PSI - Issue 78

Christian Salvatori et al. / Procedia Structural Integrity 78 (2026) 1529–1536

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As previously discussed, the proposed macroelement enables the explicit modeling of strengthening or reinforcement solutions. This is accomplished by introducing additional stripe or fiber elements with different mechanical properties or constitutive laws along the macroelement interfaces, while ensuring compatibility by enforcing an a-priori linear strain profile. Strengthening and reinforcement of masonry members typically involves applying or embedding materials with significant tensile strength to overcome one of the main deficiencies of the material. In this context, single- or double sided jacketing interventions can be modeled as additional surface layers discretized according to a stripe or fiber formulation (Salvatori et al., 2025a). On the other hand, internal or external lumped reinforcement can be represented through additional fiber elements. Unlike the axial-flexural response, which is explicitly accounted for, the shear contribution of the additional elements is not directly considered in the current implementation. 3. Validation of the macroelement formulation The proposed macroelement is adopted to simulate the experimental response of two calcium silicate (CS) masonry piers subjected to in-plane quasi-static cyclic shear-compression tests, conducted at the EUCENTRE Foundation and University of Pavia facilities in Italy (Guerrini et al., 2021). 3.1. Specimens and testing protocol The two single-wythe CS masonry piers present identical geometrical dimensions and mechanical properties, measuring 2.70 m in height, 2.00 m in length, and 0.10 m in thickness (Fig. 3). The first specimen is unstrengthened (Fig. 3a), acting as a reference, whereas the second is retrofitted through a timber frame linked to the masonry underneath, to the top reinforced concrete (RC) beam, and to the RC footing through steel connections (Fig. 3b). The timber frame is characterized by vertical posts and horizontal nogging elements. The vertical posts are fastened to the top and bottom sill plates and to the top and bottom RC elements through specific tie-down anchorages, designed to yield before reaching the timber strength (Fig. 3b). Finally, 18-mm-thick oriented strand boards (OSBs) are nailed to the timber frame to enhance the in-plane shear strength and stiffness of the masonry panel (Guerrini et al., 2021). A comprehensive characterization campaign carried out at the DICAr Laboratory of the University of Pavia (Guerrini et al., 2021) allowed obtaining the mechanical properties of the CS masonry. Table 1 summarizes the main findings in terms of Young’s modulus ( E ), tensile and compressive strength of masonry ( f t and f c ) and bricks ( f bt and f bc ), cohesion ( f v0 ) and friction ( μ ) coefficients, and density ( ρ ). The shear modulus ( G ) is conventionally taken as 0.3 E , since no dedicated tests were performed.

Fig. 3. Geometry and details of the tested masonry piers: (a) bare and (b) retrofitted configurations (Guerrini et al., 2021).