PSI - Issue 78

Sara Silvana Lucchini et al. / Procedia Structural Integrity 78 (2026) 1079–1086

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(a)

(b)

Fig. 3. (a) macro-element schematization of the building; (b) shear behavior of URM (thin line) and retrofitted masonry (thick line).

Pushover analyses were carried out by considering both force distributions prescribed by the Italian code NTC (2018): one proportional to the static forces (or to the first mode shape of the building - primary distribution), and one proportional to the masses (secondary distribution).

2.3. Comparison between different approaches

The results of nonlinear static analyses corresponding to a primary force distribution are presented below and compared with those of linear static analyses described in Section 2.1. Unstrengthened building The pushover analysis in +Y direction provided a maximum base shear (V b ) of 772 kN for the unstrengthened building (see Fig. 2b). As already highlighted by the linear analysis, damage mechanisms were primarily concentrated on the first floor. In particular, the numerical model showed diagonal shear failure of the inner piers Y4 and Y5 at the first floor, where the masonry had lower mechanical strength (see Fig. 4a). The shear capacity obtained was slightly lower (-3%) than the analytical capacity estimated for the ground floor and 51% higher than that of the first floor. This shows that the nonlinear model has a greater capacity to redistribute seismic actions, allowing it to significantly exceed the capacity of the first floor. On the other hand, the linear model provides more conservative results, suitable for simplified assessments. Retrofitted building After retrofitting, the building’s capacity increase d by 33% (V b =1027 kN). This strength lay between the analytical capacity of the first floor (+14%) and that of the ground floor (-26%), confirming that the most critical level remained the first floor. As shown by the failure mechanisms of Fig. 4b, no pier reached diagonal shear failure (blue box outside the yellow and red X-patterns). The failure modes provided by the analytical model were quite consistent with the mechanisms exhibited by the nonlinear static analyses carried out with 3DMacro, both before and after retrofitting (Table 3 vs Fig. 4b).