1 Introduction
2 Evaluation of Existing BCJ’s Shear Strength Models
3 Mechanics of BCJ’s
4 Experimental Program
4.1 Specimen Design
Specimen | Dimensions (mm) | Reinforcement | |||||
---|---|---|---|---|---|---|---|
Beam | Column | ||||||
SP1-SP7 | Beam | Column | Top | Bottom | Stirrups | Main | Ties |
200 × 250 | 200 × 250 | 4 Ø20 | 4 Ø20 | Ø8 @ 50 | 6 Ø20 | Ø8 @ 50 |
4.2 Material Properties
Specimen | Bar size (mm) | Stress (MPa) | Strain µε (Micro strain) | ||
---|---|---|---|---|---|
f
y
|
f
u
|
∈
y
|
∈
u
| ||
SP1-SP7 | Ø8 | 580 | 667 | 3000 | 10,500 |
Ø20 | 605 | 695 | 3100 | 10,600 |
4.3 Test Setup Details
4.4 Specimens Instrumentation
4.5 Loading Procedure
Specimen ID | Magnitude of axial load (kN) | Axial load ratio (ALR),
\( \frac{N}{{A_{g} f^{\prime}_{c} }} \)
| Test method |
---|---|---|---|
SP-1 | 0 | 0.00 | Monotonic |
SP-2 | 200 | 0.19 | Monotonic |
SP-3 | 600 | 0.57 | Monotonic |
SP-4 | 200 | 0.19 | Reverse cyclic |
SP-5 | 600 | 0.57 | Reverse cyclic |
SP-6 | 1050 | 0.70 | Monotonic |
SP-7 | 1050 | 0.70 | Reverse cyclic |
5 Experimental Results and Discussions
5.1 Effect of Axial Load on Shear Strength of BCJ Subjected to Monotonic Loading
5.2 Effect of Axial Load on Shear Strength of BCJ Subjected to Reverse Cyclic Loading
Specimen ID | Load | σN (f’c %) | ICL (kN) | JCL (kN) | P (kN) | T (kN) | Vu(col) (kN) | Vj(Joint) (kN) | vj(Joint) (MPa) |
---|---|---|---|---|---|---|---|---|---|
SP-1 | M | 0.00 | 16 | 16 | 37 | 166 | 28 | 137 | 2.74 |
SP-2 | M | 0.19 | 29 | 29 | 51 | 212 | 37 | 174 | 3.50 |
SP-3 | M | 0.57 | 38 | 38 | 57 | 254 | 43 | 211 | 4.23 |
SP-6 | M | 0.70 | 45 | 45 | 66 | 310 | 49 | 260 | 5.20 |
SP-4 | RC | 0.19 | 20 | 21 | 41/43 | 182/187 | 31/32 | 152/155 | 2.98/3.09 |
SP-5 | RC | 0.57 | 27 | 36 | 47/50 | 207/210 | 35/37 | 171/172 | 3.43/3.50 |
SP-7 | RC | 0.70 | 51 | 51 | 59/54 | 273/255 | 44/40 | 228/215 | 4.58/4.30 |
6 Numerical Modeling of BCJs
6.1 Finite Element Model
6.1.1 Models to Simulate Cracking in Concrete
6.1.2 Modelling of Concrete
Concrete strength (MPa) | Mass density (tonne/mm3) | Young’s modulus (MPa) | Poisson’s ratio | Dilation angle Ψ (degrees) | Plastic potential eccentricity ϵ | fbo/fco |
b
c
/b
t
|
---|---|---|---|---|---|---|---|
Varies | 2.4E−009 | Variesa | 0.19–0.20 | 36 | 0.1 | 1.16 | 0.7 |
6.1.3 Modelling of Reinforcing Steel and its Bond with Concrete
Elastic modulus (MPa) | 193600/195161 |
---|---|
Poisson’s ratio | 0.3 |
Mass density (tonne/mm3) | 7.85E−009 |
Yield stress (MPa) | 580/605 |
6.2 Validation of Finite Element Model
6.2.1 Specimen SP-1
6.2.2 Specimen SP-2
6.2.3 Specimen SP-3
6.2.4 Specimen SP-6
6.3 Parametric Study Using Finite Element Modeling
Group | M-21 | M-30 | M-36 | M-50 | M-65 |
---|---|---|---|---|---|
f’c
| 21 | 30 | 36 | 50 | 65 |
ALR | |||||
0.00 | M-21-00 | M-30-00 | M-36-00 | M-50-00 | M-65-00 |
0.10 | – | M-30-10 | M-36-10 | M-50-10 | M-65-10 |
0.20 | M-21-19 | M-30-20 | M-36-20 | M-50-20 | M-65-20 |
0.30 | – | M-30-30 | M-36-30 | M-50-30 | M-65-30 |
0.40 | – | M-30-40 | M-36-40 | M-50-40 | M-65-40 |
0.50 | – | M-30-50 | M-36-50 | M-50-50 | M-65-50 |
0.60 | M-21-57 | M-30-60 | M-36-60 | M-50-60 | M-65-60 |
