# Seismic Response of RC Beam-Column Joints Strengthened with FRP ROPES, Using 3D Finite Element: Verification with Real Scale Tests

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Characteristics of the Specimens

_{f}= 28 mm

^{2}. CFRP ropes also exhibit excellent corrosion resistance and durability, making them suitable for application in harsh environmental conditions. Additionally, CFRP ropes can be easily fabricated into various shapes and configurations, allowing for flexible application in strengthening structural elements such as beam-column joints in reinforced concrete structures. The chemical properties of CFRP ropes are primarily determined using the epoxy resin matrix, which provides adhesion between the carbon fibers and protects them from environmental degradation. Epoxy resins offer high chemical resistance, low shrinkage during curing, and excellent bonding properties, ensuring the long-term performance and durability of CFRP strengthening systems.

#### 2.2. Concrete Damage Plasticity

#### 2.2.1. Yield Function

_{c}is the ratio of the second stress invariant on the tensile meridian, q

_{(TM)}, to that on the compressive meridian, q

_{(TM)}, at initial yield for any given value of the pressure invariant p such that the maximum principal stress is negative, ${\widehat{\overline{\sigma}}}_{max}<0$,

#### 2.2.2. Uniaxial Tension and Compression Stress Behavior

_{to}, (Figure 4a), which corresponds to the onset of micro-cracking in the concrete material. In the case of uniaxial compression, a linear elastic branch is adopted until initial yield stress, σ

_{co}, (Figure 4b). The inelastic part of the response includes stress hardening followed by strain softening beyond the maximum stress, σ

_{cu}. Thus, the adopted stress–strain relationship includes the main features of the response of concrete [20,32,33]. The uniaxial stress–strain curves are converted to stress versus plastic-strain curves.

_{i}are other predefined field variables. In the case of unloading from any point on the strain-softening branch of the stress–strain curves, the unloading response exhibits lower stiffness (Figure 4), and the elastic stiffness of the material is degraded (damaged). The stiffness degradation is characterized by two damage variables, d

_{t}and d

_{c}, that are considered to be functions of the plastic strains variables:

_{0}is the initial (undamaged) elastic stiffness of the material, the stress–strain relations under uniaxial tension and compression loading are, respectively:

#### 2.2.3. Variables of Damage and Stiffness Degradation

_{o}is reduced to E as

_{0}is the initial modulus of elasticity of the undamaged concrete. This expression applies both in the tensile (σ

_{11}> 0) and the compressive (σ

_{11}< 0) direction of the cyclic loading. The stiffness degradation coefficient, d, is a function of the stress state and the uniaxial damage variables, d

_{t}and d

_{c}. Lubliner et al. [31] support plastic degradation only within the softening range, and stiffness depends on the material’s cohesion. Thus, the plastic damage factor is assumed as

_{max}where c is cohesion proportion to stress and c

_{max}is proportional to concrete strength.

_{t}and s

_{c}are functions of the stress state that are introduced to model stiffness recovery effects associated with stress reversals. They are defined according to the following:

_{t}and w

_{c}, are considered to be material properties that control the recovery of the tensile and compressive stiffness upon load reversal. Parameter r

^{*}as defined in relationship (24), denotes that in compression stiffness recovery, the recovery is not reduced as it is in the case of the tensional stress state. Figure 5 presents this phenomenon in case the load changes from tension to compression.

_{11}> 0), r

^{*}= 1; therefore,${d=d}_{c}$ as expected. In compression (σ

_{11}< 0), r

^{*}= 0 and $d=\left(1-{w}_{c}\right){d}_{t}$. If w

_{c}= 1, then $d=0$; therefore, the material fully recovers the compressive stiffness (and here is the initial undamaged stiffness, E = E

_{0}) [20,30,31,32,33,34]. Effect of the compression stiffness recovery parameter w

_{c}is shown in Figure 6.

#### 2.2.4. Postfailure Stress–strain Relation

_{t}/Ε

_{ο}, as illustrated in Figure 5.

