Buckling

buckling

Mode of failure under compression of a structural component that is thin (see shell structure) or much longer than wide (e.g., post, column, leg bone). Leonhard Euler first worked out in 1757 the theory of why such members buckle. The definition by Thomas Young of the elastic modulus significantly propelled building construction science forward. The elastic theory formed the basis of structural analysis until World War II, when the behaviour of bomb-damaged buildings forced the modification of some of the theory's underlying assumptions. See also post-and-beam system.

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buckling [′bək·liŋ]

(engineering)

Wrinkling or warping of fibers in a composite material.

(mechanics)

Bending of a sheet, plate, or column supporting a compressive load.

(nucleonics)

The size-shape factor that appears in the general nuclear reactor equation and is a measure of the curvature of the neutron density distribution in the reactor.

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buckling

The collapse of a slender vertical element which has been subjected to compression, leading to a sudden sideways deflection.

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Buckling 

in strength of materials, the bending of an originally straight column under the effect of centrally applied axial compressive forces that exceed the column’s bearing power. For a column of uniform cross section exhibiting elastic behavior, the various forms of buckling correspond to critical values of the compressive forces N_c = μ²n²EI/(μl)², where E is the modulus of elasticity of the material of the column, I is the minimum value of the axial moment of inertia of the column’s cross section, l is the length of the column, μ is the coefficient of reduced length dependent on the conditions of end support of the column, and n is an integer. The minimum value for the critical force is usually of practical interest in that for a column with pinned ends (μ = 1), this force causes bending of the column according to a half-cycle sine curve (n = 1). The magnitude of the force is calculated by the Euler formula N_c = π²EI/l². The stress σ_c = N_c/F(F is the cross-sectional area of the column) corresponds to the critical force and is called the critical stress. If the value of the critical stress exceeds the proportional limit of the column material, then buckling occurs in the zone of plastic deformations. In this case, the minimum critical force is determined by the formula N_c = π²n²TI/(μl)², where T is the modulus, which characterizes the dependence between the deformations and the stresses beyond the limits of the elastic deformations.

In structural design, buckling is taken into account in calculating column loads.

L. V. KASAB’IAN