PSI - Issue 44

Sara S. Lucchini et al. / Procedia Structural Integrity 44 (2023) 2206–2213 Lucchini et al. / Structural Integrity Procedia 00 (2022) 000–000

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regular Newton-Raphson iteration scheme was adopted. To check convergence of the iteration process, the force and displacement norms were both controlled by setting the corresponding tolerances ≤0.01. a b 100

Cyclic test - Envelope Monotonic test Bare wall, numerical Retrofitted wall, numerical

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40

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-20 Lateral load [kN]

-40

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-80

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

Midspan displacement [mm]

Fig. 4. (a) FE model of the strengthened wall. (b) Load vs. midspan displacement response: comparison between experimental and numerical results.

2.3. Comparison of results Fig. 4b shows the comparison between the experimental and the numerical load-midspan displacement response of the strengthened wall. The diagram reports also the response of the bare wall, which was simulated by removing the SFRM coating from the FE model of Fig. 4a. The results of the NLFEAs are in good agreement with the experimental curves discussed in the previous sections of the paper. Table 2 summarizes the main experimental and numerical results, including the initial secant stiffness (K i ) referred to the displacement range 0-|1.0| mm, the peak load (P max ), the deflection at peak (d max ) and the deflection (d 85% ) corresponding to a 15% reduction of the peak load on the post peak curve. Note that the negative initial stiffness of the monotonic test was not reported as loading reversal started from a non-zero value of deflection (i.e., residual deflection after un-loading). As one may note, the slope of the pre peak branch of the numerical response is very close to those exhibited by the experimental tests, thus confirming the ability of the model to well capture the initial elastic behavior as well as the response right after first cracking. As compared to the bare wall the increment of the initial stiffness after retrofitting is higher than 70% and 150% in the positive and negative loading direction, respectively. Considering the peak loads reported in Table 2 one may conclude that the potential increment of the OP capacity after strengthening is about 50% of the maximum resistance of the un strengthened member. On the contrary, because of the increased stiffness of the wall, the deflection at peak resulted lower than that of the bare wall. The failure mechanism was generally quite brittle for all the wall typologies. This fact is clearly highlighted by the values of the post-peak deflection d 85% , which are about 1.5-2 times d max for the strengthened walls and no more than 1.07 times d max for the bare wall. The numerical results confirmed the evolution of cracks observed on the external surface of the test walls and provided also additional information about the damage mechanisms acting inside the walls. According to the FE simulations, the failure mechanism of the specimens is mainly governed by shear together crushing of bricks located above the upper loading point. The shear mechanism is related to the formation of a shear crack that run diagonally from the loading plate to the end of the specimen, passing through the whole thickness of the wall. When the side of the wall strengthened with SFRM coating is subjected to tension (i.e., wall pushed out of the building), the shear crack goes diagonally through the URM wall thickness and then deviates vertically along the masonry-to-coating interface up to the restrained end of the members. Therefore,