## 3 The Purpose and Main Tasks of the Article  
The purpose of the article is to highlight the results of determining the bearing-structure load of a two-section hopper wagon under the main operational load modes. The tasks of the study are  
* To calculate the strength of the two-section hopper-wagon-supporting structure under the main operational load modes;
* To determine the vertical load of a two-section hopper wagon;
* To investigate the bearing-structure load of a two-section hopper wagon on a railway ferry. The Strength Analysis of the Two-Section Hopper-Wagon-Bearing Structure under the Main Operational Load Modes  
In order to increase the efficiency of the operation of the hopper wagon by providing the possibility of simultaneous transportation of different types of cargo, it is proposed to improve its design. This solution consists of dividing the body into two separate sections interacting with each other through a vertical wall and horizontal connecting belts (Figure 1). To increase the rigidity of the frame in the areas where the sections are supported on central part, a middle beam of the box section was installed (Figure 2). Due to the fact that the sections were supported not only in the cantilever parts of the frame but also in the middle part, increased stresses and displacements occurred in it. Therefore, a solution was proposed, aimed at increasing the rigidity of the frame by setting beam 6. A patent application has been filed for this design of the wagon. When carrying this out, the hopper wagon model 20-9749 (Figure 3), built by \"Ukxpetsvagon\", was chosen as the prototype. The useful volume of sections of the improved hopper wagon is 41 m\({}^{3}\). The wagon has a width of 3154 mm and a length along the frame end beams of 13,500 mm. The wagon base is 7800 mm. An image of the wagon is shown in Figure 4.  
To determine the strength of the two-section hopper wagon, a calculation was carried out by using the FEM in the SolidWorks Simulation [28; 29]. At the first initial stage of the study, the calculation was made for the first mode (impact). The finite element model of the hopper wagon was formed by isoparametric tetrahedrons (Figure 5). In this case, the grid was created taking into account automatic compaction in areas of possible stress concentrations. Thus, the mesh was uneven relative to the model. Figure 1: Two-section hopper wagon: 1—module of the running gear; 2—automatic coupling module; 3—brake equipment module; 4—body module; 5—frame module. Figure 4: Finite element model of the hopper wagon frame: (**a**)—general view; (**b**)—frame. Figure 3: Hopper wagon. Figure 2: The frame of a two-section wagon: 1—center girder; 2—pivot beam; 3—end beam; 4—struts; 5—intermediate transverse beams; 6—medium beam. The number of tetrahedrons was calculated by the graphic and analytic method [30]. The number of mesh elements was 90,457, and the number of nodes was 30,545. The maximum size of a mesh element was 200 mm, and the minimum one was 40 mm. The maximum and minimum sizes of the grid elements were chosen based on the calculations carried out in previous studies by the team of authors regarding other wagon designs. These calculations were confirmed experimentally through field tests. At this stage, based on the experience of previous studies, an identical size of the elements was chosen. In the future, after conducting experimental studies, this hypothesis will be refined. The calculation scheme of the hopper wagon is shown in Figure 6. The scheme is shown in the section to better visualize the application of loads. When compiling it, the following loads were taken into account: vertical static load \(\mathrm{P_{v}}^{\mathrm{st}}\), due to the weight of the cargo; the lateral pressure from the bulk cargo \(\mathrm{P_{i}}\); and the impact load \(\mathrm{P_{imp}}\), the numerical value of which, according to regulatory documents, is 3.5 MN [31]. The limitation of the design scheme is the absence of bulk cargo movements in sections and friction forces between the cargo and walls.