## 4 Numerical Model of the Retrofitted Joints
### Pushover Analysis of the Retrofitted Connection  
Once the numerical model was validated, the CFRP-retrofitted RC joint was analyzed. As stated earlier, the target of this research was to evaluate the ability of the selected CFRP retrofit scheme by shifting the place of the plastic hinges off the column face. However, the selected flange-bonded retrofitting scheme is shown in Figure 6b. In a parametric study, the thickness and number of CFRP sheets required for a successful plastic hinge relocation into the beam were to be determined.  
To this end, the non-linear pushover analysis of the joint was performed using different CFRP overlay thicknesses, and for each thickness, the strain state in the beam's tensile reinforcements was considered for locating the true position of the plastic hinge. The joint was then retrofitted with 4, 5, and 7 layers of CFRP laminates, corresponding, respectively, to thicknesses of 0.66 mm, 0.825 mm, and 1.155 mm. As shown in Figure 8b, the maximum strain variation in the longitudinal tensile reinforcements of the beam retrofitted with 4, 5, and 7 layers of CFRP is compared with reinforcement strain variation in the original (non-retrofitted) beam.  
Moreover, Figure 8b demonstrates that for the original joint, the maximum strain in steel reinforcement corresponding to plastic hinge location occurs in the vicinity of the column. While the connection is retrofitted using four layers of laminates, there will be two peaks, one close to the column and the other at the end section of CFRP sheets. These two peaks are close in value; it cannot be stated that a safe relocation of the plastic hinge has followed. However, once five layers of CFRP sheets are used to retrofit the joint, the reinforcement strain at the end of the CFRP overlay evidently dominates the strain formed at the column face. This indicates a successful relocation of the hinge over the cover. Highernumbers of CFRP layers would also lead to such relocation, and the retrofitting would then be more expensive. Therefore, for this joint, a five-layer coat is considered as the optimal thickness for successful plastic hinge relocation.  
Figure 8: Load–displacement and strain results.  
Figure 10: Strain contours of the joint.  
In Figure 9, the stress counter indicates that in the control sample (CS1), the maximum stress under applied loads appears at the contact point of the beam-column, specifically at the top part of the beam. However, in the retrofitted joint (RS1), the peak stress occurs in the beam, away from the beam-column connection surface. These results reveal that bonding the flange with CFRP leads to a shift in the position of the peak stress from the beam-column contact point to a location along the beam length, away from the joint.  
Similarly, in Figure 10, the strain counter shows that in the CS1 joint, the maximum strain (deformation) appears at the contact surface of the beam-column in the tensile part (top of the right beam and bottom of the left beam). Hence, in the RS1 joint, the peak strain and consequent plastic hinges are observed to occur in the beams, away from the beam-column connection. These results demonstrate that by employing the proposed retrofitting technique, the position of plastic hinge occurrence has successfully shifted from the near beam-column connection face to the beam length at a further distance from the joint area. Therefore, the beam-column joint is able to function during applied loads and provide structural integrity and stability.  
However, practically, in order to appropriately design for retrofitting scheme by using flange-bonded CFRP layers, it is recommended to add a large enough number of CFRP layers in the critical length of the beam beside the joint (preferably equal to the depth of the beam) in order to relocate the plastic hinge from the joint area to the length of the beam which is not critical for the stability of the structure. The number of CFRP layers can be estimated based on the amount of imposed shear force and bending moment at the beam and column in the joint.