Analysis of Loaded Beam, Cantilever, and Elongated Vertical Column via Integral Rohit Transform
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Abstract
Structural analysis is a branch of solid mechanics which utilizes straight forward models for solids. The main objective of Structural analysis is to find out the effect of loads on the physical structures and their components. A beam is a structure with a constant cross-section and is described by its significant length in comparison to its thickness and width. A cantilever, on the other hand, is a slender beam with a uniform cross-sectional shape that is fixed horizontally at one end and subjected to a load at the other end. Columns, which serve as vertical compression members in building frames, are susceptible to buckling and failure when subjected to relatively small axial loads. The analysis of loaded beams, cantilevers, and elongated vertical columns is typically carried out using the principles of calculus. However, this paper introduces the integral Rohit transform for the analysis of loaded beam supported at ends, cantilever, and elongated columns with low buckling axial loads. It is found that the depression grows as the cantilever and beam lengths that are loaded in the middle and supported at both ends rise. An attempt has been made to analyze the elongated column with low axial buckling loads and derive the Euler's formula for buckling load. The obtained solutions are graphically represented, and the results demonstrate accuracy, capability and effectiveness of the integral Rohit transform technique when compared to existing methods in the literature. The Rohit transform involves simple formulation and less computational work compared to other methods available in the literature.
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References
Ramamrutham, S.; Narayan, R. Theory of Structures. Danpat Rai Publishing Company, 9th Ed., 2014.
Khurmi, R.S.; Khurmi, N. Theory of structures. S. Chand and Company Ltd. 12th Ed. 2020.
Sharma, K. K. Mechanics Oscillations and Relativity. Sharma Publications, Revised Ed., 2019.
Arya, A.S.; Jain., O.P. Theory and analysis of structures. Nem Chand and Brothers, 2003.
Naga Prasad, Ch. S. Design and Analysis of Cantilever Beam, International Journal of Advanced Technology and Innovative Research 2017, 9(5), 0682-0685.
Karthik, K.; Unnam, N . K.; Thamilarasan, J.; Rameshkumar, R. Design and analysis of cantilever beam used Kevlar fiber composite for automobile applications, Materials Today Proceedings 2022, 59(2), 1817-1823. https://doi.org/10.1016/j.matpr.2022.04.389
Punmia, B.C. Theory of Structures, Laxmi Publications Pvt. Ltd. 9th Ed. 2000.
Alan Williams Structural Analysis-in theory and practice, Elsevier Inc. 2009. https://doi.org/10.1016/B978-1-85617-550-0.X0001-2
Gupta, R. On novel integral transform: Rohit Transform and its application to boundary value problems, ASIO Journal of Chemistry, Physics, Mathematics and Applied Sciences (ASIO-JCPMAS) 2020, 4(1), 08-13. http://doi-ds.org/doilink/06.2020-62339259/
Gupta, R.; Singh, I; Sharma, A. Response of an Undamped Forced Oscillator via Rohit Transform, International Journal of Emerging Trends in Engineering Research 2022, 10(8), 396-400. https://doi.org/10.30534/ijeter/2022/031082022
Gupta, R. Mechanically Persistent Oscillator Supplied with Ramp Signal, Al-Salam Journal for Engineering and Technology 2023, 2(2), 112–115. https://doi.org/10.55145/ajest.2023.02.02.014
Gupta, R.,; Sharma, S.; Verma, D. Analytical Treatment of The Cantilever and The Beam Supported At Ends and Loaded In The Middle (January 8, 2023). Journal of Engineering Sciences 2020, 11(2), 60-63. Available at SSRN: https://ssrn.com/abstract=4320107
Mullins, N.; Snizek, W.; Oehler, K Chapter 3 - the structural analysis of a scientific paper. Handbook of Quantitative Studies of Science and Technology, Elsevier, 1988; 81-105, ISBN 9780444705372. https://doi.org/10.1016/B978-0-444-70537-2.50008-8.
Vinay, P.; Srilaxmi., K. Structural Analysis and Design of Structural Elements of A Building. International Journal of Trend in Scientific Research and Development (IJTSRD) 2018, 2(3), 1132-1151. https://doi.org/10.31142/ijtsrd11237
Shu, B.; Xu, C. The structural analysis based on modern design method, In 2009 IEEE 10th International Conference on Computer-Aided Industrial Design & Conceptual Design, Wenzhou, 2009, 16-18. https://doi.org/10.1109/CAIDCD.2009.5375214
Kumar, C.; Singh, A.K.; Kumar, N.; Kumar, A. Model Analysis and Harmonic Analysis of Cantilever Beam by ANSYS, Global journal for research analysis 2014, 3(9), 51- 55.
Damir Hodžić, Bending Analysis Of Cantilever Beam In Finite Element Method, ANNALS of Faculty Engineering Hunedoara – International Journal Of Engineering Tome XIX 2021, 4, 23-26.
Navaee, S.; Elling, R.E. Equilibrium Configurations of Cantilever Beams Subjected to Inclined End Loads, ASME J. Appl Mech. 1992, 59(3), 572–579. https://doi.org/10.1115/1.2893762
Bisshopp, K. E.; Daniel C. Drucker. Large deflection of cantilever beams. Quarterly of Applied Mathematics 3 1945, 3(3), 272-275. https://doi.org/10.1090/QAM/13360
Li, W.; Xu, M.; Zhang, Y.; Lei, J.; Li, Z.; Huang, Y.; Tian, Y. Computational study on structures of vertical columns formed by successive droplets, Journal of Materials Processing Technology 2021, 288, 116903. https://doi.org/10.1016/j.jmatprotec.2020.116903
Sun, Y.B.; Cao, T.J.; Xiao, Y. Full-scale steel column tests under simulated horizontal and vertical earthquake loadings, Journal of Constructional Steel Research 2019, 163, 105767. https://doi.org/10.1016/j.jcsr.2019.105767