Special Cases in Column Stability

The elementary Euler model assumes an ideal straight prismatic column under centric compression. Real members may require additional stability considerations that reduce resistance or change the governing buckling mode.

Global and local buckling

Global buckling deflects the axis of the entire member. Local buckling deforms an individual plate element, such as a flange or web. Local buckling may occur first and reduce the effective cross-section.

Initial imperfections

Initial crookedness, dimensional tolerances, residual stresses, and joint imperfections produce lateral deflection before the Euler load is reached. This is one reason why design resistance is lower than the ideal elastic value.

Load eccentricity

An eccentric compression force produces bending from the beginning. Including lateral deflection gives a second-order moment

\[M=N(e+y).\]

The deformation increases the moment, and the increased moment further increases the deformation.

Stepped and non-prismatic columns

When \(EI(x)\) varies along the length, inserting a single second moment of area into the elementary Euler formula is generally inadequate. Critical loads may be obtained by a dedicated analytical, energy, or numerical model.

Intermediate and elastic restraints

Bracing can reduce the unrestrained buckling length, but its effectiveness depends on stiffness and strength. An elastic restraint is not automatically equivalent to an ideal fixed support.

Coupled modes and frames

Open thin-walled sections may buckle in torsional or flexural-torsional modes. In framed structures, joint translation and interaction between columns and the complete frame must also be considered.