PSI - Issue 44

Gianluca Salamida et al. / Procedia Structural Integrity 44 (2023) 139–146 Gianluca Salamida et al. / Structural Integrity Procedia 00 (2022) 000–000

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3. Modelling The finite element model aims to describe, through pushover analyses, the building behaviour as a whole; therefore, the modelling not only involved structural elements, but also non-structural elements such as the infill walls, since they strongly affect the structural response. Both external frames with masonry infills and internal frames were modelled in order to obtain a more accurate assessment of the structural behaviour. In particular, the structure has been modelled by placing an infilled frame and a bare frame side by side with OpenSees software (McKenna et al. 2004) assuming slabs as rigid diaphragms in their plane; the two frames, therefore, undergo the same floor displacements. 3.1. Frame members A concentrated plasticity approach was used to model frame members; a three-linear moment-rotation relationship has been assigned to rotational springs, placed at the elements ends. In the numerical model, this has been implemented using ZeroLength elements. In order to define the behaviour of plastic hinges, three characteristic points have been identified, corresponding to the yield, the ultimate condition (maximum moment) and the complete loss of strength (end of the degrading branch). Hinge rotations corresponding to the yielding and ultimate conditions, were defined based on the chord rotation limits evaluated following Eurocode 8-part 3 (2005) approach. Yielding and plastic rotations were estimated considering the complete lack of seismic details, the use of smooth bars and the presence of lapped bars. In the evaluation of the chord rotations described above, some simplifications were made; in fact, the shear span and the axial force in columns are not constant during a pushover analysis, however, the limited storeys number of the structure led to a limited variation of the axial stress in the columns, which is considered to be constant and equal to the value due to the gravitational loads only. The shear span length, L v , was assumed as a constant, equal to half the element length for beams and columns. Only for the first storey columns L v is equal to 2/3 and 1/3 of the element length, respectively for bottom and top cross-section, based on previous calibration of the parameters. The degrading branch slope of the plastic hinge envelope depends on the α c coefficient, corresponding to a percentage of the elastic stiffness, and was defined according to the Ibarra, Medina and Krawinkler (2005) model. 3.2. Masonry infills Infills can have a significant impact on the structural response of RC frames, hence it was deemed necessary to consider them in the building modelling. Infills considered in this work are 25 cm thick, with a longitudinal modulus, a shear elastic modulus and a shear cracking stress respectively equal to 1495 MPa, 598 MPa and 0.36 MPa. Since capturing the possible shear failure induced by infills is outside the scope of this study, an equivalent single diagonal strut scheme was adopted. The non-linear behaviour of masonry infills was defined following the model proposed by Panagiotakos and Fardis (1996). In particular, a tri-linear degrading envelope was adopted, which is characterized by first cracking, peak strength and reaching residual strength. The equivalent width of the strut, b w , was calculated according to equation 1, proposed by Klingner and Bertero (1976), in which d w and h w are the length of the diagonal and the effective height of the infill panel, respectively, while λ is the coefficient expressing the relative stiffness between the frame and the infill panel, evaluated according to the formulation proposed by Stafford Smith (1966). b w =d w ·0.175 ( λ ·h w ) -0.4 (1) A ratio between peak strength and first cracking strength equal to 1.3 was adopted and the slope of degrading branch was assumed equal to 3% of the initial elastic stiffness, up to the reaching of a residual strength corresponding to 1% of the peak. In addition, openings in infill walls were considered by applying a strength reductive factor, according to the formulation proposed by Asteris et al. (2012) considering an opening percentage of 14%.