1 Introduction
2 Experimental Program
2.1 Test Matrix
Beam ID | Opening size (mm) | Type of loading | Strengthening scheme | No. of specimens | Notes | |
---|---|---|---|---|---|---|
Depth, ho | Length, ℓo | |||||
BC-N-4PB | No opening | 4-point bending | Unstrengthened | 1 | Control specimen | |
BC-O1-4PB | 225 | 450 | 4-point bending | Unstrengthened | 1 | Control specimen |
BC-N-CPL | No opening | Center-point loading | Unstrengthened | 1 | Control specimen | |
BC-O1-CPL | 225 | 450 | Center-point loading | Unstrengthened | 1 | Control specimen |
BS1-O1-CPL | 225 | 450 | Center-point loading | Strengthened with scheme-1: 2 layers (0°/90°) of carbon/epoxy system (see Fig. 4) | 1 | |
BC-O2-CPL | 225 | 900 | Center-point loading | Unstrengthened | 1 | Control specimen |
BS2-O2-CPL | 225 | 900 | Center-point loading | Strengthened with scheme-2: 2 layers (0°/90°) of E-glass/epoxy system + 5 mm thick steel plates (see Fig. 6) | 1 | |
Total no. of specimens | 7 |
2.2 Test Specimen Details and Preparation
2.3 Material Properties
Concrete | |
---|---|
Material model | Type 159 (MAT_CSCM_CONCRETE) |
Density (kg/m3) | 2320 |
Uniaxial compressive strength (MPa) | 50 |
Max aggregate size (mm) | 10 |
Steel rebars, threaded rods and plates | ф8 | ф10 | ф16 | Threaded rods | Plates |
---|---|---|---|---|---|
Material model | Type 24 (MAT_PIECEWISE_LINEAR_PLASTICITY) | ||||
Density (kg/m3) | 7850 | ||||
Young’s modulus (GPa) | 200 | ||||
Poisson’s ratio | 0.3 | ||||
Yield stress (MPa) | 570 | 575 | 575 | 350 | 250 |
Tangent modulus (MPa) | 0 | 982 | 982 | 0 | 0 |
Plastic strain to failure (%) | 11.7 | 11.7 | 11.7 | 19.8 | 19.9 |
FRP material | CFRP system | GFRP system |
---|---|---|
Material model | Type 54-55 (MAT_ENHANCED_COMPOSITE_DAMAGE) | |
Density (kg/m3) | 1740 | 2550 |
Thickness per layer (mm) | 1.0 | 1.3 |
Young’s modulus in long. dir. (GPa) | 82 | 20.9 |
Young’s modulus in transverse dir. (GPa) | 3.6 | 0.9 |
Longitudinal tensile strength (MPa) | 834 | 460 |
Transverse tensile strength (MPa) | 83.4 | 46 |
2.4 Instrumentation and Test Setup
3 Discussion of Test Results
Beam ID | Results | Py (kN) | Pu (kN) | Δy (mm) | Δu (mm) | Ks (kN/mm) | μΔ | Eu (kN·m) | Failure mode |
---|---|---|---|---|---|---|---|---|---|
BC-N-4PB | EXP | 208 | 239 | 9.4 | 83.9 | 22.1 | 8.9 | 17,566 | Y-CC |
FE | 226 | 238 | 9.4 | 85.7 | 24.2 | 9.1 | 18,208 | Y-CC | |
EXP/FE | 0.92 | 1.00 | 1.00 | 0.98 | 0.92 | 0.98 | 0.96 | ||
BC-O1-4PB | EXP | 215 | 244 | 8.9 | 34.2 | 24.2 | 3.8 | 6876 | Y-CC |
