# Buckling Coefficient

## Description

In science, buckling is a mathematical instability that leads to a failure mode.

When a structure is subjected to compressive stress, buckling may occur. Buckling is characterized by a sudden sideways deflection of a structural member. This may occur even though the stresses that develop in the structure are well below those needed to cause failure of the material of which the structure is composed. As an applied load is increased on a member, such as a column, it will ultimately become large enough to cause the member to become unstable and it is said to have buckled. Further loading will cause significant and somewhat unpredictable deformations, possibly leading to complete loss of the member’s load-carrying capacity. If the deformations that occur after buckling do not cause the complete collapse of that member, the member will continue to support the load that caused it to buckle. If the buckled member is part of a larger assemblage of components such as a building, any load applied to the buckled part of the structure beyond that which caused the member to buckle will be redistributed within the structure.

In a mathematical sense, buckling is a bifurcation in the solution to the equations of static equilibrium. At a certain point, under an increasing load, any further load is able to be sustained in one of two states of equilibrium: a purely compressed state (with no lateral deviation) or a laterally-deformed state.

Buckling is a state which defines a point where an equilibrium configuration becomes unstable under a parametric change of load and can manifest itself in several different phenomena. All can be classified as forms of bifurcation.

The buckling coefficient is influenced by the aspect of the specimen, a / b, and the number of lengthwise curvatures. For an increasing number of such curvatures, the aspect ratio produces a varying buckling coefficient; but each relation provides a minimum value for each m. This minimum value can then be used as a constant, independent from both the aspect ratio and m.

Related formulas## Variables

k_{cr} | Buckling coefficient (dimensionless) |

m | Number of half sine curvatures that occur lengthwise (dimensionless) |

b | Width of specimen (m) |

a | Length of specimen (m) |