1 Introduction
2 Literature Review
2.1 Recent Research on Strengthening of Interior Slab-Column Connections Using Synthetic Sheets
2.2 Recent Research on Strengthening Beams and Columns Using HFRP Sheets
2.3 Recent Research Using Concrete Damaged Plasticity (CDP) Model to Simulate Slab-Column Connections
3 Research Significance and Scope
4 Experimental Test Program
4.1 Test Specimens and Parameters
Group | Specimen designation | Slab Thickness (mm) | Steel ratio (%) | FRP type | FRP width (cm) | No. of layers | Strengthening configuration |
---|---|---|---|---|---|---|---|
SA | SA0 | 55 | 1 | – | – | – | – |
SA-H15-A | 55 | 1 | HFRP | 15 cm | 1 | Adjacent | |
SA-H15-O | 55 | 1 | HFRP | 15 cm | 1 | Offset | |
SA-H20-A | 55 | 1 | HFRP | 20 cm | 1 | Adjacent | |
SA-C15-A | 55 | 1 | CFRP | 15 cm | 1 | Adjacent | |
SB | SB0 | 75 | 1 | – | – | – | – |
SB-H15-A | 75 | 1 | HFRP | 15 cm | 1 | Adjacent | |
SB-H15-O | 75 | 1 | HFRP | 15 cm | 1 | Offset | |
SB-H20-A | 75 | 1 | HFRP | 20 cm | 1 | Adjacent | |
SB-H15(2)-A | 75 | 1 | HFRP | 15 cm | 2 | Adjacent | |
SB-C15-A | 75 | 1 | CFRP | 15 cm | 1 | Adjacent |
4.2 Testing Materials
4.2.1 Concrete
4.2.2 Reinforcing Steel
4.2.3 HFRP Fabric Sheet
4.2.4 CFRP Sheet
CFRP Strips (SikaWrap-230 C) | |
---|---|
Width (mm) | 1000 |
Thickness (mm) | 0.129 |
Modulus of elasticity (GPa) | 230 |
Tensile strength (MPa) | 3,500 |
Elongation at break (%) | 1.59 |
Apparent density (g/cm3) | 1.82 |
4.2.5 The Adhesive Sikadur-330
Adhesive Paste (Sikadur-330) | |
---|---|
Density (Kg/L) | 1.3 |
Tensile strength at 7 days (MPa) | 30 |
Elongation at break at 7 days (%) | 0.9 |
Modulus of elasticity at 7 days (MPa) | 4,500 |
Flexural Modulus at 7 days (MPa) | 3,800 |
4.2.6 Strengthening Procedure
4.3 Test Setup
4.4 Preliminary Trial Tests
5 Experimental Test Results
5.1 Failure Modes
5.2 Presentation and Analysis of Test Results
Group | Specimen Designation | \(f\)(MPa) | Normalized ultimate load PU (kN) | Ratio of ultimate loads (%) | Deflection at ultimate load (mm) | Fracture energy (kN-m) | Energy Ductility Index | Initial stiffness (kN/mm) | Stiffness Increase (%) |
---|---|---|---|---|---|---|---|---|---|
SA | SA0* | 43.7 | 49 | - | 14.58 | 0.563 | - | 4.6 | - |
SA-H15-A | 36.5 | 59.6 | 21.63% | 11.763 | 0.3935 | 0.7 | 5.58 | 20.9% | |
SA-H15-O | 36.5 | 62.94 | 28.44% | 11.84 | 0.4466 | 0.79 | 6.32 | 37.03% | |
SA-H20-A* | 32.4 | 69.16 | 41.14% | 13.15 | 0.752 | 1.34 | 7.232 | 56.8% | |
SA-C15-A* | 38.3 | 69.7 | 42.24% | 10.94 | 0.813 | 1.44 | 7.14 | 54.8% | |
SB | SB0 | 33.6 | 93.57 | - | 11.77 | 0.711 | - | 9.81 | - |
SB-H15-A | 36.5 | 98.9 | 5.7% | 10.09 | 0.566 | 0.796 | 10.742 | 9.5% | |
SB-H15-O | 30 | 108.25 | 15.7% | 11.6 | 0.729 | 1.03 | 11.324 | 15.4% | |
SB-H20-A | 36.5 | 100.35 | 7.25% | 10.16 | 0.597 | 0.84 | 11.7 | 19.25% | |
SB-H15(2)-A | 35 | 102.43 | 9.47% | 11.32 | 0.6972 | 0.98 | 11.48 | 17% | |
SB-C15-A | 41.5 | 117.01 | 25% | 11.07 | 0.7166 | 1 | 10.89 | 11.12% |
5.2.1 Load–Deflection Response
5.2.2 Influence of the Span-to-Depth Ratio
5.2.3 Influence of the Width of HFRP Sheets
5.2.4 Influence of Location of HFRP Sheets
5.2.5 Influence of Number of Layers of HFRP Sheets
5.2.6 Influence of the Type of Strengthening Sheet: HFRP versus CFRP
5.2.7 HFRP and CFRP Strains
Specimen designation | Ultimate strain (µε) | |
---|---|---|
Location of strain gauge | ||
Bottom sheets | Top sheets | |
SA-H15-A | 3,660.8 | – |
SA-H15-O | 3,928 | 5,223.4 |
