RESEARCH PAPER
A shear effect in a bending non-standard I-beam under uniformly distributed load
1
Institute of Mathematics, Poznan University of Technology, Polska
2
Łukasiewicz Research Network - Poznan Institute of Technology, 6 Ewarysta Estkowskiego St., 61-755 Poznań, Poland
These authors had equal contribution to this work
Submission date: 2024-10-02
Final revision date: 2025-01-12
Acceptance date: 2025-01-15
Online publication date: 2025-01-19
Corresponding author
Ewa Magdalena Magnucka-Blandzi
Institute of Mathematics, Poznan University of Technology, Piotrowo, 60-965, Poznan, Polska
Institute of Mathematics, Poznan University of Technology, Piotrowo, 60-965, Poznan, Polska
KEYWORDS
TOPICS
ABSTRACT
The paper is devoted to the analytical study of the bending problem of a simply supported or clamped non-standard I-beam under a uniformly distributed load. The cross-sectional shape of this beam, as a three-part structure, is analytically described. The purpose of this research is to present a detailed analytical model of this beam, considering the shear effect and its influence on the beam's deflection. This model is formulated according to linear elastic theory, and the deformation of a planar cross-section after the bending of this beam due to the shear effect is determined. Based on the principle of stationary potential energy, two differential equations of equilibrium are obtained. These equations are analytically solved, and the dimensionless shear effect function and the relative deflection of this beam are derived. Consequently, the maximum dimensionless relative deflection and the dimensionless coefficient of the shear effect are determined. Exemplary calculations are carried out for three selected non-standard I-beams of different lengths, demonstrating a significant influence of the shear effect on the deflections of short beams, especially clamped beams.
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| eISSN: | 2719-9630 |
| ISSN: | 0138-0370 |
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