A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails

Eduard Danilenko; Vitalii Molchanov

doi:doi:10.11648/j.ajtte.20210603.12

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A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails

Eduard Danilenko, Vitalii Molchanov

Published in American Journal of Traffic and Transportation Engineering (Volume 6, Issue 3)

Received: 12 May 2021 Accepted: 1 June 2021 Published: 21 June 2021

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Abstract

The reference data given in technical literature on the characteristics of spatial stiffness and elasticity of rail threads in the conditions of joint action on the rails of vertical and horizontal lateral forces and torsion are very different and in some cases contradictory. This situation is due to the lack of an accurate analytical solution to this problem and the provision for reference materials only experimental research data, which are clearly different, not only for different railway structures, but also significantly differ in different conditions of acting external forces (P, H, M_tor). The purpose of this article is to present a new method of analytical solution of the problem of determining the spatial characteristics of stiffness and elasticity of rail threads and also computation the stresses and strains that occur in them, under conditions of complex joint action on rail threads of vertical and horizontal dynamic forces (P_dyn, H_dyn) simultaneously with the external torque moment M_tor arising from off-center forces applied to the rails from wheel loads. The complex method of solving the problem was used in the paper. It includes the theoretical part and the results of the experiment. Using the experimental researches characteristics of horizontal lateral stiffness of the rail threads of the head and sole at different constructions of the modern rail fastenings was measured. The second task of determination of the real values of the characteristics of spatial elasticity and stiffness modulus of the rail thread under joint vertical and lateral horizontal bends of the rail in conjunction with its simultaneous torsion was solved by the theoretical methods. As the results of author’s researches were obtained new values of the characteristics of spatial stiffness and elasticity modulus of rail threads under joint vertical and lateral horizontal bends of the rail in conjunction with its simultaneous torsion. These characteristics were obtained for the modern railway track constrictions with rails (R65, R50, UIC60) on concrete and wooden sleepers and with rail fastenings unlined or lined types (KB, KPP-5, KPP-1, D0). And also these characteristics were obtained in the functional dependence on the ratio of vertical and horizontal lateral forces P/H.

Published in	American Journal of Traffic and Transportation Engineering (Volume 6, Issue 3) This article belongs to the Special Issue Railway Track and Railway Structures
DOI	10.11648/j.ajtte.20210603.12
Page(s)	58-80
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Rail Thread, Stiffness, Elasticity, Torsion, Vertical Forces, Horizontal Forces, Stresses, Strains