_{b0}/f

_{c0}, parameter K of the yielding surface, and the viscosity parameter. In particular:

- −
- Dilatation angle characterizes the plastic deformation. Different values of this parameter are used in the literature [20,32]. A value equal to 56° leads to the ductile material response, which is not realistic for concrete, whereas a value close to 0 leads to an entirely brittle behavior. A value equal to 35 has been adopted for parameter ψ in the present study.
- −
- Eccentricity ε represents the rate of the deflection divergence of the plastic hyperbolic behavior to its asymptote. It is usually taken equal to the 0.10 value adopted in the present study, too.
- −
- −
- −

#### 2.3. Steel Material and FRP Ropes

_{y}550 MPa, whereas, for the analysis, the stress–strain relationship is considered to be elastic and perfectly plastic. The CFRP rope used for the strengthening of the specimens JA0Fxb and JA0F2x2b has tensile strength equal to 4000 MPa, modulus of elasticity equal to 240GPa and cross-section area A

_{s}> 28 mm

^{2}(to manufacturer’s data SikaWrap

^{®}FX-50 C, Sika Hellas SA, Kryoneri, Greece) [1,6].

## 3. Finite Element Simulation

#### 3.1. Loading, Mesh and Convergence

#### 3.2. Boundary Conditions

## 4. Test Setup and Measurement of Shear Deformations

## 5. Numerical Results-Comparison with Experimental

#### 5.1. Numerical Results and Cracking Patterns

#### 5.2. Comparison of Numerical Results with Experimental Ones

#### 5.2.1. Pilot Specimens JA0 and JA1

- −
- Specimen JA0. Experimental and numerical results of the principal stresses developing in the joint body of the specimen are presented in Figure 12a–c for the 1st, 2nd, and 3rd loading cycles of the loading steps, respectively. Red dashed lines represent the observed values, whereas blue lines represent the numerical results. From these comparisons, it is apparent that the numerical approach successfully calculates the principal stresses in the joint body. Further, Figure 13a–c presents the numerical values (blue lines) versus the experimentally measured values (red dashed lines) of the maximum displacements at each loading step for the 1st, 2nd, and 3rd loading cycles of the loading steps, respectively. From the comparisons, it is concluded that the numerical approach, in general, successfully describes the experimental ones. Perhaps a small discrepancy appears in the results of the negative loadings in the maximum loadings of the 2nd cycles under large loading, perhaps due to the experimental measurements. Finally, joint shear deformations of the joint body presented in Figure 14 show discrepancies between experimental and numerical values between experimental and numerical values in the middle part of the loading steps, perhaps due to the experimental measurements during the test procedure.
- −
- Specimen JA1. Experimental and numerical results of the principal stresses developing in the joint body of the specimen are presented in Figure 15a–c for the 1st, 2nd, and 3rd loading cycles of the loading steps, respectively. Red dashed lines represent the observed values, whereas blue lines represent the numerical results. From these comparisons, it is apparent that the numerical approach successfully calculates the principal stresses in the joint body. Further, Figure 16a–c presents the numerical values (blue lines) versus the experimentally measured values (red dashed lines) of the maximum displacements at each loading step for the 1st, 2nd, and 3rd loading cycles of the loading steps, respectively. From the comparisons, it is concluded that the numerical approach successfully describes the experimental ones. Finally, from joint shear deformations of the joint body presented in Figure 17, it can be concluded that numerical results successfully depict the tendency and are very close to the measured values obtained from the experiment.

#### 5.2.2. Strengthened Specimens JA0Fxb and FA0F2x2b

- −
- Specimen JA0Fxb. Experimental and numerical results of the principal stresses developing in the joint body of the specimen are presented in Figure 18a–c for the 1st, 2nd, and 3rd loading cycles of the loading steps, respectively. Red dashed lines represent the observed values, whereas blue lines represent the numerical results. From these comparisons, it is apparent that the numerical approach excellently calculates the principal stresses in the joint body. Further, Figure 19a–c presents the numerical values (blue lines) versus the experimentally measured values (red dashed lines) of the maximum displacements at each loading step for the 1st, 2nd, and 3rd loading cycles of the loading steps, respectively. From the comparisons, it is concluded that the numerical approach successfully describes the experimental ones. Finally, joint shear deformations of the joint body presented in Figure 17 show that numerical results successfully predict the measured shear deformations.

**Figure 12.**Experimental and Numerical results of principal stresses developing in the joint body of specimen JA0, (

**a**) for 1st loading cycles, (

**b**) for 2nd loading cycles, (

**c**) for 3rd loading cycles.

**Figure 13.**Experimental and Numerical results of force displacement of specimen JA0, (

**a**) for 1st loading cycles, (

**b**) for 2nd loading cycles, (

**c**) for 3rd loading cycles.

**Figure 14.**Experimental and Numerical results of shear deformation developing in the middle of joint body of specimen JA0.

