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Figure 8. Cloister vault (f/L = 0.5; s/L = 0.045; Tmr/amr = 1): normal stiffness decay on varying the masonry pattern.

To describe the non-linear behaviour of masonry structure, a non-linear constitutive model is used (Gambarotta & Lagomarsino 1997), already implemented in the ANSYS code. This constitutive model considers a limited tensile strength for fragile materials; a damage model allows simulation of the progressive loss of stiffness, up to a predefined strength value, and the following phase of softening, in which the material progressively loses strength with large increases in deformation. The model does not consider cracks as localized phenomena, but as a state of equivalent inelastic deformations. This constitutive law also allows description of the shear behaviour according to a Coulomb criterion and sliding in the mortar joints. Furthermore, it allows simulation of crushing in the masonry. In this way, the masonry material orthotropy is considered introducing the modeling of the bed joints.

All conditions being equal to those assumed on the elastic analyses, non-linear FEM simulations are performed. The attention is focused instead on the role played by two factors: firstly, different masonry bond types are examined (e.g. Figure 1); secondly, the ratio between some mechanical properties of strength, which characterize the bed joints is investigated, with particular regard to that between the tensile strength (amr) of the mortar joint and the cohesion (rmr). The mechanical properties assumed are representative of standard brick masonry, characterized by regular pattern and by lime mortar (friction coefficient ^ = 0.6; compressive strength of masonry fm = 6 MPa; shear strength Tmr = 0.2MPa). The moduli E and G are assumed according to the isotropic material hypothesis (E = 1.8MPa and G = 0.6MPa).

It is worth specifying that only the early non-linear response is examined. Thus, only the initial degradation of stiffness is assessed, without analysing the collapse state of the vault. The scope of defining drift limits beyond which the vault cannot be considered structurally efficient is not pursued.

In the following, the results of the axial analyses are examined.

As an example, the ones related to the response of the cloister vault (f/L = 0.5), characterized

Figure 8. Cloister vault (f/L = 0.5; s/L = 0.045; Tmr/amr = 1): normal stiffness decay on varying the masonry pattern.

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