Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability [post]

Valentin Fogang
2021 unpublished
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
more » ... 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.
doi:10.20944/preprints202011.0457.v2 fatcat:o2qdxx7zsfbvxnxbqda3owhrga