PSI - Issue 44

Giorgia Cianchino et al. / Procedia Structural Integrity 44 (2023) 219–226 Giorgia Cianchino et al. / Structural Integrity Procedia 00 (2022) 000–000

222

4

The first step was to compute the multiplier ( α 0 ) of the lateral forces that leads the activation of the kinematism, through the Virtual Work Principle. According to (Ministero delle Infrastrutture e dei Trasporti 2019), for each load multiplier the spectral acceleration a 0 *, referred to an equivalent Single-Degree Of Freedom (SDOF) system, was therefore evaluated. Subsequently, the spectral acceleration was amplified by the behavior factor q , imposed equal to 2, to consider the ductility sources of the macro-elements. This value was considered as the acceleration that led to the activation of the mechanism if the macro-element is anchored to the ground (a 0g ) (Criber et al. 2015) (Tashkov et al.2010). The analysis revealed that -for all models- the mechanism corresponding to the lower spectral and ground accelerations is the complete overturning of the front façade. The results of the linear kinematic analysis for all the six models are shown in Table 2. As expected, the lowest multipliers are associated with the out-plane mechanism of the four-story buildings for both irregular (archetype #9) and brick (archetype #21) masonry.

Table 2. Linear kinematic analyses results for the front façade of the six archetype buildings. Mechanism #Archetype α 0

a 0 * [g]

a 0g [g]

Total overturning

1 9

0,064 0,046 0,050 0,038 0,030 0,098

0,06 0,04 0,05 0,03 0,03 0,09

0,12 0,08 0,10 0,07 0,06 0,18

17 19 21 22

Afterwards, nonlinear kinematic analyses were also performed to determine the acceleration-displacement capacity curve of the most fragile mechanisms of the six archetype buildings until collapse. The capacity curves were determined according to the Italian guidelines (Ministero delle Infrastrutture e dei Trasporti, 2019): • First, the ultimate lateral displacements d k of the center of the masses of the considered macro-elements are identified by imposing a null value to α 0 . This allows to define the incipient collapse for each archetype. • Then, the lateral displacement (d 0 *) of the SDOF system is evaluated according to Eq.1: (1) where ",$ is the horizontal virtual displacement corresponding to the kinematic chain. • Finally, given d 0 *, the displacement capacity related to the Collapse Limit State (d C *= 60% · d 0 *), the Near Collapse Limit State (d NC *= 60% · d 0 *), the Damage Limit State (d D = d NC */q where q = 2 is the behavior factor accounting for the energy dissipation capacity of the structure) is determined. As for the Elastic Limit State (ELS), the following formulations are used to compute the elastic displacement capacity:

(2)

(3)