International Journal of Engineering Research

Vikas A. Jadhav ¹, Ajay G. Dahake ¹

Affiliations
1 Department of Civil Engineering, Marathwada Institute of Technology, Aurangabad, Maharshtra 431028, IN

Abstract

A trigonometric shear deformation theory for bending of deep 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 displacement field used 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 deep 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 cantilever isotropic beam subjected to uniformly varying load is examined using the present theory. Results obtained are discussed critically with those of other refined theories.

Keywords

Deep Beam, Trigonometric Shear Deformation, Principle of Virtual Work, Equilibrium Equations, Displacement, Stress.

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Satish S. Manal ¹, Rajmahendra M. Sawant ¹, Ajay G. Dahake ²

Affiliations
1 Department of Civil Engineering, Peoples Education Society’s College of Engineering, Aurangabad, Maharshtra, 431002, IN
2 Department of Civil Engineering, Marathwada Institute of Technology, Aurangabad, Maharshtra, 431028, IN

Abstract

A new trigonometric shear deformation theory for bending of thick fixed beam, 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 displacement field used in terms of sinusoidal function in thickness coordinate is replaced with z[1-4/3 z²/h²]Φ 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 beam subjected to uniformly varying load is examined using the present theory. Results obtained are discussed critically with those of other refined theories.

Keywords

Thick Beam, Trigonometric Shear Deformation, Principle of Virtual Work, Equilibrium Equation, Stress.

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