## 3 Results  
Using the design diagrams shown in Figures 6 and 7, a diagram of the bending moments acting in the framework is obtained (Figure 10). The analysis of this diagram shows that the maximum bending moment in the frame is 4.45 kN \(\cdot\) m and has a negative value. This moment occurs in the bolster beam. In the arches, the maximum moment is 3.44 kN \(\cdot\) m and it is positive. According to this bending moment M, the moment of resistance W and the known permissible stresses [\(\sigma\)], the profile of the frame arches is selected. The following classic expression is used: W = M/[\(\sigma\)]. Taking into account that [\(\sigma\)] for Steel 09G2C is 210 MPa [27], then W = 16.38 cm\({}^{3}\). Provided that the fatigue safety factor, which for the elements of the wagon bodies in accordance with [33] is n = 1.8, then W = 29.48 cm\({}^{3}\). According to this moment of resistance, the use of a rectangular tube is proposed as a profile of the frame. Technologically, this profile is quite convenient for installation and maintenance [34]. It should also be noted that this profile is more durable and lighter, thus it is more economical. In accordance with [33], several tube variants are selected with the parameters given in Table 2.  
Figure 10: Diagram of bending moments acting in the frame (kN \(\cdot\) m). Thus, according to Table 2, the use of a 100 \(\times\) 100 tube is the most rational, since it has the smallest mass. The proposed design has a 16% smaller tare weight than the prototype. Taking into account the selected profile of the arches, a spatial model of the wagon body is built and its strength is calculated. When building the model, the welds between the individual components of the structure are not taken into account. The finite-element model of the framework is formed by tetrahedra (Figure 11) since the mesh is created on a solid body [35; 36; 37]. The number of nodes is 93,440, and the number of elements is 263,648. The largest element size is 100 mm and the smallest is 20 mm. By analysing the data given in Table 3, it can be concluded that the maximum stresses in the wagon body occur during an impact due to the maximum longitudinal load acting on the body. In other diagrams, the stresses in the body have lower values. For example, in design mode I (jerk), the stress is slightly greater than that during tension. This can be explained by the fact that when jerking, a large longitudinal force acts on the frame. In design mode III, the stresses in the body are almost the same. The maximum stresses during an impact occur in the area of interaction between the centre sill and the bolster beam (Figure 12). The minimum stresses occur in the frame mounting areas, i.e., in the areas where it rests on the bogies. This occurs due to rigid connections installed here. In the end walls of the body, the stresses are about 125 MPa, while in the middle part of the frame, they are about 145 MPa. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Width and Height, cm** & **Wall Thickness, mm** & **Moment of Resistance, cm\({}^{3}\)** & **Mass of 1 m, kg** \\ \hline
70 \(\times\) 70 & 8 & 29.74 & 13.85 \\ \hline
80 \(\times\) 80 & 4.5 & 30.4 & 10.26 \\ \hline
90 \(\times\) 90 & 3.5 & 32.24 & 9.26 \\ \hline
100 \(\times\) 100 & 3 & 35.41 & 8.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of tubes for arches. Figure 11: Finite element model of the body. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Loading Mode**} \\ \cline{2-6}
**Strength Index** & \multicolumn{4}{c}{**Mode I**} & \multicolumn{4}{c}{**Mode III**} \\ \cline{2-6}  & **Impact** & **Compression** & **Jerk** & **Tension** & **Impact/ Compression** & **Jerk/ Tension** \\ \hline Stress, MPa & 308 & 278.6 & 281.4 & 275.2 & 203.5 & 201.4 \\ \hline Displacements in units, mm & 4.8 & 4.7 & 4.7 & 4.6 & 4.6 & 4.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the strength calculation of the body.