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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| Format: | Article |
| Language: | English |
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Institute of Fundamental Technological Research
2023-11-01
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| 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 |
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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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| format | Article |
| 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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