**3. Results**

### *3.1. Tensile Properties of the Materials*

In Table 5, the tensile properties corresponding to the tensile specimens cut from each component are shown. The tensile test results for the steel corresponding to the four-tab connector are identical with the ones corresponding to the five-tab connector for the same beam height because we used connectors with five tabs for all beams and we had cut the connector to obtain four-tab connectors. The decision regarding the cutting of the five-tab connector was taken in order to have the same material for both kinds of connectors.


**Table 5.** Material properties for tested components.

\* The values were obtained in tensile tests within this research carried-out by INSTRON 3369 machine.

### *3.2. Results of Bending Tests*

In this research, all upright-connector-beam assemblies presented in Table 4 were tested according to the testing procedure presented in EN 15512 [9].

First, the moment-rotation curves (M–θ) are represented by using the data acquired with the force and displacement transducers and by using Equations (1) and (2). Then, the corrected moment-rotation curves (Mn–θn) are plotted for each upright-connector-beam assembly, after the corrections caused by the different thickness and yield strength were made by using Equations (5) and (8). The moment-rotation curves (Mn–θn) corresponding to all sets of the assemblies are plotted in Appendix A. There are a total of 101 curves plotted. In Figure A1, it is shown that the curves for the beam-connector-upright assemblies containing a type A beam. In the same manner, in Figures A2 and A3, the curves for the beam-connector-upright assemblies containing a type B beam and a type C beam, respectively. In order to comparatively analyze the effects of the connector type on the mechanical behavior of the beam-upright connections in bending the moment-rotation mean curves (Mn–θn) are plotted in Figures 9–11. It may be observed that the behavior of the connections is nonlinear and the connectors with five tabs are always stiffer than the connectors with four tabs for all assemblies tested.

The shapes of the moment-rotation (Mn–θn) curves shown in Figures A1–A3 added in the Appendix A, show a good repeatability recorded for each set of beam-connector-upright assemblies tested, concerning both the initial slopes of these curves (which gives the rotational stiffness) and the maximum values of the capable bending moments.

All values for the design bending moment MRd,i and for the rotational stiffness kni (i = 1,n) are determined by bending tests of the upright-connector-beam assemblies and by using Equations (12) and (13), respectively. In order to make the comparisons for the test results, the stiffness kni was evaluated for the maximum bending moment MRd,i when η = 1. All results are presented in Table 6.

**Figure 9.** Comparison of the moment-rotation curves recorded for: (**a**) A-I-4L and A-I-5L assemblies,(**b**) A-II-4L and A-II-5L assemblies, and (**c**) A-III-4L and A-III-5L assemblies.

**Figure 10.** Comparison of the moment-rotation curves recorded for: (**a**) B-I-4L and B-I-5L assemblies, (**b**) B-II-4L and B-II-5L assemblies, and (**c**) B-III-4L and B-III-5L assemblies.

**Figure 11.** Comparison of the moment-rotation curves recorded for: (**a**) C-I-4L and C-I-5L assemblies, (**b**) C-II-4L and C-II-5L assemblies, and (**c**) C-III-4L and C-III-5L assemblies.

The average values and standard deviations are also shown in Table 6 for the design bending moment MRd and for the rotational stiffness km corresponding to each group of beam-connector-upright assemblies tested in bending. The value of the standard deviation corresponding to the design bending moment MRd for each group of assemblies, divided by the average value MRd, is generally less than 3% and this means a high level of confidence of the experimental tests. Similar remarks may also be made regarding the values of the standard deviation corresponding to the rotational stiffness km. The low values of stdev compared to the average values show that the degree of scattering of the results is small. The differences between the results obtained for assemblies of the same group are justified by the geometric imperfections of the cross sections, which are characteristic of the cold formed steel profiles, especially in the area of the slots of the upright profile.

The results regarding both the corrected moment Mni and the rotational stiffness kni are comparatively shown in Figures 12–14 for each type of beam used in the assembly, i.e., for beam A, beam B, or beam C, respectively. It notes that the degree of scattering of the results is small from the point-of-view of both the corrected moment Mni and rotational stiffness kni corresponding to each group of assemblies tested (Figures 12–14). Comparing the results corresponding to the assemblies composed by the same type of beam and upright, we noticed that the design rotational stiffness km increases as the upright thickness increases. It is also evident that the design rotational stiffness km is greater for the assembly containing the five-tab connector than the value corresponding to the assembly containing the four-tab connector (Table 6, Figures 12b, 13b and 14b).

**Figure 12.** Comparison of the results obtained for the assemblies with the beam of type A concerning: (**a**) capable corrected moment Mn, and (**b**) rotational stiffness kni of the connections.

