Theoretical mechanical properties of the panels

6.2      Theoretical mechanical properties of the panels

6.2.1     Modulus of rupture

To assure sufficient mechanical properties of the re-designed panel modulus of rupture of the original panel was calculated and was compared to the modulus of rupture of the FS welded panel.

The calculation carries inaccuracy caused by the fact that rivet joint does not carry the load the same way as monolithic structure of the welded panel. Later in this thesis simulation done using finite element methods (FEM) was used to determine more accurate value of mechanical properties of riveted and FS welded panel and allowed better comparison.

This calculation was used to determine dimensions of the stringers used on FS welded panel.     Stringer modulus of rupture comparison

The changes in the panel design lie in the change of stringer shape, dimensions and the joint type. We compared the modulus of rupture of stringers used for riveted construction and FS welded construction in order to keep the mechanical properties of the panel overall the same. This calculation cannot be taken as a proof of equivalent mechanical properties of the riveted and FS welded panel design because it does not take in consideration other types of loading than X-axis bending (as shown on Figure 17) and different character of the joint. Further comparison of mechanical properties was performed using FEM simulation involving the influence of the different joint type.     Modulus of rupture of riveted stringer

The modulus of rupture was calculated by dividing the stringer area into 3 parts, calculating the modulus for each of the parts and adding the values together. In the part 3 only the modulus towards the X-axis was calculated as its inner modulus is negligible in comparison.

Figure 17: Scheme of riveted stringer with dimensions

Equation 1: Calculation of the modulus of rupture of the stringer of riveted construction panel     Dimension design of FS welded stringers

The modulus of rupture of the FS welded stringers must not be lower the original one, thus

Modulus of rupture of the FS welded stringers can be calculated by Equation 2.

Equation 2:Calculation of modulus of rupture of the stringer of the FSW panel

For the design we fixed the width of the stringer to assure stability of the stringer as a plane under compressing stress. The width t’ was fixed to the value of 4 mm,

t’ = 4 mm

same as on the stringer used in the riveted construction, even though there is no reinforcing extension, and after getting the needed value of the stringer height a’, stability properties of the stringer was checked.

Figure 18: Scheme of FS welded stringer with dimensions

We compared the value of modulus of rupture of the FS welded stringer with the value for the riveted stringer

Equation 3: Comparison of modulus of rupture of FSW and riveted panel

And from Equation 3 we got the value of minimal stringer height a’, so we can write

Equation 4: Calculation of the minimal height of the stringer of the FSW panel

We choose the height of the stringer

a’ = 29 mm     Comparison of properties of riveted and FS welded panel

We calculated modulus of rupture for the FS welded stringer by Equation 3; in addition, we calculated cross section area of both stringers and compared their values in Table 1.


Table 2: Comparison of properties of riveted and FS welded panel


Riveted panel stringer

FS welded panel stringer

FSW/Riveted ratio

Cross section area

(representing relative weight comparison)





Modulus of rupture






The comparison shows that the FS welded stringer is lighter by almost 40 % comparing with the riveted one providing even better static mechanical properties. Translated into weight saving that would mean, considering material 2024 density [81],

r2024 = 2770 kg.m-3

that, for every meter of stringer used on the construction, we would save 208 grams of material. As a rough estimate, the change of technology from riveting to FSW would save more than 3 kg on one panel.

6.2.2     Tensile strength

Tensile properties were not compared as the panel plate dimensions remain the same and the stringers are not supposed to carry tensional load. Stringer riveting is also not capable of the full transfer of the tension from the panel plate to the stringers.