsional displacement to the translation displacement of the structure due to torsion and is one of the important indexes to measure the torsional effect for eccentric structures. It is calculated by Equation (7):  
\[\gamma=\theta r/u \tag{7}\]  
where \(\theta\) refers to the torsional angle of the characteristic point which is located at the radius of rotation from the rigid center. Herein, since a rigid floor is adopted in these models, \(\theta\) is the torsional angle of the whole floor. The parameter \(r\) is the radius of rotation, i.e., the distance between the center of mass and the rigid center in these models. The parameter \(u\) is the horizontally lateral displacement of the floor in the direction of seismic loading. At low eccentricities (eccentricity 0-10%), the relative torsional effect rises gradually; however, from 10% eccentricity, it rises quickly, with an almost linear trend. Then, the relative torsional effect appears to slow the growth rate as it approaches the high eccentricity region (eccentricity 25-30%). In contrast to the maximum IDR, the relative torsional effect exhibits a similarly linear upward trend with increasing eccentricity, but it is unable to accurately and broadly characterize the extent of damage in all structures. The relative torsional effect is zero in the symmetric structural model; however, it does not depict that  
Figure 10: Torsional angles of the structural models. Figure 9: Residual displacements of the top floor of the structural models in the Y direction. there is absolutely no damage at that time. Moreover, it needs to be calculated extensively rather than obtained directly by measuring or by a simple calculation such as an inter-story drifts ratio. Therefore, in this study, the maximum IDR is selected as the criteria indicator in earthquake scaling, as shown in Table 7, and it is used as the response indicator in the later seismic analysis work subjected to mainshock-aftershock sequences. Moreover, the maximum IDRs in the Y direction for symmetrical and eccentric structural models is obtained in the study, as shown in Figure 12. For each model, the largest IDR appears at the bottom layer. With the improvement in eccentricity, the IDR becomes larger and larger for the first floor. This illustrates that the bottom of structures is most influenced by eccentricity, and the maximum IDR is the most sensitive indicator for the increase in eccentricity. Moreover, the maximum IDR is considered to be an intuitive observation indicator of structural deformation in many national codes. It can directly present the structural damage phenomenon in the failure process. This is another justification for choosing the maximum IDR as the scaled criterion indicator in this study, as shown in Table 7.  
2.2 Responses of the Unidirectional Eccentric Structure under Unidirectional Mainshock-Aftershock Sequences  
In this section, the seismic responses of the unidirectional eccentric structure under unidirectional mainshock-aftershock sequences (Case UUS) are investigated.