## 5 Experimental Results and Discussion
### Development of Transverse Deformation Theory Based on the Obtained Experimental Results  
The relationships between the transverse and longitudinal deformations in the SLB and TLB are presented in Figure 7. The dependence between these deformations was a concave curve; i.e., as the longitudinal deformations became higher, the transverse ones grew in a non-linear form. According to the classical interpretation of Poisson deformations, there is linear relationship between the transverse and longitudinal deformations up to the elasticity limit. This concept corresponded with line 1 in the figure. Line 2 corresponded with the non-linear parts of the graphs and began from the longitudinal deformations of 0.58% for the SLB and 0.85% for the TLB. The difference between these values was 46.6%, which, consequently, increased the transverse crack resistance of the TLBs. Concrete mechanics theory does not consider transverse cracks; the transverse deformations are limited to 20% of the longitudinal ones [21,28]. Line 3 presents a conditional extension of the linear elastic transverse deformations. The theoretical interpretation of SFHSC (dependence between \(\varepsilon_{\text{trans}}/\varepsilon_{\text{c}}\) vs. \(\varepsilon_{\text{c}}\)) at a material level was previously discussed and verified for cylindrical specimens [21]. It was shown that the main feature in SFHSC behavior is that for longitudinal deformations \(\varepsilon_{\text{c}}\leq 1\%\), the ratio \(\varepsilon_{\text{trans}}/\varepsilon_{\text{c}}\) is constant; it indicates that the SFHSC behaves linearly. Figure 6: Typical load–transverse deformation diagram. Figure 7: Dependence between transverse and longitudinal deformations. Line 1: linear relationship; line 2: non-linear relationship; line 3: conditionally shown extension of linear elastic transverse deformations. The concept was further investigated in the present research for real RC beams to confirm this idea at a structural level. From a theoretical viewpoint, there are two main stages in the behavior of concrete bending elements:  
* The elastic stage, when the ratio between the transverse deformations to the longitudinal ones (\(\mu=\varepsilon_{\mathrm{trans}}/\varepsilon_{\mathrm{c}}\)) vs. the longitudinal deformations (\(\varepsilon_{\mathrm{c}}\)) is constant; i.e., for longitudinal deformations within 0 and 0.5%, the ratio \(\mu=0.2\) (Figure 8);
* The elastic-plastic stage, when the ratio between the transverse deformations to the longitudinal ones (\(\mu=\varepsilon_{\mathrm{trans}}/\varepsilon_{\mathrm{c}}\)) vs. the longitudinal deformations (\(\varepsilon_{\mathrm{c}}\)) is linear (line AB in Figure 8) and increases from \(\mu=0.2\) to \(\mu=0.4\) at \(\varepsilon_{\mathrm{c}}=0.5\%\) and \(\varepsilon_{\mathrm{c}}=2\%\), respectively. The increase in the value of \(\mu\) in the second stage was up to two times, which was as expected and corresponded with structural phenomena [4]. Consequently, and following this theoretical model, the known term \"Poisson coefficient\" was valid, but only for \(0\leq\varepsilon_{\mathrm{c}}\leq 0.5\%\). When 0.5% \(<\varepsilon_{\mathrm{c}}\leq 2\%\), this term was not correct and a suitable term was \"Poisson ratio\". Obviously, this concept and the proposed theoretical model (Figure 8) had to be verified. With this aim, the experimental data from testing the real SLB and TLB were analyzed. Figure 9 compares the above-described theoretical graph (see Figure 8) with the experimental data that were obtained in the frame of the present study for real SLB and TLB specimens (shown in Figure 1) and described in Section 4. The solid lines in Figure 9 corresponded with the experimental data and the hidden ones corresponded with the theoretical model following Figure 8. It was evident that the model accurately predicted the experimental data. Following Figure 9, for the SLB the experimental values were \(0.24\leq\mu\leq 0.46\). For the TLB (Figure 9), the corresponding limits were \(0.16\leq\mu\leq 0.28\).