Euler-Bernoulli beam theory

A beam is defined as a structure having one of its dimensions much larger than the other two. The axis of the beam is defined along that longer dimension, and a crosssection normal to this axis is assumed to smoothly vary along the span or length of the beam. Civil engineering structures often consist of an assembly or grid of beams with cross-sections having shapes such as T's or I's. A large number of machine parts also are beam-like structures: lever arms, shafts, etc. Finally, several aeronautical structures such as wings and fuselages can also be treated as thin-walled beams.

The solid mechanics theory of beams, more commonly referred to simply as “beam theory,” plays an important role in structural analysis because it provides the designer with a simple tool to analyze numerous structures. Although more sophisticated tools, such as the finite element method, are now widely available for the stress analysis of complex structures, beam models are often used at a pre-design stage because they provide valuable insight into the behavior of structures. Such calculations are also quite useful when trying to validate purely computational solutions.