# Structural Behaviour of Aluminium–Timber Composite Beams with Partial Shear Connections

^{*}

## Abstract

**:**

## 1. Introduction

_{0.6}than the screwed connection due to the hole clearance. The bolted connections had an 80% higher shear strength than the screwed connections.

## 2. Materials and Methods

#### 2.1. Aluminium Girders

_{0.2}of this alloy was 140 MPa, the characteristic value of the tensile strength f

_{u}was 170 MPa, and the modulus of elasticity E was 70 GPa. The strength parameters of this alloy were also determined in tensile tests presented in [61] (Table 1).

#### 2.2. Laminated Veneer Lumber Slabs

^{3}, respectively, based on the manufacturer’s declaration [63]. The mechanical parameters of LVL were also determined in tensile, compressive, and bending tests presented in [64] (Table 1).

Parameter | Value |
---|---|

0.2% proof strength of AW-6060 T6 | 186.7 ± 7.05 MPa |

Tensile strength of AW-6060 T6 | 210.2 ± 2.90 MPa |

Tensile strength (parallel to grain) of LVL | 41.9 ± 4.8 MPa |

Compressive strength (parallel to grain) of LVL | 50.3 ± 1.6 MPa |

Bending strength of LVL | 66.1 ± 6.9 MPa |

Tensile strength of the steel used in the screws | 553.9 ± 23.6 MPa |

#### 2.3. Screws

#### 2.4. Shear Connection Tests

_{0.4}and k

_{0.6}were 6.6 ± 4.1 kN/mm and 6.2 ± 3.1 kN/mm, respectively [58].

#### 2.5. The Experimental Programme of the Study

#### 2.6. The Numerical Models

_{u}was calculated from Eurocode 5 [68]:

_{m}is the mean density of LVL; d is the diameter of the screw.

_{0}was assumed to be 30 kN/mm for the slip ranging from 0 to 0.2 mm to take into account the low initial slip values observed in the beams in the laboratory tests.

_{y}= 186.7 MPa, f

_{u}= 210.2 MPa). The steel was modelled as a bi-linear elastic-perfectly plastic material (E = 210 GPa, f

_{y}= 235 MPa). The LVL was treated as an orthotropic material. The Hashin damage model was used to capture the failure of the LVL. The material properties of the LVL adopted in the numerical models are provided in Table 2.

## 3. Results and Discussion

#### 3.1. The Results of the Four-Point Bending Test

#### 3.2. The Theoretical Load-Carrying Capacity of the Aluminium–Timber Composite Beams with Partial Shear Connection

_{pl,η}was calculated based on the method for the steel and concrete composite beams presented in [27]:

_{pl,a}is the plastic resistance to sagging bending of the structural aluminium section alone; M

_{pl}is the plastic resistance to sagging bending of the composite section with full shear connection; η is the degree of the shear connection.

_{pl}was obtained based on the following formula [25]:

_{pl,a}was 21.5 kN·m (W

_{pl}· f

_{0.2}= 114.8 · 18.7 = 21.5 kN·m). The resistance to sagging bending of the aluminium–timber composite beams with partial shear connections from the theoretical analyses differed by 6–16% from the resistance in the laboratory tests (Figure 14).

#### 3.3. The Results of the Numerical Analyses

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The analysed beams subjected to four-point bending (1–9—linear variable differential transformers).

**Figure 3.**The numerical models: The composite beam with full shear connection (

**a**), the B120 beam (

**b**), the B160 beam (

**c**), the B200 beam (

**d**).

**Figure 13.**The model used to calculate the plastic resistance of the aluminium–timber composite beam.

**Figure 15.**The load versus deflection responses from the test and the numerical analyses: All curves (

**a**), B120 (

**b**), B160 (

**c**), B200 (

**d**).

**Figure 16.**The load versus slip responses from the test and numerical analyses: All curves (

**a**), B120 (

**b**), B160 (

**c**), B200 (

**d**).

**Figure 17.**The areas of damage initiation. Due to the compression of the fibres and due to the tension of the fibres for the ultimate load (M

_{pl}= 68.7 kN·m) and the composite beam with full shear connection (

**a**), for the ultimate load (M

_{pl}= 64.4 kN·m) and the B120 beam (

**b**), for the ultimate load (M

_{pl}= 63.3 kN·m) and the B160 beam (

**c**), for the ultimate load (M

_{pl}= 63.9 kN·m) and the B200 beam (

**d**).

**Table 2.**The properties of the LVL adopted in the numerical models (direction 1 is parallel to the LVL grain).

Properties of an Elastic Orthotropic Material (Type: Lamina) | |||||
---|---|---|---|---|---|

