PSI - Issue 78

Tommaso Petrella et al. / Procedia Structural Integrity 78 (2026) 976–983

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Table 1. Loading conditions and force locations (coordinate x and y) used for the numerical analysis. Parameter Symbol x [cm] y [cm] Value [kN] Self-weight lower block W 1 50 250 315 Self-weight upper block W 2 25 750 157,5 Vertical force first floor S V1 40 500 60 Horizontal thrust first floor S h1 40 500 30 Vertical force second floor S V1 25 1000 40 Tie force T - 450 50

These analytical values are used to calibrate the numerical model, allowing a direct comparison with the results of the non-linear static (pushover) simulations developed in SAP2000. The results of the analytical evaluation are summarized in Table 2. The computed multipliers 0 clearly indicate the beneficial effect of strengthening intervention, especially in the case of partial overturning which is significantly influenced by the presence of the tie. Table 2. Static multipliers 0 for the investigated collapse mechanisms. Collapse Mechanism Configuration α 0 θ ult Global overturning (Fig. 3c) w/o ties 4,15% 4,11% Partial overturning (Fig. 3d) w/o ties 9,66% 9,66% Global overturning (Fig. 3c) w/ ties 12,58% 12,45% Partial overturning (Fig. 3d) w/ ties 9,66% 9,66% In order to validate the effectiveness of the proposed modelling strategy, non-linear static (pushover) analyses were performed in SAP2000 for both the IS and PS configurations. The resulting capacity curves are directly compared with those derived from the analytical kinematic formulations (Figure 4). As shown in Figure 4a, the numerical results exhibit excellent agreement with the analytical predictions for both failure modes. The capacity curves overlap throughout the entire rocking collapse process, confirming the ability of the proposed model to accurately reproduce the onset and development of OOP mechanisms.

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Fig. 4. Comparison between analytical and numerical capacity curves for IS and PS configurations: (a) zoomed-in view of initial stiffness, highlighting the effect of SAP2000 zero-load initial condition; (b) full-range response showing excellent agreement in terms of collapse capacity. Deformed shapes and modelling schemes from SAP2000 are also displayed for both cases.