# Performance of Steel Bar Lap Splices at the Base of Seismic Resistant Reinforced Concrete Columns Retrofitted with FRPs—3D Finite Element Analysis

^{*}

*Fibers*)

## Abstract

**:**

## 1. Introduction

_{u}) of the columns. Modern codes for seismic design and interventions, such as Eurocode 8 part 3 (EC8.3) [40] and Greek Retrofit Code (KANEPE) [41], have adopted such equations. The extensive investigation of the recent experimental and analytical database by Anagnostou et al. [42] (see also [43]) for 261 columns with or without lap splices suggests that the existing design models for RC columns of square or rectangular sections, with or without FRP confinement, provide the predicted shear strength compared against the experimental one, with an average absolute error (AAE) of about 20%. Further, the same study reveals that the AAE of the predicted chord rotation at failure was higher than 35% (for both codes). Therefore, besides the recent research focusing on the effects of external confinement with composites on the seismic behavior of columns [44,45,46], including their deformation capacity [47,48] and the plastic hinge length [49,50,51], further research is necessary to address the unidentified gaps in our knowledge.

## 2. Experimental Database

_{R}or P

_{max}) and chord rotation at failure (θ

_{u}). In addition, the yield and ultimate chord rotation, the yield curvature, the yield moment, and the shear strength of the columns are calculated according to EC8.3 [40] and KANEPE [41].

_{anal}is the analytical value and x

_{exp}is the experimental value of the parameter (e.g., θ

_{u}, V

_{R}). It should be noticed that values of AR close to 1 and values of AAE close to 0% indicate accurate predictions of the values under investigation.

## 3. 3D Finite Elements Modelling

#### 3.1. Materials

#### 3.1.1. Concrete

#### 3.1.2. Longitudinal and Transverse Steel Bars

#### 3.1.3. Fiber Reinforced Polymer Jacket

#### 3.2. Geometry

#### 3.3. Connections

#### 3.4. Mesh

#### 3.5. Boundary Conditions and Loading

## 4. Numerical Results and Discussion

#### 4.1. Lateral Force-to-Drift (%) Curves

_{max}, P

_{u}) and the ultimate displacements (δ

_{Pu}) are presented and compared in Table 5. The experimental results refer to the average values of the two directions, push and pull.

#### 4.2. Analytical Response of the Longitudinal Bars

#### 4.2.1. Axial Force of Longitudinal Bars at the Base of Column

_{max}(or the developed stress, f

_{s}), is provided. The comparative curves of the tensile axial force of the bar versus the horizontal displacement of the columns (F-δ curves) without FRP confinement are depicted in Figure 4.

_{max}) of unretrofitted column without lap splices (R-0L0) is 145.94 kN at a displacement of 37.80 mm (at ultimate or failure), higher than the analytical yield force F

_{y}= 130.8 kN. The presence of inadequate lap splices with 15 d

_{bL}length at the base of an unretrofitted RC column results in the decrease of F

_{max}by 40% in column R-0L1 (F

_{max}= 87.95 kN at 8.57 mm, lower than the analytical yield force F

_{y}= 130.8 kN), 5% in column R-0L3 (F

_{max}= 138.33 kN at 16.64 mm), and 2% in column R-0L4 (F

_{max}= 143.30 kN at 31.36 mm) compared to R-0L0. Both columns with considered adequate lap splice lengths (R-0L3, R-0L4) may face some temporary or detrimental slip after steel bar yielding.

_{max}is 147.89 kN (at 57.78 mm) in column R-P2L0, 85.49kN (at 7.29 mm) in column R-P2L1 (lower than the analytical yield force, F

_{y}= 130.8 kN), 134.63 kN (at 55.90 mm) in column R-P2L3, and 157.42 kN (at 96.27 mm) in column R-P2L4. It is observed that the F

_{max}-to-displacement curves of R-P2L0 (without lap splices) and R-P2L4 (45 d

_{bL}lap splice length) are almost identical (also with R-0L0), confirming that a lap splice length of 45 d

_{bL}provides an equivalent tensile bar response (Figure 5). In contrast, the analyses suggest that the F

