# Maximum axial load that a long, slender, ideal column can carry without buckling

## 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. Euler’s formula gives the maximum axial load that a long, slender, ideal column can carry without buckling.

The column effective length factor K: For both ends pinned (hinged, free to rotate), K = 1.0 For both ends fixed, K = 0.50 For one end fixed and the other end pinned, K = 0.699… For one end fixed and the other end free to move laterally, K = 2 Related formulas## Variables

F_{max} | The maximum or critical force (vertical load on column) (N) |

π | pi |

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

I | The area moment of inertia (m^{4}) |

K | The column effective length factor (whose value depends on the conditions of end support of the column) (dimensionless) |

L | The unsupported length of column (m) |