## 3 Calculation Procedure for RC Flanged Beams  
This section aims to present the adopted calculation procedure to model RC flanged beams under torsion, namely T- and L-shaped beams, and which is implemented using the GSVATM. A similar calculation procedure as the one proposed by [PERSON] in 2015 [36] to model RC T- and L-shaped beams was adopted, which constitutes a generalization of the one proposed by [PERSON] and [PERSON] in 2010 [37] for RC rectangular beams under torsion wrapped with fiber reinforced polymers (FRP). The proposed calculation procedure divides the equivalent box cross section into rectangular sub-elements which are independently analyzed under torsion by using a theoretical model for RC rectangular beams. In the end, the superposition principle is used to compute the response of the original cross section. To apply this calculation procedure to RC T- and L-shaped beams, [PERSON] [36] proposed subdividing the cross section into three different ways, as shown in Figure 5 (subdivisions I, II and III), and test each of them. The idea to divide the cross section into rectangular components comes from the classical [PERSON]'s theory for thin walled cross sections under torsion. For thick walled cross sections, the connection area between the web and the flange is not negligible when compared to the area of the entire cross section. This raises doubts about how to perform the division into rectangular components. To solve this issue, [PERSON] [36] proposed dividing the cross section into different ways and test each of them to find which was the best. Figure 4: Flowchart for the GSVATM. For each subdivision, each rectangular sub-element was analyzed as an independent RC rectangular beam under torsion by using the GSVATM to compute its full response. After this, the superposition principle was applied in order to calculate the theoretical \(M_{T}-\theta\) curve for the original flanged beam. For this, by using deformation compatibility, it is assumed that the twist \(\theta\) must be the same, either for the original cross section or for each rectangular sub-element. The torque \(M_{T}\) of the original cross section is given by Equation (33), where \(M_{Ti}\) is the torque of each rectangular sub-element \(i\) which imposes the same twist \(\theta\). Parameter \(n\) represents the number of rectangular components. \[M_{T}=\sum_{i=1}^{n}M_{Ti} \tag{33}\]  
Based on the previously described calculation procedure, the main equations and solution procedure of the GSVATM do not need to be changed since each sub-element of the flanged cross section is a rectangle. The followed calculation procedure is summarized as follows:  
* 1 st step: the original flanged cross section is subdivided (subdivisions I, II and II);
* 2 nd step: the GSVATM is used to calculate independently the full \(M_{Ti}-\theta_{i}\) curve for each rectangular sub-element \(i\) and for each subdivision;
* 3 rd step: for a given subdivision (I, II or III), and from the list of point solutions \((M_{Ti};\theta_{i})\) for each rectangular sub-element \(i\), the torque \(M_{T}\) in the original cross section is computed according to Equation (33) and by using deformation compatibility;
* 4 th step: the \(M_{T}-\theta\) curve for each subdivision (I, II and III) is obtained. The curves can be compared with experimental results in order to assess which subdivision gives the best result. As explained in the next section, flanged beams under torsion partially or fully reinforced with glass fiber reinforced polymer (GFRP) bars were also incorporated in this study as reference beams to assess the predictions from the calculation procedure previously explained. For this reason, a new \(\sigma-\varepsilon\) relationship for GFRP must be incorporated in the GSVATM to model the tensile behavior of GFRP bars, either for longitudinal or transverse reinforcement.