PSI - Issue 78

980 Tommaso Petrella et al. / Procedia Structural Integrity 78 (2026) 976–983 free rotation, simulating the collapse mechanism. The constitutive relationship for the hinges adopted describe a triangular moment-rotation law: rotation is zero up to the ultimate resisting moment (denoted as A in Eq. 4), then the moment linearly tend to zero at the ultimate rotation . In the case of a post-intervention (PS) scenario, where steel ties are introduced to enhance the wall ’ s strength capacity, these additional elements are also explicitly modelled in SAP2000. The steel ties are modelled as 2-node link elements characterized, as illustrated in Figure 2b, by a multilinear elastic constitutive law. The tie is initially considered pre-tensioned, implying negligible initial displacement. Subsequently, the constitutive relationship displays a linear degrading trend, reaching zero at the maximum displacement capacity ( ) . This modelling framework enables a direct comparison between pre (IS) and PS configurations, as discussed in the following examples. 3.2. The case studies This section presents the analytical and numerical evaluation of local OOP collapse mechanisms for both IS and PS configurations. The system under consideration is a masonry wall composed of two stacked rigid blocks, with rocking motion about the pivot points (C1 or C2) as the ones illustrated in Figure 3c and Figure 3d. To simplify the calculation process and focus exclusively on the mechanism behaviour, a unitary width is assumed for the wall. The wall is idealized as two stacked rigid blocks, each with a height of 500 cm. The lower block has a thickness of 100 cm while the upper block is thinner (50 cm). Both blocks are subjected to their self-weight and additional loads, as listed in Table 1. The loading and geometric parameters remain the same in both configurations, with the sole exception of the steel tie, placed at height , providing an additional stabilizing force increasing the wall ’ s OOP strength capacity. The magnitude of the applied forces are reported in Table 1, together with the coordinates of their application – i.e. x and y coordinates. The computed collapse multipliers enable a direct comparison between the configuration with and without the steel tie, providing a quantitative assessment of the intervention ’ s effectiveness. Two collapse mechanisms are evaluated for each configuration: the global overturning of the entire wall and the partial overturning of the upper block only. The corresponding static multipliers 0 are calculated analytically for both cases, based on the simplified assumptions of the kinematic method.

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Fig. 3. (a) geometry and action of the wall case study w/o ties; (b) geometry and action of the wall case study w/ ties (c) global overturning failure mechanism; (d) partial overturning failure mechanism.