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Compression members, such as columns, are mainly subjected to axial forces. The principal stress in a compression member is therefore the normal stress,

The failure of a short compression member resulting from the compression axial force looks like,

However, when a compression member becomes longer, the role of the geometry and stiffness (Young's modulus) becomes more and more important. For a long (slender) column, buckling occurs way before the normal stress reaches the strength of the column material. For example, pushing on the ends of a business card or bookmark can easily reproduce the buckling.

For an intermediate length compression member, kneeling occurs when some areas yield before buckling, as shown in the figure below.

In summary, the failure of a compression member has to do with the strength and stiffness of the material and the geometry (slenderness ratio) of the member. Whether a compression member is considered short, intermediate, or long depends on these factors. More quantitative discussion on these factors can be found in the next section.

In practice, for a given material, the allowable stress in a compression member depends on the slenderness ratio L_eff / r and can be divided into three regions: short, intermediate, and long.

Short columns are dominated by the strength limit of the material. Intermediate columns are bounded by the inelastic limit of the member. Finally, long columns are bounded by the elastic limit (i.e. Euler's formula). These three regions are depicted on the stress/slenderness graph below,

The short/intermediate/long classification of columns depends on both the geometry (slenderness ratio) and the material properties (Young's modulus and yield strength). Some common materials used for columns are listed below:

In the table, L_eff is the effective length of the column, and r is the radius of gyration of the cross-sectional area, defined as .

Radii of gyration for standard beams, common beams, and other common areas can be found in the geometry section.