PSI - Issue 44

Carlo Vienni et al. / Procedia Structural Integrity 44 (2023) 2270–2277 Vienni et al. / Structural Integrity Procedia 00 (2022) 000–000

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4.2. Stiffness The stiffness of a generic wall can be calculated by assimilating it to a Timoshenko beam (3). An analytical formulation able to reproduce CRM efficiency accordingly to numerical results has been developed. The increase in stiffness of the panel is significantly influenced by the stiffness of the mortar plaster and the deformability of the mortar-to-masonry interface. The proposed analytical formulations shown in (4) are based on the hypothesis of perfect adhesion between mortar and wall: this assumption can be considered valid at the center of the panel where the tangential stresses in the interface are lower and shear deformations are dominant, while it is not valid at wall corners, where axial strains are dominant and the detachment usually occurs.

(3)

;

(4)

4.3. Displacement capacity Displacement capacity defines the ductility of wall panels. Despite the relevance of this parameter, especially in the case of non-linear static analysis, current Italian and European building codes provide for its definition formulations based exclusively on the failure mechanism (shear or flexural). However, experimental evidence showed a strong influence on the wall’s ductility of the aspect ratio of the wall λ = H 0 /L and compression level ν = σ 0 /f c . In Orlando et al. (2016) an analytical formulation was proposed (5) to define the drift capacity θ c as a function of these two parameters. The a i coefficients were calibrated using a numerical regression and set equal to a 1 = 0.00074, a 2 =0.00069, a 3 =1.22. The application of the proposed formulation to the sample of numerical models analyzed in the present work evidenced its reliability to predict the ultimate drift of unreinforced masonry walls, as shown in Fig.5a where a comparison between analytical and numerical results is presented.

a b Fig. 5. (a) Application of formulation proposed by Orlando et al. 2016; (b) displacement capacity amplification factor regression. For the definition of an analytical procedure able to consider CRM efficiency, therefore, it is first necessary to use the formulation proposed in (5) for calculating the displacement capacity of unreinforced panels. Hence, the assessment of the CRM effect can be fitted based on numerical analyses: as shown in Fig. 4c drift capacity increase linearly to the compression level until a compression ratio of about v=0.30 and then does not change significantly. The proposed analytical formulation (6) provides to increase the displacement capacity for compression level v higher than 0.30, considering the mechanical parameters of the unreinforced masonry. The difference between the values obtained through the analytical and numerical procedure is less than 10%. The trend of displacement capacity amplification coefficient as a function of the ratio is shown in Fig. 5b.