PSI - Issue 78

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

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In particular, the PS configuration demonstrates a noticeable increase in capacity, consistent with the analytical estimation either. Figure 4b provides a zoom on the initial part of the curves: it is possible to notice a minor discrepancy between the analytical and numerical responses, since the SAP2000 pushover analysis starts from zero horizontal force, while the kinematic approach assumes an instantaneous activation of the collapse mechanism at the threshold load. This observation offers a useful insight into the initial stiffness of the system, caught by the numerical models correctly even when the configuration varies (Additionally, the figure shows the SAP2000 deformed shapes and modelling schemes for both configurations, further illustrating the structural behaviour and the development of local collapse mechanisms. 4. Conclusions The paper proposed a simplified, yet robust, macro-element modelling strategy to simulate OOP failure mechanisms in masonry walls through numerical analysis in SAP2000. The non-linear behaviour is considered by adopting a lumped plasticity approach introducing plastic hinges at the base of the elements. Several OOP mechanisms can be activated in the model by considering different boundary conditions, i.e., simple overturning and combined flexural mechanisms, as well as various loading scenarios for each of them. By integrating the parameters derived from kinematic limit analysis into a non-linear static framework, the model accurately reproduces both the initiation and evolution of collapse mechanisms. The comparison with analytical results confirms the reliability of the approach, highlighting its capacity to capture the structural response in both pre (IS) and post-intervention (PS) configurations. In particular, the introduction of steel ties leads to a significant improvement in the OOP resistance. One of the main strengths of the proposed method lies in its practicality: it provides a quick, adaptable, and accessible tool for evaluating local collapse mechanisms, even in complex masonry structures. It also allows for an efficient assessment and design of strengthening interventions, making it particularly suitable for supporting decision making processes in seismic vulnerability assessments. Future developments may focus on extending the model to three-dimensional applications, incorporating dynamic effects, and exploring alternative constitutive relationships for the ties, to account for different mechanical behaviours and pre-tensioning conditions. Overall, the modelling framework presented herein proves to be a valuable and versatile tool for both research and engineering practice, especially in contexts where local failure mechanisms play a critical role in the seismic performance of unreinforced masonry buildings. References Casapulla, C., Argiento, L., 2017. Non-linear kinematic analysis of masonry walls out of-plane loaded. The comparative role of friction between interlocked walls. In: Proceedings of COMPDYN 2017, Rhodes Island, Greece. CNR-DT 212/2013. Istruzioni per la valutazione e la riduzione della vulnerabilità sismica degli edifici esistenti. Consiglio Nazionale delle Ricerche, Italy. Computers and Structures, Inc., SAP2000 Linear and Nonlinear Static and Dynamic Analysis and Design of Three-Dimensional Structures, 2025. EN 1998-3, 2005. Eurocode 8: Design of structures for earthquake resistance – Part 3: Assessment and retrofitting of buildings. European Committee for Standardization. Felice G., & Giannini, Renato. (2001). Out-of-plane seismic resistance of masonry walls. JOURNAL OF EARTHQUAKE ENGINEERING. 5. 253-271. 10.1080/13632460109350394. Fiorentino, G., Forte, A., Pagano, E., Sabetta, F., Baggio, C., Lavorato, D., Nuti, C., & Santini, S. (2018). Damage patterns in the town of Amatrice after August 24th, 2016, Central Italy earthquakes. Bulletin of Earthquake Engineering , 16(4), 1399 – 1423. https://doi.org/10.1007/s10518-017 0254-z Graziotti F, Tomassetti U., Sharma S., Grottoli L., Magenes G.. Experimental response of URM single leaf and cavity walls in out-of-plane two way bending generated by seismic excitation, Construction and Building Materials,Volume 195, 2019, Pages 650-670, ISSN 0950-0618, https://doi.org/10.1016/j.conbuildmat.2018.10.076. Heyman, J., 1966. The Stone Skeleton. In: International Journal of Solids and Structures, 2(2), pp. 249 – 279. Housner, G.W., 1963. The behaviour of inverted pendulum structures during earthquakes. In: Bulletin of the Seismological Society of America, 53, pp. 403 – 417. Lourenço, P.B., 2002. Computations on historic masonry structures. In: Progress in Structural Engineering and Materials, 4(3), pp. 301 – 319. Lourenco, Paulo & Mendes, Nuno & Ramos, Luís & Oliveira, Daniel. (2011). Analysis of Masonry Structures Without Box Behavior. International Journal of Architectural Heritage. 5. 369-382. 10.1080/15583058.2010.528824.