## 3 Comparison of the Experiments with Analytical Models and Discussion of the Results  
### Calculation for Pure Torsion and Combination of Torsion and Bending  
After testing, we attempted to confirm the experimental results mathematically using the truss model found in common standards (e.g., Eurocode 2 [15]). Here, the stirrup reinforcement (1) and the longitudinal reinforcement (2) for pure torsion are determined separately:  
\[\frac{A_{sw}}{s_{w}}=\frac{T}{2\cdot A_{k}\cdot f_{y,s}}\cdot tan(\theta), \tag{1}\]  
\[\frac{A_{sl}}{u_{k}}=\frac{T}{2\cdot A_{k}\cdot f_{y,l}}\cdot cot(\theta), \tag{2}\]  
where \(T\) is the torsional moment; \(A_{sw}\) is the diameter of a stirrup; \(s_{w}\) is the distance between the stirrups in the longitudinal direction of the beam; \(A_{sl}\) is the total area of longitudinal reinforcement installed in the beam; \(u_{k}\)_is_ the circumference of the centerline of the equivalent box girder, which coincides with the real cross-section for the tests performed; \(A_{k}\) is the area inside the centerlines of the equivalent box girder; \(f_{y,s}\) and \(f_{y,l}\) are the yield stresses of the stirrup (\(s\)) and the longitudinal reinforcement (\(l\)), respectively; and \(\theta\) is the inclination of the compression strut. Table 2 lists the parameters of the two test specimens for pure torsion. For TSjoint, two calculation variants were analyzed: one considering only the continuous longitudinal reinforcement in the deck and bottom slabs within \(A_{sl}\) (representing the cross-section at the restraint), and the second also considering the longitudinal reinforcement of the webs ending at the joint (representing the cross-section in the field). The fact that the ultimate load capacity has not yet been reached when the yield point of one of the two reinforcements is reached (cf. Section 1) was previously described by [PERSON] et al. in 1968 [16]. The force is redirected by a change in the inclination of the compression struts to the reinforcement that has not yet yielded. This is considered by equating the maximum torsional moment due to longitudinal reinforcement with that of the stirrup reinforcement, and then solving the equation according to the compression strut inclination (3):  
\[\theta=tan^{-1}\left( \begin{array}{c}\frac{A_{sw}\cdot f_{y,s}}{s_{w}}\\ \frac{A_{sl}\cdot f_{y,l}}{u_{k}}\end{array} \right). \tag{3}\]  
If the compression strut inclination obtained from Equation (3) is substituted into Equation (1) or (2) and the equation is solved for \(T\), a much more accurate value--when compared to the real ultimate torsion load--can be obtained, even though certain limits are set regarding the force redistribution [15; 19]. An extension to the equations for the combined loading from torsion and bending was developed in 1970 [17; 20]. In order to keep the calculation simple, the test specimens investigated by [PERSON] and [PERSON] [17; 20] were converted into cross-sections that only had reinforcement in the corners. The resulting minor inaccuracy with respect to the lever arm for the bending moment can be considered acceptable. In order to compare the experiments determined here with those investigated by [PERSON] and [PERSON] [17; 20], the same procedure was followed. The 28 O8 mm longitudinal bars of TSRef were thus converted into corner bars with an equivalent area of 7 O8 mm each. In TSjoint, a distinction \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Test Specim** & \(A_{sw}\) (cm\({}^{2}\)) & \(s_{w}\) (cm) & \(A_{sl}\) (cm\({}^{2}\)) & \(u_{k}\) (cm) & \(A_{k}\) (cm\({}^{2}\)) & \(f_{y,s}\) (N/mm\({}^{2}\)) & \(f_{y,l}\) (N/mm\({}^{2}\)) \\ \hline TS\({}_{\text{Ref}}\) & 0.79 & 15.0 & 14.07 & 420.0 & 1080.0 & 680 & 652 \\ TSjoint w/o web-reinf. & 0.79 & 15.0 & 14.07 & 420.0 & 1080.0 & 680 & 652 \\ TSjoint w/web-reinf. & 0.79 & 15.0 & 23.12 & 420.0 & 1080.0 & 680 & 652 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters for pure torsion.