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Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] 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 corresponding to small deflections of a beam that is subjected to lateral ...
The Euler–Bernoulli beam equation defines the behaviour of a beam element (see below). It is based on five assumptions: Continuum mechanics is valid for a bending beam. The stress at a cross section varies linearly in the direction of bending, and is zero at the centroid of every cross section.
Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or ... According to Euler–Bernoulli beam theory, ...
The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory. An example of the use of deflection in this context is in building construction. Architects and engineers select materials for various applications.
Simple beam bending is often analyzed with the Euler–Bernoulli beam equation. The conditions for using simple bending theory are: [4] The beam is subject to pure bending. This means that the shear force is zero, and that no torsional or axial loads are present. The material is isotropic (or orthotropic) and homogeneous.
According to Euler–Bernoulli beam theory: = Where is the Young's modulus of elasticity of the substance, is the second moment of area. Therefore, the differential equation of the central line of BP is:
1750: Euler–Bernoulli beam equation; 1700–1782: Daniel Bernoulli introduced the principle of virtual work; 1707–1783: Leonhard Euler developed the theory of buckling of columns; Leonhard Euler developed the theory of buckling of columns. 1826: Claude-Louis Navier published a treatise on the elastic behaviors of structures
A beam of PSL lumber installed to replace a load-bearing wall. The primary tool for structural analysis of beams is the Euler–Bernoulli beam equation. This equation accurately describes the elastic behaviour of slender beams where the cross sectional dimensions are small compared to the length of the beam.