PSI - Issue 78

Sara Silvana Lucchini et al. / Procedia Structural Integrity 78 (2026) 1079–1086 Table 2. Effective height and axial load of unstrengthened Y-oriented resisting masonry piers of 1 st F ( H̅ =3300mm)and GF ( H̅ =3400mm). Property Pier Y1 Pier Y2 Pier Y3 Pier Y4 Pier Y5 Pier Y6 Pier Y7 Pier Y8 Pier Y9 Pier Y10 H eff - 1 st F [mm] 3300 3300 3300 3300 3300 2512 2759 2826 3300 3300 H eff - GF [mm] 3398 3398 3398 3372 3372 2526 2781 2849 3398 3398 N - 1 st F [kN] 147.17 108.12 97.14 132.13 132.13 32.00 48.26 39.45 66.51 41.03 N - GF [kN] 237.30 167.78 158.24 214.44 214.44 52.42 78.95 66.17 108.88 60.21

1082

1600

1391kN (+35%)

1400

1200

1027kN

1000

903 kN (-12%) 799kN (+3%)

400 Base shear V b [kN] 600 800

772kN

512kN (-34%)

Unstrengthened, numerical Unstrengthened-1st F, analytical Unstrengthened-GF, analytical Retrofitted, numerical Retrofitted-1st F, analytical Retrofitted-GF, analytical

200

0

0 2 4 6 8 101214161820222426 3rd floor lateral displacement [mm]

(a)

(b)

Fig. 2. Case study: (a) designation and length of the ten Y-oriented resisting piers (Dimensions in [cm]); (b) comparison between numerical and analytical results, in terms of shear capacity, for both unstrengthened and retrofitted building.

A stiffness distribution method was used to share the seismic demand among the structural elements of the story. The initial elastic stiffness of each pier was calculated in accordance with elastic theory, accounting for both flexural and shear stiffness. Subsequently, assuming an elastic-perfect plastic behavior, in cases where the demand on one or more piers exceeded their capacity, the stiffness values were recalculated such that, for the piers in the plastic range, the demand was set equal to their capacity. The sum of the resistances of all piers of each story was compared with the corresponding seismic demand in order to identify the critical floor, considering the different mechanical properties of masonry at ground and upper floors. Unstrengthened building The weakest mechanism between diagonal shear (D) and flexure (F), according to NTC (2018), provided the capacity of each of the ten Y-oriented piers. The average axial load N, calculated at half height of each Y-oriented pier of first and ground floor of the unstrengthened building, is listed in Table 2. The linear analysis indicated that, in the as-built condition, the building was not verified in the Y direction. The seismic capacity was lower than the demand at both the ground (799 kN vs 871 kN) and first (512 kN vs 701 kN) floors, with a greater discrepancy observed at the first floor. This indicated that the most critical floor was the first one. At the ground floor, five piers (i.e. Y1, Y3, Y4, Y5, and Y9) failed due to diagonal shear and only pier Y8 due to flexure. At the first floor, instead, the two failure mechanisms were equally critical: five piers (i.e. Y1, Y3, Y4, Y5, and Y9) failed due to diagonal shear and five piers (i.e. Y2, Y6, Y7, Y8 and Y10) due to flexure. Retrofitted building The analytical model proposed by the Authors was used to determine the resistance of masonry piers retrofitted by SFRM coating on the external surface. Table 3 provides the average axial load N, calculated at half height, the shear demand V S , the shear resistances and the critical failure mechanism for the ten Y-oriented piers of first and ground floor of retrofitted building.