_{max}obtained for column R-P2L1 is lower than the F

_{y}, although the column is externally confined with FRPs. The two layers of CFRP jacketing, in this case, are inadequate to prevent the lap-spliced bars from slipping, despite the pseudo-ductile behavior observed in Figure 3f. This pseudo-ductility is attributed to the pseudo-ductile bar contribution (see Figure 5). However, the response of the column is considered to be inadequate, as there is slip and it fails to reach bar yielding. This bar response is similar to the one in R-0L1 (Figure 4). For R-P2L3, the maximum tensile force of the bars exceeds the yield one, but at a horizontal displacement of 40 mm. The column seems to suffer initially by the controlled slip of the bars, starting before the displacement at the yielding of the bars of columns R-0L0 or R-P2L0 (Figure 5). However, at around 60 mm displacement, the bars slip again. The revealed deficient performance of the lap-spliced bars in R-P2L3 is in accordance with the lower bearing horizontal load of around 180–200 kN at the pseudo-yielding point (Figure 3). The corresponding bearing horizontal load for R-P2L0 at real bar yielding is around 190–225 kN (Figure 3).

_{bL}= 280 mm = 0.67 l

_{b,min}or 40 d

_{bL}= 560 mm = 1.29 l

_{b,min}) without FRP confinement (L20d_C, L40d_C) or with FRP confinement (L20d_R2, L40d_R2). They provided the steel strain histories of starter bars at the column base during testing, measured with strain-gauges (Figure 6). The lap-splice length equal to 20 d

_{bL}is inadequate for developing the yield strain (or yield stress) of the longitudinal bars (ε

_{yL}= 523/200,000 = 2.62‰), while the slippage of lap-spliced bars is observed. Although a lap-splice length of 40 d

_{bL}is adequate to develop the yield stress of the longitudinal bars, it is not sufficient to prevent slippage, which is observed after yielding. The application of two layers of CFRP delays the slippage of the lap-spliced bars for the inadequate lap-splice length of 20 d

_{bL}, happening at higher drifts of 3.75%. However, longitudinal bars do not really surpass yielding strain, while this marginal yielding of bars initiates at a higher column drift of 3.44%. As for the adequate lap-splice length of 40 d

_{bL}, FRP confinement does not affect the drift at the yielding of the lap-spliced bars, while no slippage is observed at higher drifts up to column failure.

_{y}(Figure 7a). However, for inadequate lap splice lengths, this change occurs at a lower force (F < F

_{y}). In this case, the axial force is defined as pseudo-yield force (F

_{py}) and the corresponding displacement as pseudo-yield displacement (δ

_{py}), as shown in Figure 7b. This pseudo-ductility or delay in real tensile bar yielding development may explain the divergences in prediction in some cases in the yield flexural moment or chord rotation of the columns with lap-spliced bars, despite the fact that they are more or less affected by the mechanical characteristics of the steel bar under tension. These cases urge an assessment of the performance of such columns as acceptable or not in redesign.

#### 4.2.2. Stress along the Lap Splice Length

_{bL}= 508 mm = 0.78 l

_{b,min}). They placed strain gauges to monitor the strain histories of the lap-spliced bars (Figure 8a), which recorded at about 3% lateral drift when most of them were damaged due to the damage to the columns. They expected a triangular strain distribution before bond deterioration (Figure 8b).

_{yL,main}= 510 MPa for the main bars and f

_{yL,starter}= 521 MPa for the starter bars. For the starter bars, the strain distribution is triangular indeed (blue), while for the main bars it has a curved form (orange). A different response of the corner and middle longitudinal bars in tension during cyclic loading can also be observed.

_{bL}= 508 mm = 0.78 l

_{b,min}) predicts the increment of stress in both the starter and the main bars, for monotonic (Figure 10a) and cyclic (Figure 10b) analyses, as the drift ratio increases up to the lateral load capacity of columns (about 0.5% drift level). For both bars, the stress increases as the drift level increases. The stress of the starter bar along the lap splice length resembles a parabolic distribution at lower lateral drifts, which changes into triangular at higher lateral drifts. The stress distribution of the main bar has a wavy form.

_{yL}= 514 MPa), it has a wavy form. For higher lateral displacements and after yielding, it has a triangular form. Moreover, a longer part of the steel bar reaches the yield stress and the critical region within which the plastic hinge develops is extended up to 300 mm.

