# Experimental Study on a Novel Shear Connection System for FRP-Concrete Hybrid Bridge Girder

^{*}

## Abstract

**:**

## 1. Introduction

## 2. FRP-Concrete Hybrid Bridge Girder and Shear Connection System

^{3}. The slab was reinforced longitudinally and transversally with two grids made of 12 mm ribbed GFRP rebars spaced every 120 mm in each direction. The LWC slab was connected to FRP beam by means of novel shear connectors made of M20 class 4.8 bolts welded to a rectangular steel plate (Figure 2). The single connector consisted of 8 bolts welded in two rows to 10 mm thick steel plate of 240 × 660 mm in plan. The connectors were attached to bottom surface of beam’s top flanges with epoxy adhesive.

## 3. Shear Connection Design

_{L,Ed}and corresponding shear forces V

_{Ed}were determined according to Formulas (A6)–(A8) in Appendix A and thus the shear force per one stud was established to be assumed in testing program (Table 1).

## 4. Static Tests

#### 4.1. Specimens’ Fabrication

_{u}= 400 MPa, yield strength f

_{y}= 320 MPa and modulus of elasticity E = 200 GPa.

#### 4.2. Test Setup

_{Ed,k}= 87.92 kN, subsequently five cycles of loading up to design load level of P

_{Ed,d}= 125.36 kN, and finally loading up to specimen’s failure. The both intermediate load levels were determined taking into account the maximum shear force per stud (Table 1) multiplied by four studs of the specimen. The loading rate was 2.0 kN/s.

#### 4.3. Test Results

_{s}and corresponding slip value δ

_{1}, both necessary for slip modulus k

_{slip}estimation. Ultimate load P

_{u}and corresponding ultimate slip δ

_{u}let us to determine shear connecting capacity. The failure mode indicates the weakest elements of the connection. All of these outcomes are described and illustrated below for all specimens tested.

## 5. Fatigue Test

#### 5.1. Test Setup

_{min}, peak load F

_{max}and loading range ΔF. During the cyclic test, the load from the actuator load cell and the displacement of the specimen were measured, the latter by four LVDT’s in P1 and P3 measurement points. Cyclic tests were conducted under sinusoidal control waveforms with a load frequency of 2 Hz.

_{u,av}was determined (Table 4). This value represented the reference parameter for the relative values of loading required for cyclic tests. Cyclic tests were conducted for loading range approximately 30%–60% of P

_{u,av}with the stress ratio R = 0.1. Three load controlled cyclic tests on specimens F4, F5 and F6 were performed to determine the fatigue life N of the shear connection. The loading parameters of fatigue test are summarized in Table 5. After reaching the design number of cycles (2 million) one of these three test specimens did not fail and it was statically loaded to failure under displacement control to obtain the reduced static strength after high cycle preloading.

#### 5.2. Test Results

## 6. Discussion

#### 6.1. Load-Slip Behavior

_{slip}is often used to evaluate shear connections. The slip modulus is given as follows:

_{slip}= P

_{s}/n δ

_{1}

_{slip}is the slip modulus for a single bolt, n is the number of bolts in the specimen (here n = 4) and δ

_{1}is the slip at the load of P

_{s}, after which the nonlinear behavior becomes notable.

_{slip}for the novel connector is listed in Table 4. For specimen 2 in parenthesis k

_{slip}value is also given after deducting the premature slip 0.065 mm (Figure 10), which was rather untypical behavior of the specimen. The average slip modulus k

_{slip}is approximately 523 kN/mm, indicating that the connectors can promote the composite action very efficiently, than other solutions, where k

_{slip}was obtained in the range of –200 kN/mm [25,29,35].

#### 6.2. Failure Mechanism

#### 6.3. Shear Capacity

_{r}) was defined by Equation (2):

_{r}= P

_{u}/n

_{u}—experimentally obtained maximum load of push-out tested specimens; n-total number of bolts in specimen (here n = 4).

_{Ed}= 21.98 kN (Table 1) the global safety factor of the shear connection can be estimated as follows: 80.67/21.98 = 3.67 showing the high safety, reliability and robustness of the novel connection system.

#### 6.4. Fatigue Strength

_{R})

^{m}·N

_{R}= (Δτ

_{c})

^{m}× N

_{c}

_{R}is the stress range; m is the slope of the fatigue strength curve with the value m equal to 8; N

_{R}is the number of stress-range cycles; Δτ

_{c}is the reference value at N

_{c}= 2 million cycles with Δτ

_{c}equal to 90 MPa.

