# Seismic Tests of Full Scale Reinforced Concrete T Joints with Light External Continuous Composite Rope Strengthening—Joint Deterioration and Failure Assessment

^{1}

^{2}

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## Abstract

**:**

^{−4}rad. The composite strengthening, increases the structural performance of the joint up to 4% drift which corresponds to 68 mm of beam-end displacement and shear deformation of the joint equal to 10 × 10

^{−4}rad. The investigated cases of inadequate existing transverse reinforcement in the joint and light external FRP strengthening provide a unique insight into the required retrofits to achieve different levels of post-yielding displacement ductility under seismic loading at 2%, 3% and 4% drift. It allows for future analytical refinements toward reliable redesign analytical models.

## 1. Introduction

_{max}. The experimental investigation concludes that cyclic loading has a detrimental effect on the performance of the joint. Absence of an internal steel stirrup leads to earlier deterioration of the joint. Suitably designed light strengthening with NSM X-shaped composite ropes may upgrade remarkably the ductility of the beam–column connection, delaying the disintegration of the joint and achieving higher drift levels at failure. The carbon FRP rope follows an improved continuous versatile detailing that may allow for more layers of rope inside the grooves. The experimental results may serve for future development of redesign tools.

## 2. Specimens’ Dimensions, Reinforcement Detailing and Material Properties

#### 2.1. Main Characteristics of As-Built Specimens

_{jhd}= 377 kN and the corresponding shear stress is τ = 3.3 MPa, as considered in Eurocode 8 part 1 or Greek Retrofit Code [39]. According to ACI 318 [40], external joints have to satisfy the relationships ΣΜR

_{c}/MR

_{b}> 1.40 and φV

_{n}> V

_{u}, where φ is the strength reduction factor, V

_{n}the nominal shear strength and V

_{u}the maximum required value of shear. Since ΣMR

_{c}/MR

_{b}= 1.4, the development of a plastic hinge is expected within the critical region of the beam.

_{ult}(and γ

_{ult}= τ

_{ult}/ f

_{c}

^{0.5}). Then, the factor γ

_{ult}is compared to the developed shear τ

_{cal}(and γ

_{cal}= τ

_{cal}/f

_{c}

^{0.5}). The values of γ

_{cal}are little less than the corresponding values of the ultimate shear cracking γ

_{ult}for joints with and without a stirrup inside the joint region. Therefore, it is deduced that the cracking system is expected to be developed both in the beam and the joint body after the yielding of beam tensile reinforcement. These predictions are experimentally verified as it is presented in the subsequent sections. Similarly, the KANEPE model suggests there will be diagonal tensile cracking inside the joint region in both cases, i.e., with or without a stirrup in the joint region.

#### 2.2. Concrete and Steel

_{c}′ = 22.4 MPa, based on the mean value of three standard cylinders with diameter of 150 mm and height 300 mm, tested at 28 days. The compression machine and gathered results are presented in Figure 2. The steel used for the construction of the cages of the internal longitudinal bars and stirrups was of quality B500C, suitable for seismic-resistant structures. The tensile stress at yielding of the steel was equal to 550 MPa and the tensile strength (at ultimate) was 650 MPa.

#### 2.3. Carbon FRP Flexible Ropes and Detailing of NSM Strengthening

_{f}of the carbon fibers of the used ropes A

_{f}> 28 mm

^{2}. It corresponds to an ultimate force of 50 kN/rope cross-section. The carbon FRP rope is delivered already resin-impregnated per carbon filaments by the manufacturer and, therefore, favors easy handling. That is, the composite rope is flexible enough to follow the geometry of the concrete surface without damaging the carbon fibers during the process of the in-situ impregnation of the rope with the adhesive or during stretching of the rope against the concrete surface or against multiple rope rounds. The compressive strength of the adhesive resin for the in-situ application is 34 MPa, its tensile strength in flexure is 41 MPa, the tensile strength is 24 MPa whereas the tensile adhesion strength is given by the manufacturer as >4 MPa. Finally, the compressive strength of the resin paste after seven days is almost 114 MPa [43,44].

## 3. Test Setup and Loading Protocol

_{c}= 0.05 A

_{c}f

_{c}=134 kN throughout the testing procedure.

