Understanding Short Column Failure

Columns are structural elements primarily designed to carry axial compressive loads. The way a column fails depends largely on its slenderness ratio. The slenderness ratio relates the effective length of the column to its least radius of gyration.

Columns can be broadly classified into short columns and long columns based on this slenderness ratio. Their failure modes are distinctly different.

Failure Mode of Short Columns

A short column is a column with a low slenderness ratio. This means its length is relatively short compared to its cross-sectional dimensions. Due to its short length, a short column is very stiff laterally and does not tend to buckle under load.

When a compressive load is applied to a short column, the stress increases uniformly across the cross-section. The material reaches its yield strength or crushing strength before any significant lateral deformation (buckling) occurs.

Therefore, a short column fails by crushing of the material. This failure happens when the compressive stress exceeds the material's capacity to resist compression.

Comparing Short and Long Column Failure

• Short Columns: Fail primarily by crushing. The load capacity is governed by the material's compressive strength.
• Long Columns: Fail primarily by buckling. Buckling is a sudden lateral instability that occurs at a critical load, which is often well below the load required to crush the material. The load capacity is governed by the column's stiffness and geometry, as described by Euler's formula or similar concepts.

Analyzing the Options

Let's look at the given options in the context of short column failure:

• combined crushing and buckling: This mode is more typical for intermediate columns, which have a slenderness ratio between that of short and long columns. Short columns usually fail purely by crushing.
• crushing only: This aligns with the behavior of short columns, where the material strength is reached before buckling becomes a factor.
• buckling only: This is the characteristic failure mode for long columns, not short ones.
• bending: Bending can be a factor in columns, especially if there are eccentric loads or lateral forces, but the primary failure mode under axial load for a short column is crushing.

Based on the understanding of column behavior, short columns fail when the compressive stress causes the material to crush.