PSI - Issue 11

Siro Casolo et al. / Procedia Structural Integrity 11 (2018) 20–27 Siro Casolo & Giuseppina Uva / Structural Integrity Procedia 00 (2018) 000–000

22

3

In the present paper, the out-of-plane response under cyclic loading, is modeled by a non-linear heuristic model in which the damages are concentrated into spherical joints (springs) with suitable mechanical properties (Casolo, 2000). The adopted phenomenological description includes the peculiar aspects of the macroscopic response: very low tensile strength; dependence of the shear strength on the vertical compression stress; progressive mechanical degradation; significant post-elastic orthotropy combined with texture effects; significant amount of energy dissipation during repeated cycles of loading.

Fig. 2. An elementary cell of four square elements connected by spherical joints ( S ). Pure bending (left) and twisting (right) (Casolo, 2000).

At each connection joint, two components of rotation are singled out: one in which the axis is parallel to the edge of the abutting elements, and the other whose axis is perpendicular to the edge (flexural and twisting deformation, respectively, as sketched in Figure 2).

(c)

(a)

(b)

Fig. 3. Behaviour of the heuristic model in vertical (a) and horizontal (b) bending for a three-leaf wall (Casolo & Milani, 2013). (c) Two different types of multi-leaf textures (Casolo & Uva, 2013).

Fig. 3 shows the main features of the heuristic scheme of a multi-leaf wall, in which the layers tend to bend separately when masonry is highly damaged. According to the adopted approach, the bending moment–curvature relationship M 11 – c 11 is reproduced by a set of line springs disposed in the plane of the horizontal mortar joints. Two three-leaf textures corresponding to typical masonry of Italian historical buildings are considered (Fig. 3c). They will be used as a demonstrative application of the texture-dependent heuristic model and then exploited for the successive investigations on seismic analysis of whole masonry façades. Texture (I) is a three-leaf masonry built with large blocks and very thin mortar joints. The transversal interlocking of the blocks is rather poor and exclusively demanded to the different length of the blocks. Texture (II) is again a three-leaf masonry, but with external leaves built with clay bricks, 10 mm-thick mortar joints and a filler of thickness 250-300 mm, similar to that of texture (I). The transversal interlocking between filler and clay bricks is better, and it is expected that the second texture is more suited to be used in seismic zone. The approach has provided good estimates of macroscopic moment–curvature diagrams for both textures, by reproducing the orthotropy of flexural peak strength in relation with the texture geometry, the different shape of the post-peak response and the residual strength due to the orthotropic influence of the average vertical compression stress. (Casolo & Milani, 2013). The peculiar effects of micro-structure on the global non-linear out-of-plane response of multi-leaf masonry have been described at the macro-scale level by a Rigid Body and Spring Model (RBSM) specifically designed to describe the flexural–torsional response and implemented in a proprietary computer code (Casolo, 2000). As an application, the response of a church located in Moggio Udinese, in the North-East of Italy, has been considered. This church is an example of architecture quite frequent in small Italian towns. The façade has a width of 16.30 m, with a maximum