Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) 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 for small deflections of a beam which is subjected to lateral loads only. It is thus a special case of Timoshenko beam theory which accounts for shear deformation and is applicable for thick beams. It was first enunciated circa 1750, but was not applied on a large scale until the development of the Eiffel Tower and the Ferris wheel in the late 19th century. Following these successful demonstrations, it quickly became a cornerstone of engineering and an enabler of the Second Industrial Revolution.
Additional analysis tools have been developed such as plate theory and finite element analysis, but the simplicity of beam theory makes it an important tool in the sciences, especially structural and mechanical engineering.
... The original Euler-Bernoulli theory is valid only for infinitesimal strains and small rotations ... The theory can be extended in a straightforward manner to problems involving moderately large rotations provided that the strain remains small by using the von Kármán strains ... remain plane and normal to the axis of the beam lead to displacements of the form Using the definition of the Lagrangian Green strain from finite strain theory, we can find the von Karman strains ...
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