UkrainianProfessional Education

Abstract

The article examines the deformations of short elastic beams with different сross-sections under concentrated and uniformly distributed loads. The effect of transverse shear deformations on the stiffness of the beams is investigated. A second-order differential equation is used as a mathematical model of the problem, formed with consideration of pure bending and transverse shear deformations. Boundary conditions are specified for simply supported and cantilever beams. The boundary value problem is solved analytically and using the finite element method (FEM), allowing control over different levels of accuracy. The maximum deflections of beams with different crosssections (rectangular, I-shape, circular, and annular) are determined. Timoshenko beam theory is applied to obtain beam deflections. Modern structural design relies on computer-aided design (CAD) systems, which enable the creation of precise structural models and the analysis of their behavior under realistic conditions. CAD software with integrated finite element tools enables the analysis of the behavior and the identification of specific deformations in both individual components and the entire structures. Three-dimensional finite element modeling of beams was performed using the SCAD and LIRA software. Graphs of mesh convergence for the deflections of the I-shaped cantilever beams were plotted. A comparison of analytical and numerical solutions of the boundary value problem demonstrated a high level of accuracy, indicating the efficiency of the applied approaches. The obtained results have practical significance for structural engineers, particularly in analyzing short beam deformations during the design of beams with different cross-sections. Additionally, these research findings can be incorporated into the educational process for the "Strength of Materials" course

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