Submitted:
17 November 2020
Posted:
17 November 2020
Read the latest preprint version here
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
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