Engineering Transactions, 72, 3, pp. 285–307, 2024
10.24423/EngTrans.2024.3242

Bending of a Homogeneous Beam with a Monosymmetric Cross Section – Shear Effect

Krzysztof MAGNUCKI
ORCID ID 0000-0003-2251-4697
Łukasiewicz Research Network – Poznan Institute of Technology
Poland

Ewa MAGNUCKA-BLANDZI
ORCID ID 0000-0002-6349-5579
Institute of Mathematics, Poznan University of Technology
Poland

Dawid WITKOWSKI
ORCID ID 0000-0002-4847-5887
Łukasiewicz Research Network - Poznań Institute of Technology
Poland

Natalia STEFAŃSKA
ORCID ID 0000-0002-5377-9762
Łukasiewicz Research Network – Poznan Institute of Technology
Poland

This paper is devoted to the study of a homogeneous clamped beam with a monosymmetric cross section under uniformly distributed load or three-point bending. A nonlinear shear deformation theory of a plane beam cross section based on the classical shear stress formula known as the Zhuravsky shear stress is developed. The values of shear coefficients and maximum deflections of exemplary beams are analytically determined. Moreover, numerical FEM computations for these beams are carried out. The results of the research from both methods are shown in figures, specified in tables, and compared. The percentage relative differences between the analytical and numerical results prove that the proposed original shear deformation theory accurately describes the shear deformation problem of a beam’s planar cross‑section.

Keywords: homogeneous beam; nonlinear shear deformation theory; bending; shear effect
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DOI: 10.24423/EngTrans.2024.3242