Three-Point Bending of a Beam with Non-Homogeneous Structure in the Depth Direction

This paper is devoted to the behavior of a non-homogeneous simply supported beam under three-point bending. The individual shear deformation function of a planar cross-section is adopted, and longitudinal displacements, strains, and stresses for two parts of the beam are explained. By applying the...

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Main Authors: Krzysztof MAGNUCKI, Ewa MAGNUCKA-BLANDZI, Dawid WITKOWSKI, Leszek WITTENBECK
Format: Article
Language:English
Published: Institute of Fundamental Technological Research 2023-11-01
Series:Engineering Transactions
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Online Access:https://et.ippt.pan.pl/index.php/et/article/view/3107
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author Krzysztof MAGNUCKI
Ewa MAGNUCKA-BLANDZI
Dawid WITKOWSKI
Leszek WITTENBECK
author_facet Krzysztof MAGNUCKI
Ewa MAGNUCKA-BLANDZI
Dawid WITKOWSKI
Leszek WITTENBECK
author_sort Krzysztof MAGNUCKI
collection DOAJ
description This paper is devoted to the behavior of a non-homogeneous simply supported beam under three-point bending. The individual shear deformation function of a planar cross-section is adopted, and longitudinal displacements, strains, and stresses for two parts of the beam are explained. By applying the principle of stationary potential energy, a system of two differential equations of equilibrium is derived and solved analytically. The positions of the neutral axis, shear coefficients, and deflections are then calculated for three different beam families. Additionally, the bending problem of these beams is studied numerically using the finite element method (FEM). The results of both analytical and numerical calculations are presented in tables and figures. The main contribution of this paper lies in the development of an analytical model incorporating the individual shear deformation function and a numerical FEM model for this beam.
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id doaj-art-916d21fc1bb54f5fb85f08bdf496b264
institution Kabale University
issn 0867-888X
2450-8071
language English
publishDate 2023-11-01
publisher Institute of Fundamental Technological Research
record_format Article
series Engineering Transactions
spelling doaj-art-916d21fc1bb54f5fb85f08bdf496b2642025-08-20T03:49:51ZengInstitute of Fundamental Technological ResearchEngineering Transactions0867-888X2450-80712023-11-0171410.24423/EngTrans.3107.20231128Three-Point Bending of a Beam with Non-Homogeneous Structure in the Depth DirectionKrzysztof MAGNUCKI0Ewa MAGNUCKA-BLANDZI1Dawid WITKOWSKI2Leszek WITTENBECK3Łukasiewicz Research Network - Poznań Institute of TechnologyInstitute of Mathematics, Poznan University of TechnologyŁukasiewicz Research Network - Poznań Institute of TechnologyInstitute of Mathematics, Poznan University of Technology This paper is devoted to the behavior of a non-homogeneous simply supported beam under three-point bending. The individual shear deformation function of a planar cross-section is adopted, and longitudinal displacements, strains, and stresses for two parts of the beam are explained. By applying the principle of stationary potential energy, a system of two differential equations of equilibrium is derived and solved analytically. The positions of the neutral axis, shear coefficients, and deflections are then calculated for three different beam families. Additionally, the bending problem of these beams is studied numerically using the finite element method (FEM). The results of both analytical and numerical calculations are presented in tables and figures. The main contribution of this paper lies in the development of an analytical model incorporating the individual shear deformation function and a numerical FEM model for this beam. https://et.ippt.pan.pl/index.php/et/article/view/3107non-homogeneous beamshear deformation theorythree-point bending
spellingShingle Krzysztof MAGNUCKI
Ewa MAGNUCKA-BLANDZI
Dawid WITKOWSKI
Leszek WITTENBECK
Three-Point Bending of a Beam with Non-Homogeneous Structure in the Depth Direction
Engineering Transactions
non-homogeneous beam
shear deformation theory
three-point bending
title Three-Point Bending of a Beam with Non-Homogeneous Structure in the Depth Direction
title_full Three-Point Bending of a Beam with Non-Homogeneous Structure in the Depth Direction
title_fullStr Three-Point Bending of a Beam with Non-Homogeneous Structure in the Depth Direction
title_full_unstemmed Three-Point Bending of a Beam with Non-Homogeneous Structure in the Depth Direction
title_short Three-Point Bending of a Beam with Non-Homogeneous Structure in the Depth Direction
title_sort three point bending of a beam with non homogeneous structure in the depth direction
topic non-homogeneous beam
shear deformation theory
three-point bending
url https://et.ippt.pan.pl/index.php/et/article/view/3107
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AT dawidwitkowski threepointbendingofabeamwithnonhomogeneousstructureinthedepthdirection
AT leszekwittenbeck threepointbendingofabeamwithnonhomogeneousstructureinthedepthdirection