Engineering Transactions, 71, 4, pp. 645–665, 2023
10.24423/EngTrans.3107.20231128

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

Krzysztof MAGNUCKI
Łukasiewicz Research Network - Poznań Institute of Technology
Poland

Ewa MAGNUCKA-BLANDZI
Institute of Mathematics, Poznan University of Technology
Poland

Dawid WITKOWSKI
Łukasiewicz Research Network - Poznań Institute of Technology
Poland

Leszek WITTENBECK
Institute of Mathematics, Poznan University of Technology
Poland

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.

Keywords: non-homogeneous beam; shear deformation theory; three-point bending
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DOI: 10.24423/EngTrans.3107.20231128