Influence of Shear Strain on the Deflection of Girders

Antonia J. Lazarević, Tanja Mališ, Elizabeta Šamec, Elizabeta Jerečić

Abstract

Numerical calculations are a standard part of modern structural design. Engineers remain particularly interested in real problems where analytical and numerical solutions can be compared with experimental results. Such cases are typical examples of benchmarks because they are used to verify the assumptions introduced. This study shows in detail how shear stresses affect the deflection of a relatively short and high cantilever when the span-to-height ratio of the cross-section is less than five. Such models are frequently used in the design of cantilevers that support heavily loaded beams, for example in the cement industry (e.g., often as structural elements for a heat exchanger system) or for the assessment of short cantilever limit states that appear during excavation in rock sediments. The models are also suitable for designing the various details and joints in the industry of prefabricated elements. This work analyzes in depth the analytical solutions for the displacement field of the linear elastic plane stress theory with two displacement boundary conditions. Also, the solutions were compared with the beam, two-, and three-dimensional numerical models using SAP2000. The results highlight the fundamental principles and solutions behind plane stress and beam theories, with an insight into the advantages and limitations of such models.

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Keywords

Short Cantilever; Linear Elasticity Theory; Analytical Solution of the Displacement Field; Plane Stress State; SAP2000.

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DOI: 10.28991/CEJ-2024-010-05-04

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