**Figure 15.**Experimental and Numerical results of maximum principal stress of specimen JA1, (

**a**) for 1st loading cycles, (

**b**) for 2nd loading cycles, (

**c**) for 3rd loading cycles.

**Figure 16.**Experimental and Numerical results of force displacement of specimen JA1, (

**a**) for 1st loading cycles, (

**b**) for 2nd loading cycles, (

**c**) for 3rd loading cycles.

**Figure 17.**Experimental and Numerical results of shear deformation developing in the joint body of specimen JA1.

- −
- Specimen JA0F2x2b. Experimental and numerical results of the principal stresses developing in the joint body of the specimen are presented in Figure 21a–c for the 1st, 2nd, and 3rd loading cycles of the loading steps, respectively. Red dashed lines represent the observed values, whereas blue lines represent the numerical results. From these comparisons, it is apparent that the numerical approach excellently calculates the principal stresses in the joint body. Further, Figure 22a–c presents the numerical values (blue lines) versus the experimentally measured values (red dashed lines) of the maximum displacements at each loading step for the 1st, 2nd, and 3rd loading cycles of the loading steps, respectively. From the comparisons, it is concluded that the numerical approach successfully describes the experimental ones. Finally, joint shear deformations of the joint body are presented in Figure 23. From these comparisons, it is shown that numerical results successfully depict the tendency and are very close to the measured values obtained from the experiment. Discrepancies shown in high-story drifts may be attributed to the measurements of the damaged joint body.

**Figure 18.**Experimental and Numerical results of maximum principal stress of specimen JA0Fxb, (

**a**) for 1st loading cycles, (

**b**) for 2nd loading cycles, (

**c**) for 3rd loading cycles.

**Figure 19.**Experimental and Numerical results of force displacement of specimen JA0Fxb, (

**a**) for 1st loading cycles, (

**b**) for 2nd loading cycles, (

**c**) for 3rd loading cycles.

**Figure 20.**Experimental and Numerical results of shear deformation developing in the joint body of specimen JA0Fxb.

**Figure 21.**Experimental and Numerical results of maximum principal stress of specimen JA0F2x2b, (

**a**) for 1st loading cycles, (

**b**) for 2nd loading cycles, (

**c**) for 3rd loading cycles.

**Figure 22.**Experimental and Numerical results of force displacement of specimen JA0F2x2b, (

**a**) for 1st loading cycles, (

**b**) for 2nd loading cycles, (

**c**) for 3rd loading cycles.

**Figure 23.**Experimental and Numerical results of shear stresses developing in the joint body of specimen JA0F2x2b.

## 6. Comparisons of Numerical Results with the Experimental Ones—Discussion

_{avg}of specimens JA0, JA1, JA0Fxb, and JA0F2x2b, respectively, as yielded using the numerical approach are presented and compared with the corresponding ones as calculated based on the observed deformations of the string displacement transducers mounted on the joints body (Figure 10) during the tests [6]. From these comparisons, it is concluded that the adopted approach adequately predicts the developing shear deformations per loading step of the examined beam-column specimens in most cases.