_{yL}= 514 MPa and yield strain ε

_{sL}= 2.57‰). Both bars seem to develop the same stress at about two thirds of the lap splice length away from the bottom section, even in cases of inadequate lap splice length. Moreover, the shape of the curves representing the stress along lap splice up to yielding for starter and main bars validates more or less the analytical model provided by Chowdhury & Orakcal [108]. FE analyses suggest that in most cases the developed stress at the base of the column is not fully transferred to the end of the lap splice, as the tensile strain of the bars may be lower far from the bottom section due to lower moment values along the column. Therefore, the loading along the lap-splice length is obviously not symmetrical.

_{bL}= 810 mm = 1.53 l

_{b,min}) and no slippage is observed, the total bearing tensile stress by both bars at any section (gray line in Figure 12 and Figure 13) is lower at the end of the lap splice in accordance with the developed moments, similar to the column without laps (Figure 11). For higher column drift, the same pattern is valid (see R-0L4 and R-P2L4), as the bars achieve hardening behavior in response to the increased bearing stress. Further, it is interesting to note that in column R-0L0, the plastic hinge length is around 300 mm, defined by the length the tensile steel bars surpass the yield stress. In the case of R-0L4 with adequate lap-splice, the plastic hinge length is extended to 400 mm, as we consider the sum of the stress developed in both bars at an identical column length (gray line in Figure 12). Similarly, in R-P2L4, the FRP jacketing further extends the plastic hinge length to around 620 mm.

_{bL}(540 mm = 1.02 l

_{b,min}), the bars develop their yielding, but clearly, a slip occurs at ultimate drift (see R-0L3, Figure 15, and R-P2L3, Figure 16). When the column is confined with two layers of FRP, slip occurs at a far higher ultimate drift. Further, in the case of R-0L3, the plastic hinge length is extended to 325 mm, as we consider the sum of the stress developed in both bars at an identical column length (gray line in Figure 14). Similarly, in R-P2L3, the FRP jacketing further extends the plastic hinge length to around 450 mm. In R-P5L3, the corresponding plastic hinge length is developed at higher drifts but extends to 540 mm.

_{bL}= 270 mm = 0.51 l

_{b,min}), the total tensile stress by both bars at any section remains rather constant all along the lap-splice, and lower than the yield stress of the bars. This pattern is not affected by external FRP confinement. The total stress of the main bar may be higher than the starter’s for different horizontal drifts of the column. No plastic hinge length may be defined based on steel yielding.

_{f}) is 600 mm (Table 1). It barely exceeds the lap splice length of 30 d

_{bL}(h

_{f}= 600 mm > l

_{o}= 540 mm), while it is shorter than a lap splice length of 45 d

_{bL}(h

_{f}= 600 mm < l

_{o}= 810 mm). The height of the provided FRP confinement seems to affect the transfer mechanism of stress along the lap splice, as the diagrams in Figure 13 show a sudden stress decrease at 600 mm from the column bottom, at the end of the FRP jacket.

#### 4.2.3. Proposed Modifications

_{y}must be multiplied by an additional relation c (Equation (4)), regarding the RC columns with insufficient lap splices (0 < l

_{b}/l

_{b,min}< 1).

_{b}< 0.5 l

_{b,min}. If the bars reach the yield stress (c = 1), then the hardening of the steel bar is taken into consideration (1.25·f

_{y}). The (Equation (4)) is inserted in the yield curvature to calculate M

_{y}and θ

_{y}, and in the mechanical ratios of reinforcement to calculate θ

_{u}and therefore μ

_{δ}for adequate FRP strengthening (at least two layers). Obtained values of μ

_{δ}lower than 3.5 are avoided and higher FRP strengthening is recommended. Further, it should be secured that the shear force required to develop the full flexural strength of the column after the tensile yielding of the bars is lower than the shear capacity of the column. In cases where the lap length is adequate (higher than l

_{b,min}), c equals 1. It should be noted that, based on the proposed modification, the l

_{b,min}is different from that in seismic codes.

#### 4.2.4. Comparison of Analytical and Experimental Values

_{R}and an AAE of 37.48% and AR 0.97 for θ

_{u}, according to KANEPE. The corresponding values, according to EC8.3, are 19.40% and 0.87 for V

_{R}and 41.45% and 0.91 for θ

_{u}.

