"We consider the case of a horizontal rod or beam slightly bent by vertical forces applied to it. The state of strain is no longer of the simple character appertaining to pure flexure; in particular there will be a relative shearing of adjacent cross-sections, and also a warping of the sections so that these do not remain accurately plane. We shall assume, however, that the additional strains thus introduced are on the whole negligible, and consequently that the bending moment is connected with the curvature of the axis..."
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Sir , Statics, Including Hydrostatics and the Elements of the Theory of Elasticity (1916) p. 314.
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Euler–Bernoulli beam theory
(also known as engineer's beam theory or classical beam theory) is a simplification of the linear and provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case for small deflections of a beam that are subjected to lateral loads only, and is thus a special case of . It was first enunciated circa 1750, but was not generally applied until the development of the and the in the late 19th century. Following these successful demonstrations, it quickly
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