_{R}replaced by η

_{E}Δτ

_{R}and Δτ

_{c}replaced by η

_{E}Δτ

_{c}, where η

_{E}is given in Eurocode 2 [34] as 0.955.

_{c}are calculated as 12.95 and 142.6 MPa, respectively. Thus, the fatigue strength obtained from the fatigue test is 142.6/(0.955· 90) = 1.66 higher when compared to the fatigue strength according to Eurocode 4 [32].

## 7. Conclusions

- •
- the load—slip behavior of the GFRP–concrete specimens is more ductile than that of typical steel-concrete specimens;
- •
- the average slip modulus k
_{slip}value is approximately 523 kN/mm, indicating that the connectors can promote the composite action very efficiently; - •
- bolt shank fracture is the only failure mode, found in the static tests, while the weld toe fracture in welds joining shear bolts to steel plate was the failure mode in fatigue; these may be a preferable failure modes for designing of FRP–concrete hybrid girders with the use of the novel shear connectors;
- •
- the average ultimate resistance obtained from the test is about 12% higher than the characteristic resistance of shear studs according to Eurocode 4 [32];
- •
- the fatigue strength curve slope m = 12.95 and the reference value Δτ
_{c}= 42.6 MPa at two million cycles are determined; thus, the fatigue strength obtained from the test is 1.66 higher when compared to the fatigue strength of shear studs according to Eurocode 4 [32]; - •
- the global safety factor of the shear connection is estimated as 3.67 showing the high safety, reliability and robustness of the novel connection system,
- •
- Eurocode 4 [32] slightly underestimates the shear capacity and the fatigue strength of the novel connection; however, despite this conservatism this code can be used to predict the strength of the connection and to check its ULS/SLS design provisions.

## 8. Patents

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{Rk}was calculated according to Eurocode 4 [32] as:

_{Rk}= min(P

_{Rk1},P

_{Rk2}),

_{Rk1}= 0.8 × f

_{u}× ( πd

_{s}

^{2})/4—shear resistance of stud’s shank,

_{Rk2}= 0.29 × α

_{s}× d

_{s}

^{2}× √(f

_{ck}× E

_{cm})—concrete crushing resistance,

_{u}—specified ultimate tensile strength of stud’s material, f

_{ck}—characteristic cylinder compressive strength of concrete at the age considered, E

_{cm}—secant modulus of elasticity of concrete, d

_{s}—nominal diameter of bolt shank, while α

_{s}:

_{S}= 0.2 × (h

_{sc}/d

_{s}+ 1) for 3 ≤ h

_{sc}/d

_{s}≤ 4 or α

_{s}= 1 for h

_{sc}/d

_{s}> 4a = 1,

_{sc}—the overall nominal height of the stud.

- •
- f
_{u}= 400 MPa—for 4.8 class bolt acc. to Eurocode 3–1-8 [34], - •
- f
_{ck}= 35.0 MPa—approved by testing for 35/38 class LWC acc. to Eurocode 2–1-1 [36], - •
- E
_{cm}= 26.968 GPa—determined by testing for 35/38 class LWC acc. to Eurocode 2–1-1 [36] and for concrete density ρ = 1968 kg/m^{3}, - •
- d = 16.94 mm—nominal dimeter for M20 bolt acc. to [37],
- •
- h
_{sc}= 150 mm,

- •
- γ
_{V}= 1.25—the partial factor for ultimate limit states (ULS), - •
- k
_{s}= 0.75—the reduction factor for serviceability limit states (SLS),

_{Rd,ULS}= P

_{Rk}/1.25,

_{Rd,SLS}= 0.75 × P

_{Rd,ULS},

- •
- P
_{Rk1}= 72.15 kN—shear resistance of stud’s shank, - •
- P
_{Rk2}= 80.91 kN—concrete crushing resistance, - •
- P
_{Rd,ULS}= 57.72 kN—design resistance for ULS verification, - •
- P
_{Rd,SLS}= 43.29 kN design resistance for SLS verification.

_{Ed}, V

_{Ed}) were determined and considered to prepare the test program for the structural performance verification of shear connection system as described below.

_{L,Ed}at the interface between the concrete slab and the FRP beam was determined as follows:

_{L,Ed}(x) = V

_{Ed}(x) × (S

_{c}/I

_{c}),

_{Ed}(x)—shear force for the considered load case, S

_{c}—static moment of area of concrete slab with respect to the center of gravity of the composite cross-section and un-cracked cross-section properties; I

_{c}—second moment of area (moment of inertia) of the hybrid (composite) cross-section.

