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The Timoshenko–Ehrenfest beam theory was developed by Stephen Timoshenko and Paul Ehrenfest [1] [2] [3] early in the 20th century. [ 4 ] [ 5 ] The model takes into account shear deformation and rotational bending effects, making it suitable for describing the behaviour of thick beams, sandwich composite beams , or beams subject to high ...
In general, the yield strength of a material is an adequate indicator of the material's mechanical strength. Considered in tandem with the fact that the yield strength is the parameter that predicts plastic deformation in the material, one can make informed decisions on how to increase the strength of a material depending on its microstructural ...
For thin beams (beam length to thickness ratios of the order 20 or more) these effects are of minor importance. For thick beams, however, these effects can be significant. More advanced beam theories such as the Timoshenko beam theory (developed by the Russian-born scientist Stephen Timoshenko) have been developed to account for these effects.
Stepan Prokopovich Timoshenko [3] (Ukrainian: Степан Прокопович Тимошенко, romanized: Stepan Prokopovych Tymoshenko; Russian: Степан Прокофьевич Тимошенко, romanized: Stepan Prokofyevich Timoshenko, [sʲtʲɪˈpan prɐˈkofʲjɪvʲɪtɕ tʲɪmɐˈʂɛnkə]; December 22 [O.S. December 10] 1878 – May 29, 1972), later known as Stephen ...
The stress-strain behavior of materials is not strictly linear even below the yield point, hence the modulus of elasticity decreases as stress increases, and significantly so as the stresses approach the material's yield strength. This reduced material rigidity reduces the buckling strength of the structure and results in a buckling load less ...
Timoshenko improved upon that theory in 1922 by adding the effect of shear into the beam equation. Shear deformations of the normal to the mid-surface of the beam are allowed in the Timoshenko–Rayleigh theory. The equation for the bending of a linear elastic, isotropic, homogeneous beam of constant cross-section under these assumptions is [7 ...
(0) real beam, (1) shear and moment, (2) conjugate beam, (3) slope and displacement. The conjugate-beam methods is an engineering method to derive the slope and displacement of a beam.
Plastic bending [1] is a nonlinear behavior particular to members made of ductile materials that frequently achieve much greater ultimate bending strength than indicated by a linear elastic bending analysis. In both the plastic and elastic bending analyses of a straight beam, it is assumed that the strain distribution is linear about the ...