Euler-Bernoulli beam equation
Overview

Eulerâ€“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
Deflection (engineering)
In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.The deflection distance of a member under a load is directly related to the slope of the deflected shape of the member under that load and can be calculated by...

characteristics of beams
Beam (structure)
A beam is a horizontal structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a bending moment.- Overview...

. It covers the case for small deflections of a beam
Beam (structure)
A beam is a horizontal structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a bending moment.- Overview...

which is subjected to lateral loads only. It is thus a special case of Timoshenko beam theory
Timoshenko beam theory
The Timoshenko beam theory was developed by Ukrainian-born scientist Stephen Timoshenko in the beginning of the 20th century. The model takes into account shear deformation and rotational inertia effects, making it suitable for describing the behaviour of short beams, sandwich composite beams or...

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
Eiffel Tower
The Eiffel Tower is a puddle iron lattice tower located on the Champ de Mars in Paris. Built in 1889, it has become both a global icon of France and one of the most recognizable structures in the world...

and the Ferris wheel
Ferris wheel
A Ferris wheel is a nonbuilding structure consisting of a rotating upright wheel with passenger cars attached to the rim in such a way that as the wheel turns, the cars are kept upright, usually by gravity.Some of the largest and most modern Ferris wheels have cars mounted on...

in the late 19th century.