## 7. Conclusions

- The differences between the Experimental and Numerical results are small, considering the load–displacement curves, the maximum principal stress, and the shear deformations. It shows that the material input in the program and the FE modeling have been accurately done.
- The only considerable difference was found in the shear deformation of specimen JA0.
- Further, the importance and effectiveness of the application of FRP ropes for the improvement of the seismic response of the joints have also been proved.
- The cracking patterns of the examined specimens, as predicted using the finite elements in specimens, are very close to those of the experimental ones. This shows that the used CDP can accurately predict the crack propagation in concrete, and it can simulate the concrete’s triaxial behavior accurately.
- The favorable influence of the ropes is evaluated based on their real characteristics in order to achieve a more realistic prediction of SFRC behavior under compression and tension. The cyclic loading tests of retrofitted joints exhibit improved hysteretic responses in terms of stiffness, load-bearing capacity, deformation, and cracking behavior.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Karayannis, C.G.; Golias, E. Strengthening of deficient RC joints with diagonally placed external C-FRP ropes. J. Earthq. Struct.
**2021**, 20, 123–132. [Google Scholar] [CrossRef] - Golias, E.; Lindenthal, H.; Schlüter, F.H.; Karabinis, A. Ertüchtigung seismisch beschädigter Rahmenknoten aus Stahlbeton mittels FRP-Filamentbündelverbindungen. Bautechnik
**2020**, 97, 268–278. [Google Scholar] [CrossRef] - Golias, E.; Zapris, A.G.; Kytinou, V.K.; Kalogeropoulos, G.I.; Chalioris, C.E.; Karayannis, C.G. Effectiveness of the novel Rehabilitation method of seismically damaged RC joints using C-FRP ropes and comparison with widely applied method using C-FRP sheets—Experimental Investigation. Sustainability
**2021**, 13, 6454. [Google Scholar] [CrossRef] - Golias, E.; Zapris, A.G.; Kytinou, V.K.; Osman, M.; Koumtzis, M.; Siapera, D.; Chalioris, C.E.; Karayannis, C.G. Application of X-shaped CFRP ropes for structural upgrading of reinforced concrete beam-column joints under cyclic loading—Experimental study. Fibers
**2021**, 9, 42. [Google Scholar] [CrossRef] - Karayannis, C.G.; Golias, E. Full-scale experimental testing of RC Beam-column joints strengthened using CFRP Ropes as external reinforcement. Eng. Struct.
**2022**, 250, 113305. [Google Scholar] [CrossRef] - Karayannis, C.; Golias, E.; Kalogeropoulos, G.I. Influence of carbon fiber-reinforced ropes applied as external diagonal reinforcement on the shear deformation of RC Joints. Fibers
**2022**, 10, 28. [Google Scholar] [CrossRef] - Golias, E.; Vougioukas, E.A.; Wittemann, K.; Kalogeropoulos, G.I.; Karayannis, C. Cyclic response of RC Beam-column joints strengthened with transverse steel bars and with C-FRP Rope connections through the joint area. Acta Polytech.
**2022**, 62, 274–282. [Google Scholar] [CrossRef] - Karayannis, C.G.; Golias, E.; Naoum, M.C.; Chalioris, C.E. Efficacy and damage Diagnosis of reinforced concrete columns and joints strengthened with FRP ropes using piezoelectric transducers. Sensors
**2022**, 22, 8294. [Google Scholar] [CrossRef] - Bathe, K.J.; Walczak, J.; Welch, A.; Mistry, N. Nonlinear analysis of concrete structures. Comput. Struct.
**1989**, 32, 563–590. [Google Scholar] [CrossRef] - Kotsovos, M.D.; Spiliopoulos, K.V. Modeling of crack closure for finite-element analysis of structural concrete. Comput. Struct.
**1998**, 69, 383–398. [Google Scholar] [CrossRef] - Carpinteri, A.; Valente, S.; Ferrara, G.; Imperato, L. Experimental and numerical fracture modeling of a gravity dam. In Fracture Mechanics of Concrete Structures (Proceedings of the 1st FraMCoS Conference, Breckenridge, USA, 1992); Bazant, Z.P., Ed.; Elsevier Applied Science: London, UK, 1992; pp. 351–360. [Google Scholar]
- Panagiotou, M.; Lu, Y. Three-Dimensional cyclic beam-truss model for nonplanar reinforced concrete walls. J. Struct. Eng. ASCE
