Euler-Bernoulli and Timoshenko Beam Theories Analytical and Numerical Comprehensive Revision



Abstract Views
3252

Downloads
10924

Citations

Share

##plugins.themes.bootstrap3.article.sidebar##

Submitted Oct 12, 2021
Published Nov 12, 2021
10.24018/ejeng.2021.6.7.2626

Abstract viewed = 3252 times

Table of Contents

##plugins.themes.bootstrap3.article.main##

Obtaining reliable and efficient results of a specified problem solution depends upon understanding the strategy of the method of analysis, which is emanated from all related physical basics of the problem, formulated with master mathematical tools to give its governing mathematical model. These two categories require deep study in a wide range of references and literature in order not only to apply the method professionally, but also to look for improvements, developments, and contributions in the field of the method. Consequently, although Euler-Bernoulli and Timoshenko beam theories are the oldest ones, but surely, they represent a cornerstone for most modern methods in structural analysis; In what follows, a detailed revision of these theories and their applications analytically and in numerical style is presented in a proper and simplified entrance to be able to understand more advanced topics such as thin and thick plate theories. Illustrative examples will be used to show and discuss the methods.

Keywords: Euler-Bernoulli Beam Theory, First order Shear Deformation; Timoshenko, Beam Theory

Downloads

Download data is not yet available.

References

  1. Timoshenko S. Strength of Material Part I & II, 2nd Edition,1930, D Van Nostrand Company Inc.
     Google Scholar
  2. Timoshenko S. (1878-1972), Gere JM. Mechanics of Materials, Third Si Edition, Springer Science+ Business Media, B.V, 1991.
     Google Scholar
  3. Stephen H. Crandall and Norman C. Dahl, et al., An Introduction to The Mechanics of Solids, 2nd Edition, Mcgraw Hill, 1978.
     Google Scholar
  4. Egor P. Popov, Engineering Mechanics of Solids, Prentice Hall.
     Google Scholar
  5. Benham PP, Warnock FV, Mechanics of Solids and Structures, Pitman Publishing Ltd. Uk, First Reprinted Edition 1978.
     Google Scholar
  6. S. Timoshenko, J. N. Goodier, Theory of Elasticity, Mcgraw Hill, 1951.
     Google Scholar
  7. Reddy JN. Appendix-B_Notes-On-Beam-Theories.Pdf, Evpm 3ed02, 2016.
     Google Scholar
  8. On the Correction for Shear of The Deferential Equation for Transverse Vibrations of Prismatic Bars. By: Prof. S. P. Timoshenko,1921, Phil. Mug. 41 744-6.
     Google Scholar
  9. On the Transverse Vibrations of Bars of Uniform Cross-Section. By Prof. S. P. Timoshenko, 1922 Phil. Mag. 43 125-31.
     Google Scholar
  10. Roark RJ. Formulas for Stress and Strain. 3rd Ed. New York: Mcgraw-Hill;1954. P. 119–21.
     Google Scholar
  11. Newlin JA and Trayer GW, Deflection of Beams with Special Reference to Shear Deformations, Report National Advisory Committee for Aeronautics, University of Wisconsin.
     Google Scholar
  12. Cowper Gr. The Shear Coefficient in Timoshenko's Beam Theory. J Appl Mech Trans, Asme 1966;33:335–40.
     Google Scholar
  13. Hutchinson JR, Shear Coefficients for Timoshenko Beam Theory, Journal of Applied Mechanics, January 2001, vol. 68.
     Google Scholar
  14. Klaus-Jurgen Bathe, Finite Element Procedures, Second Edition, Prentice Hall, Pearson Education, Inc. 2nd Edition: Fourth Printing 2016.
     Google Scholar
  15. Zienkiewicz OC, Cbe, Frs, Taylor RL, Zhu JZ, The Finite Element Method: Its Basis and Fundamentals, Seventh Edition, Elsevier Ltd.
     Google Scholar
  16. Clive L. Dym Irvin 2013 G H. Shames, Solid Mechanics, A Variational Approach, Augmented Edition, Springer Science+Business Media New York 2013.
     Google Scholar
  17. Yu-Qiu Long, Song Cen, Zhi-Fei Long, Advanced Finite Element Method in Structural Engineering, Springer-Verlag Gmbh Berlin Heidelberg, 2009.
     Google Scholar
  18. Reddy JN.-2nd Ed. An Introduction to the Finite Element Method, 1993, Mcgraw-Hill.
     Google Scholar
  19. Reddy JN. Mechanics of Laminated Composite Plates and Shells Theory and Analysis, 2nd Edition, Crc Press, 2003.
     Google Scholar
  20. J. N. Reddy, Theory and Analysis of Elastic Plates and Shells,2nd Ed. Crc Press,2007.
     Google Scholar
  21. Reddy JN, Energy Principles & Variational Methods in Applied Mechanics, 2nd Edition, John Wiley & Sons Inc. 2002.
     Google Scholar
  22. Wang CM, Reddy JN, Lee KH. Shear Deformable Beams and Plates: Relationships with Classical Solutions, 1st Ed., Elsevier Science Ltd. 2000.
     Google Scholar
  23. Bertoti E. A Comparison of Primal- And Dual-Mixed Finite Element Formulations for Timoshenko Beams, Engineering with Computers, Springer-Verlag London, 2013.
     Google Scholar
  24. Ahmed A. and Barony S. Derivation of Explicit Augmented Spline Finite Strip Matrix Using Mixed Formulation for Plate Bending. European Journal of Engineering and Technology Research. 4, 8 (Aug. 2019), 99-106. DOI: https://doi.org/10.24018/ejers.2019.4.8.1421.
     Google Scholar
  25. Ahmed A. and Barony S. Plate Bending Spline Finite Strip Models Using Mixed Formulation and Combined Spline Series. European Journal of Engineering and Technology Research. 4, 10 (Oct. 2019), 42-51. DOI: https://doi.org/10.24018/ejers.2019.4.10.1489.
     Google Scholar
  26. Ahmed A. and Barony S. Mixed Finite Element Matrix for Plate Bending Analysis Using Weighted-Residual Integral and Weak Formulation. European Journal of Engineering and Technology Research. 5, 8 (Aug. 2020), 990-999. DOI: https://doi.org/10.24018/ejers.2020.5.8.2041.
     Google Scholar
  27. Abdarrhim M. Ahmed and Salah Y. Barony, Mixed Formulation of Spline Finite Strip Method Using Equally Spaced B2-Spline Series, IJISET - International Journal of Innovative Science, Engineering & Technology, 2(8), Aug 2015.
     Google Scholar
  28. Angelo Simone, An Introduction to The Analysis of Slender Structures, Draft September 4, 2011, Delft University of Technology, The Netherlands.
     Google Scholar