## 5 Investigation of Segments of Arch-Shaped Steel Sheets
### Multi-Camera DIC System with Overlapping Field of View  
Considering the length of 12 m of arch segments, the measurements have been carried out with the use of multi-camera DIC system in which the field of view of neighboring 3D setups overlapped each other. As a result, the obtained, stitched FOV was 7 \(\times\) 4 m (Figure 7a). For stitching we used the method described in the papers [13; 24; 25], while the general measurement procedure of the segments of arch-shaped steel sheets are presented in [13]. The multi-camera DIC system used in this measurements comprised eight 5 MPx (2448 \(\times\) 2048) Pointgrey cameras equipped with 8 mm focal length lenses. The cameras were connected to the control computer in order to synchronize the data acquisition procedure. The calibration procedure comprised two steps. In the first stage, 3D DIC setups have been calibrated separately with the checkerboard before the measurements. The quality of calibrations has been expressed as a reprojection error, which was smaller than 0.05 px for all 3D DIC setups. After the scaling (from pixels to mm), the accuracy of displacement measurements of each 3D DIC setup can be estimated at 0.05 mm. In the second stage, the transformation of individual coordinate systems  
Figure 5: The comparison of V displacement functions obtained for three numerical models and experimental data (results for point 2) [2].  
Figure 6: V displacement maps derived from (**a**) experiment and (**b**) the C model, and U displacement maps derived from (**c**) experiment and (**d**) the C model [2].  
of separate 3D DIC systems into a common coordinate system has been determined. The fields of view of neighboring 3D DIC setups overlapped each other (Figure 7) in order to make it possible to capture the images of the same calibration target (checkerboard in this case) with two systems simultaneously. Checkerboard corners (markers) viewed by each camera have been detected and their positions in two 3D DIC coordination systems were obtained. The knowledge of position of markers in two separate coordination systems was used to obtain geometrical transformation between these two systems. The common coordination system (CS) is associated with one of the two systems. Here the coordination system of DIC setup 2 has been selected as the global CS. The transformation between CSs of setup no. 1 and 3 into CS of setup no. 2 has been determined directly. The transformation of CS of setup no. 4 was obtained indirectly--at the beginning, the transformation into CS of setup no. 3 was obtained, and then transformation from CS of setup no. 3 into CS of setup no. 2 was performed. The transformation errors obtained were below 0.5 mm. In order to correlate CSs of the measurements with numerical simulations, the data from the global coordination system (associated with setup no. 2) was transferred to the coordinate system, in which the xy plane was parallel to the ground and z axis was perpendicular to the ground (Figure 7b). AOI covers the area of corrugated web surface of two middle arches and additionally eight points on two external arches, corresponding to the locations of force extortion. Data obtained from upper (flat lip according to Figure 1) and middle (corrugated flange according to Figure 1) surfaces of the middle arches have been thresholded due to a higher correlation error (because of the loss of depth of focus).