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 horizontal; = effective depth of FRP shear reinforcement (mm); = center-to-center spacing of FRP laminates (mm); = Area of FRP shear reinforcement (mm 2 ); n = the number of FRP plies; = thickness of FRP ply (mm); = width of FRP laminates (mm); = FRP elastic modulus (MPa); = effective strain in the FRP (mm/mm); = ultimate strain in the FRP (mm/mm); = reduction coefficient; = effective bond length (mm); 1 = modification factor to account for the concrete compressive strength; 2 = modification factor to account for the type of wrapping scheme; ′ = concrete compressive strength (MPa); = beam web width (mm); = effective depth (mm); = acute angle of fiber direction to member axis; = orientation angle of the fibers with respect to longitudinal axis of the member; . = design value of the shear force which can be sustained by the externally applied reinforcement (N); = area of externally bonded shear reinforcement measured perpendicular to the direction of the fibers (mm 2 ); h f = height of FRP crossed by the shear crack (taken equal to h-0.1 d s in the case of full-depth FRP) (mm); = angle between beam axis and shear crac k; α = angle between fibers and the member axis perpendicular to the shear force; f fwd = design value of the average stress in the FRP intersected by the shear crack in the ultimate limit state (MPa); = width of the FRP strips (mm); = effective thickness (mm); = thickness of a single FRP layer (mm); n = number of FRP layers; = reduction factor; = long term loading factor; R = radius at the corner (mm); = design tensile strength of FRP (MPa); l e = maximum bond length (mm) ; = characteristic bond strength (MPa); = material safety factor (1.5 for persistent, 1.2 for accidental); n = number of strips crossed by the shear crack; m = number of strips for which the bond length is less than l e ; = effectiveness coefficient of an anchorage system; 1 = characteristic bond shear strength (MPa); = characteristic ultimate slip (mm); = concrete compressive strength (MPa); = tensile strength of concrete (MPa); , = anchorage length required to develop full anchorage capacity (mm); = angle between principal fibers and a line perpendicular to the longitudinal axis of the member; = characteristic tensile strength of concrete (MPa); = effective strain in the FRP laminates; = design ultimate strain capacity of FRP. 4. Experimental Database In this research, a total of seven experimental studies (Cao et al. (2005); Colalillo and Sheikh (2014); Koutas and Triantafillou (2013); Leung et al. (2007); Mhanna et al. (2021); Ozden et al. (2014); Saribiyik et al. (2021)) were used to evaluate the accuracy of the design models. The database was divided into three parts: U-wrapped specimens, completely wrapped specimens, and anchored U-wrapped specimens. Note that side bonded wrapping scheme was not included as several guidelines, such as fib bulletin 90 (2019), recommend preventing it. A total of 58 RC beam specimens were used in this study. The specimens varied between T-sections and rectangular sections as shown in Table 2. In addition, some of the specimens were reinforced with transverse steel reinforcement and some without stirrups. The compressive strength of concrete ( f’ c ) varied between 12 – 53 MPa. The FRP sheets used to strengthen the beams were made up of CFRP (40 specimens), GFRP (11 specimens), and BFRP (7 specimens) as shown in Table 2. The FRP sheets were bonded in the form of strips with specific width and spacing (49 specimens), or continuous without spacing (9 specimens). Furthermore, most of the sheets were bonded perpendicular to the beams’ longitudinal axis. However, three specimens were externally bonded with FRP sheets inclined at an angle of 45 º . The mechanical properties of the FRP fibers used to strengthen the specimens in the database are within the following range: elastic modulus: 5.3-640 GPa, tensile strength: 112-4300 MPa, ultimate strain: 0.004-0.047 mm/mm, and total composite thickness: 0.11-1.27 mm. 4

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Table 2. Experimental database Study

No. of specimens

Transverse steel

Wrapping method 2 U, AU U, C U, AU U, C U, C, AU

Fiber distribution 3

f’ c (MPa) 47-53 16.9 40

Section 1

FRP type

Mhanna et al. (2021) Colalillo and Sheikh (2014) Saribiyik et al. (2021)

T R R T R R T

10

0

S

CFRP CFRP BFRP

8 7 5

0, ✓

S, C S, C

✓ ✓ ✓ ✓

Ozden et al. (2014) Leung et al. (2007) Cao et al. (2005)

12 27

S S S C

CFRP, GFRP

12 11

CFRP

14-24 22-23

C

CFRP, GFRP CFRP, GFRP

Koutas and Triantafillou (2013)

5

0

U, AU

1 T: T-section; R: rectangular section 2 U: U-wrapped, AU: Anchored U-wraps; C: Complete wraps 3 S: strips; C: continuous 5. Results and Discussion

The experimental values of the FRP shear contribution ( V f ) were obtained directly from the literature. In addition, the analytical values were calculated as per the guidelines of the design standards (ACI440.2R-17 (2017); CSA S806.12 (2017); fib bulletin 90 (2019); TR55 (2000)). Figure 1 shows the comparison plots of the experimental ( V f (exp) ) values versus the predicted ones ( V f (pred) ). As previously mentioned, the database was divided depending on the