The idea of beams on elastic foundation has been widely applied in the design of geotechnical structures such railway tracks, rigid and flexible highway pavement, building and habour structures. Winkler was the first to present the analysis of a beam on an elastic foundation for the analysis of railroad track deflection, based on the premise that the foundation reaction forces are proportionate to the deflection of the beam at that location. An elastic material regains its original shape on unloading whereas plastic material do not; an elastoplastic material undergoes coupled elastic (recoverable) and plastic (unrecoverable) deformations during loading and unloading. Soils are really elastoplastic material. At stresses below the yield stresses soil to responds elastically, whereas at stresses beyond yield stress soil to respond elastoplastically. The conventional analysis of plate on elastic foundation is inadequate which necessitated this study. This study focuses on the analysis of a beam on an elastoplastic foundation. Though the derivation started with winkler’s model, elastoplastic condition was considered. It was also assumed that the soil is homogeneous and isotropic; and that the beam on elastoplastic system is symmetrical with law of superposition applying. The derivation was further confirmed using Buckingham Pi theorem for dimensional analysis.
| Published in | Journal of Civil, Construction and Environmental Engineering (Volume 7, Issue 4) |
| DOI | 10.11648/j.jccee.20220704.11 |
| Page(s) | 40-45 |
| 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 |
Beam on Elastic Foundation, Winkler’s Model, Beam on Elastoplatic Foundation, Soil Structure Interaction
| [1] | Binesh S. M., Hataf N. and Ghahramani A. (2010). Elasto plastic analysis of reinforced soils using mesh free method. Applied Mathematics and Computation, 215: 4406-4421. doi: 10.1016/j.amc.2010.01.004. |
| [2] | Akhazhanov, B., Omarbekova, N., Mergenbekova, A., Zhunussova and Abdykeshova (2020). Analytical solution of beams on elastic foundation. International Journal of GEOMATE, Sept., 2020, Vol. 19, Issue 73, pp. 193–200. |
| [3] | Avramidis, I. E. and Morfidis, K. (2005). Bending of beams on three-parameter elastic foundation. International Journal of Solids and Structures 43 (2006) 357–375. |
| [4] | Nizameev, V., Basharov, F., & Nizameev, L. (2021). Evaluation of bearing capacity of a beam on an elastic foundation using the methods of the theory of limiting balance. In E3S Web of Conferences (Vol. 274). EDP Sciences. |
| [5] | Belkom, A. A. (2020). A simplified method for calculating load distribution and rail deflections in track incorporating the influence of sleeper stiffness. Advances in Structural Engineering, 23 (11): 2358-2372. |
| [6] | Shinkin, V. N. (2018). Springback coefficient of round steel beam under elastoplastic torsion. CIS Iron and Steel Review, 15: 23-27. |
| [7] | Zhu, B. T., & Yang, M. (2006). Comparison between elastoplastic method and m-method for retaining structures. Yantu Gongcheng Xuebao/Chinese Journal of Geotechnical Engineering, 28 (SUPPL.), 1387–1394. |
| [8] | Winkler, E. (1867). Theory of elasticity and strength, H. Dominicus, Czechoslovakia, Prague. |
| [9] | Arinze, E. E. (2019). Effect of angle of inclinations of structural loads on the normal and shear stresses of elastoplastic material. Nigerian International Material Congress at University of Ilorin, Nigeria, pp 216-218. |
| [10] | Cinoglu, I. S., Begley, M. R., Deaton, J. D., Beran, P. S., McMeeking, R. M., & Vermaak, N. (2019). Elastoplastic design of beam structures subjected to cyclic thermomechanical loads. Thin-Walled Structures, 136, 175–185. |
| [11] | Tan, Z., Cong, Z and Yao, Y. (2019). Re-discussion on Elastic- plastic Solution of the Ultimate Bearing Capacity of a Plate on a Winkler Foundation, Chin. J. Highway Transp. 32 (11) 129-136. |
| [12] | Liang, F., Zhang, H. and Yang, K (2014). "A variational solution for nonlinear response of laterally loaded piles with elasto-plastic winkler spring model", KSCE Journal of Civil Engineering, 19: 74-80. |
| [13] | Madhav, M. R., Rao, N. S. V. K., & Madhavan, K. (1971). Laterally loaded pile in elasto-plastic soil. Soils and Foundations, 11 (2), 1–15. |
| [14] | Hetenyi, M. (1946). Beam on elastic foundation: theory with applications in the fields of civil and mechanical engineering. The University of Michigan press, London. |
| [15] | Potts, D. M. and Zdravkovic, L. (2001). Finite Element analysis in geotechnical engineering-theory. Thomas Telford LTD, London. |
