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Flexural Analysis of Thick Beam Subjected to Sine Load Using Refined Shear Deformation Theory

Pallavi Murlidhar Pankade

Abstract


A Hyperbolic Shear Deformation Theory (HPSDT) taking into account transverse shear deformation effects is used for the static flexure analysis of thick isotropic beams. The displacement field of the theory contains two variables. The hyperbolic sine and cosine function is used in the displacement field in terms of thickness coordinate to represent shear deformation. The transverse shear stress can be obtained directly from the use of constitutive relations, satisfying the shear stress-free boundary conditions at top and bottom of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. General solutions of thick isotropic simply supported beam subjected to Single sine load are obtained. Expressions for transverse displacement of beams are obtained and contribution due to shear deformation to the maximum transverse displacement is investigated. The results of the present theory are compared with those of other refined shear deformation theories of beam to verify the accuracy of the theory.

Keywords- Thick beam, shear deformation, isotropic beam, transverse shear stress, static flexure, hyperbolic shear deformation theory, principle of virtual work.

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References


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DOI: https://doi.org/10.37628/jsea.v2i2.116

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