## 2 Computational Model  
The task is complex and complicated since the dimensions of the studied objects are large, and the deformations are significant. In this case, non-linear effects occur that do not allow us to obtain an accurate solution even when using specialized software SolidWorks 2014 SP5. In the literature, there are studies investigating beams where the deformations are large [23; 24; 25; 26; 27]. In them, the following task is solved: at a given load, the bending line of the beam is sought. In the present work, the reverse task should be solved: determining the forces that arise at the support points at a given deformation of the investigated beam. For this purpose, a linear analysis method was used, and the research methods from [23; 24; 25; 26; 27] can be used to assess the accuracy of the solution. The transportation of long rails can be carried out with wagons that have different parameters (length, base, width, own weight, load capacity, etc.). After analyzing the mentioned parameters, the authors propose as the most efficient version of the specialized train composition, one that should consist of nine wagons with precisely defined parameters. The idea is to obtain maximum use of both the wagons' carrying capacity and their length, and to have the necessary safety factor against derailment. Therefore, the specific technical parameters of the wagon, which in our opinion are the most efficient, are described. When using another modification in the wagons, the mentioned efficiency cannot be guaranteed. Basic data and prerequisites for solving the task at these conditions are:  
* In accordance with [28], the train composition is in a curve with radius \(R=150\) m (Figure 2a). The locomotive is not shown in the figure. * The composition consists of nine wagons; the rails are located on support frames (Figure 2b) and are grouped in separate sections of five rails each. * The middle wagon is equipped with a system to guarantee the immobility of the rails (so called \"fixing block\") (Figure 2b), and the load/pressure forces are shown in Figure 2c. * On the remaining wagons (not equipped with fixing blocks), three or two (for the end wagons) support frames [29] (Figure 2b) are installed, depending on the length of the transported rails and the number of wagons. * In the support frames, the rails are placed freely, and unlimited longitudinal displacement is allowed as well as limited lateral displacement within \(\Delta h\), (Figure 2d). Movements along the vertical direction are limited by the supporting beams of the frames and the clearances \(\Delta v\) (Figure 2d). * It is assumed that the first four wagons have entered the curve. The last premise allows for only one half of the train composition to be considered (Figure 3). Element A\({}_{0}\) defines the position of the fixing block in the middle wagon, and the remaining elements (A\({}_{1}\) to A\({}_{12}\)) define the position of the support frames. The front wagon is equipped with two support frames (A\({}_{11}\) and A\({}_{12}\)) in accordance with the requirements of [29]. The locomotive is not illustrated in Figure 3.  
The following additional assumptions were made during the compilation of the computational model:  
* The bending of a group of five rails (corresponding to one separate section) in the plane _Oxy_, referred to as \"group of rails\" or \"beam\" for brevity (Figures 4 and 5);
* Each rail group has a moment of inertia \(I_{\text{zi}}=0.00000486\) m\({}^{4}\)[30,31]. The total moment of inertia for five rails is \(I_{\text{z}}=5\). \(I_{\text{zi}}\);  
Figure 3: Half of the train composition with elements needed for calculation. Figure 2: Train composition for transportation of long rails: (**a**) composition in the curve; (**b**) middle wagon with frames; (**c**) load/pressure forces in the fixing block; (**d**) movement limitations in support frames. * The friction between the rails is neglected due to the peculiarities of the investigated structure.