# Experimental Study on the Torsional Behaviour of Prestressed HSC Hollow Beams
## 3 Global Analysis of the Experimental Results  
### Torsional Moments vs. Twists  
Figure 8 presents the graphs of torque (\(T\)) _versus_ the average twists (\(\theta_{m}\)) for the tested beams. The torque, \(T\), was obtained multiplying the load applied by the actuator by the horizontal projection of the level arm, 0.85 m, which remained constant (see Figure 5). The average twist, \(\theta_{m}\), was obtained by dividing the experimental angle measured in Section A-A to the distance between Sections A-A and J-J, 5.35 m (Figure 5). In each \(T\)-\(\theta_{m}\) curve, identification marks were used to highlight the points corresponding to cracking () and to yielding of the transverse (\(\square\)) and longitudinal (\(\triangle\)) reinforcement. The yielding points were calculated from the experimental values of the strains recorded by the strain gauges stuck to the reinforcement bars. As expected, Figure 8 shows the high influence of prestress in the cracking torque. It is known that prestress delays the formation of cracking. For a moderate concrete stress (induced by prestress) of 1.79 MPa (Beam D-1.79) an increase of approximately 32.5% on the cracking torque is observed, when compared with the beam without prestress (Beam D-0). This shows the efficiency of uniform longitudinal prestress to delay the cracking in beams under torsion. This high influence of prestress can be explained because in torsion the concrete is under a lower and more uniform level of tensile stresses (in the whole section) when compared with the bending situation. Therefore, even for low levels of prestress, the cracking stage is delayed. It is also observed that, in State I (non-cracked state), the steel bars, including the prestressed wires, generally have little influence on the stiffness of the beams. In fact, the \(T\)-\(\theta_{m}\) curves are almost coincident at this state. In State II (cracked state), the \(T\)-\(\theta_{m}\) curves are almost parallel to each other. This shows that the contribution of the longitudinal prestress for the stiffness of the beams is small at this state. This is due to the adopted prestressing technique (external longitudinal and centred prestress). As expected, Figure 8 also shows that the use of prestress increases the resistant torque, \(T_{r}\), of the beams. However, there is not a clear tendency with respect to the associated twist at the ultimate torque, \(\theta_{T_{r}}\). In fact, since prestress induces a compressive stress state in concrete, it would be expected that the deformation capacity of concrete in the compressed areas of the beam (namely in the struts) would decrease as the level of prestress increases. As a consequence, the twist corresponding to the ultimate torque should decrease as the stress induced by prestress increases. This is not the case for Beam D-3.08, which has the highest level of prestress and reaches a twist \(\theta_{T_{r}}\) that exceeds the same one of the other beams. However, this observation can be explained due to the type of failure of Beams D-0 and D-1.79, which was fragile and somehow premature (failure by pull off of the concrete corners). This subject will be discussed later. This aspect also justifies the different shape of the descending branches of \(T\)-\(\theta_{m}\) curves that is observed and the absence of yielding points before the peak torque is reached for Beam D-0. \(T\)-\(\theta_{m}\) curves of Figure 8 also show that, before the peak torque is reached, the prestressed beams only present points corresponding to yielding of the transverse reinforcement. It is observed that the yielding of longitudinal reinforcement only occurs after the peak torque. After cracking, the longitudinal prestress reinforcement starts working as ordinary reinforcement under the torsional loading. Consequently, the beams with balanced longitudinal to transverse reinforcement ratios will lose this balance because of the influence of the prestress wires.