PSI - Issue 37

Haya H. Mhanna et al. / Procedia Structural Integrity 37 (2022) 359–366 Mhanna et al./ Structural Integrity Procedia 00 (2021) 000 – 000

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6

% = ̅ ∗ 100 % = 1 ∑ | ( ) − ( ) | =1 ∑ *100 = √ 1 ∑ ( ( ) − ( ) ) 2 =1

(3)

(4)

(5) where is the number of samples; is the experimental FRP capacity (kN); and is the predicted FRP capacity (kN). Table 3. Evaluation of V f prediction models for U-wraps, complete wraps, and anchored U-wraps. Scheme U-wraps Complete Wraps Anchored U-wraps Design code ACI440. 2R-17 CSA S806.12 fib bulletin 90 TR55 ACI440. 2R-17 CSA S806.12 fib bulletin 90 TR55 ACI440. 2R-17 CSA S806.12 fib bulletin 90 TR55 ̅ 0.86 0.88 0.88 0.89 2.33 1.73 1.33 2.62 1.47 1.34 0.85 2.02 0.74 0.77 0.67 0.68 1.39 1.02 0.67 1.36 1.11 1.03 0.32 1.12 (%) 86 87 76 76 60 59 50 52 76 77 38 55 (%) 80 74 41 59 46 29 28 60 27 24 39 49 74 69 38 54 72 45 51 99 25 22 50 43 Table 4. Evaluation of V f prediction models for all wrapping schemes. Design code ACI440.2R-17 CSA-S806.12 fib bulletin 90 TR55 ̅ 1.62 1.35 1.04 1.92 1.28 1 0.61 1.31 (%) 79 74 59 68 (%) 49 38 34 56 62 49 48 72 It can be seen from Fig. 1 that there is a relatively good correlation between the experimental and predicted V f values. In general, it is clear that all design provisions provide unsafe predictions for the U-wrapped specimens, with most of the U-wrapped points falling below the unity line in Fig. 1, and overall average of V f(exp) to V f(pred) of less than 1.0. However, the results are reasonable considering that the strength reduction factors were not included in the analysis. In addition, the experimental values in Leung et al. (2007) study were significantly lower than the predicted values which may have affected the overall average values. It is suggested that more data is used in future studies with more variations in the geometrical and mechanical properties of the beams and FRP to verify these results. Overall, the least error (MAE and RMSE) in the U-wraps category was provided by fib bulletin 90 (2019) guidelines and the highest error was given by the ACI440.2R-17 (2017) predictions. When considering completely wrapped specimens, most data points in Fig. 1 fall above the unity line, and all ̅ values in Table 3 are higher than 1.0, which indicates that all design provisions provide safe predictions for fully wrapped specimens. This could be due to the low strain limitation imposed on the complete wraps by all design guidelines to prevent loss of aggregate interlock, while practically, this wrapping scheme is the most effective one. In addition, many of the fully wrapped specimens failed by rupture of the laminates. As a result, the strain in the FRP was fully utilized and the shear capacity was significantly enhanced. The least errors, standard deviation, and CoV values were depicted by fib bulletin 90 (2019) and CSA-S806.12 (2017) as shown in Table 3. On the other hand, TR55 (2000) provided the most conservative predictions for the complete wraps ( ̅ =2.62) with the highest error values of MAE = 60% and RMSE = 99. This is due to cautious design procedure that TR55 adopts for FRP shear strengthening, where the code imposes three limitations on the effective strain in the FRP for completely wrapped members. This strain limit, in many specimens, was computed to be lower than the 0.004 limit proposed by the ACI440.2R-17 guidelines. A similar trend was portrayed in the anchored U-wrapped laminates. The results in Fig. 1 and Table 3 indicate that all design guidelines (except for fib bulletin 90 (2019)) provide conservative and safe predictions with ̅ values greater