# Self-buckling critical height ( for a free-standing, vertical 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. The maximum load, sometimes called the critical load, causes the column to be in a state of unstable equilibrium; that is, the introduction of the slightest lateral force will cause the column to fail by buckling. A free-standing, vertical column, will buckle under its own weight if its height exceeds a certain critical height.

Related formulas## Variables

h_{crit} | critical height (in m) (dimensionless) |

E | modulus of elasticity / Young's modulus (in Pa) (dimensionless) |

I | second moment of area of the beam cross section (in m^4) (dimensionless) |

ρ | density of the vertical column (in kg/m^3) (dimensionless) |

g | Standard gravity (Earth: 9.80665 m/s^2) (dimensionless) |

A | vertical column cross-sectional area (m^2) (dimensionless) |