# Structural Behaviour of Aluminium-Timber Composite Beams with Partial Shear Connections
## 2 Materials and Methods
### The Numerical Models
Figure 10: Slip distribution in the B200 composite beam. The authors observed one distinctive mode of failure in all of the tested beams (Figure 12). When the collapse load was applied, the veneers separated from each other in the LVL panel sections subjected to tension. Then, the veneers cambered near the loading plates in the LVL panel sections subjected to compression. At the serviceability deflection limit (\(L/250=10.8\) mm), the load reached ca. 30% of the failure load. The deflections of the specimens were large because of the low values of the modulus of elasticity for aluminium and LVL. The Young's modulus of aluminium (70 GPa) is three times lower than that of steel (210 GPa). For this reason, the deflection of the tested beams was large. However, in the presented tests, the LVL slab width was limited by the dimensions of the laboratory stand. The LVL slabs were located between the columns of the testing machines. The dimensions of the LVL panel and the cross-section of the aluminium beam were selected to obtain the neutral axis located in the LVL. In the case of the floor, the effective LVL slab will be wider, and the girder will be higher. As a result, the deflections will be lower. Therefore, the combination of aluminium and timber is beneficial. The transformed slab area for the cross-section of an aluminium- timber composite beam is approximately three times larger (\(n=70.0/14.0=5.0\)) than the transformed slab area for the cross-section of a steel-timber composite beam (\(n=210.0/14.0=15.0\)). This means that the second moment of area of an ideal cross-section of a composite beam is larger for an aluminium and timber composite beam than for a steel and timber composite beam. Due to this fact, the impact of the low modulus of elasticity of aluminium on large deflection may be decreased. The Theoretical Load-Carrying Capacity of the Aluminium-Timber Composite Beams with Partial Shear Connection  
The plastic resistance to bending of the aluminium-timber composite beam with partial shear connection \(M_{pl,q}\) was calculated based on the method for the steel and concrete composite beams presented in [27]:  
\[M_{pl,q}=M_{pl,a}+(M_{pl}-M_{pl,a})\eta \tag{2}\]  
Figure 12: Failure modes of the aluminium–timber composite beams: B120 (a), B160 (b), B200 (c). where \(M_{pl,a}\) 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; \(\eta\) is the degree of the shear connection. The calculations of the plastic resistance of the aluminium-timber composite beam were conducted using the stress block method for the steel-concrete composite beams (Figure 13) and are presented in Table 4. The timber subjected to tension was additionally taken into account. Due to fact that the LVL slabs were subjected to both tension and compression in the composite beams with partial shear connections, the bending strength of the LVL was used as the LVL strength. This assumption was made based on the fact that timber structural elements are stronger in bending than in compression or tension [71]. This is because when a timber structural element is subjected to bending, only about 10% of its volume is subjected to high stresses, whereas when a timber structural element is subjected to pure tension or compression, all of its volume is subjected to the same value of stress [72]. The position of the plastic axis \(x_{pl}\) was obtained based on the following formula [25]:  
Figure 3:0  
The plastic resistance to sagging bending of the aluminium-timber composite beam was calculated from [25]:  
Figure 3:1  
The calculations of the plastic resistance of the aluminium-timber composite beam with partial shear connection are presented in Figure 3:2 The normal force in the aluminium beam section was \(18.79\cdot 18.7=351.0\) kN.