Euler-Bernoulli Beam Equation

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available from Wikipedia or other free sources online. Euler-Bernoulli
beam theory (also known as Engineer's beam theory, Classical beam theory
or just 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 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.