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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coefficient, α , equal to 0.7. This was modelled using the Hysteretic material in the OpenSees library, adopting an elastic-perfectly plastic behaviour. The backbone curve relating to the infills was obtained by subtracting the force displacement curve of the frames from the capacity curve of the overall system, assuming that the displacements corresponding to the yielding of the RC elements and the attainment of residual strength in the infills coincided. Shear slip behaviour was assumed for the infills, which were modelled using the Pinching4 material. A damping ratio corresponding to 0.05 was assumed. An example of the behaviour of the infills, of the RC frame alone, and the overall force-displacement behaviour of the system is shown in Fig. 2.

Fig. 2. Example of hysteretic behaviour of the SDoF system. (a) RC frame behaviour; (b) infills shear-slip behaviour; (c) whole system response.

5. Fragility analysis

The behaviour of the building under investigation was studied from a probabilistic point of view, with the aim of obtaining a fragility model that expresses the probability of exceeding the damage levels previously defined as a function of a certain ground motion IM. Various types of uncertainties are involved in the problem under investigation. In particular, the behaviour of the building depends on the response of its elements, the characteristics of the materials and the uncertainty in their value, but also on the seismic input features, i.e. the characteristics of the ground shaking. A series of Random Variables (RVs) governing the building response were identified. In particular, the following have been considered: the concrete compressive strength, f c , with a median value equal to 23.5 MPa; steel yield stress, f y , with a median value of 369.9 MPa; chord rotation at yielding, θ y , and ultimate, through the plastic rotation component, θ pl ; the stiffness coefficient of the degrading branch in plastic hinges behaviour, α c ; and the force and displacement behaviour of masonry infills, through the coefficients F inf and D inf . In particular, F inf and D inf are related to the first cracking and the peak points, to which different levels of uncertainty are associated. A log-normal probability distribution was assumed for each RV and a corresponding Coefficient of Variation (CoV) was defined. The CoV for concrete compressive strength was defined on the base of the limits set for acceptance criteria. The uncertainty for α c coefficient was defined based on range tested by Ibarra and Krawinkler (2005) and assuming a median value equal to 0.17, comparable to the formulation used by Haselton (2008). The RVs considered in this study and the uncertainty parameters are shown in Table 2.

Table 2. RVs and coefficients of variations

f c

f y

θ y

θ pl

α c

F inf

D inf

RV

CoV

0.20

0.08

0.331

0.54

0.55

[0.3; 0.3]

[0.4; 0.7]

Reference -

Verderame et al. (2001)

Verderame et al. (2014)

Haselton (2008)

-

Verderame et al. (2014)

Verderame et al. (2014)

A series of pushover analyses were carried out using 27 permutation in RVs values, according to a Latin Hypercube Sampling (LHS), thus considering the uncertainty in the building capacity. Uncertainty in displacement demand was considered by using different ground motion recordings in the non-linear dynamic analyses on the SDoF systems. A