### Loading

Loading of the panel samples was chosen to simulate bending loading. The typical loading of the panel on a real construction would be tensional or compression/buckling. However, thanks to the low dimension of the sample in the longitudinal direction stability features of compression/buckling loading would not appear on the sample in correct way. The applied loading approximates buckling load by introducing the bending moment into the sample. The simulation was not designed to reveal the stability threshold.

On these samples, we investigated bending loading of the panel as shown on Figure 28 for the loading in the direction of positive Z-axis, which simulates loading where the panel plate carries tensional stress and stringers carry compression. Due to the dimensions of the sample is unlikely that the simulation would reveal buckling of the stringer.

The residual stresses after welding were not introduced as a part of loading of the sample, because we did not have enough data about its distribution for the given type of FS welded joint.

Figure 28: Loading of the panel in direction of the positive Z-axis

Figure 29 shows the case of loading in the negative Z-axis direction. In this case, the panel plate is compressed and we expect tendency towards buckling and stringers carry tensional load.

Figure 29: Loading of the panel in direction of the negative Z-axis

For the purpose of further calculation, we considered the plane, the surface of the panel plate (where the stringers are attached), as the neutral plane for both cases of bending. Asymmetry caused by the slightly asymmetrical cut-outs in the panel plate is neglected, as their influence towards the deformation and stress distribution in the observed area is not significant.

The values of the bending loads are the same for the both cases only the directions are opposite.

The value of the loading q is chosen to be

q = 0.44 N.mm-1

The loading force for the investigated width of the panel ws = 250 mm thus, is

Equation 5: Calculation of the force applied on the FEM model samples

that would equal total force, applied to the full-scale panel of width wp = 1926 mm, which is

Equation 6: Calculation of the force applied on the tested panels

The moment caused by the force in the investigated plane of symmetry for the panel sample would be

Equation 7: Calculation of the moment caused by the loading force in the plane of symetry

where lp is the length of the full scale panel.

We did not introduce the moment into the plane of symmetry of the panel but into the surface that lies in the distance

ls = 60 mm

from the plane of symmetry thus, the moment we introduced into the sample is

Equation 8: Calculation of the moment introduced into the FEM model samples

The gained value of the moment cannot be introduced directly into the tested sample. The used FEM simulation program, Ansys Workbench 10, distributes the load equally according the surface area of selected part surfaces. However, the moment has to be distributed according to the modulus of rupture towards the bend axis. Herein below, we showed how we calculated the modulus of rupture for respective riveted and FS welded panel sample

##### 6.4.1.2.1     Riveted panel sample loading

The total values of the load introduced into the sample are

The moment distribution depends on the modulus of rupture of the stringer and the panel plate sample. We have already calculated the modulus of rupture of the riveted panel stringer

We have to calculate the modulus of the part of the panel plate involved in the simulation. Figure 30 shows the dimensions of the panel plate.

Figure 30: Scheme of the panel plate part used in FEM simulations

Modulus of rupture of the sample panel part is

Equation 9: Modulus of rupture of the sample panel part

###### 6.4.1.2.1.1       Moment load distribution between stringer and the panel plate

The moment Ms is distributed proportionally to the modulus of rupture value between the stringer and the panel plate. Thus, moment carried by the stringer is

Equation 10: Moment carried by the stringer of riveted panel construction sample

and the moment carried by the panel plate part is

Equation 11: Moment carried by the panel plate of riveted panel construction sample

###### 6.4.1.2.1.2       Shear force load distribution between stringer and the panel plate

The force is distributed proportionally to the surface area values. Thus, for the stringer we can write

Equation 12: Force carried by the stringer of riveted panel construction sample

and for the panel plate

Equation 13: Force carried by the panel plate of riveted panel construction sample

where SR,st is the cross section area of the stringer for the riveted panel calculated previously.

###### 6.4.1.2.1.3       Sample loading

The forces are distributed automatically and evenly on surface area of the selected surfaces, we can apply the calculated loads on the FEM model as shown in Figure 31.

Figure 31: Load placement on the riveted panel FEM sample

##### 6.4.1.2.2     FS welded panel sample loading

Similar calculations were performed for the FS welded panel sample. The modulus of rupture of the panel plate sample is the same as for the riveted sample.

###### 6.4.1.2.2.1       Moment load distribution between stringer and the panel plate

To calculate the moment carried by the stringer we used adapted Equation 10 and thus,

Equation 14: Moment carried by the stringer of FSW panel construction sample

and the moment carried by the panel plate from the adapted Equation 11 is

Equation 15: Moment carried by the panel plate of FSW panel construction sample

###### 6.4.1.2.2.2       Shear force load distribution between stringer and the panel plate

The force is distributed proportionally to the surface area values. Thus, for the stringer we can write

Equation 16: Force carried by the stringer of FSW panel construction sample

and for the panel plate

Equation 17: Force carried by the panel plate of FSW panel construction sample

where SR,st is the cross section area of the stringer for the riveted panel calculated previously.

###### 6.4.1.2.2.3       Sample loading

Again the force introduced into the sample is in total FS = 110 N and is automatically distributed on the cross section surfaces of the stringer and the panel plate as shown in Equation 16and Equation 17. The moment is distributed as shown in Equation 14 and Equation 15. All the loads are shown in Figure 31.

Figure 32: Load placement on the FS welded FEM sample

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