SA-H20-A | – | 5,773.2 |
SA-C15-A | 3,219.8 | 3,105.1 |
SB-H15-A | 6,517.5 | 4,184.2 |
SB-H15-O | 9,750.8 | 2,572.5 |
SB-H20-A | 9,137.4 | – |
SB-H15(2)-A | 4,226.2 | 4,858.1 |
SB-C15-A | 6,767.1 | 5,223.8 |
6 Numerical and Analytical Investigations
6.1 Numerical Modeling
6.1.1 Finite-Element Model Construction
Parameters | Sikadur 330 | |
---|---|---|
Elastic modulus of adhesive (GPa) | Ea | 4.82 |
Nominal stress normal mode only (MPa) | tn | 31.28 |
Nominal stress shear directions (MPa) | ts, tt | 31.28 |
Elastic stiffness of the adhesive in normal direction (N/mm3) | Knn | 4.72 × 1013 |
Elastic stiffness of the adhesive in shear directions (N/mm3) | Kss, Ktt | 2.36 × 1013 |
Fracture energy of the adhesive in normal direction (N/mm) | Gn | 1 |
Fracture energy of the adhesive in shear directions (N/mm) | Gs, Gt | 1.25 |
-
Dilation angle (\(\boldsymbol{\varphi }\)): According to Genikomsou (2015), the effective range of the dilation angle is between 30º and 40º; a value of 36º was used in the analysis.
-
Shape factor coefficient (Kc): For normal concrete strength, this factor ranges between 0.64 and 0.8; a value of 0.67 was used (Smith, 2009).
-
Eccentricity (\({\varvec{\varepsilon}}\)): A default value of 0.1 was taken for the potential flow eccentricity (Smith, 2009).
-
Stress parameters (Fb0/fc0): For normal strength concrete, the value ranges between 1.10 and 1.16; a value of 1.16 was used in this research (Lee & Fenves, 1998).
-
The viscosity parameter (\({\varvec{\mu}})\): This parameter was determined by conducting a sensitive analysis (0.0001).
Dilation Angle (\(\boldsymbol{\varphi }\)) | Eccentricity (\({\varvec{\varepsilon}})\) | Stress parameters (Fb0/fc0) | Shape factor (Kc) | Viscosity Parameter (\({\varvec{\mu}})\) |
---|---|---|---|---|
36 | 0.1 | 1.16 | 0.667 | 0.0001 (calibrated) |
Parameter | Value |
---|---|
Modulus of elasticity (GPa) | 210 |
Poison's ratio | 0.3 |
Yield stress (MPa) | 570 |
Failure stress (MPa) | 640 |
Parameter | CFRP | HFRP |
---|---|---|
Tensile strength (MPa) | 3500 | 30 |
Modulus of elasticity (MPa) | 230,000 | 3700 |
Poison's ratio | 0.25 | 0.3 |
Thickness (mm) | 0.13 | 1.2 |
6.1.2 Calibration of the Model
6.1.3 FEM Results and Discussion
Specimen designation | Experimental results | Numerical results | PUFEM / PUexp | ∆FEM / ∆exp | ||
---|---|---|---|---|---|---|
Ultimate Load PUexp (kN) | Deflection at PU∆exp (mm) | Ultimate Load PUFEM (kN) | Deflection at PU∆FEM (mm) | |||
SB0 | 93.57 | 11.77 | 93.93 | 11.45 | 1.004 | 0.973 |
SB-H15-A | 98.9 | 10.09 | 98.5 | 11.23 | 0.996 | 1.113 |
SB-C15-A | 117.02 | 11.07 | 112.4 | 12.24 | 0.961 | 1.106 |
6.2 Analytical Modeling
Specimen designation | Pu test (kN) | Afrp (mm2) | m (kN-m/m) | Pflex (kN) | Pu calc (kN) | Pu test/Pu calc |
---|---|---|---|---|---|---|
SA-H15-A | 59.6 | 180 | 7.524 | 60.43 | 58.97 | 1.011 |
SA-H15-O | 62.9 | 313.2 | 7.807 | 62.7 | 59.8 | 1.052 |
SA-H20-A | 69.16 | 240 | 7.65 | 61.45 | 59.35 | 1.165 |
SA-C15-A | 69.7 | 19.5 | 8.7 | 69.88 | 62.2 | 1.121 |
SB-H15-A | 98.9 | 180 | 17 | 136.57 | 114.247 | 0.866 |
SB-H15-O | 108.25 | 378 | 17.57 | 141.08 | 115.32 | 0.939 |
SB-H15(2)-A | 102.43 | 360 | 17.52 | 140.67 | 115.22 | 0.889 |
SB-H20-A | 100.35 | 240 | 17.176 | 137.94 | 114.58 | 0.876 |
SB-C15-A | 117.01 | 19.5 | 18.58 | 149.22 | 117.14 | 0.999 |
Average | 0.991 | |||||
Standard deviation | 0.108 | |||||
Coefficient of variation (%) | 10.9 |