## 4. Experimental Test Results

_{max}(see [39,41,48]). Therefore, Figure 6 suggests that specimen CON0 fails at a bearing load of 104.5 kN during the 2nd reversal at step 5 which corresponds to 2% drift. Specimen CON1 fails at 106.4 kN load during the 2nd reversal of the 6th step corresponding to 3% drift. Similarly, specimen CON0F2X fails at 105 kN during the 2nd cycle at 3% drift. Finally, CON1F2X fails at 107.4 kN during the 3rd cycle of step 6 at 3% drift. However, the bearing load of the 1st cycle at 4% drift is at 0.76 P

_{max}which is reasonably close to 0.8 P

_{max}limit for CON1F2X. The above results, for all the specimens, are similar and symmetrical for both push and pull directions.

## 5. Elaboration of the P-δ Test Results

#### 5.1. Envelope Curves

#### 5.2. Joint Shear Deformation γ_{avg}

_{avg}is the average value of the joint shear deformation in rad, Δl1 and Δl2 represent the variations in the length of the strings of the diagonal string displacement transducers, L is the initial length of their strings and they are equal to 420 mm, θ is the inclination angle of the diagonals to the vertical direction and in these cases θ = 45.

_{avg}30 × 10

^{−4}rad. The drift level for similar shear deformations for CON0F2X occurs at 3% drift, 2nd cycle, for CON1 at 3% drift, 2nd cycle, and for CON0 at 2% drift, 3rd cycle. From the figures it is apparent that as the imposed displacement increases, the observed joint shear deformations of specimen CON1F2X are substantially reduced compared to the corresponding ones of the unstrengthened specimen CON1. The low deformations observed for the strengthened specimen CON1F2X are apparently attributed to the shear strengthening imposed by the X-shaped CFRP ropes externally applied on the joint body. From these observations it can be concluded that the strengthening technique improves the joints in terms of shear bearing capacity. The limit drifts for elastic joint cyclic behavior are clearly assessed. No cyclic loading effect is evidenced for CON1F2X up to 3% drift, for CON0F2X up to 2% drift, for CON1 up to 2% drift and for CON0 up to 2% drift. Specimens CON1 and CON0F2X reveal an almost identical variation of shear deformations with the beam drift for the 1st, 2nd or 3rd cycles.

## 6. Conclusions

_{max}), that is at 0.8 P

_{max}, and (ii) the beam drift and reversal in which the shear deformation of the joint (diagonal deformation γ) exceeds the elastic range, denoting initiation of severe joint deterioration.

- All T specimens reveal improved and symmetric P-δ response in the presence of steel stirrups in the joint region or/and external rope strengthening when compared with as-built joints. No fracture of the rope is evidenced even for beam drifts higher than the global “failure” drifts. The proposed continuous detailing of the rope offers improved versatility and efficiency.
- All T specimens under investigation reach the shear force of the beam (P) that corresponds to the yielding of its tensile steel reinforcement.
- The higher the shear reinforcement in the form of an internal steel stirrup or/and X-shaped CFRP ropes, the higher the displacement ductility measured at the beam end at failure point of 0.8 P
_{max}and the higher the number of cycles they sustain. That is, the unstrengthened joint without an internal steel stirrup CON0 fails at drift 2% during the 2nd reversal, CON1 with one internal steel stirrup as well as CON0F2X without a stirrup but with versatile X-shaped continuous CFRP rope strengthening fail at drift 3% during the 2nd reversal, and finally CON1F2X with a stirrup and CFRP rope fails at a drift close to 4% during the 1st cycle. Interestingly, CON1 and CON0F2X reveal rather equivalent mechanical response up to failure. This is extremely interesting for future redesign elaborations. - The beam displacement ductility includes the contribution of the rotation of the joint based on the stiffness of the columns and of the beam, as well as the shear deformation of the joint. The results suggest that, in the absence of a stirrup in the CON0 joint, the γ values exceed the elastic range simultaneously with the 0.8 P
_{max}failure point; that is, the deterioration of the joint initiates at 2% drift 2nd cycle and is, therefore, abrupt. In the presence of a steel stirrup, or alternatively of X-shaped elastic rope, the disintegration of the joint initiates at 2% drift during the 3rd cycle but it develops at a lower rate, as the shear load of the specimen is kept high up to the 2nd cycle at 3% drift. The best response is revealed for CON1F2X with elastic joint response up to the 1st cycle of 3% drift. Then, the joint starts to deteriorate while during the next cycles the load is kept high up to 4% drift. - No failure of the rope strengthening is evidenced in any case.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Abbreviation | Definition |

