PSI - Issue 44

Alessandra Maione et al. / Procedia Structural Integrity 44 (2023) 1372–1379 Alessandra Maione et al. / Structural Integrity Procedia 00 (2022) 000 – 000

1378

7

3. Optimization of the strengthening solution through parametric analyses The proposed simplified approach is herein applied to a T-shaped connection to identify the best strengthening solution to achieve a target performance. Several solutions are investigated by varying two design parameters, i.e., the number m of rows and the length L a of the anchors. In addition, two values are considered for the orthogonal wall thickness t s , i.e., 0.3 m and 0.5 m, with the other parameters listed in Section 2.2. The horizontal capacity  0 related to the unreinforced condition is obtained as 0.16 and 0.2 for t s = 0.3 m and 0.5 m, respectively. The horizontal capacity   for the strengthened condition is plotted in Fig. 5a-b together with the target capacity  d (dashed red line), as a function of the considered design parameters. The seismic demand related to a definite limit state  d for only illustration purposes is assumed equal to 0.35, which is about 2 times and 1.75 times the horizontal capacity  0 of the unreinforced condition.

(a)

(b)

Fig. 5. Horizontal capacity   vs. the number m of rows, for different lengths L

a of the anchors related to (a) t s = 0.3 m; (b) t s = 0.5 m.

The graphs show that   increases with the number of rows m and the length L a of the anchors for both t s ; in particular, when m = 12 and L a = 2 m, the maximum percentage increase with respect to the unreinforced condition is 188% for t s = 0.3 m and 158% for t s = 0.5 m, respectively. Moreover, the same strengthening solution, identified by fixed values of m and L a , performs better when t s is larger; for example, for m = 3 and L a = 2 m,  * increases by about 22% from t s = 0.3 m to t s = 0.5 m, respectively. Finally, the results of the parametric analyses can be used to identify the “minimum” strengthening solution complying with the target performance  d . For this purpose, for both values of t s and each value of L a , the minimum number m min of rows required by the target capacity is indicated on the horizontal axis in Fig. 5a-b, by using dot vertical lines. The design solutions identified by m min and related L a are detailed in Table 2. for each t s in terms of the geometry of the expected failure mechanism ( r and   c ). It arises that for all of them, the hinge of the expected failure mechanism in the strengthened condition coincides with that related to the unreinforced one, being r = 0. Moreover, for both values of t s, the minimum design solution is obtained with a length of the anchors L a = 2 m, although for t s = 0.3 m, a larger number of anchors is required than for t s = 0.5 m (5 vs. 3 rows) due to the lower stabilizing moment of masonry. As a general trend, however, longer length may significantly reduce the minimum number of rows, allowing sensible saving of time and cost of installation. Table 2. Design solutions in terms of the minimum number of anchors and the geometry of the expected failure mechanism. L a = 1.5 m L a = 1.8 m L a = 2 m m min r   c m min r   c j 0 m min r   c t s = 0.3 m 10 0 37° 7 0 43° 4 0 38° t s = 0.5 m 8 0 37° 5 0 33° 3 0 43° 4. Conclusions In this paper, an improvement of a modelling approach, previously proposed by the authors to assess the onset of the out-of-plane (OOP) response of a strengthened T-shaped wall connection, is presented. In applying the kinematic