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# Compressive stress

Compressive stress is the stress applied to materials resulting in their compaction (decrease of volume). When a material is subjected to compressive stress then this material is under compression. Usually compressive stress applied to bars, columns, etc. leads to shortening.

Loading a structural element or a specimen will increase the compressive stress until the reach of compressive strength. According to the properties of the material, failure will occur as yield for materials with ductile behaviour (most metals, some soils and plastics) or as rupture for brittle behaviour (geomaterials, cast iron, glass, etc).

In long 'slender' structural elements (such as columns or truss bars), increase of compressive force F leads to structural failure due to buckling at lower stress than the compressive strength, according to Euler;

Fb = π2 × E × I / l2

The 'slenderness' of the element depends on its length, the way the ends are supported and its cross section. The slenderness is expressed with the letter lambda as; λ = lb / √(I/A).

With λ and σ = F/A, Euler's formula can be rewritten for the buckling stress as; σb = π2 × E / λ2

Compressive stress has stress units (force per area), usually with negative values to indicate the compaction. However in geotechnical engineering, compressive stress is represented with positive values.

Compare tensile stress.