Displacements in Thick Cantilever Beam Using V Order Shear Deformation Theory

  • Girish Joshi
  • Sagar Gaikwad
  • Ajay DahakeEmail author
  • Amardip Girase
Conference paper


Paper presents the study of displacements in cantilever thick beam via 5th order function of study of shear deformation when exposed to a cosine loading. The theory is based upon the elementary theory of beam by considering shear deformation effects applying function of 5th order using variables of thickness. This study gratified the zero shear stress condition on top and bottom of the beam. As the deflection is more definite in cantilever sections, the cantilever beam is considered here. For obtaining equilibrium equations a well-known source of virtual work is used. To demonstrate the worth of the theory, the longitudinal and axial displacements are worked out for beam which is thick in nature, when subjected to cosine load as such type of load is very common in aerospace and marine structures. Outcomes are likened with the other theories.


Cantilever Thick beam V order 


  1. 1.
    Bernoulli, J.: Curvatura laminae elasticae. Acta Eruditorum Lipsiae 1694, 262–276 (1744). (Also in Jacobi Bernoulli Basileensis Opera (2 vols.), 1, (LVIII), p. 576,, (1694), (1744)Google Scholar
  2. 2.
    Bernoulli, J.: Explicationes, annotations et additions. Acta Eruditorum Lipsiae 1695, 537–553 (1695). (Also in Jacobi Bernoulli Basileensis Opera (2 vols.), 1(LXVI), p. 639., (1695), (1744)Google Scholar
  3. 3.
    de Saint Venant, B.: Memoire sur la flexion des prismes. Journal de Mathematiques Pures et Appliquees, (Liouville),2(1), pp. 89–189 (1856)Google Scholar
  4. 4.
    Timoshenko, S.P.: On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Phil. Mag. 41(6), 744–746 (1921)CrossRefGoogle Scholar
  5. 5.
    Ghugal, Y.M., Shmipi, R.P.: A review of refined shear deformation theories for isotropic and anisotropic laminated beams. J. Reinf. Plast. Compos. 20(3), 255–272 (2001)CrossRefGoogle Scholar
  6. 6.
    Krishna Murty, A.V.: Towards a consistent beam theory. AIAA J. 22(6), 811–816 (1984)CrossRefGoogle Scholar
  7. 7.
    Ghugal, Y.M., Sharma, R.: A hyperbolic shear deformation theory for flexure and vibration of thick isotropic beams. Int. J. Comput. Methods 6(4), 585–604 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ghugal, Y.M., Sharma, R.: A refined shear deformation theory for flexure of thick beams. Latin Am. J. Solids Struct. 8, 183–193 (2011)CrossRefGoogle Scholar
  9. 9.
    Ghugal, Y.M., Dahake, A.G.: Flexure of simply supported thick beams using refined shear deformation theory. Int. J. Civil Environ. Struct. Constr. Archit. Eng. 7(1), 99–108 (2013)Google Scholar
  10. 10.
    Dahake, A.G., Ghugal, Y.M.: A trigonometric shear deformation theory for flexure of thick beam. Proc. Eng. 51, 1–7 (2013)CrossRefGoogle Scholar
  11. 11.
    Jadhav, V.A., Dahake, A.G.: Bending analysis of deep beam using refined shear deformation theory. Int. J. Eng. Res. 5(3), 526–531 (2016)Google Scholar
  12. 12.
    Sayyad, A.S., Ghugal, Y.M.: Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature. J. Compos. Struct. 171, 486–504 (2017)CrossRefGoogle Scholar
  13. 13.
    Ghumare, S.M., Sayyad, A.S.: A new fifth-order shear and normal deformation theory for static bending and elastic buckling of P-FGM beams. Latin Am. J. Solid Struct. 14, 1893–1911 (2017)CrossRefGoogle Scholar
  14. 14.
    Ghugal, Y.M., Gajbhiye, P.D.: Bending analysis of thick isotropic plates by using 5th order shear deformation theory. J. Appl. Comput. Mech. 2(2), 80–95 (2016)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Girish Joshi
    • 1
  • Sagar Gaikwad
    • 1
  • Ajay Dahake
    • 1
    Email author
  • Amardip Girase
    • 1
  1. 1.Civil Engineering DepartmentG. H. Raisoni College of Engineering and ManagementPuneIndia

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