Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
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)
de Saint Venant, B.: Memoire sur la flexion des prismes. Journal de Mathematiques Pures et Appliquees, (Liouville),2(1), pp. 89–189 (1856)
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)
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)
Krishna Murty, A.V.: Towards a consistent beam theory. AIAA J. 22(6), 811–816 (1984)
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)
Ghugal, Y.M., Sharma, R.: A refined shear deformation theory for flexure of thick beams. Latin Am. J. Solids Struct. 8, 183–193 (2011)
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)
Dahake, A.G., Ghugal, Y.M.: A trigonometric shear deformation theory for flexure of thick beam. Proc. Eng. 51, 1–7 (2013)
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)
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)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Joshi, G., Gaikwad, S., Dahake, A., Girase, A. (2020). Displacements in Thick Cantilever Beam Using V Order Shear Deformation Theory. In: Gunjan, V., Singh, S., Duc-Tan, T., Rincon Aponte, G., Kumar, A. (eds) ICRRM 2019 – System Reliability, Quality Control, Safety, Maintenance and Management. ICRRM 2019. Springer, Singapore. https://doi.org/10.1007/978-981-13-8507-0_35
Download citation
DOI: https://doi.org/10.1007/978-981-13-8507-0_35
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-8506-3
Online ISBN: 978-981-13-8507-0
eBook Packages: EngineeringEngineering (R0)