1 Introduction
2 Research Significance
3 Experimental Work
Beam | L (mm) | L/d | f′c (MPa) | Ec (GPa) | Tension long. steel | Shear reinforcement | ||||
---|---|---|---|---|---|---|---|---|---|---|
Nos. | ϕ (mm) | fy (MPa) | ϕ (mm) | s (mm) | fy (MPa) | |||||
B3.4-2 | 1020 | 3.37 | 21.73 | 23.5 | 2 | 12 | 596.6 | 6 | 150 | 425.8 |
B3.4-3 | 1020 | 3.37 | 25.52 | 22.5 | 3 | 85 | ||||
B2.7-2 | 825 | 2.72 | 31.65 | 26.1 | 2 | 110 | ||||
B2.7-3 | 825 | 2.72 | 26.59 | 24.2 | 3 | 60 |
4 Finite Element Analysis
4.1 Material Constitutive Model
4.2 Bond-Slip Interface
4.3 Finite Element Model
5 Results and Discussions
5.1 Load-Deformation Analysis
Beam | Pmax (kN) | ∆max (mm) | ||||
---|---|---|---|---|---|---|
Exp | FEM | FEM/Exp | Exp | FEM | FEM/Exp | |
3.4-2 | 85.6 | 86.9 | 1.09 | 19.4 | 19.5 | 1.01 |
3.4-3 | 125.4 | 123.8 | 0.99 | 36.4 | 17.4 | 0.48 |
2.7-2 | 111.1 | 110.5 | 0.99 | 44.5 | 29.9 | 0.67 |
2.7-3 | 164.3 | 157.9 | 0.96 | 33.1 | 21.9 | 0.66 |
5.2 Deformation Components
5.3 Crack Pattern and Failure Mode
5.4 Effective Stiffness
Beam | \(\kappa_{exp}\) | \(\kappa_{FEA}\) | \(\kappa_{Eq}\) | \(\kappa_{FEA}\)/\(\kappa_{exp}\) | \(\kappa_{Eq}\)/\(\kappa_{exp}\) |
---|---|---|---|---|---|
B3.4-2 | 15.1 | 10.6 | 10.5 | 0.70 | 0.69 |
B3.4-3 | 8.72 | 12.4 | 11.8 | 1.42 | 1.35 |
B2.7-2 | 5.43 | 10.3 | 6.79 | 1.90 | 1.25 |
B2.7-3 | 8.71 | 12.2 | 9.13 | 1.39 | 1.05 |
6 Conclusions
- Modeling the bond-slip is necessary to better simulate the overall behavior of the beams. When a perfect bond is assumed, it is observed that there is a sudden drop in the maximum capacity due to stress redistribution in the elements. This phenomenon is eliminated when the slip of reinforcement is modeled, with improvement in the prediction of stiffness.
- The model developed is able to predict the behavior of the beams accurately, especially the maximum load capacity. The maximum deformation was found to be underestimated, due to the inability of the model to accurately determine the shear deformation.
- The deformation of the beam was divided into two different components, namely shear and flexural deformations. The shear deformation was found to increase beyond cracking, becomes significant before yielding (20 to 27 percent of the total deformation), and is found to be larger for a shorter beam. The shear deformation was underestimated for all beams, signifying the inability of the finite element model to accurately estimate the shear deformation. The flexural deformation (including slip) in the finite element model was well determined, where the slip becomes significant as the concrete cracks. This shows that the slip is very important in coupling beams and should be modeled.
- The finite element model developed was found to be able to predict the failure mode, where most of the beams fail in flexure.
- The effective stiffness from the experiment is compared to the one obtained from the finite element and an analytical equation. It is found that the equation estimated the effective stiffness better than the finite element result. Hence, the finite element might not be suitable for its determination, as it generally gives an over prediction of the effective stiffness.