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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 ...
Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula: [1] where. P c r {\displaystyle P_ {cr}} , Euler's critical load (longitudinal compression load on column), E {\displaystyle E} , Young's modulus of the column material, I {\displaystyle I ...
In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. [1][2] The most common or simplest structural element subjected to bending moments is the beam. The diagram shows a beam which is simply supported (free to rotate and ...
M is the moment in the beam; c is the maximum distance from the neutral axis to the outermost fiber in the bending plane; I is the second moment of area; For a simple supported beam as shown in Fig. 3, assuming the load is centered between the supports, the maximum moment is at the center and is equal to:
Continuum mechanics. In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or ...
A column under a concentric axial load exhibiting the characteristic deformation of buckling The eccentricity of the axial force results in a bending moment acting on the beam element. The ratio of the effective length of a column to the least radius of gyration of its cross section is called the slenderness ratio (sometimes expressed with the ...
Section modulus is a geometric property of a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness. Any relationship between these properties is ...
The Timoshenko–Ehrenfest beam theory was developed by Stephen Timoshenko and Paul Ehrenfest [1][2][3] early in the 20th century. [4][5] The model takes into account shear deformation and rotational bending effects, making it suitable for describing the behaviour of thick beams, sandwich composite beams, or beams subject to high- frequency ...