**Assembly code Design Moment Rotational Sti**ff**ness Assembly code Design Moment Rotational Sti**ff**ness Assembly code Design Moment Rotational Sti**ff**ness Mni MRd Stdev kni km Stdev Mni MRd Stdev kni km Stdev Mni MRd Stdev kni km Stdev (kNm) (kNm) (kNm) (kNm**/ **rad) (kNm**/ **rad) (kNm**/ **rad) (kNm) (kNm) (kNm) (kNm** / **rad) (kNm** / **rad) (kNm** / **rad) (kNm) (kNm) (kNm) (kNm** / **rad) (kNm** / **rad) (kNm** / **rad) A-I-4L** 2.11 1.54 0.12 40 39.0 1.34 **B-I-4L** 2.03 1.84 0.02 34 35.9 1.38 **C-I-4L** 2.12 1.70 0.08 44 43.7 1.26 1.99 38 2.06 36 2.13 44 2.08 38 2.08 35 2.13 45 1.90 37 2.07 38 1.95 41 1.81 40 2.07 37 2.14 44 1.96 40 **A-I-5L** 2.68 2.3 0.07 47 48.0 6.18 **B-I-5L** 2.69 2.24 0.12 55 57.8 7.29 **C-I-5L** 2.84 2.15 0.20 72 77.4 5.71 2.65 45 2.75 59 3.05 73 2.77 48 2.62 46 3.01 73 2.60 40 2.58 61 2.60 80 2.78 55 2.76 58 2.61 81 2.64 56 2.92 68 2.69 86 **A-II-4L** 2.73 2.43 0.05 41 42.0 3.37 **B-II-4L** 3.04 2.03 0.18 56.1 56.0 1.65 **C-II-4L** 3.08 2.74 0.03 50.1 52.4 2.97 2.75 37 2.67 54.3 3.03 49.3 2.72 40 2.87 57.6 3.07 52.8 2.84 45 3.11 53.1 2.77 45 3.08 56.8 2.81 45 **A-II-5L** 2.54 2.21 0.09 63 76.0 13.5 **B-II-5L** 2.66 2.36 0.10 65 86.1 15.7 **C-II-5L** 3.29 2.95 0.06 79 83.7 7.25 2.69 57 2.78 77 3.39 93 2.79 74 2.75 76 3.36 81 2.60 81 2.85 100 3.35 80 2.59 91 2.87 105 3.47 93 2.57 88 2.94 94 3.35 77 **A-III-4L** 2.57 2.16 0.06 41 45.0 3.57 **B-III-4L** 2.76 2.43 0.03 50 51.2 2.97 **C-III-4L** 3.28 2.89 0.03 63 63.0 2.93 2.48 43 2.74 50 3.27 67 2.40 42 2.78 47 3.24 64 2.49 44 2.75 53 3.20 64 2.50 48 2.70 55 3.27 61 2.52 50 2.71 52 3.24 58 **A-III-5L** 2.36 2.09 0.02 73 77.0 8.90 **B-III-5L** 2.52 2.18 0.07 80 102 20.9 **C-III-5L** 2.92 2.61 0.06 107 115 9.76 2.34 65 2.49 86 3.01 101 2.34 72 2.55 98 2.99 116 2.34 81 2.55 114 2.94 121 2.31 84 2.68 131 3.00 119 2.37 89 3.08 128

**Table 6.** Test results in bending tests for all assemblies tested.

**Figure 13.** Comparison of the results obtained for the assemblies with the beam of type B concerning: (**a**) capable corrected moment Mn and (**b**) rotational stiffness kni of the connections.

**Figure 14.** Comparison of the results obtained for the assemblies with the beam of type C concerning: (**a**) capable corrected moment Mn, and (**b**) rotational stiffness kni of the connections.

Regarding the capable load, the design moment MRd corresponding to the assembly containing the upright II having a thickness of 1.75 mm is greater than the design moment MRd corresponding to the assembly containing the upright I with a thickness of 1.5 mm (Table 6, Figures 12a, 13a and 14a). However, the design moment MRd corresponding to the assembly containing the upright III with a thickness of 1.5 mm and the five-tab connector is less than the design moment MRd for the assembly with the same upright region and with four connectors, even if the stiffness is bigger for the assembly with a five-tab connector comparatively with the stiffness for the assembly with a four-tab connector. Moreover, the design moment MRd for the assembly containing upright III and a four-tab connector is much closer to the design moment MRd for the assembly containing upright II and a five-tab connector in the case of all types of beams (A, B, or C).

### *3.3. Failure Modes in Bending Tests*

The failure mode was changed from assembly to another assembly tested. Upright is the main failure mode, especially when the upright thickness is 1.50 mm (Figure 15). This happens because, when the beam is loaded and the connector rotates, the first two tabs are tearing the upright's slots because the upper part of the beam is subjected to tensile stresses (Figure 15c).

It was observed that, when the thickness of the upright increases, for the upright having a thickness of 1.75 mm, the failure mode was changed. All the elements (upright, beam, and beam end connector) start to be a part of the failure mode (Figure 16). In this case, the rotation angle θ deceases (Figure 16a), especially as the beam height increases and the bottom part of the beam is compressed and it starts to locally buckle (Figure 16b). The connector is also bending (Figure 16a).

**Figure 15.** Failure modes of the upright region with a thickness equal to 1.50 mm: (**a,b**) failure mode of the connector and (**c**) failure mode of the upright region.

**Figure 16.** Failure modes in case of the assembly with an upright region having a thickness equal to 1.75 mm: (**a**) failure mode of the connector, (**b**) failure mode of the beam, and (**c**) failure mode of the upright region.

For uprights having a thickness of 2.00 mm, the effects of the action of the connector tabs on the upright region is very small, especially for the five-tab connector (Figure 17a,c). The rotation of the connection is even smaller (Figure 17a), which means that the biggest rotational stiffness corresponds to this situation. The main failure modes were bending of the connector and the local buckle of the beam near the connector (Figure 17b). For assembly with a four-tab connector (Figure 18) because the beam rotates more than in a situation of the assembly with a five-tab connector, the first top tab still leaves a mark on the upright slots (Figure 18c).

**Figure 17.** Failure modes in case of the assembly with the upright region having a thickness equal to 2.00 mm and a connector with five tabs: (**a**) failure mode of the connector, (**b**) failure mode of the beam, and (**c**) failure mode of the upright region.

**Figure 18.** Failure modes in case of the assembly with an upright region having a thickness equal to 2.00 mm and a connector with four tabs: (**a**) failure mode of the connector, (**b**) failure mode of the beam, and (**c**) failure mode of the upright region.