- •
- V
_{Ed,k}= 21.98 kN—maximum characteristic shear force for SLS checking, - •
- V
_{Ed,d}= 31.34 kN—maximum design shear force for ULS checking.

_{c}and I

_{c}is the same as the one used to calculate the corresponding shear force contribution for each single load case. Taking into account the following values [31,38] we obtained:

- •
- E
_{FRP}= 71.924 GPa—equivalent modulus of elasticity of FRP beam with respect to bottom edge, - •
- E
_{cz}(t) = 26.986—short term modulus of elasticity of concrete slab, - •
- E
_{cw}(t) = 18.549—long term modulus of elasticity of concrete slab, - •
- n
_{Lz}= E_{FRP}/E_{cz}(t) = 71.924/26.986 = 2.665—modular ratio for short term loads, - •
- n
_{Lw}= E_{FRP}/E_{cw}(t) = 71.924/18.549 = 3.878—modular ratio for long term loads including creep,

- •
- A
_{c}= 0.18 × 2.62 = 0.472 m^{2}—cross-section area of concrete slab, - •
- z
_{z}= 97.18 mm—distance between gravity center of concrete slab and neutral axis of hybrid (composite) girder for short term loads, - •
- z
_{w}= 133.20 mm—distance between gravity center of concrete slab and neutral axis of hybrid (composite) girder for long term loads including creep,

_{L,Ed}are as follows:

- •
- S
_{cz}= 0.0172 m^{3}—static moment of area for short term loads, - •
- S
_{cw}= 0.0162 m^{3}—static moment of area for long term loads, - •
- I
_{cz}= 0.0188 m^{4}—second moment of area for short term loads, - •
- I
_{cw}= 0.0180 m^{4}—second moment of area for short term loads.

- •
- max (v
_{L,Ed,k}) = 488.40 kN/m, - •
- max (v
_{L,Ed,d}) = 696.43 kN/m.

_{L,Ed,k}) and max (v

_{L,Ed,d}) values shrinkage is also included. In each cross-section of the girder there should be enough studs to take up all the shear force per unit length. The following should be therefore verified at all abscissa x:

_{L,Ed,k}(x) ≤ (N

_{i}/l

_{i}) × P

_{Rd,SLS}—for SLS verification,

_{L,Ed,d}(x) ≤ 1.1 × (N

_{i}/l

_{i}) × P

_{Rd,ULS}—for ULS verification,

- •
- l
_{i}—length of segment (the girder total length is divided into n segments), - •
- N
_{i}—number of studs per row in segment (constant density per segment).

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**Figure 1.**Bridge girder’s cross-section: (

**a**) fiber-reinforced polymer (FRP) beam; (

**b**) hybrid FRP- lightweight concrete (LWC) girder (unit: mm).

**Figure 4.**Specimen’s fabrication: (

**a**) glass fiber-reinforced polymer (GFRP) reinforcement of concrete slab; (

**b**) steel connectors inside the tube; (

**c**) ready specimen.

**Figure 6.**Location of linear variable differential transducer (LVDT) measurement points on specimen.

**Figure 9.**Failure mode of specimen S1: concrete surface—no cracks (

**top**); GFRP surface—no bearing or shear-out failure (

**bottom**).

**Figure 11.**Failure mode of specimen S2: (

**a**) general mode; (

**b**) concrete surface—no cracks; (

**c**) GFRP surface—initial bearing (right).

**Figure 12.**Failure mode of specimen S3: (

**a**) concrete surface protrusion crushed; (

**b**) concrete surface—no cracks.

**Figure 13.**Load–slip curves of specimen S3 in the range of 0–200 kN: premature slip at 140 kN (one side only).

**Figure 16.**Fatigue failure mode of specimen F4: (

**a**) fracture at weld toe on steel plate; (

**b**) fractured bolt shanks; (

**c**) slight shear-out failure in GFRP laminate.

Load | Total Shear Force Per Unit Length v_{L,Ed} | Maximum Shear Force V_{Ed} | Maximum Shear Force Per Study P_{Ed} |
---|---|---|---|

[kN/m] | [kN] | [kN] | |

Characteristic | 488.40 | 349.44 | 21.98 |

Design SLS | 488.40 | 349.44 | 21.98 |

Design ULS | 696.43 | 523.02 | 31.34 |

Constant, Parameter | Unit | Symbol, Direction | Lamina | ||
---|---|---|---|---|---|

