PSI - Issue 44

Greta Agata Venneri et al. / Procedia Structural Integrity 44 (2023) 291–298 Greta Agata Venneri et al. / Structural Integrity Procedia 00 (2022) 000–000

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through elements but inserted through floor loads and assigning a rigid constraint to the nodes of each level. The applied static loads were: self-weight, permanent loads, snow loads, wind loads, live loads; their values are those given in the original design documents. The adopted material model had a bi-linear stress-strain behavior, with modulus of elasticity E = 210000 N/mm 2 and Poisson’s ratio υ = 0.3. Yielding strength and ultimate strength values of material were selected according to the steel grade of the elements. Two finite element models were developed for each building, differing in terms of joint modelling: the “theoretical model” with rigid joints and the “actual model” with semi-rigid joints whose behavior was modeled according to the real behavior. 3.2. Joint modelling In the model of the as-built frames, the semi-rigid joints were modelled as nonlinear rotational springs at the ends of the elastic elements (Zareian and Medina 2010). Hence, springs were placed at the ends of beams to model beam to-column joints, and at the end of columns to model column bases. The rotational springs accounted for the hysteretic cyclic behavior, also in terms of degradation (i.e., strength and stiffness degradation), using the Bouc-Wen model (Bouc 1967; Wen 1976; Charalampakis 2010). The strength and stiffness properties of the springs were derived through the application of the Component Method, which provided the Moment-rotational (M- θ ) curve. The rotational springs were modelled in MIDAS Gen platform through General link elements. Rigid link elements, which constrain all relative translational movements of the connected nodes, were used for modelling the translational degrees of freedom of semi-rigid joints. Fig. 3(a) shows the general link elements implemented at the end of the column and the beam. Fig. 3(b) illustrates the generic Bouc-Wen behavior of the general links. On the contrary, for the theoretical frames, nodal tie constraints were implemented to simulate the rigid joints of the MRFs. Since fixed supports had to be implemented, translational and rotational degrees of freedom were blocked to the base nodes of the columns.

Fig. 3. (a) General link elements; (b) Bouc-Wen hysteretic behavior of general link elements.

3.3. The implemented analyses

Conventional modal analyses and linear and nonlinear analyses were performed on the structural models. In particular, for the seismic vulnerability assessment dealt with in this paper, nonlinear dynamic time history analyses were carried out. Natural records were applied on the theoretical and on the as-built frames, as described in more detail in the next section. In the time history analysis setup, end of time, time increment and incremental step were defined according to the duration of the ground motions and the desired accuracy of the results. Time history analyses were performed by applying the Newmark method with constant acceleration ( γ = 0.5 and β = 0.25) (Midas GEN 2021).