References

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[3]	Smirnov M. P. Osnovy rascheta jelementov verhnego stroenija puti na prochnost' [Basics of strength calculation of track superstructure elements] in the book: ''Osnovy ustrojstva i raschetov zheleznodorozhnogo puti'' [Fundamentals of the device and calculations of the railway track]. Moscow, Transport Publ., 1990. pp. 264–318.
[4]	Pravyla rozrakhunkiv zaliznychnoi kolii na mitsnist' i stijkist' [Rules for calculating the railway track for strength and stability] under editor Danilenko E. I. Kyiv, Transport of Ukraine, 2006. 168 p.
[5]	Danilenko E. I., Velinets V. P. Eksperymentalni doslidzhennia kharakterystyk horyzontalnoi poperechnoi zhorstkosti i modulia pruzhnosti zaliznychnoi kolii pry riznykh konstruktsiiakh reikovykh skriplen [Experimental studies of characteristics of horizontal and lateral stiffness and elasticity modulus of railway track in various designs of rail fasteners]. Zaliznychnyi transport Ukrainy – Railway Transport of Ukraine, (Journal) 2015, no. 4, pp. 3-11.
[6]	Danilenko E. I. Raschet harakteristik zhestkosti i uprugosti rel'sovoj niti pri kruchenii pod vozdejstviem vertikal'nyh i gorizontal'nyh sil [Calculation of the characteristics of stiffness and elasticity of a rail thread in torsion under the influence of vertical and horizontal forces]. Nauka ta prohres transportu. Visnyk Dnipropetrovs'koho natsional'noho universytetu zaliznychnoho transportu [Science and progress of transport. Bulletin of Dnipropetrovsk National University of Railway Transport], 2016, issue 5 (65), pp. 79–91.
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[8]	Timoshenko S. P. Metod issledovaniy statisticheskikh i dinamicheskikh napryazheniy v relse [Method of research of statistical and dynamic stresses in the rail]. Statisticheskiye i dinamicheskiye problemy teorii uprugosti [Statistical and dynamic problems of the elasticity theory]. Kyiv, Science Publ., 1975, pp. 209-220.
[9]	Timoshenko S. P. Napryazheniya v zheleznodorozhnom relse [Stresses in the rail]. Statisticheskiye i dinamicheskiye problemy teorii uprugosti [Statistical and dynamic problems of the elasticity theory]. Kyiv, Science Publ., 1975, pp. 318-355.
[10]	Stepkin S. A. O mestnyh naprjazhenijah v rel'sah pri kruchenii [About local torsional stresses in rails] Sbornik trudov Leningradskogo institutu inzhenerov transporta [Proceedings of the Leningrad Institute of Transport Engineers], 1937, issue 127.
[11]	Golovanov D. G. Vlijanie modulja uprugosti osnovanija rel'sa v otnoshenii kruchenija na naprjazhenija i deformacii v rel'se, zagruzhennom poperechnoj gorizontal'noj siloj [Influence of the modulus of elasticity of the rail base in relation to torsion on stresses and deformations in a rail loaded with a lateral horizontal force]. Trudy Tashkentskogo instituta inzhenerov transporta [Proceedings of the Tashkent Institute of Transport Engineers], 1956, issue V.
[12]	Golovanov D. G. Vlijanie modulja uprugosti osnovanija rel'sa v otnoshenii izgiba na deformacii i naprjazhenija v rel'se, zagruzhennom poperechnoj gorizontal'noj siloj [Influence of the modulus of elasticity of the rail base in relation to bending on deformations and stresses in a rail loaded with a lateral horizontal force]. Trudy Tashkentskogo instituta inzhenerov transporta [Proceedings of the Tashkent Institute of Transport Engineers], 1954, issue IV.
[13]	Yershkov O. P. Kharakteristiki prostranstvennoy uprugosti relsovoy niti [Characteristics of the spatial elasticity of rail thread]. Trudy Vserossiyskogo nauchno-issledovatelskogo instituta zheleznodorozhnogo transporta [Proc. of All-Russian Research Institute of Railway Transport], Moscow, 1960, issue 192, pp. 59-101.
[14]	Yershkov O. P. Raschet relsa na deystviye bokovykh sil v krivykh [Rail Calculation of the rail under the action of the lateral forces in the curves]. Trudy Vserossiyskogo nauchno-issledovatelskogo instituta zheleznodorozhnogo transporta [Proc. of All-Russian Research Institute of Railway Transport], Moscow, 1960, issue 192, pp. 5-59.
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[16]	Timoshenko S. P. K voprosu o prochnosti rels [To the question about rail strength] in the book: ''Prochnost i kolebaniya elementov konstruktsiy'' [Strength and vibration of construction elements], Moscow, Science Publ., 1975, pp. 322-358.
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[22]	Darenskiy O. M., Tuley Yu. L., Ovchynnikov O. O., Leibuk Ya. S. Numerical investigations of dynamic transverse forces in curves, in the zones of rail varieties. Proc. of scientific works of Ukrainian State University of Railway Transport. Kharkiv, 2018, issue 179, pp. 51–58.

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Eduard Danilenko, Vitalii Molchanov. (2021). A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails. American Journal of Traffic and Transportation Engineering, 6(3), 58-80. https://doi.org/10.11648/j.ajtte.20210603.12

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ACS Style

Eduard Danilenko; Vitalii Molchanov. A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails. Am. J. Traffic Transp. Eng. 2021, 6(3), 58-80. doi: 10.11648/j.ajtte.20210603.12

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AMA Style

Eduard Danilenko, Vitalii Molchanov. A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails. Am J Traffic Transp Eng. 2021;6(3):58-80. doi: 10.11648/j.ajtte.20210603.12