_{R}with an AAE of 20.83% and an AR of 0.80, while they predict the θ

_{u}with an AAE of 38.86% and an AR of 0.64. As for EC8.3, the corresponding values are 18.73% and 0.83 for V

_{R}and 46.11% and 0.54 for θ

_{u}. The above performance of the existing design models suggests that the error of prediction of the existing models is significant. As was already proposed in Section 4.2.3, the variable performance of the lap splices with inadequate length should be incorporated into the models to better address the variable beneficial effects of different quantities of external FRP confinement and their upper and lower limits.

## 5. Conclusions

- In most cases, the developed stress at the base of the column is not fully transferred to the end of the lap splice, as the tensile strain of the bars may be lower far from the bottom section (because of lower moment values). Both bars (starter and main) seem to develop the same stress at about two thirds of the lap splice length away from the bottom section (even in cases of inadequate lap length).
- In cases where the lap splice length is adequately long (45 d
_{bL}), the total bearing tensile stress by both bars at any section is lower at the end of the lap in accordance with the developed moments, similar to the column without laps. For higher column drift, the same pattern is valid, as the bars achieve the hardening behavior of increased bearing stress. Further, if we consider the sum of the developed stress for the lapped bars at any point, the plastic hinge length is extended from 300 mm for R-0L0 without lap, to 400 mm for R-0L4, and to more than double (620 mm) for FRP jacketing at the lap region in R-P2L4. - In cases the lap splice is 30 d
_{bL}the bars develop their yielding, but clearly a slip occurs at ultimate drift. When a column is confined with two layers of FRP, it initially suffers a temporary controlled slip of the bars, starting before the displacement at yielding of the columns R-0L0 or R-P2L0. After delayed bar yielding, the detrimental slip occurs at a far higher ultimate drift. The plastic hinge length is lower than in R-0L4 but higher than in R-0L0 (325 mm). Again, the plastic hinge length extends to around 450 mm or 540 mm for two or five layers of FRP jacketing, based on which is higher for higher lap length or FRP jacketing. - In cases where the lap splice length is inadequate (lap length of 15 d
_{bL}), the total tensile stress of both bars at any section remains rather constant all along the lap-splice and lower than the yield stress of the bars. This pattern is not affected by external FRP confinement. The total stress of the main bar one may be higher than the starter’s for different horizontal drifts of the column. No plastic hinge length may be defined in these cases, as no bar yielding occurs (despite pseudo-yielding). - Increased tensile bar stresses occur at the steel stirrups levels for different columns, as they tend to resist the opening of the potential crack along the spliced bars that leads to their relative slip. The CFRP retrofit seems to improve the axial force transfer mechanism and to result in a better bar stress distribution. The sum of the tensile stress received by both lapped bars increases for more layers of FRP.
- The height of the provided FRP confinement seems to affect the transfer mechanism of stress along the lap splice. If the FRP does not cover all lap splice regions, then a sudden bar stress decrease at the end of the FRP jacketing occurs.
- For the first time, cases of smooth bar slip together with delayed bar yielding or without bar yielding are identified that may be recorded through a “ductile” P-d seismic response. Such pseudo-ductile response cases are revisited through suitably revised redesign criteria for adequate FRP jacketing that identify if the lapped bar will yield.
- The authors propose that composite jacketing that leads to pseudo-ductile P-d behavior while the lapped bar does not yield due to slip (temporary or not) should be considered as inadequate in redesign, and additional FRP layers should be provided as per the framework presented in Section 4.2.2.
- The high potential of advanced dynamic 3D FEA should be further utilized to extend investigations in several challenging real cases of deficient existing columns with different cross-section geometry, multiple side steel bars inside the lap region, and different detailing of existing steel stirrups or of composite jacketing to assist successful redesign.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Parts of FE model (

