PSI - Issue 64

Luigi Granata et al. / Procedia Structural Integrity 64 (2024) 1073–1080 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 7 In view of the numerical model assessment, the comparison between numerical and experimental results available in [6] are reported in Table 4 for both criteria adopted in terms of the ratio , ⁄ (strength of bent and straight reinforcement, respectively). Furthermore, in the same tables, comparisons with numerical results obtained by empirical formula, ACI 440 [12] and Lee et al. [10] are also reported. The , strength values are obtained for each type of specimen by dividing the corresponding failure load F u,b by the cross-section area A WFRP (Table 1). Table 4. Model assessment and comparisons in terms , ⁄ . Number of Layers Spadea et al. [11] ACI 440 [28] Lee et al. [16] Numerical (Tsai-Hill criterion) Numerical (Tsai-Wu criterion) 1 2 3 1 2 3 1 0,622 0,415 0,605 0,631 0,737 0,828 0,608 0,714 0,798 2 0,496 0,383 0,567 0,404 0,494 0,575 0,393 0,478 0,556 3 0,482 0,370 0,547 0,341 0,417 0,491 0,331 0,404 0,475 4 0,468 0,362 0,534 0,310 0,383 0,452 0,302 0,371 0,436 5 0,459 0,357 0,526 0,306 0,378 0,446 0,298 0,365 0,431 6 0,450 0,353 0,519 0,308 0,378 0,447 0,297 0,364 0,429 In Figure 4, the ratio , ⁄ is plotted against the number of layers varying the shear strength of the composite S. The comparison was performed also referring to the numerical values obtained by empirical formulations of ACI440 [12] and Lee et al. [10] as well as the experimental values obtained by Spadea et al. [11]. 1079

(a) (b) Fig. 4. Comparison between numerical and experimental results in terms of , ⁄ : a) Tsai-Hill criterion; b) Tsai-Wu criterion. 5. Conclusions Based on the present study, the following conclusions can be drawn: • As expected, increasing the curvature radius increases the strength of bent corners, tending to the strength of the straight reinforcement when the radius is infinite. The present mechanical model captures this well, while empirical formulations are unable to fully describe the physical phenomenon; • The empirical formulas seem to either overestimate (Lee et al.) or underestimate (ACI 440) the experimental values. • The Tsai-Wu criterion leads to more conservative numerical results with respect to those obtained on the basis of the Tsai-Hill criterion; • The numerical results are generally able to capture the trend of the experimental trend and are in particularly good agreement for a number of wound layers larger than three, especially if the Tsai-Hill criterion with a composite shear strength S3 is employed.