Analytical Solution of a Guided Simply Supported Beam under Three Point Bending

1
Mohammad Ikthair Hossain Soiket
Mohammad Ikthair Hossain Soiket
2
Shabbir Ahmed
Shabbir Ahmed
1 Bangladesh University of Engineering and Technology (BUET)

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GJRE Volume 14 Issue J7

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In the present paper, elastic field parameters of a guided simply supported beam under three point bending has been investigated by a new approach called displacement potential formulation. Guided beams involve mixed mode of boundary conditions which the classical beam theory cannot handle. In displacement potential formulation, all the elastic field parameters has been expressed in terms of a single function Ψ which gives rise to a fourth order partial differential equation. The solution of this equation has been determined by trial and error process satisfying all the boundary conditions. This solution is then inserted to reduce the partial differential equation into an ordinary one. The obtained analytical solution of the beam has been presented as graphs. The stress concentration occurs mainly at the point of application of the load and the support at two corners. The analytical solution has further been verified by finite element analysis.

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No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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Not applicable for this article.

Mohammad Ikthair Hossain Soiket. 2015. \u201cAnalytical Solution of a Guided Simply Supported Beam under Three Point Bending\u201d. Global Journal of Research in Engineering - J: General Engineering GJRE-J Volume 14 (GJRE Volume 14 Issue J7): .

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Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

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December 31, 2015

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English

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In the present paper, elastic field parameters of a guided simply supported beam under three point bending has been investigated by a new approach called displacement potential formulation. Guided beams involve mixed mode of boundary conditions which the classical beam theory cannot handle. In displacement potential formulation, all the elastic field parameters has been expressed in terms of a single function Ψ which gives rise to a fourth order partial differential equation. The solution of this equation has been determined by trial and error process satisfying all the boundary conditions. This solution is then inserted to reduce the partial differential equation into an ordinary one. The obtained analytical solution of the beam has been presented as graphs. The stress concentration occurs mainly at the point of application of the load and the support at two corners. The analytical solution has further been verified by finite element analysis.

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Analytical Solution of a Guided Simply Supported Beam under Three Point Bending

Shabbir Ahmed
Shabbir Ahmed
Mohammad Ikthair Hossain Soiket
Mohammad Ikthair Hossain Soiket Bangladesh University of Engineering and Technology (BUET)

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