# Critical buckling stress of a column

## 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).

Related formulas## Variables

σ | The allowable critical stress of the column (Pa) |

π | pi |

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

l | The unsupported length of column (m) |

r | The least radius of gyration of column's cross section (m) |