*3.1. Laboratory Tests*

In the first step of the laboratory analysis, the four-pinned frame of the experimental set-up (see Figure 2a) was tested without the sheeting. The force–displacement outcomes confirmed the assumption that the frame alone, not including trapezoidal sheeting, has a mechanism of negligible stiffness, with regard to shear stiffness of the analysed panel; see Figure 6.

**Figure 6.** Force–displacement paths obtained in experimental tests.

Next, major tests of trapezoidal sheeting panels were conducted. In the first step, the constant displacement increase was applied leading to panel failure. The force–displacement and force–time path of the main nodes were registered; see "T\_0\_increasing" in Figures 6 and 7. Moreover, strains were measured by SG (for the location of the SG; see point 2.3), leading to the corresponding stresses: SG1 and SG5—stresses in the direction perpendicular to the corrugation (top and bottom side of the sheeting respectively) and SIG\_1 and SIG\_2—the principal stresses linked with the outcomes of strain gauge rosette; see Figure 7. Note that the stresses related to profile distortion (in the location of strain gauges SG1 and SG5) start to increase earlier and become much greater than the stresses related to global shear of the panel (in the location of strain gauges SG2, 3, 4). It confirms the prediction that in this variant of panel geometry (relatively high trapezoidal sheeting compared to the panel planar dimensions), the profile distortion dominates the shear strain. What is more, the absolute values of SIG\_2 principal stresses were about 1.5–2 times greater than the values of SIG\_1 principal stresses. The values were affected by the orthotropy of the trapezoidal sheeting and the location of the SGs on the bottom flange.

**Figure 7.** Force–time and stress–time paths obtained in experimental tests for increasing loading.

In the next step, three cyclic loading tests were conducted on trapezoidal sheeting panels. The diaphragms were loaded six times in every test; each step brought an increasing force level. The last increment led to failure of the panel. The force–displacement path of the main nodes registered by the testing machine is presented in Figures 6 and 8; see "T\_1\_cyclical," "T\_2\_cyclical" and "T\_3\_cyclical".

**Figure 8.** Force–displacement paths obtained in experimental tests—the extract of the outcomes.

The force–displacement relations corresponding to the repeated loading revealed a wider characteristic of the panel compared to the permanently increasing load (compare T\_1-3\_cyclical with the T\_0\_increasing in Figure 8). Hence the diaphragm displays two types of stiffnesses: primary and secondary. When the panel bears a particular force level for the first time, its stiffness is lower (primary stiffness); when the force level is achieved again, after unloading, the stiffness is greater (secondary stiffness). In the course of primary loading, the displacements between elements (e.g., loose

space, clearances) are successively removed, some of them permanently. As a result, during reloading the displacement does not reach the level prior to the primary loading. Moreover, stiffness depends on the direction of change which is represented graphically by the hysteresis curves. The area in the centres of hysteresis loops can be interpreted as the energy dissipation mainly due to friction between elements of the panel. The scale of the hysteresis can rely on the rapidity of the loading/reloading.

The trend line for the test with increasing load is shown in Figure 8, where: *F* is force and Δ is displacement. According to the trend line equation, the primary stiffness of the panel is 0.424 kN/mm. The force–displacement relations for increasing and repeated loading make us conclude that both primary and secondary stiffness of the panels in four tests are comparable. Simultaneously, translation of the diagrams is observed. It can arise from different initial clearances in particular panels triggered by assembly imperfections, thus means it can also occur in real structure situation.

Similarly to the increasing loading case, in the case of repeated loading strains were also measured by strain gauges (the location of the strain gauges is addressed in point 2.3), leading to stresses: SG1 and SG5—the stresses in the direction perpendicular to the corrugation (top and bottom side of the sheeting respectively); and SIG\_1 and SIG\_2—the principal stresses in the location of strain gauges rosette, as presented in Figure 9.

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**Figure 9.** Force–time and stress–time paths obtained in experimental tests for repeated loading.

After reaching a particular load level, the force was fixed for the time equal to 30 s. During that time, the displacements were increasing while the force and the stresses in the sheeting remained constant; see Figures 8 and 9. It can signalise the local plasticity of the trapezoidal sheeting, e.g., in the area of screws and the longitudinal fold lines of the sheeting—even in the case of load increments when the stresses (indirectly) measured by strain gauges SG1 and SG5 in the area close to the support were below the yield stress.

Permanent displacements increased at every loading; the stresses followed; see Figure 9. That confirms the theory of local plasticity of the trapezoidal sheeting, which can lead to leakage or even failure of the sheeting.

Figure 10 shows deflection modes observed during tests. First of all, profile distortion occurs; next comes hole elongation, leading to the rotation of the sheeting. Hole elongation due to plasticity of the sheeting turned out to be a crucial failure mechanism in this series of tests.

**Figure 10.** Deflections of trapezoidal sheeting observed during laboratory tests: (**a**) profile distortion—global view; (**b**) profile distortion—local view; (**c**) hole elongation; (**d**) rotation of the sheeting due to hole elongation.

At the first stage of the unloading, both displacements and stresses decrease rapidly (small decrease of the displacements means that the structure is rigid at the beginning of the uploading). Visual observations confirm that the profile distortion decreases significantly. It is interpreted as the fact that in first unloading stage the traction between elements supresses the displacements between members and the stiffness is mostly influenced by taking back the profile distortion.
