PSI - Issue 44

Stefano Bracchi et al. / Procedia Structural Integrity 44 (2023) 442–449 Stefano Bracchi, Maria Rota, Andrea Penna / Structural Integrity Procedia 00 (2022) 000–000

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and an equivalent thickens ( t eq = b * t /0.0001), where b and t are the width and thickness of the real flange. Single walls analyses were performed with different values of b , ranging from zero to half of the length of the entire orthogonal wall (i.e. 2.04 m). In this way, in the single wall model the mass of the flange is equal to the mass of flange in the entire building. Fig. 3a,b shows the adopted modelling strategy.

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(b)

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Fig. 3. Bi-dimensional modelling of a single wall with flanges: façade (a), three-dimensional view (b) and indication of the nodes of the orthogonal wall, whose mass has to be accounted for in the single wall’s model (c).

Piers modelling flanges need to have the same deformable height of corresponding elements belonging to the entire building. In case of flanges with no openings, the height corresponds to the interstory height, whereas in case openings are present, it is lower than the interstory height. In the latter case, the masses of the nodes belonging to the entire building have to be added as nodal forces in the single wall model, to guarantee the consistency of the total mass. With this modeling strategy, it is possible to capture the real axial stiffness of the flange, without altering the flexural stiffness. In the bi-dimensional model of the wall it is obviously not possible to include floor elements. To model floors’ contribution on the single wall, linear beams with zero moment of inertia were introduced at the floor and roof level. The beam’s area is equal to the area of floors pertaining to the considered wall. It is therefore necessary to define an area equal to s * l w , where s is the floor’s thickness and l w is the pertaining length of the wall. The material of the linear beam is characterized by a value of E equal to the E 1 or E 2 of the floor’s membrane depending on the spanning direction ( E = E 1 if floor’s span is parallel to the wall, E = E 2 if floor’s span is orthogonal to the wall). Since the beam element is underestimating shear stiffness, to obtain consistency between the single wall model and the entire building, it was necessary to reduce the G 1,2 modulus of the floor of the entire building. 4. Results of the analysis Nonlinear static analysis were performed on the entire buildings (Building 2 with the two simplified configurations and STD geometry) and on the single wall models defined with the developed strategy and adopting various flange lengths. Fig. 4 shows the pushover curves obtained for the West wall modelled as single wall (with maximum flange’s length) and considered as belonging to the entire buildings, with all the different elements adopted and in case of transversal walls with no openings. It is possible to notice that the strength predicted by the code-compliant element is approximately half of the one obtained with the refined macroelements. As evident from comparison with experimental tests (e.g. Penna et al. 2016 for the experimental tests from which the case studies have been derived) the macroelements better approximate the real behavior of the structure. This is due to the fact that these elements are modelling phenomena such as cracking of masonry, uplift of piers and shear damage through mechanics-based approaches. These aspects are not always captured by the bilinear element, which instead is a phenomenological code-compliant model, implying a certain degree of conservativeness due to the embedded simplifications. As regards the comparison single wall vs. entire building, a good agreement is obtained between the two models for all the elements adopted, with the only significant difference being represented by the stiffness, which tends to be larger for the single wall models when refined macroelements are adopted. The sign of the variation of axial load in the West wall is also reported. In this case, this parameter for all the piers is consistent between the entire building