**a**) concrete, (

**b**) internal (steel) reinforcement, (

**c**) external reinforcement (FRP jacket).

**Figure 3.**Lateral Force-Drift curves for columns (

**a**) R-0L0, (

**b**) R-0L1, (

**c**) R-0L3, (

**d**) R-0L4, (

**e**) R-P2L0, (

**f**) R-P2L1, (

**g**) R-P2L3, (

**h**) R-P2L4 and (

**i**) R-P5L3.

**Figure 6.**Peak pull and push steel strain of starter bars at the base of column (

**a**) L20d_C, (

**b**) L20d_R2, (

**c**) L40d_C and (

**d**) L40d_R2 at each loading cycle (based on results by [19]).

**Figure 8.**(

**a**) Strain gauges layout. (

**b**) Expected strain distribution along lap-spliced bars (based on [107]).

**Figure 10.**Predicted steel stress distribution on starter and main bar, for (

**a**) monotonic analysis, and (

**b**) cyclic analysis (based on results by [108]).

**Figure 11.**Developed stress along starter longitudinal bars in tension at a displacement of (

**a**) 3.39 mm, (

**b**) 9.74 mm (δ

_{y}), (

**c**) 23.88 mm (δ

_{Pmax}) and (

**d**) 36.86 mm (δ

_{u}), for column R-0L0.

**Figure 12.**Developed stress along lap splice length at a displacement of (

**a**) 3.15 mm, (

**b**) 8.19 mm (δ

_{y}), (

**c**) 22.34 mm (δ

_{Pmax}), and (

**d**) 31.36 mm (δ

_{u}), for column R-0L4.

**Figure 13.**Developed stress along lap splice length at a displacement of (

**a**) 4.70 mm, (

**b**) 8.91 mm, (

**c**) 12.02 mm (δ

_{y}), (

**d**) 26.50 mm (δ

_{Pmax}), and (

**e**) 96.27 mm (δ

_{u}), for column R-P2L4.

**Figure 14.**Developed stress along lap splice length at a displacement of (

**a**) 3.16 mm, (

**b**) 8.22 mm (δ

_{y}), (

**c**) 16.64 mm (δ

_{Pmax}), and (

**d**) 27.20 mm (δ

_{u}), for column R-0L3.

**Figure 15.**Developed stress along lap splice length at a displacement of (

**a**) 2.07 mm, (

**b**) 4.20 mm, (

**c**) 6.58 mm (δ

_{py}), (

**d**) 36.21 mm (δ

_{P€}), (

**e**) 49.30 mm (δ

_{y}), and (

**f**) 69.11 mm (δ

_{u}), for column R-P2L3.

**Figure 16.**Developed stress along lap splice length at a displacement of (

**a**) 3.44 mm, (

**b**) 7.23 mm, (

**c**) 10.14 mm (δ

_{py}), (

**d**) 37.83 mm (P

_{max}), (

**e**) 51.20 mm (δ

_{y}), and (

**f**) 97.17 mm (δ

_{u}), for column R-P5L3.

**Figure 17.**Developed stress along lap splice length at a displacement of (

**a**) 3.15 mm, (

**b**) 8.57 mm (δ

_{py}), (

**c**) 16.95 mm (δ

_{Pmax}), and (

**d**) 28.50 mm (δ

_{u}), for column R-0L1.

**Figure 18.**Developed stress along lap splice length at a displacement of (

**a**) 2.24 mm, (

**b**) 4.49 mm, (

**c**) 7.29 mm (δ

_{py}), (

**d**) 26.28 mm (δ

_{Pmax}), and (

**e**) 49.36 mm (δ

_{u}), for column R-P2L1.

Column | f_{c}(MPa) | Geometry | FRP | Longitudinal Bars | Stirrups | v | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

b_{w}(m) | h (m) | L_{s}(m) | Type of FRP | Height of FRP (mm) | t_{j}(mm) | E_{j}(GPa) | ε_{ju} | r (mm) | d_{bL}(mm) | Lap-splice Length (d _{bL}) | f_{yL}(MPa) | f_{uL}(MPa) | d_{w}(mm) | f_{yw}(MPa) | s (m) | f_{uw}(MPa) | |||

R-0L0 | 31.0 | 0.250 | 0.500 | 1.60 | - | - | - | - | - | 18 | - | 514 | 659 | 8 | 425 | 0.2 | 596 | 0.26 | |

R-0L1 | 27.4 | 0.250 | 0.500 | 1.60 | - | - | - | - | - | 18 | 15 | 514 | 659 | 8 | 425 | 0.2 | 596 | 0.23 | |

R-0L3 | 27.4 | 0.250 | 0.500 | 1.60 | - | - | - | - | - | 18 | 30 | 514 | 659 | 8 | 425 | 0.2 | 596 | 0.28 | |

R-0L4 | 27.4 | 0.250 | 0.500 | 1.60 | - | - | - | - | - | 18 | 45 | 514 | 659 | 8 | 425 | 0.2 | 596 | 0.28 | |

R-P2L0 | 32.9 | 0.250 | 0.500 | 1.60 | CFRP | 600 | 0.26 | 230 | 0.015 | 30 | 18 | - | 514 | 659 | 8 | 425 | 0.2 | 596 | 0.23 |

