# Experimental Studies on the Strength of a Flatar during Shunting Impacts
## 3 Theoretical Determination of the Strength of the Flatcar  
The strength of the flatcar loaded with containers during a shunting collision was studied with the FEM in SolidWorks Simulation (France) [20; 21; 22]. The model 13-401M flatcar built by the Dniprovagonmash Car Building Plant was chosen as a base model. The frame of the flatcar was of welded construction. The main bearing beam of the frame was the center sill. It consisted of two I-beams, which were shaped to resemble a beam of equal bending resistance. The main longitudinal beams also consisted of I-beams of variable length and height. The center sill and the main longitudinal beams were connected by two box-section end beams (bent angle and sheet), two closed box-section pivot beams, and rolled I-beams. The end beam had a handrail for the stacker and a socket, which was molded together with the front stops of the car coupler. The load-bearing elements were made of Steel 09G2S. To transport containers, fixed fittings were installed on the bearing structure of the flatcar. They could be either stationary, i.e., welded to the longitudinal beams of the frame, or hinged. They are usually installed on the flatcar structure during modernization at car repair or car building enterprises. When creating a spatial model of the frame, welding joints between its individual components were not taken into account. That is, the model was considered as a monolith. At the same time, the model was an assembly unit, in which each element was made according to the album of drawings. Therefore, operational wear and tear of an individual component was not taken into account. The model was assembled in SolidWorks (France). Then, it was saved as a neutral format (SAT) file and imported to AutoCad (US). There it was assembled and re-imported to SolidWorks. It was necessary to follow this procedure during the calculation because in the assembly unit the stresses were distributed asymmetrically in some zones. The calculation included that the flatcar was loaded with two ICC containers. It was assumed that they were equally loaded. The gross weight of one container was assumed to be equal to 240 kN, which is the maximum permissible value for this type. The design diagram of the flatcar frame included the impact force \(P_{l}\) = 3.5 MN (Figure 1), the vertical impact force \(P_{v}\) to the fixed fitting from the containers, and the horizontal force \(P_{h}\) as a result of a collision between the container fitting and the fixed fitting (Figure 2). The magnitude of the horizontal force applied to the pin of the fixed fitting was determined by mathematical modeling on the basis of the models developed in previous publications by the authors' team. Figure 1: Design diagram of the flatcar frame. The flatcar was fixed on the horizontal surfaces of the center plates. The frictional forces between the center plates and center bowls were not taken into account. The design values of the forces were taken equal to the values given in [20]. Tetrahedrons were taken as finite elements [23; 24; 25; 26]. The graphic analytical method was used [27; 28]. The method was based on a graphical (geometric) representation of admissible solutions and the objective function of the problem. The essence of the method in solving this problem is to build a dependence of the maximum equivalent stresses on the number of finite elements. When this dependence began to be described by a horizontal line, that indicated the optimum number of finite elements. In this case, the number of elements forming the mesh was previously calculated. In the areas where there was a connection between the frame beams or parts, the mesh was automatically compacted. The number of nodes in the mesh was 311,601, and the number of elements was 932,166. The maximum element size was 100 mm, and the minimum was 20 mm. The finite element model of the bearing structure of the flatcar is shown in Figure 3.  
The model was fastened in the areas of support on the bogies.