# Experimental Study on the Torsional Behaviour of Prestressed HSC Hollow Beams
## 4 Failure Modes and Cracking Patterns  
Figures 10 and 11 show some photographic records of the failure zone of the tested beams. From these photos and from the analysis of the \(T\)-\(\theta_{m}\) graphs at their final part it is possible to distinguish two failure modes.  
Figure 10: Fragile failure by concrete break off at the corners: (**a**) Beam D-0 and (**b**) Beam D-1.79.  
Figure 9: \(F_{ps}\)–\(\theta_{m}\) curves.  
With a low level of prestress (1.79 MPa), Beam D-1.79 had the same failure mode as Beam D-0 (with no prestress), characterized by concrete break off at the corners (Figure 10). It should be mentioned that this particular fragile failure mode, somehow frequent in hollow beams, was observed and reported in previous studies [6; 10]. For a moderate prestress level (3.08 MPa), Beam D-3.08 clearly shows a fragile failure by crushing of concrete in the struts due to compression. This failure mode was particularly destructive and explosive (Figure 11). These results seem to show that the prestress level influences the failure mode. The results seem to indicate that, as the initial prestress increases, the failure becomes more fragile. This reveals an unfavourable effect of the prestress, which is observed for moderate levels of prestress.  
To analyse the cracking pattern of the tested beams, photographs were taken and posterior graphic tools were used to produce graphic type images for the three visible faces (lateral faces and top face) for all the beams. Such illustrations are presented in Figures 12-14.  
Figure 11: Fragile failure by crushing of concrete: Beam D-3.08.  
Figure 12: Cracking pattern: Beam D-0.  
Figures 12-14 do not seem to show a significant influence of the prestress level in the distribution of cracking.  
Table 4 presents, for each beam, the average longitudinal distance between cracks (\(d_{m}\)) and the average angle of such cracks to the longitudinal axis of the beams (\(\alpha_{m}\)). Only diagonal cracks that cross the entire width of the faces were considered to compute \(d_{m}\). Minors cracks or those associated to localized concrete spalling were not accounted. The angles \(\alpha_{m}\) were taken at the mid-width of the faces.  
\begin{table}
\begin{tabular}{c c c} \hline
**Beam** & \(d_{m}\)**cm** & \(\alpha_{m}\)\({}^{\circ}\) \\ \hline D-0 & 13.0 & 46.3 \\ D-1.79 & 12.9 & 44.8 \\ D-3.08 & 13.6 & 44.2 \\ \hline \end{tabular}
\end{table}
Table 4: Cracking parameters.  
Figure 14: Cracking pattern: Beam D-3.08.  
Figure 13: Cracking pattern: Beam D-1.79.  
Table 4 confirms that prestress does not seems to influence the distribution of cracking, since the values of \(d_{m}\) are similar for the three beams. The values of \(\alpha_{m}\) varied from 44.2\({}^{\circ}\) to 46.3\({}^{\circ}\), not far from the expected theoretical value of 45\({}^{\circ}\) for beams with balanced reinforcement and without prestress. For beams with prestress, the referred angle is slightly smaller to the one of the similar beam without prestress. This shows a small influence of prestress (the prestress levels were not high either). It is known that the existence of an axial compressive force in beams symmetrically reinforced under torsion causes the angle of the diagonal cracks to decrease [17].