R-P2L1 | 26.9 | 0.250 | 0.500 | 1.60 | CFRP | 600 | 0.26 | 230 | 0.015 | 30 | 18 | 15 | 514 | 659 | 8 | 425 | 0.2 | 596 | 0.30 |

R-P2L3 | 26.9 | 0.250 | 0.500 | 1.60 | CFRP | 600 | 0.26 | 230 | 0.015 | 30 | 18 | 30 | 514 | 659 | 8 | 425 | 0.2 | 596 | 0.28 |

R-P2L4 | 26.9 | 0.250 | 0.500 | 1.60 | CFRP | 600 | 0.26 | 230 | 0.015 | 30 | 18 | 45 | 514 | 659 | 8 | 425 | 0.2 | 596 | 0.28 |

R-P5L3 | 27.0 | 0.250 | 0.500 | 1.60 | CFRP | 600 | 0.65 | 230 | 0.015 | 30 | 18 | 30 | 514 | 659 | 8 | 425 | 0.2 | 596 | 0.29 |

_{c}: concrete compressive strength, b

_{w}: width of cross-section, h: depth of cross-section, L

_{s}: shear span length, t

_{j}: total thickness of FRP jacket, E

_{j}: elastic modulus of CFRP, ε

_{ju}: strain at failure of CFRP, r: bend radius of FRP at the corners of the member, d

_{bL}: diameter of longitudinal steel bar, f

_{yL}: yield stress of longitudinal steel bar, f

_{uL}: ultimate stress of longitudinal steel bar, d

_{w}: diameter of transverse steel bar, f

_{yw}: yield stress of transverse reinforcement, s: stirrup spacing, f

_{uw}: ultimate stress of transverse reinforcement, v: normalized axial force.

Property | Value |
---|---|

Density (kg·m^{−3}) | 2314 |

Tensile Strength ft/fc | 0.1 |

Shear Strength fs/fc | 0.18 |

Intact Failure Surface Constant A | 1.6 |

Intact Failure Surface Exponent n | 0.61 |

Tension/Compression Meridian Ratio Q2.0 | 0.6805 |

Brittle to Ductile Transition BQ | 0.0105 |

Hardening Slope | 2 |

Elastic Strength/ft | 0.7 |

Elastic Strength/fc | 0.53 |

Property | Value | |
---|---|---|

Density (kg·m^{−3}) | 7850 | |

Isotropic elasticity | Young’s Modulus (MPa) | 2 × 10^{5} |

Poisson’s Ratio | 0.3 | |

Bulk Modulus (Pa) | 1.6667 × 10^{11} | |

Shear Modulus (Pa) | 7.6923 × 10^{10} | |

Plastic Strain | Stress | |

Multilinear isotropic hardening(Steel stirrups) | 0 | 425 |

0.05 | 550 | |

0.1 | 580 | |

0.195 | 596 | |

Multilinear isotropic hardening(Longitudinal bars) | 0 | 514 |

0.05 | 630 | |

0.1 | 650 | |

0.17 | 659 |

Property | Value |
---|---|

Density (kg·m^{−3}) | 1.451 × 10^{−9} |

Young’s Modulus X direction (MPa) | 59,160 |

Young’s Modulus Y direction (MPa) | 59,160 |

**Table 5.**Comparative experimental and numerical results of columns R-0L0, R-0L1, R-0L3, R-0L4, R-P2L0, R-P2L1, R-P2L3, R-P2L4, and R-P5L3.

