PSI - Issue 78

Emanuele Rizzi et al. / Procedia Structural Integrity 78 (2026) 1420–1427

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in the C2 model, the formation of hinge C at a load multiplier of 0.054 precedes that of the uplift at the base of the column, which occurs at a load multiplier of 0.090. As the mechanism progresses, the horizontal load gradually decreases until equilibrium is completely lost at displacement values of the centers of mass of the column and nave wall portion, equal to 515 mm and 1034 mm for model C1, and 252 mm and 509 mm for model C2, respectively. In the strengthened models IP R (dashed lines), the initial behavior is similar to IP U , though the response is stiffer by about 17% for the column and 23% for the nave wall. For the C1 model, the column uplift begins at a higher value of the load multiplier, namely 0.203. Then the stiffness reduces with a second linear slope due to the progressive loss of contact between the top of the column and the base of the arcade until a load multiplier value of 0.225. In contrast, in the C2 model, the formation of hinge C at a load multiplier of 0.073 precedes that of the uplift at the base of the column, which occurs at a load multiplier of 0.109. In both models, a subsequent hardening phase is observed due to the presence of the springs representing the roof bracing system. The maximum load multipliers attained values of 0.315 (C1) and 0.212 (C2). Then, the capacity curves exhibit a softening branch, as the yielding of steel ties and subsequent failure occur. After failure, the curves of the reinforced models almost attain those of the unreinforced ones, reaching comparable ultimate displacements.

(a)

(b)

Fig. 6. Capacity curves of the IP models: configuration (a) C1 and (b) C2.

5.1.2. Out-of-plane models results (OOP) The unstrengthened models OOP U exhibit a typical bilinear response (dashed lines in Fig. 7), with an initial linear phase ending with the onset of uplift at the column base, corresponding to peak load multipliers of 0.065 and 0.038 for C1 and C2 models, respectively. Beyond this, the kinematic mechanism is activated, and the horizontal load gradually decreases as the mechanism progresses, until equilibrium is lost. The ultimate displacement values of the centers of mass of the column and nave wall portion are equal to 186 mm and 744 mm (C1) and 115 mm and 463 mm (C2). In the strengthened models OOP R (solid lines in Fig. 7) the behavior is trilinear, due to the formation of an additional hinge and the column/wall contact. The initial elastic behavior is significantly stiffer than OOP U , by about 145% for the column and 667% for the nave wall, because of the change in failure mechanism. Also, the column uplift begins at higher values of load multiplier: 0.143 (C1) and 0.087 (C2). Then the stiffness reduces with a second linear slope, due to the progressive loss of contact between the column and the wall, until maximum load multiplier values of 0.192 (C1) and 0.104 (C2) are reached. As the kinematic mechanism fully develops, the horizontal load gradually decreases until equilibrium is completely lost at displacement values of the centers of mass of the column and nave wall portion, equal to 429 mm and 286 mm for model C1, and 234 mm and 167 mm for model C2.