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@article{10.11648/j.ajtte.20210603.12,
  author = {Eduard Danilenko and Vitalii Molchanov},
  title = {A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails},
  journal = {American Journal of Traffic and Transportation Engineering},
  volume = {6},
  number = {3},
  pages = {58-80},
  doi = {10.11648/j.ajtte.20210603.12},
  url = {https://doi.org/10.11648/j.ajtte.20210603.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtte.20210603.12},
  abstract = {The reference data given in technical literature on the characteristics of spatial stiffness and elasticity of rail threads in the conditions of joint action on the rails of vertical and horizontal lateral forces and torsion are very different and in some cases contradictory. This situation is due to the lack of an accurate analytical solution to this problem and the provision for reference materials only experimental research data, which are clearly different, not only for different railway structures, but also significantly differ in different conditions of acting external forces (P, H, Mtor). The purpose of this article is to present a new method of analytical solution of the problem of determining the spatial characteristics of stiffness and elasticity of rail threads and also computation the stresses and strains that occur in them, under conditions of complex joint action on rail threads of vertical and horizontal dynamic forces (Pdyn, Hdyn) simultaneously with the external torque moment Mtor arising from off-center forces applied to the rails from wheel loads. The complex method of solving the problem was used in the paper. It includes the theoretical part and the results of the experiment. Using the experimental researches characteristics of horizontal lateral stiffness of the rail threads of the head and sole at different constructions of the modern rail fastenings was measured. The second task of determination of the real values of the characteristics of spatial elasticity and stiffness modulus of the rail thread under joint vertical and lateral horizontal bends of the rail in conjunction with its simultaneous torsion was solved by the theoretical methods. As the results of author’s researches were obtained new values of the characteristics of spatial stiffness and elasticity modulus of rail threads under joint vertical and lateral horizontal bends of the rail in conjunction with its simultaneous torsion. These characteristics were obtained for the modern railway track constrictions with rails (R65, R50, UIC60) on concrete and wooden sleepers and with rail fastenings unlined or lined types (KB, KPP-5, KPP-1, D0). And also these characteristics were obtained in the functional dependence on the ratio of vertical and horizontal lateral forces P/H.},
 year = {2021}
}

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TY  - JOUR
T1  - A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails
AU  - Eduard Danilenko
AU  - Vitalii Molchanov
Y1  - 2021/06/21
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtte.20210603.12
DO  - 10.11648/j.ajtte.20210603.12
T2  - American Journal of Traffic and Transportation Engineering
JF  - American Journal of Traffic and Transportation Engineering
JO  - American Journal of Traffic and Transportation Engineering
SP  - 58
EP  - 80
PB  - Science Publishing Group
SN  - 2578-8604
UR  - https://doi.org/10.11648/j.ajtte.20210603.12
AB  - The reference data given in technical literature on the characteristics of spatial stiffness and elasticity of rail threads in the conditions of joint action on the rails of vertical and horizontal lateral forces and torsion are very different and in some cases contradictory. This situation is due to the lack of an accurate analytical solution to this problem and the provision for reference materials only experimental research data, which are clearly different, not only for different railway structures, but also significantly differ in different conditions of acting external forces (P, H, Mtor). The purpose of this article is to present a new method of analytical solution of the problem of determining the spatial characteristics of stiffness and elasticity of rail threads and also computation the stresses and strains that occur in them, under conditions of complex joint action on rail threads of vertical and horizontal dynamic forces (Pdyn, Hdyn) simultaneously with the external torque moment Mtor arising from off-center forces applied to the rails from wheel loads. The complex method of solving the problem was used in the paper. It includes the theoretical part and the results of the experiment. Using the experimental researches characteristics of horizontal lateral stiffness of the rail threads of the head and sole at different constructions of the modern rail fastenings was measured. The second task of determination of the real values of the characteristics of spatial elasticity and stiffness modulus of the rail thread under joint vertical and lateral horizontal bends of the rail in conjunction with its simultaneous torsion was solved by the theoretical methods. As the results of author’s researches were obtained new values of the characteristics of spatial stiffness and elasticity modulus of rail threads under joint vertical and lateral horizontal bends of the rail in conjunction with its simultaneous torsion. These characteristics were obtained for the modern railway track constrictions with rails (R65, R50, UIC60) on concrete and wooden sleepers and with rail fastenings unlined or lined types (KB, KPP-5, KPP-1, D0). And also these characteristics were obtained in the functional dependence on the ratio of vertical and horizontal lateral forces P/H.
VL  - 6
IS  - 3
ER  -

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Author Information

Eduard Danilenko

Department of Railway Track and Track Facilities, State University of Infrastructure and Technology, Kyiv, Ukraine
Vitalii Molchanov

Department of Railway Track and Track Facilities, State University of Infrastructure and Technology, Kyiv, Ukraine

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APA Style

Eduard Danilenko, Vitalii Molchanov. (2021). A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails. American Journal of Traffic and Transportation Engineering, 6(3), 58-80. https://doi.org/10.11648/j.ajtte.20210603.12

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ACS Style

Eduard Danilenko; Vitalii Molchanov. A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails. Am. J. Traffic Transp. Eng. 2021, 6(3), 58-80. doi: 10.11648/j.ajtte.20210603.12

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AMA Style

Eduard Danilenko, Vitalii Molchanov. A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails. Am J Traffic Transp Eng. 2021;6(3):58-80. doi: 10.11648/j.ajtte.20210603.12

