PSI - Issue 37

Haya H. Mhanna et al. / Procedia Structural Integrity 37 (2022) 359–366 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

361

3

shear strengthening compared to flexural strengthening. Several guidelines adopted models that predicts the contribution of FRP to the shear capacity of structural members. The accuracy of these models is dependent on many factors, such as but not limited to, the wrapping scheme, wrapping angle, shear crack angle, concrete compressive strength, number of FRP layers, and FRP type. Hence, the predictions of the design models could widely vary depending on the geometry and mechanical properties of the beam’s section and FRP. Therefore, the main objective of this research is to compare and evaluate the accuracy of common available FRP shear design guidelines. The design standards considered in this study are: ACI440.2R-17 (2017), CSA-S806.12 (2017), fib bulletin 90 (2019), and TR55 (2000). The accuracy of the models was assessed against an experimental database collected from the literature. 3. Analytical Models This section provides the equations used to calculate shear strength of FRP constituent ( V f ) as provided in the design guidelines. All V f models presented herein limit the effective strain in the FRP ( ε fe ) to a fraction of the ultimate strain depending on the wrapping scheme, to prevent premature failure either by FRP debonding (in case of U-wraps) or loss of aggregate interlock (in case of complete wraps and anchored U-wraps). It should be noted that the ACI (ACI440.2R 17 (2017)) assumes a shear crack angle of 45º, while the CSA (CSA-S806.12 (2017)), fib (fib bulletin 90 (2019)), and TR55 (TR55 (2000)) guidelines allow the truss angle to range between 21.8º-45º. In this study, the shear crack angle was conservatively chosen as 45 º to allow comparison between the models that do not account for the shear crack angle with those that accounts for the shear crack angle. In addition, all reduction factors were set to unity (1.0) to allow for true comparison between the experimental and predicted results. Table 1 presents the models available in the ACI440.2R-17 (2017), CSA-S806.12 (2017), fib bulletin 90 (2019), and TR55 (2000) design provisions to determine V f . = ( + ) ; = 2 ; = ; Well anchored and complete wraps: = 0.004 ≤ 0.75 ; U-wraps: = ≤ 0.004 ; = 1 2 11900 ; = 23300 ( ) 0.58 ; 1 = ( ′ 27 ) = ( + ) ; = greater of 0.9d or 0.72h; = 2 For completely wrapped sections: = 0.006 ≤ 0.75 ; For U-wrapped with anchorage: = 0.005 ≤ 0.75 ; For unanchored U-wrapped: = < 0.004; = 1 2 11900 ≤ 0.75; 1 = ( ′ 27 ) 2 3 ; 2 = − ; = 23300 ( ) 0.58 , = ℎ ( + ) ; = 2 ; ℎ = ℎ − 0.1 in case of full-depth FRP = for n < 4, = 0.85 for n ≥ 4; For complete wraps: , = ; = 0.8; = 0.5 5 0 (2 − 5 0 ) for R<50 mm; = 0.5 f or R≥50 mm For U-wraps: = min( , , ) (a) For ℎ ≥ and ≤ ( + ) ≤ ℎ : = (b) For ℎ ≥ and ( + ) ≤ : = [1 − (1 − 2 3 ) ] (c) For ℎ ≤ and ( + ) ≤ ℎ : = 2 3 ( )/[( + ) ] = 2 √ 1 ; = ( + )/ ; = (( + ) / ; = √ 1 ; = 0.37 ; 1 = 0.37√ ; = 0.62√ For U-wraps with anchors: = , ; ≤ 0.9 ; = 2 ; , = 0.7√ ; = 0.21( ′ ) 2 3 ; For complete wraps: = 0 ; For U-wraps: = 1; = min ( 2 , 0.5√ , 0.004) Designations: = FRP shear contribution (N); = effective stress in the FRP (MPa); = angle of applying FRP laminates with respect to the 2 3 ; 2 = − CSA-S806.12 (2017) fib bulletin 90 (2019) TR55 (2000) , = ( − 3 , ) ( + ) Table 1. Summary of FRP shear strengthening design provisions. Design guideline Equations ACI440.2R-17 (2017)