PSI - Issue 64

1036 Veronica Bertolli et al. / Procedia Structural Integrity 64 (2024) 1033–1040 4 Veronica Bertolli, Lesley H. Sneed, Francesco Focacci, Tommaso D’Antino/ Structural Integrity Procedia 00 (2019) 000–000

 fd is the peak load attained in direct or indirect shear tests (i.e., it is the smaller of the stress associated with the onset of debonding,  lim,conv , and the fiber tensile strength,  u,f ), l eff is the effective bond length, and L max is the maximum bonded length of fibers crossing the crack. If information about the effective bond length is not available, l eff is taken equal to 300 mm. The model proposed by the American ACI 549.4R (2020) guideline computes  fe from the ultimate strain and tensile modulus of cracked FRCM,  fu and E FRCM , respectively, obtained by clevis-grip tensile tests of the specific FRCM composite. The model considers a fixed value of the compressed strut angle (  =45°). If a textile with multiple fiber directions is used, V f is computed as the sum of contributions of each fiber direction, provided that PD fibers contribute to at least half of the composite shear strength.   ε ε ,0.004 fu fe  (5) The limit 0.004 is intended to limit the opening of the shear crack to promote the different concrete shear resisting mechanisms (i.e., concrete, steel (if present), and FRCM shear strength contributions). It is enforced also by ACI 440.2R (2023) for beams with FRP composites. 3. Database description and assessment methodology The database used to assess the design models proposed by the design guidelines considered comprises 103 beams shear strengthened with U-wrapped FRCM without anchors. Basalt, carbon, glass, PBO, and steel fibers were considered. Four and 13 beams were strengthened with basalt and glass FRCM, respectively, whereas 23 beams were strengthened with PBO FRCM. Thirty-two and 31 beams were strengthened with carbon and steel FRCM, respectively. The beams had different cross-section shapes and dimensions, lengths, and amounts of internal longitudinal and transverse steel reinforcement. In Fig. 2, they are grouped based on the type of fibers used in the FRCM and depending on the concrete compressive strength of the RC beams, f c , which ranged between 13.8 MPa and 45.0 MPa. Fig. 2 illustrates the number of layers applied to strengthen each beam (1 ≤ n ≤ 7) and the equivalent thickness of the textile used (0.03 mm  t f ≤ 0.3 mm). The number of specimens within each subset is also reported. Detailed descriptions of geometry, amount of internal reinforcement, type of EB FRCM reinforcement, and mechanical properties of the RC beams collected in the database can be found in Bertolli et al. (2024). FRCM and textile geometrical and mechanical properties were taken from results published in works of the same research group who experimentally tested the beams. When not possible, they were gathered from the available literature considering tensile and direct shear tests performed on the same FRCM (Bertolli et al. (2024)). For each beam in the database, the experimental shear strength was compared with the analytical predictions of the models considered. The experimental composite shear strength, ,exp nor f V , was computed as the difference between the shear strength of the strengthened beam,   c f exp V V  or   c s f exp V V V   , for beams without and with transverse steel reinforcement, respectively, and the normalized shear strength of the control beam, which was computed as: σ ε FRCM fe E  fe (6)

   exp V f c

 0.5

  c V

nor exp

(7)

ctrl

str

f



c

c

   exp V V f c s

 0.5





nor exp

(8)

ctrl

str

V V

f

  

c

s

c

c

for beams without and with transverse steel reinforcement, respectively. ctrl c f and str c f are the mean concrete compressive strength of control (i.e., unstrengthened) and corresponding strengthened beams, respectively. To provide a consistent comparison between the two models, a fixed value of the compressed strut angle (  =45°) was assumed for both models.