PSI - Issue 78

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

1081

Table 1. Mechanical properties considered in analytical and numerical models. Material E [MPa] f m [MPa] τ 0 [MPa] f v0 [MPa] f c [MPa] f ct [MPa]

f Ft-0,25 [MPa]

f Ftu [MPa]

MasonryGF

2910 2.91 0.06 0.21 -

-

-

-

Masonry 1 st -2 nd F 444

0.44 0.04 0.07

SFRM

21000 -

-

-

25.40 1.82 1.56 1.36

In addition to the self-weight of the walls, total vertical loads of 8 kN/m 2 (8.8 kN/m 2 for areas used as a loggia) and 6.5 kN/m 2 , which included both the permanent and the variable actions, were applied to first and second floors and to third floor, respectively. A reinforced concrete (RC) chord running along the whole perimeter of the building connects the seismic floor diaphragms with the URM walls. So, a structural idealization characterized by strong spandrels and weak piers can be assumed and the piers can be schematized as double fixed-end walls.

2.1. Linear analyses based on behavior factor “q”

Linear analyses using the behavior factor “q” were performed by implementing an analytical, code -oriented model developed by the authors. As discussed in detail in Facconi et al. (2023), the shear failure may be governed either by the formation of diagonal shear cracks or by the attainment of shear resistance along potential sliding sections. In this case study, to be consistent with the numerical analyses described below, the shear-sliding failure mechanism was neglected. Assuming perfect bond condition between masonry and SFRM coating, the total in-plane diagonal shear capacity of reinforced masonry (V R,t ) is obtained by adding the two resisting components and assuming the upper limit V R,max as the shear force causing diagonal crushing of masonry. The capacity of URM (V t,m ) was calculated by the method proposed by Turnšek and Cačovic (1971) , assuming a shape factor b constantly equal to 1.5, consistent with the assumptions adopted by the commercial code used for the numerical analyses. The shear resistance of coating (V t,coat ), instead, was calculated by considering the simple Strut-and-Tie model proposed by the authors (see Fig. 1). The flexural resistance was calculated by equilibrium considering the contribution of masonry, SFRM coting and steel rebars, if present. Note that the tensile contribution of coating must be neglected along sections presenting discontinuities (e.g. the wall-to-foundation interface). Fig. 2a reports the designation and the length of the ten Y- oriented piers of each floor. The Dolce’s (1991) approach was used to determine the effective height H eff , whose values are listed in Table 2. In this preliminary phase of research, the seismic demand was calculated by applying a behavior factor q, in accordance with the provisions of the Italian standard NTC (2018). In particular, the ratio α u /α 1 was taken equal to 1.5, while the behavior factor q 0 was set to 1.75 for the unstrengthened building, consistent with the provisions for existing hollow clay block masonry structures, and to 2.5 for the retrofitted building, consistent with the provisions for new reinforced masonry structures. As a result, the overall behavior factor q was 2.63 and 3.75, respectively.

Fig. 1. Analytical model developed by the authors: shear resistance of coating [Facconi et al. (2023)].