*3.2. Results*

All the beam models (altogether 12 elements) were loaded at a constant speed right up to their failure. The failure of beams in series A resulted from the shearing of fibres in the bottom part of the central area of the beam where earlier there were no visible cracks (except for cracks in the vicinity of knots in the beams). Sudden failure with no prior signs occurred. Generally, the failure of beams in

series E, F, and G involved a loosening of the joint in the lower zone of the central part of the beam and the appearance of cracks and fractures on the edges of the joint and in points weakened as a result of earlier flaws (such as knots or primary cracks of the beam). The tested joint was unsymmetrical. In the right part of the joint, the beam elements were bent and pressed to each other. In the left part of the joint, the elements were also bent, but the bottom element was not pressed and the joint was loosened. Destruction occurred in the left part of the joint by breaking the upper element (visible cracks above the edge of the joint). The cross-section of the destruction was in the joint area. Failure resulted from delamination due to stretching across the fibres. The failure views of selected experimental models are presented in Figure 15.

**Figure 15.** Failure views for selected beams (**a**) A01, (**b**) E03, (**c**) F01, (**d**) G02.

Table 1 presents the value of the ultimate forces Fu obtained for each of the beam series. Ratio of mean destruction force for specified series to reference beam series is FuX/FuA, where X stands for E, F, or G (and expresses mean destructive force for this series).


**Table 1.** Ultimate forces for beams in each series.

Load-deflection plots (in the central part of the beam span, i.e., in point 1) for beams in the various series are presented in Figure 16.

Deformations in the area of point 1 in the central part of the beams are presented in Figure 17. The deformation profiles are consistent with expected curves: for beam A01, the standard image of deformation in the cross-section for the continuous beam was obtained, whereas for beams E02, F02, and G02, it was noted that the typical curve shape for the composite cross-section was as presented inter alia in [18].

**Figure 16.** *Cont.*

**Figure 16.** Load-deflection plots for beams in series A, E, F, and G.

**Figure 17.** *Cont.*

**Figure 17.** Strain profile in the cross-section for selected beams subjected to bending.

### *3.3. Analysis of Results*

The mean ultimate force value for beams in series A (continuous beams) was 46.07 kN. The value of the mean load bearing for bending for this series was 24.88 kNm. Compared to the reference beams, beams joined with stop-splayed scarf joints, i.e., beams in series E, F and G, achieved lower load-bearing levels, which were comparable to one another. The highest values were obtained for series G beams with a mean ultimate force of 14.26 kN (load-bearing for bending of 7.70 kNm), which constituted 31.0% load-bearing in relation to reference beams. The largest variation in results was obtained for this series (variation coefficient exceeds 30%). Beams of series E and F obtained lower ultimate force values: series E—12.67 kN (load-bearing for bending 6.86 kNm), series F—13.04 kN (load bearing for bending 7.04 kNm) which constitutes respectively 27.5% and 28.3% load-bearing in relation to the reference beam. The results of series E were characterised by the smallest variation with an indicator of not much more than 10%. A comparison of the values of ultimate force values for beams in series A, E, F, and G is presented in Table 2 and in the curve in Figure 18.

**Table 2.** Comparison of load-bearing for beams in the various series.

**Figure 18.** Comparison of values obtained for ultimate force values for beams of series A, E, F, and G.

As part of the comparative analysis, in Figure 19, a comparison of the load-deflection plots of the beams of series E, F, and G to the reference beams of series A is presented. It should be noted that the tested beam series attained similar values for final deflection, but with different levels of force, which are several times higher for series A, whereas the values for beams of series E, F, and G were similar to one another.

**Figure 19.** Comparison of load-deflection plots of beams of series E, F, G to the reference beam of series A.

An analysis of the graph (curves for series E, F, and G) shows a change in the nature of the static behaviour of the joint when strain η is equal to approximately 60% of the elastic to ductile state. Estimations on the basis of the load-deflection plots of the 'stiffness parameter' in the elastic state, calculated as the ratio of loading force value to deflection (1) for the beams representing series A, E, F, and G, are as follows: for A01—0.94 kN/mm, for E01—0.31 kN/mm, for F01—0.32 kN/mm, and for G02—0.45 kN/mm.

$$\mathbf{k} = \mathbf{t} \mathbf{g} \boldsymbol{\alpha} = \frac{\mathbf{F}\_{\mathrm{i}}}{\mathbf{u}\_{\mathrm{i}}} [\mathbf{k} \mathbf{N} / \mathrm{mm}] \tag{1}$$

It should be noted that the parameters for beam E01 and F01 are close to one another and amount to approximately 30% of the stiffness parameter for the continuous beam A01, whereas in the case of beam G02, the parameter amounts to approximately 50% of the reference value. The most important test results obtained for the beams from the specified series in relation to the reference beam (continuous beam) are presented in Table 3.


**Table 3.** Presentation of results for beams from specified series.
