# Seismic Response of a Three-Dimensional Asymmetric Multi-Storey Reinforced Concrete Structure
## 6 Torsional Behavior  
The SMART 2013 RC structure is asymmetric in plan view, as shown in Figure 2. In general, asymmetric structures often exhibit coupled flexural and torsional behaviors against lateral loads, since the line of action of the lateral load does not pass through the center of the stiffness of the structure when viewed in plan [36; 37; 38; 39; 40; 41]. Figure 33 shows the displacement trace at the sampling points of the third floor of the building during the Northridge main shock with Run 19. The displacement traces indicate that the building was not only bent by seismic forces, but also twisted. Figure 34 shows the distortion of each floor of the building at 8.6 s, when the seismic response was the largest, as can be seen in Figure 27. For the calculated torsional response, the phase was similar to what was obtained from the shaking table test. Furthermore, the calculated torsional response seems to reflect the test result in that the degree of twist was more substantial on the higher floors. However, the numerical plan view deformation seems to be more correlated to a horizontal translation rather than a twisting mode. The difference could be because the numerical model did not accurately reflect the reduced torsional stiffness of the damaged structure. Figure 31: Frequency spectrum of the \(x\) directional displacement at point A on the third floor. Figure 30: Damages in the lower part of the concrete walls connected to the foundation [23; 30]. Figure 32: Frequency spectrum of the \(y\) directional displacement at point A on the third floor. In order to further investigate the torsional effect, we compared the seismic response of the asymmetric SMART 2013 structure with the response of a hypothetical symmetric structure. Figure 35 shows a plan view of the symmetric structure and the corresponding three-dimensional finite element model. The number of floors, thickness of the floors and walls, dimensions of the column, length in the \(x\) and \(y\) directions, mass of each floor, and materials used were the same as for the asymmetric SMART 2013 structure. In Figure 36, the displacement responses of the asymmetric SMART 2013 structure and the hypothetical symmetric structure due to the Northridge main shock are compared with each other. The responses are sampled at point D. On the first floor, the responses were similar to each other. However, the difference in response became more substantial on the higher floors. The tendency of the greater response of the asymmetric structure also appeared in the frequency response spectrum, as shown in Figure 37. Figures 38 and 39 compare the absolute maximum displacement for the two cases. For all of the sampling points and all of the floors, the displacement response of the asymmetric structure was larger than that of the hypothetical symmetric structure. It can also be seen that the response difference increased on the higher floors. The difference in the x directional absolute  
Figure 34: Distortion of each floor due to the Northridge main shock (Run 19) at 8.6 s.  
Figure 35: Finite element modeling of a hypothetical symmetric structure for comparison with the SMART 2013 RC structure. Figure 33: Displacement trace at sampling points during the Northridge main shock of Run 19.  
maximum displacement between the asymmetric and symmetric structures was up to 15%, while the difference in the y directional absolute maximum displacement was up to 31%. The results indicate that, similar to previous studies [36; 37; 38; 39; 40; 41], a larger seismic response should be considered in the seismic design of an asymmetric structure compared to a symmetric structure with same design conditions. Figure 38: Absolute maximum displacement in the \(x\)-direction of the asymmetric and the hypothetical symmetric structures due to the Northridge earthquake (Run 19).