# Railway Track Stress-Strain Analysis Using High-Precision Accelerometers
## 5 Analysis  
The results of modeling the impact of rolling stock on a section of a railway track with intermediate rail fastenings ZhBR-65 SH are presented below in the form of contours of normal stresses and deformations in the elements of the railway track (see Figures 5-8 and Table 1). The axial load was 30 ton-force (tf), and the lateral force was 10 tf. As can be seen from the figures, the highest stress was in the Y direction longitudinally. The side stresses were more important for the control of destructive effects. The data presented in Table 1 enabled determination of the boundaries of rail movements dependent on vertical and side forces. Approximations of these simulation results provided the dependences of the lateral forces acting on the rail on the magnitude of the displacements at various axial loads (see Figure 9):  
\[ \begin{array}{l}\text{y}=-126.066\text{x}^{2}+418.748\text{x}-231.351,\text{ R}^{2}=1.0;\\ \text{y}=-191.104\text{x}^{2}+615.992\text{x}-391.266,\text{ R}^{2}=1.0;\\ \text{y}=-246.606\text{x}^{2}+829.830\text{x}-596.294,\text{ R}^{2}=1.0\end{array} \]  
where x--displacement in mm. Figure 5: Bending stresses on the inner edge of the rail. Figure 8: Stresses at the main site of the subgrade. Figure 6: Bending stresses on the outer edge of the rail. Figure 7: Movement of a rail under the influence of a train load. The coefficient of accuracy of the approximation was equal to one, which indicated the maximum degree of compliance of the trend model with the initial data. There was an obvious dependence of the increase in the growth of displacements with the addition of lateral forces for certain axial loads. Thus, knowing the type of rolling stock with the corresponding axle load, and by measuring the rail movement, it was possible to determine the lateral forces acting on the rail from the wheels of the rolling stock, and to establish the parameters of the stress-strain state of the track elements using the equations of approximation and linear interpolation. The corresponding rail deflections are presented in Figure 10. Using high-precision accelerometers with the distance between the sensors 1.5-2 m, it was possible to obtain the maximum and minimum values of the deflections on adjacent sensors. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Vertical Wheel Force, kN** & **Side Force, kN** & **Inner Sole Edge** & **Outer Sole Edge** & **Moving the Rail** & **Subgrade** \\  & & & & **(Wheel between** & **(Wheel between** \\  & & & & **the Sleepers)** & **the Sleepers)** \\ \hline \(98.1\) & \(0\) & \(43.88\) & \(31.29\) & \(0.7\) & \(-0.04787\) \\ \(98.1\) & \(49.05\) & \(2.341\) & \(82.409\) & \(0.93\) & \(-0.047068\) \\ \(98.1\) & \(98.1\) & \(-18.344\) & \(133.28\) & \(1.28\) & \(-0.049891\) \\ \(122.63\) & \(0\) & \(54.495\) & \(39.002\) & \(0.87\) & \(-0.057487\) \\ \(122.63\) & \(49.05\) & \(10.511\) & \(90.069\) & \(1.07\) & \(-0.05667\) \\ \(122.63\) & \(98.1\) & \(-13.764\) & \(140.91\) & \(1.42\) & \(-0.058574\) \\ \(147.15\) & \(0\) & \(65.134\) & \(46.598\) & \(1.04\) & \(-0.067109\) \\ \(147.15\) & \(49.05\) & \(18.719\) & \(97.654\) & \(1.22\) & \(-0.066353\) \\ \(147.15\) & \(98.1\) & \(-9.1453\) & \(148.53\) & \(1.56\) & \(-0.068139\) \\ \hline \hline \end{tabular}  
* Normal stresses, MPa; displacement, mm; 1840 \(\mathrm{hp}/\mathrm{km}\); ballast, 45 cm.  
\end{table} 
Table 1: Simulation results under loading of a track section 1. Figure 9: Restored side forces acting on the rail for the corresponding rail movements at various axial loads. Therefore, the proposed approach is suitable for studying the deflections of one rail, and the influences of adjacent wheels of the carriage bogie. Simulation results are presented in Table 2.  
That is, for example, when a coach with a mass of 90 tons passed (corresponding to a wheel load of 110.4 kN) and the rail moved directly under the wheels of a rolling stock 1 mm in size, the resulting forces and stresses were calculated in several stages:  
1. The wheel load of 110.4 kN was between 98.1 and 122.63 kN (step 1);
2.