PSI - Issue 78

Melina Bosco et al. / Procedia Structural Integrity 78 (2026) 1087–1094

1092

5. Numerical analyses The seismic performance of the designed structures is assessed by multiple stripe analysis. The numerical simulations are performed by the OpenSees computer program. 5.1. Numerical model Two-dimensional numerical models are developed in both the x- and y-directions. To account for P–Δ effects, a leaning column is included in the model. Link beams are modelled as proposed by Bosco et al. (2015). Specifically, each link is represented by a series of three elements connected in series. The central element (EL0) is modelled through a modified version of the “elasticBeamColumn” that simulates the elastic flexural behavior of the link. This element has the same length and moment of inertia as the actual link and infinite shear stiffness. The modified version of the elasticBeamColumn used in this study differs from the standard elasticBeamColumn available in OpenSees because it allows the definition of an optional parameter. The optional parameter defines the plastic rotational capacity of the member. At both ends of the link, the connection with the nodal panels occurs via a zero-length element. This zero-length element comprises three nonlinear springs: a vertical spring (EL1) that simulates the elastic and inelastic shear behavior of half a link, a rotational spring (EL2) that captures the inelastic flexural behavior of the ending part of the link (the elastic stiffness of this element is assumed to be infinite) and a horizontal spring with elastic stiffness assumed equal to infinity. At each step of the numerical analysis, the plastic rotation demand in links γ pl,l is calculated at each end according to the following expression where V is the shear force at the end of the link, K 0,EL1 is the elastic stiffness of the vertical spring EL1, δ v is the vertical relative displacement between the two nodes connected by the vertical spring EL1, ϕ M is the relative rotation between the two nodes connected by the rotational spring EL2 and e * is the geometric length of the link, calculated taking into account the effective linked column depth. When the plastic rotation demand reaches the rotational capacity, the stiffness of the element EL0 is set to zero so as to simulate the link failure. Beams and columns belonging to the MRFs are modelled by “forceBeamColumn” elements with the HingeRadau integration rule. The plastic hinge length is set equal to the depth of the cross-section. Linked columns, which are considered fragile members, are modelled by “elasticBeamColumn” elements. Panel zones at both beam-to-column and link-to-column intersections are modeled using rigid elements arranged to form an articulated quadrilateral (Gupta and Krawinkler, 1999). The nonlinear rotational behavior of the panel zone is concentrated in a rotational spring located at one of the quadrilateral's corners. The behavior of this spring is defined according to the model proposed by Skiadopoulos et al. (2021). 5.2. Seismic input For the site under investigation, seismic hazard data on stiff soil conditions (Soil Type A) are provided by the National Institute of Geophysics and Volcanology (INGV). Specifically, INGV reports three percentiles of spectral acceleration (i.e., 16%, 50%, and 84% percentiles) for eleven periods of vibration T i ranging from to 0.0 to 2.00 s and for nine probabilities of exceedance PVR (and, therefore, for nine return periods T R ), ranging from 81% to 2% in 50 years. For exceedance probabilities not directly covered in the INGV database, the corresponding spectral accelerations are derived using the interpolation procedure developed by Barbagallo et al. (2020). For each considered PVR, a suite of 50 accelerograms is generated by the SIMQKE computer program. Considering the above accelerograms as seismic input at the bedrock, the corresponding input motions at the surface of the investigated site (i.e., soil type B with v s30 = 550 m/s) have been obtained through one-dimensional local site response analysis by Bosco et al (2024b). pl,L M * 0, 1 EL V K e     2 γ δ v        (4)