**2014**, 140, 04013071. [Google Scholar] - Said, A.; Elmorsi, M.; Nehdi, M. Nonlinear Model for Reinforced Concrete under Cyclic Loading. Mag. Concr. Res.
**2005**, 57, 211–224. [Google Scholar] [CrossRef] - Vecchio, F.G.; Collins, M.P. The modified compression field theory for reinforced concrete elements subjected to shear. J. Am. Concr. Inst.
**1986**, 83, 219–231. [Google Scholar] - Panagiotou, M.; Restrepo, J.I.; Schoettler, M.; Kim, G. Nonlinear cyclic truss model for reinforced concrete walls. ACI Struct. J.
**2012**, 109, 205–214. [Google Scholar] - Mergos, P.E.; Kappos, A.J. A distributed shear and flexural flexibility model with shear–flexure interaction for R/C members subjected to seismic loading. Earthq. Eng. Struct. Dyn.
**2008**, 37, 1349–1370. [Google Scholar] [CrossRef] - Bazant, Z.P.; Planas, J. Fracture and Size Effect in Concrete and Other Quasibrittle Materials, 1st ed.; Routledge: London, UK; CRC Press: Boca Raton, FL, USA, 1998. [Google Scholar]
- Xu, S.; Zhang, J. Hysteretic shear–flexure interaction model of reinforced concrete columns for seismic response assessment of bridges. Earthq. Eng. Struct. Dyn.
**2011**, 40, 315–337. [Google Scholar] [CrossRef] - Park, H.; Eom, T. Truss model for nonlinear analysis of RC members subject to cyclic loading. J. Struct. Eng.
**2007**, 133, 1351–1363. [Google Scholar] [CrossRef] - ABAQUS/CAE User’s Manual; Hibbitt, Karlsson & Sorensen, Inc.: USA. 2000. Available online: https://www.researchgate.net/file.PostFileLoader.html?id=557a68c45e9d9734b28b458e&assetKey=AS:273794663419904@1442289142232 (accessed on 20 February 2024).
- Mundeli Salathiel, M.; Pilate Moyo, L. Finite element modeling of reinforced concrete beam patch repaired and strengthened with fiber-reinforced polymers. Int. J. Eng. Tech. Res.
**2016**, 4, 47–54. [Google Scholar] - Ibrahim, A.M.; Mahmood, M.S. Finite element modeling of reinforced concrete beams strengthened with FRP laminates. Eur. J. Sci. Res.
**2009**, 30, 526–541. [Google Scholar] - Shakor, P.; Gowripalan, N.; Rasouli, H. Experimental and numerical analysis of 3D printed cement mortar specimens using inkjet 3DP. Arch. Civ. Mech. Eng.
**2021**, 21, 58. [Google Scholar] [CrossRef] - Rezazadeh, M.; Costa, I.; Barros, J. Influence of prestress level on NSM CFRP laminates for the flexural strengthening of RC beams. Compos. Struct.
**2014**, 116, 489–500. [Google Scholar] [CrossRef] - Kmiecik, P.; Kamiński, M. Modelling of reinforced concrete structures and composite structures with concrete strength degradation taken into consideration. Arch. Civ. Mech. Eng.
**2011**, 11, 623–636. [Google Scholar] [CrossRef] - Panagiotakos, T.; Fardis, M. Deformations of reinforced concrete members at yielding and ultimate. ACI Struct. J.
**2001**, 98, 135–148. [Google Scholar] - Stevens, N.J.; Uzumeri, S.M.; Collins, M.P.; Will, T.G. Constitutive model for reinforced concrete finite element analysis. ACI Struct. J.
**1991**, 88, 49–59. [Google Scholar] - Tsonos, A.G. Ultra-high-performance fiber reinforced concrete: An innovative solution for strengthening old R/C structures and for improving the FRP strengthening method. In Proceedings of the 4th International Conference on Computational Methods and Experiments in Materials Characterization, Materials Characterization, New Forest, UK, 17–19 May 2009. [Google Scholar]
- Pohoryles, D.A.; Melo, J.; Rossetto, T.; Varum, H.; Bisby, L. Seismic retrofit schemes with FRP for deficient RC beam-column joints: State-of-the-art review. J. Compos. Constr.
**2019**, 23, 03119001. [Google Scholar] [CrossRef] - Lee, J.; Fenves, G. Plastic-Damage model for cyclic loading of concrete structures. J. Eng. Mech. ASCE
**1998**, 124, 892–900. [Google Scholar] [CrossRef] - Lubliner, J.; Oliver, J.; Oller, S.; Onate, E. A plastic-damage model for concrete. Int. J. Solids Struct.
**1989**, 25, 299–326. [Google Scholar] [CrossRef] - Genikomsou, A.S.; Polak, M.A. Finite element analysis of punching shear of concrete slabs using damaged plasticity model in ABAQUS. Eng. Struct.
**2015**, 98, 38–48. [Google Scholar] [CrossRef] - Hany, N.F.; Hantouche, E.G.; Harajli, M.H. Finite element modeling of FRP-confined concrete using modified concrete damaged plasticity. Eng. Struct.
**2016**, 125, 1–14. [Google Scholar] [CrossRef] - Chi, Y.; Yu, M.; Huang, L.; Xu, L. Finite element modeling of steel-polypropylene hybrid fiber reinforced concrete using modified concrete damaged plasticity. Eng. Struct.
**2017**, 148, 23–35. [Google Scholar] [CrossRef] - Xiong, Q.; Wang, X.; Jivkov, A.P. A 3D multi-phase meso-scale model for modelling coupling of damage and transport properties in concrete. Cem. Concr. Compos.
**2020**, 109, 103545. [Google Scholar] [CrossRef]

