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Ductility index_
| Beam symbol | Beam ID | P y (kN) | Δ y (mm) | P u (kN) | Δ u (mm) | μ ε u (steel-tension) | P u /Δ u | Ductility index Δ u /Δ y (μd) | Increase in μd % | Area under curve (kN mm) | Increase in area under curve % |
|---|---|---|---|---|---|---|---|---|---|---|---|
| BF-L | F1 | 48.4 | 6.7 | 51 | 16 | 2,364 | 3.2 | 2.39 | — | 138 | — |
| BF-L-LB | F2 | 58.2 | 7 | 73.4 | 10.8 | 3,398 | 6.8 | 1.54 | −36% | 192 | 39% |
| BF-L-SB-2 | F3 | 46 | 5.9 | 73.4 | 20.1 | 2,871 | 3.7 | 3.41 | 43% | 413 | 199% |
| BF-L-LB-UE | F4 | 67.2 | 6.4 | 76.4 | 17.6 | 2,942 | 4.7 | 2.75 | 15% | 411 | 198% |
| BF-L-LB-UE5 | F5 | 104 | 7.2 | 111.8 | 18.6 | 3,580 | 6.0 | 2.58 | 8% | 510 | 270% |
| BF-L-SB-UE | F6 | 60.8 | 11.1 | 71.6 | 30.2 | 2,900 | 2.4 | 2.72 | 14% | 696 | 404% |
| BF-L-SB-UE2 | F7 | 67 | 10.7 | 78.2 | 22.8 | — | 3.4 | 2.13 | −11% | 547 | 296% |
| BF-L-LBT-UE | F8 | 60.6 | 6.1 | 72.8 | 11.3 | 2,872 | 6.4 | 1.85 | −23% | 195 | 41% |
Details of strengthened RC beams_
| Label | Beam symbol | FRP material | Scheme | Notes |
|---|---|---|---|---|
| F1 | BF-L | Flexural control beam | ||
| F2 | BF-L-LB | CFRP strip | 1-layer 100 mm | Bottom soffit |
| F3 | BF-L-SB-2 | CFRP sheet | 2-layer 100 mm | Bottom soffit |
| F4 | BF-L-LB-UE | CFRP strip/sheet | 1-layer 100 mm/1-layer 100 mm at both ends | Bottom soffit/U-wrapped only ends |
| F5 | BF-L-LB-UE5 | CFRP strip/sheet | 1-layer 100 mm/1-layer 500 mm at both ends | Bottom soffit/U-wrapped only ends |
| F6 | BF-L-SB-UE | CFRP sheet/sheet | 1-layer 100 mm/1-layer 100 mm at both ends | Bottom soffit/U-wrapped only ends |
| F7 | BF-L-SB-UE2 | CFRP sheet/sheet | 2-layer 100 mm/1-layer 100 mm at both ends | Bottom soffit/U-wrapped only ends |
| F8 | BF-L-LBT-UE | CFRP sheet/strip | 1-layer 100 mm/1-layer 100 mm/1 layer at both ends | Bottom soffit/top soffit center compression/U-wrapped only ends |
Results of RC beams critical in flexural (F1–F11)_
| Beam ID | P cr (kN) | M cr (kN m) | V cr (kN) | Δ cr (mm) | P y (kN) | M y (kN m) | V y (kN) | Δ y (mm) | P u (kN) | P u/P u.control | M u (kN m) | V u (kN) | Δ u (mm) | Failure mode |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| F1 | 9 | 3.0 | 4.5 | 0.76 | 48.4 | 16.1 | 24.2 | 6.7 | 51 | — | 17.0 | 25.5 | 16 | Flexural tension failure |
| F2 | 22 | 7.3 | 11.0 | 2.06 | 58.2 | 19.4 | 29.1 | 7 | 73.4 | 43.9% | 24.5 | 36.7 | 10.8 | Concrete cover separation and flexural tension failure |
| F3 | 14 | 4.7 | 7.0 | 1.33 | 46 | 15.3 | 23.0 | 5.9 | 73.4 | 43.9% | 24.5 | 36.7 | 20.1 | CFRP plate debonding and concrete cover separation and flexural tension failure |
| F4 | 12.5 | 12.6 | 4.2 | 0.91 | 67.2 | 67.2 | 22.4 | 6.4 | 76.4 | 62.7% | 27.7 | 41.5 | 17.6 | CFRP plate debonding and flexural tension failure |
| F5 | 23 | 7.7 | 11.5 | 1.9 | 104 | 34.7 | 52.0 | 7.2 | 111.8 | 119.2% | 37.3 | 55.9 | 18.6 | CFRP plate debonding and flexural tension failure |
| F6 | 16.5 | 5.5 | 8.2 | 1.91 | 60.8 | 20.3 | 30.4 | 11.1 | 71.6 | 40.4% | 23.9 | 35.8 | 30.2 | CFRP plate debonding and flexural tension failure |
| F7 | 22 | 7.6 | 11.4 | 2.69 | 67 | 22.3 | 33.5 | 10.7 | 78.2 | 53.3% | 26.1 | 39.1 | 22.8 | CFRP plate debonding and flexural tension failure |
