Issue 60

F. Greco et alii, Frattura ed Integrità Strutturale, 60 (2022) 464-487; DOI: 10.3221/IGF-ESIS.60.32

the transversal macro-element have been reported, which is believed to be more vulnerable due to its peculiar configuration and location with respect to the other structural elements of the Cathedral. This macro-element involves two different masonry types, i.e. irregular soft stone masonry for the two lateral portions, and squared block stone masonry for the central part. The inelastic parameters required to perform the nonlinear static analysis by using the two models presented in the following section are reported in Tab. 2. In particular, the strength parameters (tensile strength f t , uniaxial and biaxial compressive strengths, f c and f b ) were deduced starting from the average compressive strength reported in the Italian code [35], whereas the fracture energies G f are assumed on the basis of typical values adopted in the technical literature for these masonry types.

Figure 7: Vertical section generating from the global geometrical model: longitudinal macro element (A) and transverse macro element (B).

f t (MPa)

f c (MPa)

f b (MPa)

G f (J/m 2 )

Material

Irregular soft stone masonry Squared block stone masonry

3.24

3.89

100

0.095

0.189 500 Table 2: Inelastic parameters of the masonry elements. 8.40 10.08

Limit analysis of local collapse mechanisms In addition to the global analysis of the structure, the seismic vulnerability assessment of an existing masonry building also requires the study of local collapse mechanisms, that are local portions of the structure that are susceptible to rigid overturning falls under moderate seismic actions. Indeed, most of the existing masonry structures present several vulnerable portions, such as unconstrained perimeter bearing walls (because of the lack of orthogonal connections) or soaring sub- structures ready to fail because of equilibrium losses rather than strength exceedance. For an existing masonry building, the equilibrium loss of local portions represents undoubtedly an unsafe condition. In extreme cases, the sudden loss of a local masonry portion can trigger a sequence of consecutive local collapse mechanisms up to the fall of the entire structure. Hence, the vulnerability of all unrestrained elements of a masonry structure against overturning risks represents an essential investigation, which is also helpful in achieving timely information for adopting proper retrofitting strategies to avoid them (including those based on the external application of FRP-like systems [39]). The study of local collapse mechanisms consists of comparing the horizontal load capacity of all the vulnerable portions of the masonry structure with the seismic demand of the building site. To this end, the Italian Codes prescribe using the kinematic approach of limit analysis to evaluate the horizontal capacity of a vulnerable masonry element, under the assumption for the masonry of being ( i ) rigid in compression, ( ii ) with no tensile strength, and ( iii ) unsusceptible to sliding failures. Quantifying the horizontal capacity of a masonry portion via the kinematic approach comprises several consecutive steps. The analysis begins by extracting the vulnerable element from the building, together with all the vertical and horizontal forces acting on it (i.e., all the actions transmitted by the structure, that are, for instance, all floor and service loads, and the

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