E_{1}[MPa] | E_{2}[MPa] | ν_{12}[–] | G_{12}[MPa] | G_{13}[MPa] | G_{23}[MPa] |

24 000 | 430 | 0.48 | 650 | 650 | 96 |

Hashin damage parameters | |||||

σ_{t}_{1}[MPa] | σ_{c}_{1}[MPa] | σ_{t}_{2}[MPa] | σ_{c}_{2}[MPa] | σ_{v}_{12}[MPa] | σ_{v}_{23}[MPa] |

73 | 73 | 10 | 15 | 10 | 5 |

Longitudinal tensile fracture energy [kJ/m ^{2}] | Longitudinal compressive fracture energy [kJ/m ^{2}] | Transverse tensile fracture energy [kJ/m ^{2}] | Transverse compressive fracture energy [kJ/m ^{2}] | Viscosity coefficient | |

45 | 45 | 0.1 | 0.1 | 1.0 × 10^{−6} |

**Table 3.**The ultimate load (F

_{ult}), the ultimate load-carrying capacity (M

_{ult}), the deflection corresponding to the ultimate load (ν

_{ult}), and the slip corresponding to the ultimate load (u

_{ult}) from the bending tests.

Parameter | B120 | B160 | B200 |
---|---|---|---|

F_{ult} [kN] | 151.9 | 148.7 | 145.9 |

M_{ult} [kN·m] | 68.4 | 66.9 | 65.7 |

ν_{ult} [mm] | 83.2 | 80.7 | 87.9 |

u_{ult} [mm] | 3.5 | 4.0 | 5.6 |

**Table 4.**The calculations of the plastic resistance of the aluminium–timber composite beam with full shear connection.

Parameter | Value |
---|---|

Aluminium I-section area A_{a} [cm^{2}] | 18.8 |

Aluminium alloy yield strength of f_{0.2} [kN/cm^{2}] | 18.7 |

LVL bending strength f_{m} [kN/cm^{2}] | 7.3 |

LVL slab effective width b_{eff} [cm] | 37.0 |

LVL slab height h_{ts} [cm] | 7.5 |

Aluminium I-section height h [cm] | 16.0 |

Position of the plastic axis x_{pl} [cm] | 4.4 |

Plastic resistance M_{pl} [kN·m] | 78.2 |

**Table 5.**The plastic resistance to sagging bending of the aluminium–timber composite beams with partial shear connections.

Beam | η [–] | M_{pl,η} fromEquation (2) [kN·m] | M_{pl,η,test} fromthe Tests [kN·m] | M_{pl,η}/M_{pl,η,test} |
---|---|---|---|---|

B120 | 0.90 | 72.5 | 68.4 | 1.06 |

B160 | 0.70 | 61.2 | 66.9 | 0.91 |

B200 | 0.60 | 55.5 | 65.7 | 0.84 |

Analysis | η [–] | M_{pl},_{simulation} [kN·m] | M_{pl},_{theory} [kN·m] | M_{pl}_{,test}[kN·m] | M_{pl,simulation}/M_{pl,test} |
---|---|---|---|---|---|

1 | 1.00 | 68.7 | 78.2 | – | – |

2 (B120) | 0.90 | 64.4 | 72.5 | 68.4 | 0.94 |

3 (B160) | 0.70 | 63.3 | 61.2 | 66.9 | 0.95 |

4 (B200) | 0.60 | 63.9 | 55.5 | 65.7 | 0.97 |

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**MDPI and ACS Style**

Chybiński, M.; Polus, Ł. Structural Behaviour of Aluminium–Timber Composite Beams with Partial Shear Connections. *Appl. Sci.* **2023**, *13*, 1603.
https://doi.org/10.3390/app13031603

**AMA Style**

Chybiński M, Polus Ł. Structural Behaviour of Aluminium–Timber Composite Beams with Partial Shear Connections. *Applied Sciences*. 2023; 13(3):1603.
https://doi.org/10.3390/app13031603

**Chicago/Turabian Style**

Chybiński, Marcin, and Łukasz Polus. 2023. "Structural Behaviour of Aluminium–Timber Composite Beams with Partial Shear Connections" *Applied Sciences* 13, no. 3: 1603.
https://doi.org/10.3390/app13031603