Copy | Download

@article{10.11648/j.ajtte.20210603.12,
  author = {Eduard Danilenko and Vitalii Molchanov},
  title = {A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails},
  journal = {American Journal of Traffic and Transportation Engineering},
  volume = {6},
  number = {3},
  pages = {58-80},
  doi = {10.11648/j.ajtte.20210603.12},
  url = {https://doi.org/10.11648/j.ajtte.20210603.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtte.20210603.12},
  abstract = {The reference data given in technical literature on the characteristics of spatial stiffness and elasticity of rail threads in the conditions of joint action on the rails of vertical and horizontal lateral forces and torsion are very different and in some cases contradictory. This situation is due to the lack of an accurate analytical solution to this problem and the provision for reference materials only experimental research data, which are clearly different, not only for different railway structures, but also significantly differ in different conditions of acting external forces (P, H, Mtor). The purpose of this article is to present a new method of analytical solution of the problem of determining the spatial characteristics of stiffness and elasticity of rail threads and also computation the stresses and strains that occur in them, under conditions of complex joint action on rail threads of vertical and horizontal dynamic forces (Pdyn, Hdyn) simultaneously with the external torque moment Mtor arising from off-center forces applied to the rails from wheel loads. The complex method of solving the problem was used in the paper. It includes the theoretical part and the results of the experiment. Using the experimental researches characteristics of horizontal lateral stiffness of the rail threads of the head and sole at different constructions of the modern rail fastenings was measured. The second task of determination of the real values of the characteristics of spatial elasticity and stiffness modulus of the rail thread under joint vertical and lateral horizontal bends of the rail in conjunction with its simultaneous torsion was solved by the theoretical methods. As the results of author’s researches were obtained new values of the characteristics of spatial stiffness and elasticity modulus of rail threads under joint vertical and lateral horizontal bends of the rail in conjunction with its simultaneous torsion. These characteristics were obtained for the modern railway track constrictions with rails (R65, R50, UIC60) on concrete and wooden sleepers and with rail fastenings unlined or lined types (KB, KPP-5, KPP-1, D0). And also these characteristics were obtained in the functional dependence on the ratio of vertical and horizontal lateral forces P/H.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - A New Method for Solving the Problem of Determining the Characteristics of Spatial Stiffness and Elasticity of the Rail Threads and Stresses and Strains in Rails
AU  - Eduard Danilenko
AU  - Vitalii Molchanov
Y1  - 2021/06/21
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtte.20210603.12
DO  - 10.11648/j.ajtte.20210603.12
T2  - American Journal of Traffic and Transportation Engineering
JF  - American Journal of Traffic and Transportation Engineering
JO  - American Journal of Traffic and Transportation Engineering
SP  - 58
EP  - 80
PB  - Science Publishing Group
SN  - 2578-8604
UR  - https://doi.org/10.11648/j.ajtte.20210603.12
AB  - The reference data given in technical literature on the characteristics of spatial stiffness and elasticity of rail threads in the conditions of joint action on the rails of vertical and horizontal lateral forces and torsion are very different and in some cases contradictory. This situation is due to the lack of an accurate analytical solution to this problem and the provision for reference materials only experimental research data, which are clearly different, not only for different railway structures, but also significantly differ in different conditions of acting external forces (P, H, Mtor). The purpose of this article is to present a new method of analytical solution of the problem of determining the spatial characteristics of stiffness and elasticity of rail threads and also computation the stresses and strains that occur in them, under conditions of complex joint action on rail threads of vertical and horizontal dynamic forces (Pdyn, Hdyn) simultaneously with the external torque moment Mtor arising from off-center forces applied to the rails from wheel loads. The complex method of solving the problem was used in the paper. It includes the theoretical part and the results of the experiment. Using the experimental researches characteristics of horizontal lateral stiffness of the rail threads of the head and sole at different constructions of the modern rail fastenings was measured. The second task of determination of the real values of the characteristics of spatial elasticity and stiffness modulus of the rail thread under joint vertical and lateral horizontal bends of the rail in conjunction with its simultaneous torsion was solved by the theoretical methods. As the results of author’s researches were obtained new values of the characteristics of spatial stiffness and elasticity modulus of rail threads under joint vertical and lateral horizontal bends of the rail in conjunction with its simultaneous torsion. These characteristics were obtained for the modern railway track constrictions with rails (R65, R50, UIC60) on concrete and wooden sleepers and with rail fastenings unlined or lined types (KB, KPP-5, KPP-1, D0). And also these characteristics were obtained in the functional dependence on the ratio of vertical and horizontal lateral forces P/H.
VL  - 6
IS  - 3
ER  -

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