Column | Results | P_{max}(kN) | AE (%) | P_{u,exp}(kN) | δ_{Pu}(mm) | δ_{Pu} AE(%) | δ_{u,exp}(mm) | P_{δu}(kN) | P_{δu} AE(%) |
---|---|---|---|---|---|---|---|---|---|

R-0L0 | Experimental | 196.50 | 0.79 | 157.20 | 40.00 | 6.93 | 40.00 | 157.20 | 2.06 |

numerical | 194.95 | 157.20 | 37.23 | 40.00 | 153.96 | ||||

R-0L1 | Experimental | 148.00 | 5.63 | 123.40 | 30.40 | 10.79 | 30.40 | 123.40 | 12.77 |

numerical | 139.67 | 123.40 | 27.12 | 30.40 | 107.64 | ||||

R-0L3 | Experimental | 173.75 | 7.67 | 139.00 | 30.40 | 1.78 | 30.40 | 139.00 | 1.64 |

numerical | 187.07 | 139.00 | 30.94 | 30.40 | 141.28 | ||||

R-0L4 | Experimental | 205.00 | 6.32 | 164.00 | 39.00 | 22.92 | 39.00 | 164.00 | 19.62 |

numerical | 192.05 | 164.00 | 30.06 | 39.00 | 131.82 | ||||

R-P2L0 | Experimental | 217.00 | 0.33 | 173.60 | 67.20 | 14.02 | 67.20 | 173.60 | 5.67 |

numerical | 217.73 | 173.60 | 76.62 | 67.20 | 183.44 | ||||

R-P2L1 | Experimental | 171.50 | 3.13 | 137.20 | 52.20 | 15.31 | 52.20 | 137.20 | 11.84 |

numerical | 176.86 | 137.20 | 60.19 | 52.20 | 153.45 | ||||

R-P2L3 | Experimental | 211.50 | 1.13 | 169.20 | 70.10 | 5.34 | 70.10 | 169.20 | 7.29 |

numerical | 209.11 | 169.20 | 66.36 | 70.10 | 156.86 | ||||

R-P2L4 | Experimental | 208.50 | 1.24 | 166.80 | 87.30 | 10.27 | 87.30 | 166.80 | 4.46 |

numerical | 211.08 | 166.80 | 96.27 | 87.30 | 174.24 | ||||

R-P5L3 | Experimental | 225.25 | 1.04 | 180.00 | 89.30 | 8.81 | 89.30 | 180.00 | 4.73 |

numerical | 222.90 | 180.00 | 97.17 | 89.30 | 188.52 |

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|

Column | Lap Length (d _{bL}) | Layers CFRP | θ_{u,exp} | θ_{u,pred}(KANEPE) | AE (%) | θ_{u,pred}(EC8.3) | AE (%) | θ_{u,prop}(Proposed- Including Equation c) | AE (%) |

R-P2L0 | 0 | 2 | 0.044 | 0.0422 | 4.1 | 0.0419 | 4.9 | 0.0419 | 4.8 |

R-P2L1 | 15 | 2 | 0.034 | 0.0121 | 64.5 | 0.0167 | 50.9 | 0.0352 | 3.5 |

R-P2L3 | 30 | 2 | 0.047 | 0.0231 | 51.0 | 0.0227 | 51.7 | 0.0442 | 5.9 |

R-P2L4 | 45 | 2 | 0.056 | 0.0303 | 45.9 | 0.0298 | 46.8 | 0.0467 | 16.5 |

R-P5L3 | 30 | 5 | 0.056 | 0.0256 | 54.3 | 0.0252 | 55.0 | 0.0632 | 12.8 |

AAE(%) | 44.0 | 41.9 | 8.7 | ||||||

AR | 0.56 | 0.58 | 0.98 |

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**MDPI and ACS Style**

Anagnostou, E.; Rousakis, T.
Performance of Steel Bar Lap Splices at the Base of Seismic Resistant Reinforced Concrete Columns Retrofitted with FRPs—3D Finite Element Analysis. *Fibers* **2022**, *10*, 107.
https://doi.org/10.3390/fib10120107

**AMA Style**

Anagnostou E, Rousakis T.
Performance of Steel Bar Lap Splices at the Base of Seismic Resistant Reinforced Concrete Columns Retrofitted with FRPs—3D Finite Element Analysis. *Fibers*. 2022; 10(12):107.
https://doi.org/10.3390/fib10120107

**Chicago/Turabian Style**

Anagnostou, Evgenia, and Theodoros Rousakis.
2022. "Performance of Steel Bar Lap Splices at the Base of Seismic Resistant Reinforced Concrete Columns Retrofitted with FRPs—3D Finite Element Analysis" *Fibers* 10, no. 12: 107.
https://doi.org/10.3390/fib10120107