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

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In applying this model to strengthen a T-shaped connection, it was assumed that the portion to be tied coincides with the macro-block involved in the most likely failure mechanism for the unreinforced condition; thus, it has height H c,0, measured from the hinge O 0 of such a mechanism (Fig. 1a). (a) (b)

Fig. 1. (a) T-shaped connection of masonry walls; (b) experimental pull-out curves related to wrapped CFRP tubes from Ceroni and Di Ludovico (2020) and bi-linear load-slip relationship proposed by Maione et al. (2021).

The strengthening system consists of m rows of CFRP grouted anchors, with the first one ( j = 1) at the distance d t from the top of the wall. The anchors have the length L a and are equally spaced by d along the height H c − d t of the walls. Thus, the distance of the j th row from O 0 is: H j = ( m– + 1) (1) In the unreinforced condition, the geometry of the possible rocking failure mechanisms depends on two variables: the vertical position of the cylindrical hinge, which defines the height of the involved macro-block, and the inclination angle of the main crack to the vertical axis. However, for the strengthened systems, only the latter variable was considered by Maione et al. (2021) since it was assumed that the position of the hinge is unchanged from the unreinforced condition. Therefore, verifying such a reasonable assumption is the first novel contribution of this paper, by considering the variable vertical position of the hinge in addition to the crack inclination angle. In pursuing the geometry of the failure mechanism that minimizes the load multiplier in the strengthened condition, discrete values of these two variables are considered. Regarding the vertical position of the hinge O r , the r possible values of its vertical distance from O 0 are given by: = (2) being 0 ≤ r ≤ ( m – 1), while r = m is excluded to avoid O r too close to the upper edge of the wall. Eq. (2) implies that O r coincides with O 0 , when r = 0; otherwise, its distance from O 0 coincides with that of the row j = m – r +1 given by Eq. (1). For each position of the hinge O r , the height of the potential macro-block is H c ,r = H c,0 – H O r, whereas the number m r of rows found along H c ,r is m r = m – r ; consequently, the rows j > m r are not involved in the rocking mechanism around O r (these are represented as dashed yellow lines in Fig. 1a). Then, for each position of O r , the possible failure mechanisms are characterized by m r definite crack inclination angles  c j,r ( j = 1, …, m r ); they involve the active contribution of a number k r of rows of anchors, being k r = m r – j, starting from the row j + 1. Indeed, the model assumes that the active anchors are those crossed by the crack and adequately embedded in the resting portion of the orthogonal wall to exploit their pull-out strength. This means that the embedded length L e must be greater than a conventional limit value L 0d . For the wrapped CFRP anchors considered in this paper, it is assumed L 0d = 245 mm, based on the pull-out tests in Ceroni and Di Ludovico (2020). Thus, when the crack line intersects the row j at the distance L 0d from its end, i.e., at point A j , it is safely assumed that the row j