| [16] | Kondner, R. L. (1963). Hyperbolic Stress-Strain Response. Cohesive Soils. J. of Soil Mech. and Foundn. Div., Proc. ASCE, 89 (1): 115-143. |
| [17] | Cong, Z., Tan, Z. and Zhu, T. (2020). Ultimate bearing capacity of plate on Winkler foundation subjected to a circular uniform load. International Journal of Pavement Research and Technology 14 (2021) 668-675. |
APA Style
Emmanuel Emeka Arinze, Emeka Ogbonnaya Oti. (2022). Analyzing the Beam's Deformation Behavior on an Elastoplastic Foundation. Journal of Civil, Construction and Environmental Engineering, 7(4), 40-45. https://doi.org/10.11648/j.jccee.20220704.11
ACS Style
Emmanuel Emeka Arinze; Emeka Ogbonnaya Oti. Analyzing the Beam's Deformation Behavior on an Elastoplastic Foundation. J. Civ. Constr. Environ. Eng. 2022, 7(4), 40-45. doi: 10.11648/j.jccee.20220704.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.jccee.20220704.11,
author = {Emmanuel Emeka Arinze and Emeka Ogbonnaya Oti},
title = {Analyzing the Beam's Deformation Behavior on an Elastoplastic Foundation},
journal = {Journal of Civil, Construction and Environmental Engineering},
volume = {7},
number = {4},
pages = {40-45},
doi = {10.11648/j.jccee.20220704.11},
url = {https://doi.org/10.11648/j.jccee.20220704.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jccee.20220704.11},
abstract = {The idea of beams on elastic foundation has been widely applied in the design of geotechnical structures such railway tracks, rigid and flexible highway pavement, building and habour structures. Winkler was the first to present the analysis of a beam on an elastic foundation for the analysis of railroad track deflection, based on the premise that the foundation reaction forces are proportionate to the deflection of the beam at that location. An elastic material regains its original shape on unloading whereas plastic material do not; an elastoplastic material undergoes coupled elastic (recoverable) and plastic (unrecoverable) deformations during loading and unloading. Soils are really elastoplastic material. At stresses below the yield stresses soil to responds elastically, whereas at stresses beyond yield stress soil to respond elastoplastically. The conventional analysis of plate on elastic foundation is inadequate which necessitated this study. This study focuses on the analysis of a beam on an elastoplastic foundation. Though the derivation started with winkler’s model, elastoplastic condition was considered. It was also assumed that the soil is homogeneous and isotropic; and that the beam on elastoplastic system is symmetrical with law of superposition applying. The derivation was further confirmed using Buckingham Pi theorem for dimensional analysis.},
year = {2022}
}
TY - JOUR T1 - Analyzing the Beam's Deformation Behavior on an Elastoplastic Foundation AU - Emmanuel Emeka Arinze AU - Emeka Ogbonnaya Oti Y1 - 2022/07/05 PY - 2022 N1 - https://doi.org/10.11648/j.jccee.20220704.11 DO - 10.11648/j.jccee.20220704.11 T2 - Journal of Civil, Construction and Environmental Engineering JF - Journal of Civil, Construction and Environmental Engineering JO - Journal of Civil, Construction and Environmental Engineering SP - 40 EP - 45 PB - Science Publishing Group SN - 2637-3890 UR - https://doi.org/10.11648/j.jccee.20220704.11 AB - The idea of beams on elastic foundation has been widely applied in the design of geotechnical structures such railway tracks, rigid and flexible highway pavement, building and habour structures. Winkler was the first to present the analysis of a beam on an elastic foundation for the analysis of railroad track deflection, based on the premise that the foundation reaction forces are proportionate to the deflection of the beam at that location. An elastic material regains its original shape on unloading whereas plastic material do not; an elastoplastic material undergoes coupled elastic (recoverable) and plastic (unrecoverable) deformations during loading and unloading. Soils are really elastoplastic material. At stresses below the yield stresses soil to responds elastically, whereas at stresses beyond yield stress soil to respond elastoplastically. The conventional analysis of plate on elastic foundation is inadequate which necessitated this study. This study focuses on the analysis of a beam on an elastoplastic foundation. Though the derivation started with winkler’s model, elastoplastic condition was considered. It was also assumed that the soil is homogeneous and isotropic; and that the beam on elastoplastic system is symmetrical with law of superposition applying. The derivation was further confirmed using Buckingham Pi theorem for dimensional analysis. VL - 7 IS - 4 ER -
Information
Email: