## 4 Nonlinear Pushover Analyses
The structural continuity provided by the tie beams resulted in nearly symmetric deformation responses in the lateral walls of the naive (Figure 12b). The damage started with cracking at the connections between the lateral walls and the baptistery and sacristy. As the deformation increased, diagonal and horizontal cracks formed, leading to the full development of an out-of-plane collapse mechanism of the complete north wall (Figure 13b). The north buttress exhibited crushing at the base and shear failure along its connection with the north wall, resulting in detachment. By the end of the analysis, all three buttresses on the north side had separated from the main structure (Figure 13b). As in the case of the south wall, the failure of the north wall was primarily driven by insufficient out-of-plane restraint and a lack of mechanical connection between the structural elements. The adobe material properties contributed to its vulnerability, but the absence of structural continuity, particularly the lack of ring beams, stiff horizontal diaphragms, and transverse walls, was the dominant factor in the formation of this failure mode. The relatively long vertical and horizontal spans further exacerbated the wall's vulnerability. The detachment of the buttresses was again the result of inadequate anchorage and low shear strength, highlighting the need for improved detailing in future strengthening strategies. Figure 12: Capacity curves and deformed shapes at the ultimate displacement for the (**a**) +X direction, (**b**) \(-\)X direction, (**c**) +Y direction, and (**d**) \(-\)Y direction. As seen in Figure 12c, in the +Y direction (positive longitudinal direction), the rear (east) facade exhibited an initially stiff response, followed by a strength drop at 0.12 g and a partial recovery leading to a peak at 0.17 g, with a displacement of 5.40 cm. The post-peak  
Figure 13: Principal tensile strains for the (**a**) +X direction at ultimate displacement, (**b**) -X direction at ultimate displacement, (**c**) +Y direction at 0.12 g (left) and at the peak load (right), and (**d**) -Y direction at ultimate displacement. phase was characterized by a short plateau, reaching a maximum displacement of 7.00 cm (Figure 12c). In general, the damage was concentrated primarily at the intersections of the rear facade with the lateral walls, with the onset of cracking observed at a load factor of 0.12 g. This damage started at the corners, with vertical cracks propagating downward, followed by diagonal cracking near the presbytery window (north wall) and the formation of a horizontal hinge at the base of the rear facade (Figure 13c). At peak load, the out-of-plane collapse mechanism was completely developed, characterized by full detachment of the rear facade, with vertical cracks at both corners and the formation of a horizontal hinge along the base of the foundation (Figure 13c). This collapse mechanism is directly associated with the stress concentration at the corners and the poor mechanical properties of the material, along with weak continuity between the rear facade and the adjoining lateral walls. That is, in the absence of proper anchors, ring beams, and rigid roof, the facade relies only on the tensile strength of adobe, which is very limited. Once the tensile capacity is exceeded, vertical cracking and detachment occur. The rear facade has no buttresses, which increases its susceptibility to out-of-plane overturning. The observed failure is thus the result of inadequate mechanical restraint and unfavorable geometry. In the -Y direction, the main (west) facade and its buttresses experienced the most significant deformations. The structure exhibited the highest lateral load capacity among all directions, with a peak of 0.26 g and a displacement of 1.53 cm (Figure 12d). However, this response was characterized by brittle behavior. The initial drop in stiffness at 0.19 g was associated with the onset of vertical cracks at the upper corners, which propagated downward as the lateral load increased.