PSI - Issue 78

Joud Habib et al. / Procedia Structural Integrity 78 (2026) 799–806

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Structural damage is categorized into five discrete states — No Damage, Slight, Moderate, Extensive, and Complete — in line with the SERA project classification. The engineering demand parameter (EDP) used to assess damage is the maximum inelastic absolute displacement. Four displacement thresholds are used to define the damage states, based on the methodology proposed by Villar-Vega et al. (2017). Slight damage ( 1 ) is assumed to occur when the maximum displacement reaches or exceeds 75% of the yield displacement 2 . Complete damage ( 4 ) corresponds to the ultimate displacement capacity 4 . The intermediate thresholds for Moderate ( 2 ) and Extensive ( 3 ) damage are defined as 0.5 2 + 0.33 4 and 0.25 2 + 0.67 4 respectively, to ensure a progressive and physically meaningful transition between damage states.

Fig. 1. (a) Generic capacity curve defined by four points; (b) Capacity curves for Code Design Null.

Fig. 2. (a) Hysteretic behaviour of CDL-H6-10; (b) Distribution of Records Across PGA Ranges.

2.2. Numerical modelling Using the concept of Equivalent Single-Degree-of-Freedom (ESDoF) systems and the previously defined capacity curves, the considered typologies are modelled in OpenSees (Open System for Earthquake Engineering Simulation) (McKenna, 2000; 2011). A damping ratio of 5% is adopted, consistent with the SERA project recommendations for reinforced concrete (RC) structures. For each typology, a numerical model is implemented in OpenSees using zeroLength element. The stiffness and overall structural response are governed by the Pinching4 material, which is specifically used to represent the hysteretic behaviour of RC structures (McKenna, 2000). This material describes both strength and stiffness degradation under cyclic loading. This feature enables multi-seismic sequence analysis, allowing the model to account for the cumulative effects of prior earthquake events (Altoontash, 2004). The Pinching4 parameters are calibrated using the capacity curves in combination with the values proposed by Orlacchio et al. (2024), ensuring a realistic representation of each typology’s nonlinear response. An example of the hysteretic behaviour captured using Pinching4 material for the typology CDL-H6-10 is shown in Fig. 2. (a).