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)
How to cite:
Fogang, V. Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability. Preprints2020, 2020110457. https://doi.org/10.20944/preprints202011.0457.v2
Fogang, V. Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability. Preprints 2020, 2020110457. https://doi.org/10.20944/preprints202011.0457.v2
Fogang, V. Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability. Preprints2020, 2020110457. https://doi.org/10.20944/preprints202011.0457.v2
APA Style
Fogang, V. (2021). Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability. Preprints. https://doi.org/10.20944/preprints202011.0457.v2
Chicago/Turabian Style
Fogang, V. 2021 "Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability" Preprints. https://doi.org/10.20944/preprints202011.0457.v2
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.
Commenter: Valentin Fogang
Commenter's Conflict of Interests: Author