International Journal of Civil and Structural Engineering

Volume 3 Issue 2 2012          Pages: 321 - 335                         << Previous      Next>>

Flexure of thick beams using refined shear deformation theory

Author Information:

Yuwaraj M. Ghugal1, Ajay G. Dahake2
1- Professor, Applied Mechanics Department, Govt. College of Engineering, Karad, India

2- Research Scholar, Applied Mechanics Department, Govt. College of Engineering, Aurangabad, India

ABSTRACT

A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick isotropic beams are considered for the numerical studies to demonstrate the efficiency of the theory.  It has been shown that the theory is capable of predicting the local effect of stress concentration due to fixity of support. The fixed isotropic beams subjected to parabolic and cosine loads are examined using the present theory. Results obtained are discussed critically with those of other theories.

Keywords:Thick beam, trigonometric shear deformation, principle of virtual work, equilibrium equations, displacement, stress

doi:10.6088/ijcser.201203013031

Copyright: © 2012 by the author(s), licensee Integrated Publishing Association. This is an open-access article distributed under the terms of the Creative Commons Attribution License (3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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