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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compared: a) a non-linear kinematic (NLK) approach, proposed and experimentally validated by Maione et al. (2021); and b) a new simplified approach proposed in this paper (second novel contribution). Both assume, with some approximation, that the maximum resultant moment occurs at the onset of a failure mechanism. The NLK approach requires a load-slip law to describe the non-linear behavior of the anchors; to this aim, an average bi-linear relationship was derived from the experimental curves obtained by Ceroni and Di Ludovico (2020) for wrapped CFRP anchors (see Fig. 1b). Hence, for each  c j,r , the resultant moment provided by the active anchors is evaluated in a sequence of kinematic configurations varied by the finite angle  until its maximum value is reached. In a generic kinematic configuration varied by  ( Fig. 3a), the position of the force T j+i,r (1 ≤ i ≤ k r ) is identified by the cartesian coordinates: ′ + , = + , ∙ ( + , + ) ′ + , = + , ∙ ( + , + ) (6) being R j+i,r the position radius from the hinge O r and  j+i,r its inclination angle to the horizontal axis when  = 0. These are respectively: + , ( , ) = √ 2 + , + 2 + , + , ( , ) = −1 ( + , + , ⁄ ) (7) being (see Fig. 1a): + , ( , ) = − ∙ ∙ , + , ( , ) = , − ∙ (8) Using the bilinear load-slip relationship T-s in Fig. 1b , the force T j+i,r can be calculated for the horizontal slip s defined as: = ′ + , − + , (9) Hence, considering Eq. (6), the resultant moment provided by the k r forces T j+i,r is: ( ) = ∑ [ + , ∙ + , ∙ ( + , + )] =1 (10) When the maximum resultant moment is evaluated for a given  , it is used in Eq. (4) to define the load multiplier  j,r . Note that in the same Eq. (4), the contributions of the gravitational forces are instead evaluated for  = 0, being the onset of the failure mechanism under consideration. Such an approximation can be accepted since the maximum resultant moment occurs for  very close to zero due to the high initial stiffness of the anchors.

(a)

(b)

Fig. 3. Data required for the maximum resultant moment provided by the anchors according to (a) NLK approach; (b) simplified approach.