0.70 | – | M-30-70 | M-36-70 | M-50-70 | M-65-70 |
0.80 | M-21-80 | M-30-80 | M-36-80 | M-50-80 | M-65-80 |
0.90 | – | M-30-90 | M-36-90 | M-50-90 | M-65-90 |
1.00 | – | M-30-100 | M-36-100 | M-50-100 | – |
1.05 | – | – | – | – | M-65-AC |
1.08 | – | – | – | M-50-AC | – |
1.10 | M-21-AC | M-30-AC | M-36-110 | – | – |
1.13 | – | – | M-36-AC | – | – |
7 Shear Strength Equation for BCJs
7.1 Development of Shear Strength Equation
7.2 Proposed Shear Strength Equation for BCJs
Axial load ratio \( \frac{N}{{A_{g} f^{\prime}_{c} }} \) | Shear co-efficient | ||
---|---|---|---|
α | β | γ | |
0.00 < ALR ≤ 0.50 | 351 | 100 | 0.21 |
0.50 < ALR ≤ 0.70 | 4 | 0.03 | 1 |
0.70 < ALR ≤ 0.90 | 425 | − 5 | 0.25 |
7.3 Validation of Shear Strength Equation
Researchers | Specimens | Joint type | Joint aspect ratio | \(f^{\prime}_c\) (MPa) | Beam | Axial load ratio (ALR) | VTest (MPa) | VPredicted (MPa) |
\( \frac{{V_{\text{Predicted}} }}{{V_{\text{Test}} }} \)
| ||
---|---|---|---|---|---|---|---|---|---|---|---|
ρbb (%) | ρtb (%) | fyb (MPa) | |||||||||
Hakuto et al. (2000) | 06 | Exterior | 1.1 | 31 | 0.66 | 1 | 308 | 0 | 3.75 | 3.23 | 0.86 |
07 | Exterior | 1.1 | 31 | 0.66 | 1 | 308 | 0 | 4.05 | 3.23 | 0.80 | |
Clyde et al. (2000) | SP 2 | Exterior | 0.89 | 46.2 | 2.45 | 2.45 | 454 | 0.10 | 6.26 | 6.31 | 1.01 |
SP 6 | Exterior | 0.89 | 40.9 | 2.45 | 2.45 | 454 | 0.10 | 6.26 | 5.85 | 0.93 | |
SP 4 | Exterior | 0.89 | 37.0 | 2.45 | 2.45 | 454 | 0.25 | 7.07 | 6.20 | 0.88 | |
SP 5 | Exterior | 0.89 | 40.1 | 2.45 | 2.45 | 454 | 0.25 | 6.83 | 6.54 | 0.96 | |
Pantelides et al. (2008) | SP 1 | Exterior | 1.00 | 33.0 | 1.90 | 1.90 | 459 | 0.10 | 5.39 | 4.65 | 0.86 |
SP 2 | Exterior | 1.00 | 33.0 | 1.90 | 1.90 | 459 | 0.25 | 5.24 | 5.22 | 0.99 | |
SP 3 | Exterior | 1.00 | 34.0 | 1.90 | 1.90 | 459 | 0.10 | 5.08 | 4.74 | 0.93 | |
SP 4 | Exterior | 1.00 | 34.0 | 1.90 | 1.90 | 459 | 0.25 | 5.66 | 5.32 | 0.94 | |
SP 5 | Exterior | 1.00 | 31.6 | 1.90 | 1.90 | 459 | 0.10 | 5.46 | 4.53 | 0.83 | |
SP 6 | Exterior | 1.00 | 31.6 | 1.90 | 1.90 | 459 | 0.25 | 5.46 | 5.07 | 0.93 | |
Wong (2005) | BS-L | Exterior | 1.50 | 30.8 | 0.94 | 0.94 | 520 | 0.15 | 4.05 | 3.47 | 0.86 |
BS-U | Exterior | 1.50 | 30.9 | 0.94 | 0.94 | 520 | 0.15 | 4.06 | 3.47 | 0.86 | |
BS-LL | Exterior | 1.50 | 42.1 | 0.94 | 0.94 | 520 | 0.15 | 5.39 | 4.22 | 0.78 | |
BS-L-LS | Exterior | 1.50 | 31.6 | 0.94 | 0.94 | 520 | 0.15 | 5.06 | 3.52 | 0.70 | |
BS-V2T10 | Exterior | 1.50 | 32.6 | 0.94 | 0.94 | 520 | 0.15 | 3.19 | 3.59 | 1.13 | |
BS-V4T10 | Exterior | 1.50 | 28.3 | 0.94 | 0.94 | 520 | 0.15 | 4.76 | 3.29 | 0.69 | |
BS-L600 | Exterior | 2.00 | 36.4 | 0.68 | 0.68 | 520 | 0.15 | 3.38 | 3.26 | 0.97 | |
Ghobarah and Said (2001) | T 1 | Exterior | 1.00 | 30.9 | 1.20 | 1.20 | 425 | 0.19 | 5.58 | 4.27 | 0.77 |
T 2 | Exterior | 1.00 | 30.9 | 1.20 | 1.20 | 425 | 0.10 | 5.63 | 3.97 | 0.70 | |
Antonopoulos and Triantafillou (2003) | C1 | Exterior | 1.50 | 19.4 | 0.77 | 0.77 | 585 | 0.05 | 2.57 | 2.30 | 0.90 |
C2 | Exterior | 1.50 | 23.7 | 0.77 | 0.77 | 585 | 0.05 | 2.95 | 2.57 | 0.87 | |
Average = 0.88 | |||||||||||
Standard deviation = 0.10 |