FE | 216 | 231 | 9.5 | 35.7 | 22.8 | 3.8 | 7179 | Y-CC | |
EXP/FE | 0.99 | 1.05 | 0.94 | 0.96 | 1.06 | 1.02 | 0.96 | ||
BC-N-CPL | EXP | 180 | 217 | 7.5 | 76.9 | 24.0 | 10.3 | 15,283 | Y-CC |
FE | 178 | 204 | 7.0 | 85.0 | 25.3 | 12.1 | 16,358 | Y-CC | |
EXP/FE | 1.01 | 1.06 | 1.07 | 0.90 | 0.95 | 0.85 | 0.93 | ||
BC-O1-CPL | EXP | NY | 181 | NY | 7.0 | 25.8 | – | 766 | SF-TC |
FE | NY | 172 | NY | 7.6 | 22.7 | – | 827 | SF-TC | |
EXP/FE | – | 1.05 | – | 0.92 | 1.14 | – | 0.93 | ||
BS1-O1-CPL | EXP | NY | 193 | NY | 8.6 | 22.4 | – | 1001 | DB-SF-TC |
FE | NY | 185 | NY | 9.1 | 20.3 | – | 1039 | DB-SF-TC | |
EXP/FE | – | 1.05 | – | 0.95 | 1.10 | – | 0.96 | ||
BC-O2-CPL | EXP | NY | 106 | NY | 3.5 | 30.2 | – | 181 | SF-TC |
FE | NY | 96 | NY | 3.9 | 25.0 | – | 211 | SF-TC | |
EXP/FE | – | 1.10 | – | 0.91 | 1.21 | – | 0.86 | ||
BS2-O2-CPL | EXP | NY | 201 | NY | 6.4 | 31.4 | – | 788 | BKL-FF-TC |
FE | NY | 192 | NY | 5.7 | 33.8 | – | 637 | BKL-FF-TC | |
EXP/FE | – | 1.05 | – | 1.13 | 0.93 | – | 1.24 |
Beam ID | Results | Strain in bottom rebars at mid-span (με)a | Strain in top rebars at mid-span (με)a | Strain in first FRP layer at mid-span (με) | Strain in second FRP layer at mid-depth of opening edge (με) | Mid-span steel plate strain at mid-depth of top chord (με)a | |
---|---|---|---|---|---|---|---|
At mid-depth of bottom chord | At mid-depth of top chord | ||||||
BC-N-4PB | EXP | NA |
−
14,841
| – | – | – | – |
FE |
69,540
|
−
14,036
| – | – | – | – | |
EXP/FE | – | 1.06 | – | – | – | – | |
BC-O1-4PB | EXP |
26,705
|
−
7683
| – | – | – | – |
FE |
31,354
|
−
7797
| – | – | – | – | |
EXP/FE | 0.85 | 0.99 | – | – | – | – | |
BC-N-CPL | EXP | NA |
−
5407
| – | – | – | – |
FE |
81,413
|
−
4980
| – | – | – | – | |
EXP/FE | – | 1.09 | – | – | – | – | |
BC-O1-CPL | EXP | 2609 | 434 | – | – | – | – |
FE | 2583 | 460 | – | – | – | – | |
EXP/FE | 1.01 | 0.94 | – | – | – | – | |
BS1-O1-CPL | EXP | 2549 | 350 | 2526 | 858 | 1931 | – |
FE | 2711 | 380 | 2771 | 691 | 2116 | – | |
EXP/FE | 0.94 | 0.92 | 0.91 | 1.24 | 0.91 | – | |
BC-O2-CPL | EXP | NA |
19,297
| – | – | – | – |
FE | 1303 |
21,894
| – | – | – | – | |
EXP/FE | – | 0.88 | – | – | – | – | |
BS2-O2-CPL | EXP | 1990 |
8995
| 1366 | – | 762 |
2807
|
FE | 2296 |
7768
| 1202 | – | 824 |
3033
| |
EXP/FE | 0.87 | 1.16 | 1.14 | – | 0.92 | 0.93 |
4 Finite Element Modeling
5 Validation of Finite Element Analysis
5.1 Mode of Failure
5.2 Load-Deflection Curves
5.3 Strain Gage Results
6 Parametric Study
6.1 Effect of Strengthening Scheme
