# Critical Buckling Stress of a Column with Buckling Coefficient

## Description

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. An ideal column is one that is perfectly straight, homogeneous, and free from initial stress. Buckling is characterized by a sudden failure of a structural member subjected to high compressive stress, where the actual compressive stress at the point of failure is less than the ultimate compressive stresses that the material is capable of withstanding. Euler’s formula gives the maximum axial load that a long, slender, ideal column can carry without buckling. The allowable stress of the column is depended on the slenderness ratio (l / r).

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.

Given stress is found by the buckling coefficient the critical stress can be calculated as shown here.

Related formulas## Variables

σ_{cr} | The allowable critical stress of the column (Pa) |

k_{cr} | Buckling coefficient (dimensionless ) (dimensionless) |

π | pi |

E | Modulus of elasticity ( Young's modulus) (Pa) |

ν | Poisson's ratio (dimensionless ) (dimensionless) |

b | Width of specimen (m) |

t | Thickness (m) |