X-E ±45° | B-E 0/90° | U-E 0° (90°) | |||

1210 g/m^{2} | 800 g/m^{2} | 1210 g/m^{2} | |||

Longitudinal modulus of elasticity | GPa | E_{x} | 20.50 | 20.00 | 42.13 |

E_{y} | 20.50 | 20.00 | 10.87 | ||

Transverse modulus of elasticity | GPa | G_{xy} | 3.90 | 3.90 | 4.40 |

G_{yz} | 3.04 | 2.83 | 2.71 | ||

G_{xz} | 3.04 | 2.83 | 2.71 | ||

Poisson’s ratio | - | ν_{xy} | 0.019 | 0.029 | 0.29 |

ν_{yz} | 0.019 | 0.029 | 0.075 | ||

ν_{xz} | 0.019 | 0.029 | 0.075 | ||

Tensile strength | MPa | X_{t} | 520.0 | 522.0 | 855.0 |

Y_{t} | 520.0 | 522.0 | 44.0 | ||

Compressive strength | MPa | X_{c} | 320.0 | 321.0 | 537.0 |

Y_{c} | 320.0 | 321.0 | 84.0 | ||

Shear strength | MPa | S_{xy} | 60.0 | 60.0 | 51.0 |

S_{yz} | 30.0 | 30.0 | 25.0 | ||

S_{xz} | 30.0 | 30.0 | 25.0 |

Constant, Parameter | Unit | Symbol, Direction | Value |
---|---|---|---|

Modulus of elasticity | GPa | E_{c} | 26.986 |

Tensile strength | MPa | f_{t} | 2.46 |

Compressive strength | MPa | f_{c} | 25.76 |

Ultimate compressive strain | [‰] | ε_{lcu1} | 1.749 |

Density | kg/m^{3} | ρ | 1968 |

Specimen | First Slip | Failure | |||||
---|---|---|---|---|---|---|---|

Slip Load P_{s} | First Slip δ_{1} | Modulus k_{slip} | Ultimate Load P_{u} | Ultimate Slip δ_{u} | Ultimate Resistance P_{r} | Mode | |

[kN] | [mm] | [kN/mm] | [kN] | [mm] | [kN] | ||

S1 | 255 | 0.12 | 531.3 | 311 | 4.2 | 77.75 | bolt shank fracture |

S2 | 245 | 0.30 (0.235) | 204.2 (260.6) | 315 | 4.3 | 78.75 | bolt shank fracture |

S3 | 405 | 0.16 | 632.8 | 342 | 4.5 | 85.50 | bolt shank fracture |

F6 | 320 | 0.12 | 666.7 | 315 | 4.9 | 78.75 | bolt shank fracture |

Average ^{1} | 522.8 | 322.67 | 80.67 |

^{1}Without specimen F6.

Specimen | F_{min} | F_{max} | R = F_{min}/F_{max} | ΔF | ΔF/P_{u,av} |
---|---|---|---|---|---|

[kN] | [kN] | [kN] | [%] | ||

F4 | 22.2 | 222.2 | 0.1 | 200 | 61.9 |

F5 | 16.6 | 166.6 | 0.1 | 150 | 46.5 |

F6 | 11.0 | 111.0 | 0.1 | 100 | 31.0 |

Specimen | Stress Range Δτ_{R} | Crack Initiation | Number of Cycles at Failure N_{R} | Log (N_{R})/Log (N_{c}) acc. to [32] |
---|---|---|---|---|

[MPa] | [cycles] | [cycles] | ||

F4 | 217.7 | 8.384 × 10^{3} | 8.412 × 10^{3} | |

F5 | 163.3 | 2.945 × 10^{5} | 3.488 × 10^{5} | 1.66 |

F6 | 108.9 | – | run-out |

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## Share and Cite

**MDPI and ACS Style**

Rajchel, M.; Kulpa, M.; Siwowski, T. Experimental Study on a Novel Shear Connection System for FRP-Concrete Hybrid Bridge Girder. *Materials* **2020**, *13*, 2045.
https://doi.org/10.3390/ma13092045

**AMA Style**

Rajchel M, Kulpa M, Siwowski T. Experimental Study on a Novel Shear Connection System for FRP-Concrete Hybrid Bridge Girder. *Materials*. 2020; 13(9):2045.
https://doi.org/10.3390/ma13092045

**Chicago/Turabian Style**

Rajchel, Mateusz, Maciej Kulpa, and Tomasz Siwowski. 2020. "Experimental Study on a Novel Shear Connection System for FRP-Concrete Hybrid Bridge Girder" *Materials* 13, no. 9: 2045.
https://doi.org/10.3390/ma13092045