Beam ID | Opening size (mm) | ℓo/hc | Type of loading | Strengthening scheme | FE results | |||||
---|---|---|---|---|---|---|---|---|---|---|
h
o
| ℓo | Pu (kN) | εsu,b (με) | εsu,t (με) | εspu (με) | Failure mode | ||||
Effect of strengthening scheme | ||||||||||
BS1-O1-CPL | 225 | 450 | 4.00 | CPL | Scheme-1 | 185 | 2711 | 380 | – | DB-SF-TC |
BS3-O1-CPL | 225 | 450 | 4.00 | CPL | Scheme-3 | 236 | 11,620 | 468 | – | FF-BM |
BS4-O1-CPL | 225 | 450 | 4.00 | CPL | Scheme-4 | 239 | 12,285 | 477 | 15,657 | FF-BM |
BS5-O1-CPL | 225 | 450 | 4.00 | CPL | Scheme-5 | 239 | 11,530 | 710 | 9334 | FF-BM |
BS6-O1-CPL | 225 | 450 | 4.00 | CPL | Scheme-6 | 241 | 11,492 | 706 | 5203 | FF-BM |
BS2-O2-CPL | 225 | 900 | 8.00 | CPL | Scheme-2 | 192 | 2296 | 7768 | 43,317 | BKL-FF-TC |
BS3-O2-CPL | 225 | 900 | 8.00 | CPL | Scheme-3 | 201 | 2420 | 7989 | 49,394 | FF-TC |
BS4-O2-CPL | 225 | 900 | 8.00 | CPL | Scheme-4 | 204 | 2424 | 4464 | 48,903 | FF-TC |
BS5-O2-CPL | 225 | 900 | 8.00 | CPL | Scheme-5 | 209 | 2435 | 6429 | 33,688 | FF-TC |
BS6-O2-CPL | 225 | 900 | 8.00 | CPL | Scheme-6 | 214 | 2609 | 3781 | 30,634 | FF-TC |
Effect of opening size | ||||||||||
BU-0.0-CPLa | No opening | 0 | CPL | Unstrengthened | 204 | 81,413 | –4980 | – | FF-BM | |
BU-1.0-CPL | 225 | 113 | 1.00 | CPL | Unstrengthened | 203 | 55,071 | 2575 | – | FF-BM |
BU-2.0-CPL | 225 | 225 | 2.00 | CPL | Unstrengthened | 200 | 39,071 | 2319 | – | FF-BM |
BU-3.0-CPL | 225 | 338 | 3.00 | CPL | Unstrengthened | 198 | 24,286 | 2184 | – | FF-BM |
BU-4.0-CPLb | 225 | 450 | 4.00 | CPL | Unstrengthened | 172 | 2583 | 460 | – | SF-TC |
BS4-4.0-CPLc | 225 | 450 | 4.00 | CPL | Scheme-4 | 239 | 12,285 | 477 | 15,657 | FF-BM |
BU-5.0-CPL | 225 | 563 | 5.00 | CPL | Unstrengthened | 138 | 2040 | 689 | – | SF-TC |
BS4-5.0-CPL | 225 | 563 | 5.00 | CPL | Scheme-4 | 234 | 6444 | 852 | 18,523 | FF-BM |
BU-6.0-CPL | 225 | 675 | 6.00 | CPL | Unstrengthened | 127 | 2006 | 12,855 | – | SF-TC |
BS4-6.0-CPL | 225 | 675 | 6.00 | CPL | Scheme-4 | 221 | 2881 | 1208 | 20,500 | FF-BM |
BU-8.0-CPLd | 225 | 900 | 8.00 | CPL | Unstrengthened | 96 | 1303 | 21,894 | – | SF-TC |
BS4-8.0-CPLe | 225 | 900 | 8.00 | CPL | Scheme-4 | 204 | 2424 | 4464 | 48,903 | FF-TC |
BU-10.0-CPL | 225 | 1125 | 10.00 | CPL | Unstrengthened | 54 | 755 | 27,289 | – | FF-TC |
BS4-10.0-CPL | 225 | 1125 | 10.00 | CPL | Scheme-4 | 169 | 1880 | 11,180 | 55,100 | FF-TC |
BU-12.0-CPL | 225 | 1350 | 12.00 | CPL | Unstrengthened | 42 | 211 | 30,687 | – | FF-TC |
BS4-12.0-CPL | 225 | 1350 | 12.00 | CPL | Scheme-4 | 132 | 1388 | 13,344 | 62,224 | FF-TC |