PSI - Issue 42

Mariana Jesus et al. / Procedia Structural Integrity 42 (2022) 1074–1081

1076

Jesus and Silva Lobo / Structural Integrity Procedia 00 (2019) 000–000

3

3. Proposals for the prediction of failure of the FRP

The equations found in literature for the prediction of failure of the FRP are presented in Table 2. Some of the authors proposed equations of the prediction of failure of FRP regarding reduction factors observed during the exper imental tests (Ilky et al. (2004); Lam and Teng (2003); Toutanji et al. (2010)). Others proposed equations regarding the influence of the geometry, as is the corner radius and the side of the column (Diego et al. (2019); Faustino et al. (2014); Lin and Teng (2020); Manfredi and Realfonzo (2001); Wang et al. (2016)). In the particular case of Lim and Ozbakkaloglu (2014), the authors related the failure strain of the FRP with the unconfined concrete strength and with the Young’s modulus of the FRP.

Table 2. Equations of ε lu / ε ju for columns with square and rectangular cross-section. Author ε lu /ε ju Geometry

Note:

B B

0 . 46 × 2 r 0 . 70 × 2 r 0.70

0 . 25

Diego et al. (2019)

+ 0 . 14

(1)

Square

for CFRP

0 . 23

Faustino et al. (2014)

(2)

Square

for CFRP

Ilky et al. (2004)

(3)

Square / rectangular

for CFRP

Lam and Teng (2003)

0.586 0.788 0.851 0.624 0.632

(4)

Square / rectangular

for CFRP for HM CFRP

for AFRP for GFRP for FRP

0 . 9 − 0 . 75 × E j

2 . 3 × f co 10 3

(5)

Square / rectangular

for FRP

Lim and Ozbakkaloglu (2014)

10 6 −

0 . 727 × 2 r 1 . 17 × r 0.43

B

0 . 288

Lin and Teng (2020)

(6)

Square

for FRP

B + 0 . 10

(7)

Square

for FRP

Manfredi and Realfonzo (2001)

Toutanji et al. (2010)

(8)

Square / retangular

for FRP

100

1 − 0 . 38 × B 0.33

0 . 41

(9)

Square with B ∈ [100 , 400] mm Square with B > 400 mm

for CFRP for CFRP

Wang et al. (2016)

4. Comparison of numerical and experimental results

The comparison between numerical results and experimental tests, regarding di ff erent proposals for the prediction of the failure of the FRP, focus on the analysis of di ff erent parameters such as f cc , ε cc and strain energy density ( W ) for all three FRP. Each model was combined with the equations presented in Table 2. The error of columns with square cross-section confined with CFRP, regarding f cc and ε cc , is presented in Table 3. The error can be obtained by: error (%) = [( t v − n v ) / t v ] × 100, were t v is the value of the specimen and n v is the value of the numerical model. Table 3. Error of model predictions compared to experimental results for columns with square cross-section confined with CFRP. Equation (1) Equation(2) Equation (3) Equation (4) Equation (5) Equation (6) Equation (7) Equation (8) Equation (9) Specimen Model f cc ε cc f cc ε cc f cc ε cc f cc ε cc f cc ε cc f cc ε cc f cc ε cc f cc ε cc f cc ε cc QR2C2 Faustino et al. (2014) 25.54 71.28 47.71 16.28 35.92 -11.42 43.54 6.15 37.89 -6.99 48.84 19.09 60.39 6.18 52.54 28.55 45.62 11.15 Lam and Teng (2003) 40.70 59.09 38.59 55.14 30.16 37.85 35.44 48.96 31.48 40.72 39.50 56.86 50.58 75.13 42.57 62.44 37.00 52.07 Manfredi and Realfonzo (2001) 39.34 48.31 35.66 40.54 20.52 3.04 30.05 27.70 22.88 9.46 37.24 43.92 54.79 77.36 42.62 55.07 32.80 34.12 Wei and Wu (2012) 49.24 44.62 48.03 41.58 43.31 30.11 46.26 37.21 44.04 31.85 48.55 42.88 54.95 59.93 50.30 47.35 47.14 39.36 QR2C3 Faustino et al. (2014) 20.89 68.98 42.82 9.56 31.92 -20.36 40.02 -1.39 34.01 -15.58 45.65 12.59 57.92 -1.35 49.57 22.81 42.23 4.01 Lam and Teng (2003) 37.00 55.81 34.75 51.54 25.80 32.86 31.41 44.86 27.21 35.96 35.72 53.40 47.50 73.13 38.98 59.42 33.07 48.22 Manfredi and Realfonzo (2001) 35.55 44.16 31.65 35.77 15.56 -4.74 25.68 21.90 18.06 2.19 33.32 39.42 51.97 75.55 39.04 51.46 28.61 28.83 Wei and Wu (2012) 46.07 40.17 44.79 36.89 39.77 24.50 42.90 32.17 40.54 26.38 45.34 38.29 52.14 56.71 47.20 43.12 43.83 34.49 S2R15 Faustino et al. (2014) 33.12 -19.52 32.08 -29.05 7.14 -611.60 28.75 -56.14 14.89 -68.08 32.85 -22.04 36.73 42.02 33.61 -14.81 29.92 -47.07 Lam and Teng (2003) 9.82 5.53 7.94 -0.91 -3.40 -44.10 2.61 -20.33 0.28 -29.29 9.31 3.81 21.89 40.79 10.73 8.53 4.39 -13.66 Manfredi and Realfonzo (2001) 10.26 -14.81 6.54 -27.44 -17.71 -121.58 -4.54 -67.62 -9.71 -88.29 9.25 -18.25 29.87 48.34 12.02 -9.07 -0.83 -53.85 Wei and Wu (2012) 20.06 -7.44 19.08 -11.40 13.17 -34.26 16.29 -22.35 15.08 -27.03 19.80 -8.48 26.58 20.78 20.55 -5.46 17.20 -18.85 S4R15 Faustino et al. (2014) 38.43 -59.51 35.34 -71.87 14.41 -148.15 25.97 -107.40 8.33 -102.46 26.37 -42.01 54.98 14.84 39.91 -53.43 29.16 -95.64 Lam and Teng (2003) 18.34 -12.20 15.10 -22.68 -4.52 -93.23 5.90 -54.32 -0.17 -76.61 17.47 -15.00 39.25 45.58 19.93 -7.19 8.96 -43.50 Manfredi and Realfonzo (2001) 21.54 -11.55 17.24 -25.58 -7.96 -129.11 5.04 -71.00 -2.71 -104.40 20.44 -14.89 47.80 59.25 23.67 -4.87 8.97 -55.63 Wei and Wu (2012) 37.46 -27.02 35.85 -34.38 26.24 -69.97 31.32 -51.46 28.35 -62.37 37.02 -29.84 48.04 15.78 38.25 -25.04 32.81 -45.90