Flexure and vibration of thick beams using trigonometric shear deformation theory
Palavras-chave:
Thick beam, trigonometric shear deformation, principle of virtual work, equilibrium equations, transverse deflection, axial stress, transverse shear stress, free vibration.Resumo
A trigonometric shear deformation theory is used for flexural analysis of thick beams, taking into account transverse shear deformation effect. The theory accounts for cosine distribution of transverse shear strain through the thickness of the beam. The governing differential equations and boundary conditions are obtained by using the principle of virtual work. The general solutions for the transverse displacement and rotation are presented for transversely loaded beams. The solutions for static flexure are given for beams with fixed end and subjected to uniformly distributed load and concentrated load. The solutions obtained address the accurate flexural behavior of shear deformable beams. It has been shown that the theory is capable of predicting the local effects due to concentrated load and fixity of support. The results of displacements and stresses obtained from static flexure of cantilever and fixed beams and results of free vibration frequencies for simply supported beam are presented and discussed critically with those of other theories. The results are found to agree well with the exact elasticity results wherever applicable. It is observed that the present theory yields the exact shear coefficient (p2/12) from the free vibration analysis of the simply supported beam. Keywords: Thick beam, trigonometric shear deformation, principle of virtual work, equilibrium equations, transverse deflection, axial stress, transverse shear stress, free vibration.Downloads
Publicado
Edição
Secção
Licença
Declaration and Copyright Transfer Form
(to be completed by authors)
I/ We, the undersigned author(s) of the submitted manuscript, hereby declare, that the above manuscript which is submitted for publication in the STM Journals(s), is not published already in part or whole (except in the form of abstract) in any journal or magazine for private or public circulation, and, is not under consideration of publication elsewhere.
· I/We will not withdraw the manuscript after 1 week of submission as I have read the Author Guidelines and will adhere to the guidelines.
· I/We Author(s ) have niether given nor will give this manuscript elsewhere for publishing after submitting in STM Journal(s).
· I/ We have read the original version of the manuscript and am/ are responsible for the thought contents embodied in it. The work dealt in the manuscript is my/ our own, and my/ our individual contribution to this work is significant enough to qualify for authorship.
· I/We also agree to the authorship of the article in the following order:
Author’s name
1. ________________
2. ________________
3. ________________
_______________
We Author(s) tick this box and would request you to consider it as our signature as we agree to the terms of this Copyright Notice, which will apply to this submission if and when it is published by this journal. |