| F8 | 24 | 8.1 | 12.1 | 2.38 | 60.6 | 20.2 | 30.3 | 6.1 | 72.8 | 42.7% | 24.3 | 36.4 | 11.3 | CFRP plate debonding and flexural tension failure and flexural compression failure |
Material properties of CFRP fabric and CFRP laminate provided by the manufacturer_
| Characteristics | Manufacturer data | |
|---|---|---|
| CFRP fabric | CFRP laminate | |
| Ultimate tensile strength (MPa) | 4,000 | 3,100 |
| Fiber modulus (GPa) | 230 | 170 |
| Ultimate tensile elongation (%) | 1.7 | 1.8 |
| Thickness (mm) | 0.167 | 1.4 |
| Fiber density (g/cm3) | 1.82 | 1.6 |
CFRP composite material properties_
| Coupon | Ave. width (mm) | Ave. thick. (mm)a | Max load (kN) | Max tensile stress (MPa) | Max tensile strain | Modulus of elasticity (GPa) | Poisson’s ratio |
|---|---|---|---|---|---|---|---|
| CFRP sheet (0.167 mm/ply) | |||||||
| 1 | 50.1 | 0.71 | 21 | 2,560 | 0.0122 | 209.8 | — |
| 2 | 50.3 | 0.73 | 21 | 2,530 | 0.0121 | 209.1 | — |
| 3 | 50.5 | 0.78 | 23 | 2,700 | 0.0131 | 206.1 | — |
| 4 | 50.0 | 0.82 | 22 | 2,606 | 0.0125 | 208.5 | 0.28 |
| 5 | 50.8 | 0.88 | 23 | 2,690 | 0.0127 | 211.8 | — |
| 6 | 50.1 | 0.90 | 22 | 2,620 | 0.0126 | 207.9 | — |
| Average | 50.3 | 0.80 | 22 | 2,618 | 0.0125 | 208.9 | |
| CFRP laminate (1.4 mm plate thickness) | |||||||
| 1 | 50 | 1.4 | 133 | 1,897 | 0.0114 | 166.4 | — |
| 2 | 50 | 1.4 | 131 | 1,872 | 0.0105 | 178.3 | — |
| 3 | 50 | 1.4 | 127 | 1,808 | 0.0093 | 194.4 | 0.26 |
| 4 | 50 | 1.4 | 134 | 1,908 | 0.0114 | 167.4 | — |
| 5 | 50 | 1.4 | 130 | 1,863 | 0.0103 | 180.9 | — |
| 6 | 50 | 1.4 | 131 | 1,871 | 0.0105 | 178.2 | — |
| Average | 50 | 1.4 | 131 | 1,870 | 0.0106 | 177.6 | — |
Mechanical properties of LSC_
| () MPa | (f t) MPa | (f r) MPa | (E) GPa | Poisson’s ratio | Slump test (mm) | Velocity based on UPV test mm/μ s | Density (kg/m3) | |
|---|---|---|---|---|---|---|---|---|
| LSC | 17.3 | 2.38 | 3.59 | 21.36 | 0.172 | 65 | 4.25 | 2,246 |
Number of cracks at ultimate load_
| Beam symbol | Beam ID | Number of shear cracks diagonal | Number of flexural cracks | Crack width at failure-mid span (mm) | Failure mode |
|---|---|---|---|---|---|
| BF-L | F1 | 0 | 13 | 2.2 | Diagonal tension failure |
| BF-L-LB | F2 | 1 | 16 | 1.0 | Flexural compression failure |
| BF-L-SB-2 | F3 | 2 | 17 | 1.0 | Flexural compression failure |
| BF-L-LB-UE | F4 | 2 | 15 | 1.0 | Flexural tension failure and flexural compression failure |
| BF-L-LB-UE5 | F5 | 0 | 17 | 1.5 | Flexural compression failure |
| BF-L-SB-UE | F6 | 2 | 19 | 2.0 | Flexural tension failure and flexural compression failure |
| BF-L-SB-UE2 | F7 | 1 | 19 | 1.0 | Flexural tension failure |
| BF-L-LBT-UE | F8 | 0 | 15 | 1.0 | Flexural compression failure |
Comparison between experimental, numerical, and analytical analysis_
| Exp. | GiD | Analy. | Evaluation | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Beam ID | P u (kN) | M u (kN m) | V u (kN) | Δ u (mm) | P u (kN) | M u (kN m) | V u (kN) | Δ u (mm) | P u (kN) | M u (kN m) | V u (kN) | Δ u (mm) | P u.Exp./P u.GiD | P u.Exp./P u.Analy. | Δ u.Exp./Δ u.GiD | Δ u.Exp./Δ u.Analy. |
| F1 | 51 | 17.0 | 25.5 | 13 | 49.8 | 17 | 25.5 | 12 | 54.2 | 15.4 | — | 9.4 | 1.024 | 0.941 | 1.08 | 1.38 |
| F2 | 61.4 | 20.5 | 30.7 | 10.8 | 67.5 | 22.5 | 33.8 | 7.5 | 64 | 21.4 | — | 10.1 | 0.909 | 0.959 | 1.44 | 1.07 |
| F5 | 111.8 | 37.3 | 55.9 | 18.5 | 100.5 | 33.5 | 50.3 | 18 | — | — | — | — | 1.112 | — | 1.03 | — |