## 7 Seismic Analysis
### Results of the Viceregal Building Models
#### 7.3.2 Reinforced Model  
Steel tie rods and rigid connections between beams and walls were used to strengthen the structure, since both techniques are considered less invasive and enhance the global seismic performance. The steel components are assumed to behave elastically, with a Young's modulus of 210 GPa. To limit stress concentrations, steel plates measuring 0.30 \(\times\) 0.30 m were added at each end of the tie rods. For the reinforced models, the initial amplitude was 75% and gradually increased until considerable damage was caused. As in the previous case, a 10% tolerance in the artificial energy was accepted for the validation of the results. First, the results of the model representing the facade and the transversal wall with openings (WWO) are discussed. The increment of the fundamental frequencies demonstrated that rigid connections (4.66 Hz) and tie rods (3.44 Hz) increased the stiffness of the model. These frequencies corresponded to the OOP motion of the facade. Figure 24 presents the results at a 75% amplitude for the model WWO. The model strengthened with rigid connections exhibited a numerical problem concerning the artificial energy, and thus the results are assumed to be valid up to 7.50 s. Conversely, the model with ties performed consistently throughout the analysis, below the 10% limit. Tie rods seemed to have a better performance in terms of energy and residual displacements (approximately 0.15 m). This technique induced less damage to the spandrel of the lower level. Although both techniques prevent the OOP collapse of the facade, the inertia forces were transmitted to the transversal wall, resulting in greater base shear forces (see Figure 25). Figure 23: Results for 75% of amplitude at 6.00 s: (**a**) wall with openings; (**b**) solid wall; (**c**) Ratio between artificial and internal energies; (**d**) displacement at the top of the wall. Further analyses were conducted on the WWO model by increasing the amplitude. At 100%, both models were validated based on the artificial energy criterion. In Figure 25, the tensile damage contours at 6.00 s are presented for amplitudes of 75%, 100%, and 112.5%. The time history results in Figure 26 show that the damage induced by the ties was larger than that caused by the rigid connection of the floor and roof. However, the ties  
Figure 24: Time history results for 75% amplitude of unreinforced and strengthened WWO model (wall with openings). Figure 25: Tensile damage contour at 6.00 s for amplitudes of 75%, 100%, and 112.5% in the strengthened WWO models (wall with openings). exhibited better control over the OOP displacement of the facade. Additionally, by the end of the analysis, the rigid connection led to more local damage in the facade, resulting in an increase in the damage energy similar to that observed in the case of the tie rods. In the case of the 112.5% amplitude, the model strengthened with ties maintained stability throughout the entire analysis. In the model with rigid connections, the OOP collapse of the facade occurred before surpassing the energy tolerance at 17.50 s. Hence, the results of both models can be considered reliable. In the model with rigid connections, vertical cracks developed in the spandrels, leading to the complete detachment of the transversal wall from the facade, culminating in its subsequent collapse. The extent of the damaged zone was larger when using rigid connections compared to ties. For the 112.5% amplitude scenario with ties, the shear-diagonal damage did not appear. This was due to the facade's damage occurring before the full transmission of the inertia forces to the transversal wall could take place. At the end of the analysis, both spandrels collapsed and the facade exceeded the significant damage limit state with a residual displacement of 0.37 m. Finally, it is worth mentioning that both strengthening techniques induce large shear forces in the transversal wall. Next, the seismic performance of the model featuring a solid transversal wall (SW) is explained.