# Non-Destructive Multi-Method Assessment of Steel Fiber Orientation in Concrete +
## 3 Results  
### X-ray Computed Tomography (CT)  
Fiber identification and orientation analysis was completed using the program VGSTu-dioMAX 3.3 (Volume Graphics GmbH). The results of the analysis are presented in terms of spherical coordinates (Figure 7, top left). As the fibers are oriented in all three spatial directions, this representation is the most suitable. In our opinion, a cylindrical coordinate system (using polar coordinates supplemented by a Cartesian coordinate for the height) would have been better to represent the data layer by layer focussing then only on the fiber orientation within one respective cylindrical section in 2D. In this study, though, we aim to analyse all fiber orientations in one sample in 3D.  
In the spherical coordinate system we use, orientations are characterized by angles \(\Theta\) and \(\Phi\). In the Cartesian coordinate system used for these measurements, the cylindrical axis of the sample is denoted as the z-axis. The angle \(\Theta\) represents the azimuthal angle in the x-y plane from the x-axis, with \(0<\Theta<360^{\circ}\). The angle \(\Phi\) represents the polar angle from the positive z-axis, with \(0<\Phi<180^{\circ}\).  
Figure 7 provides fiber renderings and orientation histograms for all five cylindrical samples shown in Table 1. The orientation histograms are shown in the form of orthographic projections, where the centre of the projection is the z-axis (i.e., the cylindrical axis). Thus, these projections represent, effectively, the portion of the fiber orientation histogram plotted on the upper half of the sphere shown in the upper left of Figure 7. Since the fibers are considered to be symmetric about their lengths, it is assumed that differences between the lower and upper halves of the histogram sphere are negligible, which has also been verified visually during data analysis.  
During fiber orientation analysis, the fibers were not individually identified, separated and analysed. Rather, composite orientation information was calculated for all steel fiber material in the specimens. This means that the resulting orientation measurements contain not only orientation data related to the primary axis of the fibers, but also orientation data related to the hooked ends of the fibers. Although this effect introduces a partial distortion of the data, the hook-based effects are considered to be acceptable given the relatively small size of the fiber hooks in comparison to the overall fiber dimensions.  
The \"Fiber Composite Analysis\" module automatically scales the colour coding in the polar colour plot to the deviations found from the orientation with the highest frequency. Since there is no fibre material in sample Q0F, the module scales the colour coding to the orientation values determined on dense aggregates. These aggregate related orientation values are no longer visible in the samples containing fibres with the same parameter setting. Therefore, the colour coding for Q0F was manually adjusted so that the colour scale is comparable with the other polar plot representations. Clear differences in the histogram characteristics can, for instance, be observed between the three samples Q40--, Q40 \(||\) \(||\) and Q40* in Figure 7.