## 1 Introduction  
The space truss analogy (STA) constitutes a comprehensive theoretical model which allows to understand and model the torsional behavior of reinforced concrete (RC) beams. It is used by several researchers and actually constitutes the base model for most of the current codes of practice. In its early versions, proposed in the first years of the 20 th century, the STA was only able to compute the resistance of RC beams to torsion. Since then, and mainly in the last three decades, the STA has been further developed by several researchers. Nowadays, the model is able to predict the full response of RC beams under torsion, including low loading levels. This is important because some requirements from codes of practice include design rules for service loads. Among the developments of the STA that are proposed in the literature, the generalized softened variable angle truss-model (GSVATM) is one of the most recent. The GSVATM was firstly proposed by [PERSON] et al. in 2015 [1] for RC rectangular plain beams. The derivation of this model was based on the generalization of a previous one, the variable angle truss model (VATM) from [PERSON] and [PERSON] in 1985 [2; 3]. This model aimed to unify RC and prestressed concrete (PC) rectangular beams with small or large cross sections. The VATM was able to model correctly the torsional behavior of RC beams only for the ultimate stage because the concrete tensile strength was neglected. However, this concrete property is an important one because it governs in the early loading stages. By correcting this drawback, and by incorporating adequate smeared constitutive relationships for the materials [4], the GSVATM correctly predicted the full torque (\(M_{T}\))-twist (\(\theta\)) curve of RC beams. In the last years, the GSVATM has been continuously refined to cover RC rectangular hollow beams under torsion [5], PC rectangular beams [6] and RC rectangular beams under torsion with external axial forces [7]; and the work is ongoing. In general, the theoretical predictions from the GSVATMcompare well with the experimental results of RC and PC rectangular beams under torsion, including the cracking and ultimate torques. Beams with flanged cross sections are used in many structural systems, such as buildings and bridges. T- and L-shaped beams are widely used to support precast members (slabs and beams, (Figure 1a)) or walls (Figure 1b). In current RC pavements of buildings (Figure 1c), part of the slabs can be considered as a component of the cross section of the spandrel beams located at the perimeter. Such end beams with slab on only one side are designed as flanged cross sections, namely as L-shaped beams. Due to asymmetric or eccentric loading (Figure 1b,c) and due to the torsional stiffness of the end beam (Figure 1c), such beams may have to withstand high torsional moments, among other internal forces. Thick flanges, in addition to the web, are favorable for the torsional strength of RC beams. This is because the torsional moment is distributed between the web and the flanges (without warping of the cross section if the components are thick), while the web and its transverse reinforcement carry most of the shear force. However, the behavior of flanged beams under torsion is more complicated when compared with rectangular beams and highly depends on the cross section shape, on the relative dimensions of the components of the cross section and also on the detailing of the reinforcement (both longitudinal and transverse) [8; 9; 10; 11]. For the case of L-shaped beams, the non-symmetric shape induces an additional complex behavior under torsion which needs to be assessed [12]. This explains the small number of articles on the theoretical behavior of RC flanged beams under torsion. In fact, previous studies mainly deal with the torsional behavior of rectangular beams (for instance [13; 14; 15; 16; 17]).