2.1.4. Elastic Curves

The instant elastic curves are given by the di fference between the spline relative to the point cloud acquired on the structure subject to load, and the spline relative to the unloaded structure. As for the spline relative to the loaded structure, it will be necessary to respect the structural constraints (no displacements of the supports of a simply supported beam, no displacement and rotation at the fixed support of a cantilever beam, etc.). Comparing the displacements obtained by the TLS surveying and those obtained by means of the FEM analysis, it is possible to verify whether the behavior of a structure under various loading conditions is that expected in the design phase.

It is worth noting that the spline for the unloaded structure will be obtained from the entire point cloud sampled by the TLS in line scanner mode, composed of several line scans. The same observation can be made in the case of static loads.

In the case of dynamic loads, the goal of the surveying is to obtain instantaneous displacements, so we should derive a spline for each single sampled line. Therefore, we must first extract all the lines scanned by the TLS, with their timestamps. The software provided with TLS allows automatic extraction of the lines, once the instrument has been used in line scanner mode. This software generally returns the lines extracted in graphic form, but not as a sequence of 2D coordinates of the acquired points. In this way it is not possible to carry out most of the elaborations useful for understanding the behavior of the monitored structure.

It is therefore necessary to extract the individual lines from the overall file supplied by the instrument; for this purpose a code has been created in Matlab ® which returns a file in text format, for each extracted line, containing, for each acquired point, the 3D coordinates. Once the files with the points of the single scanned lines are obtained, the interpolating lines to be used for the elaborations are found. Due to the large number of points detected, a high computing time is required.

Using the GNSS receiver supplied with the TLS, it is possible to associate to each extracted line also the position of the mobile load, obtained from synchronized videos or from a GNSS receiver mounted on the load itself. In this way a displacement line is obtained for each position of the mobile load.

The deformation lines can also be used to identify the natural frequencies of a monitored structure, if these are much lower than the sampling rate of the lines The elastic lines obtained by a Riegl VZ 1000 TLS, with a sampling rate of up to 120 lines per second, can be e ffectively used to derive the natural frequencies of high structures. This topic is outside the aims of this article, and it is object of a di fferent investigation.
