## 5 Comparative Analyses  
This section discusses the comparative analyses performed between the theoretical results obtained from the calculation procedure presented in Sections 2 and 3, by using the GSVATM, with the  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Beam** & \(\mathbf{A_{\mathit{sl}}}\)**cm\({}^{2}\)** & \(\mathbf{A_{\mathit{st1}}}\)**/s cm\({}^{2}\)/m** & \(\mathbf{A_{\mathit{sl2}}}\)**/s cm\({}^{2}\)/m** & \(\mathbf{A_{\mathit{fl}  
experimental results for the reference RC flanged beams presented in Section 4. Such comparative analyses include the \(M_{T}-\theta\) curves and the torsional strength. It must be referred that subdivisions I, II and III for T- and L-shaped beams, as shown in Figure 5, only show how the concrete cross section is divided into concrete rectangular components. In [36] it is not clearly explained how the reinforcement is divided for each concrete rectangle component. For this study the following criteria are assumed:  
* for the transverse reinforcement, since two independent closed stirrups exist (one for the web and another one for the flange, see Figure 6), it is assumed that the closed stirrup of the web constitutes the transverse reinforcement of sub-element 1 and that the closed stirrup of the flange constitutes the transverse reinforcement of sub-element 2 (see Figure 5);
* for the longitudinal reinforcement, it is assumed that the total area of reinforcement is divided among the concrete rectangular components 1 and 2 (see Figure 5) as a function of their area with respect to the total area of concrete in the cross section. Figures 7-14 present, for each reference beams, the \(M_{T}-\theta\) curves. Each graph includes the experimental curve and three theoretical curves, one for each subdivision. Figures 7-14 show high variability between the theoretical curves computed with subdivision II and those computed with subdivisions I and III. These latter are quite similar for most of the beams. Figure 11: \(M_{T}-\theta\) curves for beam LB5. Figure 10: \(M_{T}-\theta\) curves for beam LB4. Figure 9: \(M_{T}-\theta\) curves for beam LB3. When the experimental curves are compared with the theoretical ones, it can be stated that, as far as the ultimate state is concerned, the theoretical curves computed with subdivision II are in general better than the other ones. In fact, when subdivision II is used good results are observed for the  
Figure 14: \(M_{T}-\theta\) curves for beam TB1. Figure 12: \(M_{T}-\theta\) curves for beam BL1. Figure 13: \(M_{T}-\theta\) curves for beam BK-T.  
maximum torque, although the corresponding twist is overestimated for most of the beams. In general, the \(M_{T}-\theta\) curves computed with subdivision I and III highly underestimate the maximum torque. The overestimation of the ultimate twists can be explained because the deformations in the ultimate state are more difficult to capture correctly with analytical models. This drawback is also observed for RC rectangular beams and is due to the complexity to correctly model the effect of the damages in the torsional stiffness for the ultimate state [1]. However, since the ultimate deformations are not very important for the design, this drawback turns out to be less important. For the ultimate state, the results agree with those observed by [PERSON] in 2015 [36], which also observed that subdivision II shows better results. Figures 7-14 also show that, for most of the beams, the theoretical \(M_{T}-\theta\) curves from the model with subdivision II do not follow well with the experimental ones in the transition zone from the uncracked state to the cracked state. Except for beams BL1 and BK-T, the cracking torque is highly overestimated. For beams LB1 and TB1, the torsional stiffness for the uncracked state is also highly overestimated. The previous observations show that the theoretical model does not predict well the response of most the reference beams for low loading levels.