PSI - Issue 78

Sara Silvana Lucchini et al. / Procedia Structural Integrity 78 (2026) 1079–1086 1083 Table 3. Axial load, shear demand and resistance of retrofitted Y-oriented resisting masonry piers of 1 st F ( H̅ =3300mm) and GF ( H̅ =3400mm). +Y _ 1 st F Pier Y1 Pier Y2 Pier Y3 Pier Y4 Pier Y5 Pier Y6 Pier Y7 Pier Y8 Pier Y9 Pier Y10 N [kN] 161.66 109.85 103.70 139.78 139.78 34.15 51.50 42.85 72.68 42.69 V S [kN] 251.09 11.37 38.04 35.96 40.22 5.48 30.74 27.19 80.09 9.76 V R,t [kN] 691.72 94.81 76.11 81.07 81.07 18.86 94.89 98.01 196.56 73.58 V R,flex [kN] 475.81 32.83 107.85 121.14 121.14 8.54 30.74 27.19 80.09 9.89 V R [kN] 475.81 32.83 76.11 81.07 81.07 8.54 30.74 27.19 80.09 9.89 V R / V S 1.89 2.89 2.00 2.25 2.02 1.56 1.00 1.00 1.00 1.01 Failure mode F F D D D F F F F F +Y _ GF Pier Y1 Pier Y2 Pier Y3 Pier Y4 Pier Y5 Pier Y6 Pier Y7 Pier Y8 Pier Y9 Pier Y10 N [kN] 259.25 170.40 168.17 226.12 226.12 55.73 83.92 71.77 118.71 62.70 V S [kN] 2340.79 8.52 70.83 67.60 70.45 8.76 37.94 42.73 100.43 2.45 V R,t [kN] 743.88 110.43 107.63 115.44 115.44 26.98 108.53 111.57 216.40 77.83 V R,flex [kN] 745.64 51.79 210.73 266.48 266.48 19.85 50.25 45.51 127.93 13.66 V R [kN] 743.88 51.79 107.63 115.44 115.44 19.85 50.25 45.51 127.93 13.66 V R / V S 3.17 6.08 1.52 1.71 1.64 2.27 1.32 1.06 1.27 5.59 Failure mode D F D D D F F F F F After retrofitting the shear capacity significantly exceeded the demand at both ground (1391 kN vs 645 kN) and first (903 kN vs 519 kN) floor. Only piers Y7, Y8 and Y9 at first floor were not verified; therefore, the first floor remained the most critical. Regarding the failure modes, as reported in Table 3, after retrofitting, the building response was mainly governed by flexure both on the first and on the ground floor. The diagonal shear was the weakest mechanism only for piers Y3, Y4 and Y5 on both floors and for pier Y1 on the ground floor. Nonlinear static analyses (pushover) were carried out using a macro-element modeling approach implemented in the commercial code 3DMacro (see Fig. 3a). Fig. 3b shows the shear behavior of each pier before and after retrofitting. The lower thin curve represents the elastic-perfect plastic response of URM. After the retrofitting by SFRM coating, the shear strength of the reinforced panel is calculated as the maximum between the shear strength of the URM and that of the SFRM layer, where the latter is defined as the minimum between the strut and tie strengths along the two diagonals of the panel. T he shear strength of the retrofitted panel (τ 0,r ) is therefore calculated as follows: τ 0,r = ∙ ∙min ( , ; , )≥ 0, ∙ (1) where τ 0,m is the shear strength of URM, calculated according to Turnšek and Cačovic (1971) , t m is the thickness of URM, t a is the total thickness of retrofitting (thickness of a single SFRM layer per number of layers), t r is the total thickness of retro fitted panel, δ is the angle between the diagonal of the panel and the base, β c =0.65 is a reduction factor of the retrofitting contribution to the compressive strength, accounting for potential local instability phenomena , α c =0.66 and α t =0.65 are coefficients that account for the ratio between the area of the strut or the tie and the area along the diagonal. Finally, f c,a and f t,a are the compressive and the tensile strength of SFRM, respectively, corresponding to f c and f ct listed in Table 1. In addition to the increase in stiffness and shear strength, the fibers also provide an additional contribution in the post-cracking phase. As a result, the constitutive law is modified by introducing a hardening branch, quantified through the ratio between the post-elastic stiffness and the initial stiffness (see 3DMacro theoretical manual). 2.2. Nonlinear static analyses based on macro-element modeling