## 5 Conclusions  
1. The design of the detachable module for the transportation of long cargoes is proposed. The peculiarity of the detachable module is its frame-based construction. The loading platform is the frame. The profiles of the detachable module are determined based on the resistance moments of its components.  
Mathematical modeling is carried out to determine the dynamic load of the detachable module. It is found that the maximum acceleration acting on a flat car with two detachable modules is about 37 m/s\({}^{2}\). The resulting acceleration is taken into account in further calculations for the detachable module. Channel No. 27, reinforced with a vertical sheet, 4 mm thick, is chosen as the frame profile; channel No. 20, reinforced with a sheet, 3.5 mm thick, is chosen for the end superstructures and vertical posts.  
2. The strength of the detachable module under longitudinal loads is calculated. The maximum stresses in the structure of the detachable module amount to 286.5 MPa and occur in the cross bearers in the areas of their interaction with the fittings. These stresses are 7.7% lower than permissible ones. The maximum displacements in the structure of the detachable module occur in the upper belt of the end superstructure and are 4.1 mm.  
3. The strength of the detachable module under lateral loads is calculated. The maximum stresses in the structure of the detachable module are 292.4 MPa. These stresses are concentrated in the areas of interaction between the main longitudinal beam and the fitting stops. They do not exceed the permissible stresses and are 5.8% lower. The maximum displacements are recorded in the central posts on the tilt side of the detachable module and amount to 6.2 mm.  
This research also includes a modal analysis and the determination of the natural frequencies and oscillation shapes of the detachable module. The first natural oscillation frequency of the detachable module is found to be 20 Hz. Thus, according to the frequency analysis, the safety of the detachable module is ensured.  
This research will help to create recommendations for the design of modern modular vehicles and improve the efficiency of the transport industry.  
**Author Contributions:** Conceptualization, J.G. and A.L.; methodology, J.G., A.L. and M.P.; software, A.L. and M.P.; validation, J.G., A.L. and M.P.; formal analysis, A.L. and M.P.; investigation, J.G. and A.L., resources, A.L. and M.P.; data curation, J.G., A.L. and M.P.; writing--original draft preparation, J.G., A.L. and M.P.; writing--review and editing, J.G. and A.L.; visualization, [PERSON], A.L. and M.P.; supervision, [PERSON] and A.L., and M.P.; funding acquisition, J.G., A.L. and M.P. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This publication was issued thanks to the support from the Cultural and Educational Grant Agency of the Ministry of Education of the Slovak Republic in project KEGA 031 ZU-4/2023: Development of key competencies of the graduate of the study program Vehicles and Engines. This research was also supported by the Slovak Research and Development Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic in the Educational Grant Agency of the Ministry of Education of the Slovak Republic in the project and VEGA 1/0513/22, \"Investigation of the properties of railway brake components in simulated operating conditions on a flywheel brake stand\". Funded by the EU NextGenerationEU through the Recovery and Resilience Plan for Slovakia under the project No. 09I03-03-V01-00131.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.