RC | Reinforced Concrete |

NSM | Near-Surface Mounted |

FRP | Fiber-Reinforced Polymer |

CFRP | Carbon Fiber-Reinforced Polymer |

ETS | Embedded Through Section |

KANEPE | Greek Retrofit Code |

LVDT | Linear Variable Differential Transformer |

Symbol | Definition |

Vjhd | Horizontal shear force in the joint region |

Φ | Diameter of reinforcement |

τ | Shear stress |

ΣMRc | Summarized Moment on column |

ΣMRb | Summarized Moment on beam |

φ | Strength reduction factor |

Vn | Nominal shear strength |

Vu | Maximum required shear value |

γ_{ult} | Value for ultimate shear cracking- Tsonos model factor |

τ_{ult} | Ultimate shear stress |

f_{c} | Compressive strength of concrete |

τ_{cal} | Calculated shear stress |

A_{f} | Cross-section of CFRP ropes |

N_{c} | Column axial compressive load |

P | Beam load |

δ | Beam end displacement |

γ | Diagonal deformations of joint |

γ_{avg} | Average value of joint shear deformation in rad |

Δl | Variation in length of diagonal strings displacement transducers |

L | Initial length of strings |

θ | Inclination angle of the diagonals to the vertical direction |

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**Figure 3.**Strengthened specimens CON0F2X, CON1F2X; C-FRP ropes are applied in an X-shape form on the joint body.

**Figure 7.**Damage states of unstrengthened specimens. (

**a**) Specimen CON0. Damage state at the 5th step (drift 2%). (

**b**) Specimen CON0. Damage state at the 7th step (drift 4%). (

**c**) Specimen CON1. Damage state at the 5th step (drift 2%). (

**d**) Specimen CON1. Damage state at the 7th step (drift 4%).

**Figure 8.**Damage states of strengthened specimens. (

**a**) Specimen CON0F2X. Damage state at the 5th step (drift 2%). (

**b**) Specimen CON0F2X. Damage state at the 7th step (drift 4%). (

**c**) Specimen CON0F2X. Damage state at the 8th step (drift 5%). (

**d**) Specimen CON1F2X. Damage state at the 5th step (drift 2%). (

**e**) Specimen CON1F2X. Damage state at the 7th step (drift 4%). (

**f**) Specimen CON1F2X. Damage state at the 8th step (drift 5%).

**Figure 9.**Comparative presentation of the envelope curves of the hysteretic responses of the specimens. (

**a1**–

**a3**) Maximum loads of 1st, 2nd and 3rd cycles of unstrengthened specimens. (

**b1**–

**b3**) Maximum loads of 1st, 2nd and 3rd cycles of strengthened specimens.

**Figure 10.**Shear deformation of CON0-CON1 (

**a**) and CON0F2X-CON1F2X (

**b**) at (

**a1**,

**b1**) 1st cycle, (

**a2**,

**b2**) 2nd cycle, (

**a3**,

**b3**) 3rd cycle. Shear deformations of the specimens’ joint body as obtained by the diagonally mounted string displacement transducers (LVDTs).

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## Share and Cite

**MDPI and ACS Style**

Karabini, M.; Rousakis, T.; Golias, E.; Karayannis, C. Seismic Tests of Full Scale Reinforced Concrete T Joints with Light External Continuous Composite Rope Strengthening—Joint Deterioration and Failure Assessment. *Materials* **2023**, *16*, 2718.
https://doi.org/10.3390/ma16072718

**AMA Style**

Karabini M, Rousakis T, Golias E, Karayannis C. Seismic Tests of Full Scale Reinforced Concrete T Joints with Light External Continuous Composite Rope Strengthening—Joint Deterioration and Failure Assessment. *Materials*. 2023; 16(7):2718.
https://doi.org/10.3390/ma16072718

**Chicago/Turabian Style**

Karabini, Martha, Theodoros Rousakis, Emmanouil Golias, and Chris Karayannis. 2023. "Seismic Tests of Full Scale Reinforced Concrete T Joints with Light External Continuous Composite Rope Strengthening—Joint Deterioration and Failure Assessment" *Materials* 16, no. 7: 2718.
https://doi.org/10.3390/ma16072718