Article
Version 1
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Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability
Version 1
: Received: 17 November 2020 / Approved: 17 November 2020 / Online: 17 November 2020 (14:55:23 CET)
Version 2 : Received: 5 April 2021 / Approved: 5 April 2021 / Online: 5 April 2021 (16:06:31 CEST)
Version 3 : Received: 14 July 2021 / Approved: 15 July 2021 / Online: 15 July 2021 (10:30:53 CEST)
Version 2 : Received: 5 April 2021 / Approved: 5 April 2021 / Online: 5 April 2021 (16:06:31 CEST)
Version 3 : Received: 14 July 2021 / Approved: 15 July 2021 / Online: 15 July 2021 (10:30:53 CEST)
How to cite: Fogang, V. Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability. Preprints 2020, 2020110457. https://doi.org/10.20944/preprints202011.0457.v1 Fogang, V. Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability. Preprints 2020, 2020110457. https://doi.org/10.20944/preprints202011.0457.v1
Abstract
This paper presents an exact solution to the Timoshenko beam theory (TBT) for bending, second-order analysis, and stability. The TBT covers cases associated with small deflections based on shear deformation considerations, whereas the Euler–Bernoulli beam theory neglects shear deformations. A material law (a moment-shear force-curvature equation) combining bending and shear is presented, together with closed-form solutions based on this material law. A bending analysis of a Timoshenko beam was conducted, and buckling loads were determined on the basis of the bending shear factor. First-order element stiffness matrices were calculated. Finally second-order element stiffness matrices were deduced on the basis of the same principle.
Keywords
Timoshenko beam; Moment shear force curvature equation; Closed-form solutions; Stability; Second-order element stiffness matrix
Subject
Engineering, Automotive Engineering
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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