Table 1.
Mixture composition of concrete mixture
| Material | Weight (kg/m3) |
|---|---|
| Cement | 650 |
| Silica sand | 528 |
| Coarse aggregate (Nominal size = 10 mm) | 770 |
| Crush sand | 264 |
| Water (w/c = 0.25) | 162.5 |
| Super-plasticizer(Gli-110) | 3 Liters |
Table 2.
Mechanical characterization of steel reinforcement
| Mechanical Property | Bar diameter | Test Standard | |
|---|---|---|---|
| 10 mm | 6 mm | ||
| Yield strength, (MPa) | 525 | 280 | ASTM A370 (2017) |
| Ultimate strength, (MPa) | 578 | 380 | |
| Modulus of elasticity, (GPa) | 200 | 200 | |
Table 3.
Characteristics of the strengthening materials
| Item | Value |
|---|---|
| CFRP composite | |
| Type of FRP | Unidirectional CFRP sheet |
| Longitudinal elastic modulus of the primary fibers. (GPa) | 77.3 |
| Transverse elastic modulus relative to the primary fiber direction. (MPa) | 40.6 |
| Strain at fracture along the primary fiber direction (%) | 1.1 |
| Maximum tensile strength along the primary fiber direction (MPa) | 846 |
| Thickness of each individual layer, tf (mm) | 1.0 |
| Epoxy | |
| Density (kg /l) | 1.16 |
| Tensile strength of the adhesive (MPa) | > 4.0 (7 days) |
| Tensile modulus of elasticity (GPa) | 3.5 (7 days) |
| Sikadur_31 Thixotropic epoxy_resin mortar | |
| Tensile strength of the adhesive (MPa) | 15 |
| Density (kg /l) | 1.65 |
| Modulus of Elasticity (GPa) | 4.3 |
Fig. 1.
Test specimens: (a) DB-S-F; (b) DB-NS0; and (c) DB-FRP. (All dimensions are in mm)
Table 4.
Overview of test samples
| Specimen | Left half span | Right half span | ||
|---|---|---|---|---|
| Shear stirrups | Shear strengthening | Shear stirrups | Shear strengthening | |
| DB-S-F | 2L-f6@100 | None | 2L-f6@100 | None |
| DB-NS0 | 2L-f6@100 | None | None | None |
| DB-FRP | 2L-f6@100 | Yes | None | The specimen has two layers of U-wraps of FRP (25 mm wide) spaced at 100 mm intervals, along with a single layer of horizontally bonded FRP strips (50 mm wide) placed at the mid-depth on each face. |
Fig. 2.
Strain gauge locations
Fig. 3.
Failure pattern of specimen DB-S-F
Fig. 4.
Failure pattern of specimen DB-NS0
Fig. 5.
Failure pattern of specimen DB-FRP
Fig. 7.
Load displacement of specimen DB-NS0
Fig. 9.
The idealized stress-strain curve for steel reinforcement
Fig. 6.
Load displacement of specimen DB-S-F
Fig. 8.
Load displacement of specimen DB-S
Table 5.
Test results of all tested specimens
| Beam description of half span part | Shear strength (kN) | Note |
|---|---|---|
| Beam part with no stirrups | 67.1 (DB-NS0) | – |
| Beam part having stirrups in all span | 82.5 (DB-S-F) | 23% improvement as compared to DB-NS0 |
| RC beam part with no stirrups but strengthened using NSM U-wrap CFRP strips | 112 (DB-FRP) | 82% improvement as compared to DB-NS0 |
Table 6.
Constitutive material models parameters of concrete, Sikadur resin, and CFRP
| Material | Parameters | Values | Denotation |
|---|---|---|---|
| Concrete | Dilation angle (ψ) | 32° | Calibrated value |
| Eccentricity (ε) | 0.1 | ABAQUS (default value) | |
| Stress ratio (σb0/σc0) | 1.16 | ABAQUS (default value) | |
| Shape factor (Kc) | 0.667 | ABAQUS (default value) | |
| Sikadur mortar | Dilation angle (ψ) | 40° | Calibrated value |
| Eccentricity (ε) | 0.1 | ABAQUS (default value) | |
| Stress ratio (σb0/σc0) | 1.16 | ABAQUS (default value) | |
| Shape factor (Kc) | 0.667 | ABAQUS (default value) | |
| CFRP sheet | Poisson’s ratio (ν) | 0.3 | Widely used in FE modeling |
| Modulus of Elasticity (E) | 230000 MPa | Given by the manufacturer | |
| Tensile strength (longitudinal: σt1) | 1122 MPa | Experimental Value | |
| Compressive strength (longitudinal: σc1) | 10 MPa | Al-Mekhlafi, et al. [11] | |
| Shear strength (longitudinal: τf1) | 10 MPa | ||
| Transversal tensile strength (σt2) | 10 MPa | ||
| Compressive strength (transversal: σc2) | 10 MPa | ||
| Shear strength (transversal: τf2) | 10 MPa |
Fig. 10.
FE model set-up: (a) Finite elements types; (b) Loading and boundary conditions; (c) Meshing size.
Table 7.
Mesh convergence analysis results
| Mesh types | Beam elements size | Experimental flexural strength (kN) | FE flexural strength (kN) | Experimental/FE |
|---|---|---|---|---|
| Type 1 | 25 | 165 | 185 | 89.2% |
| Type 2 | 15 | 178 | 92.7% | |
| Type 3 | 7 | 172 | 95.6% |
Fig. 11.
Failure modes for FE and experimental deep beams: (a) DB-S-F; (b) DB-NS0; (c) DB-FRP
Fig. 12.
FE and experimental load versus mid-span deflection curves for deep beams