**Figure 1.**Geometrical characteristics of specimens JA0 and JA1 (dimensions in mm) and steel reinforcements (see also Table 1).

**Figure 2.**Location of the CFRP ropes applied as NSM strengthening reinforcement in specimens JA0Fxb and JA0F2x2b. (

**a**) CFRP ropes of Specimen JA0Fxb. (

**b**) CFRP ropes of Specimen JA0F2x2b.

**Figure 3.**Yield surfaces (

**a**) in the deviatoric plane correspond to different values of K

_{c}and (

**b**) in plane stress.

**Figure 5.**Effect of the compression stiffness recovery in case the load changes from tension to compression.

**Figure 7.**Finite element simulation of the parts of the specimen, (

**a**) concrete elements, (

**b**) stirrups, (

**c**) steel bars, and (

**d**) CFRP ropes.

**Figure 10.**Test setup, loading sequence, and instrumentation for the measurement of shear deformation of the joint body of the tested specimens. (

**a**) Experimental setup. (

**b**) Loading sequence. (

**c**) Specimen JA0 at the end of the test.

**Figure 11.**Comparison between Experimental and Numerical cracking patterns, in the final step (step 7), (

**a**,

**b**) specimen JA0, (

**c**,

**d**) specimen JA1, (

**e**,

**f**) specimen JA0Fxb, (

**g**,

**h**) specimen JA0F2x2b.

Reinforcements | JA0 | JA1 | JA0Fxb | JA0F2x2b |
---|---|---|---|---|

① | - | 1Ø8 | - | - |

② | 2Ø14 | 2Ø14 | 2Ø14 | 2Ø14 |

③ | 4Ø12 | 4Ø12 | 4Ø12 | 4Ø12 |

FRP ropes of joint | - | - | X-type Single rope | X-type Double rope |

FRP ropes of beam | - | - | Single rope | Double rope |

**Table 2.**Definition of concrete parameters in ABAQUS: (

**a**) damage plasticity parameters, (

**b**) concrete compressive behavior, and (

**c**) concrete tensile behavior.

(a) Concrete Damage Plasticity Parameters [20,32,33,34,35] | (b) Concrete Compressive Behavior | (c) Concrete Tensile Behavior | |||
---|---|---|---|---|---|

Stress | Inelastic | Stress | Inelastic | ||

Strain | Strain | ||||

Dilation Angle | 35 | 12.50 (yield) | 0.000000 | 3.0000 (yield) | 0.000000 |

Eccentricity | 0.1 | 14.78 | 1.5 × 10^{−5} | 1.66400 | 0.000281 |

fb0/fc0 | 1.16 | 16.89 | 4.0 × 10^{−5} | 1.78900 | 0.000507 |

K | 0.667 | 18.81 | 8.0 × 10^{−5} | 0.92300 | 0.000718 |

Viscosity Parameter | 0.008% | 26.60 | 0.000130 | 0.76383 | 0.000923 |

28.60 | 0.000202 | 0.65420 | 0.001124 | ||

29.20 | 0.000300 | ||||

30.00 | 0.000396 |

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**MDPI and ACS Style**

Golias, E.; Touratzidis, P.; Karayannis, C.G.
Seismic Response of RC Beam-Column Joints Strengthened with FRP ROPES, Using 3D Finite Element: Verification with Real Scale Tests. *CivilEng* **2024**, *5*, 395-419.
https://doi.org/10.3390/civileng5020020

**AMA Style**

Golias E, Touratzidis P, Karayannis CG.
Seismic Response of RC Beam-Column Joints Strengthened with FRP ROPES, Using 3D Finite Element: Verification with Real Scale Tests. *CivilEng*. 2024; 5(2):395-419.
https://doi.org/10.3390/civileng5020020

**Chicago/Turabian Style**

Golias, Emmanouil, Paul Touratzidis, and Chris G. Karayannis.
2024. "Seismic Response of RC Beam-Column Joints Strengthened with FRP ROPES, Using 3D Finite Element: Verification with Real Scale Tests" *CivilEng* 5, no. 2: 395-419.
https://doi.org/10.3390/civileng5020020