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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 ...
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 ...
The starting point is the relation from Euler-Bernoulli beam theory = Where is the deflection and is the bending moment. This equation [7] is simpler than the fourth-order beam equation and can be integrated twice to find if the value of as a function of is known.
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
Timoshenko–Ehrenfest beam theory This page was last edited on 2 December 2023, at 20:20 (UTC). Text is available under the Creative Commons Attribution ...
1922: Timoshenko corrects the Euler–Bernoulli beam equation; 1936: Hardy Cross' publication of the moment distribution method, an important innovation in the design of continuous frames. 1941: Alexander Hrennikoff solved the discretization of plane elasticity problems using a lattice framework; 1942: R. Courant divided a domain into finite ...
The non-linearity of the material derivative in balance equations in general, and the complexities of Cauchy's momentum equation and Navier-Stokes equation makes the basic equations in classical mechanics exposed to establishing of simpler approximations. Some examples of governing differential equations in classical continuum mechanics are
They have been developed mostly for Euler–Bernoulli beam theory; [citation needed] They were developed in a few cases for Timoshenko beam theory or plate theories with expressions provided only for particular boundary conditions and beam or plate shapes [citation needed]; They did not include mass change when applicable [citation needed]; and