# Compressive strength

Compressive strength or compression strength is the capacity of a material or structure to withstand loads tending to reduce size, as opposed to tensile strength, which withstands loads tending to elongate. In other words, compressive strength resists compression (being pushed together), whereas tensile strength resists tension (being pulled apart). In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.

Some materials fracture at their compressive strength limit; others deform irreversibly, so a given amount of deformation may be considered as the limit for compressive load. Compressive strength is a key value for design of structures.

Measuring the compressive strength of a steel drum

Compressive strength is often measured on a universal testing machine; these range from very small table-top systems to ones with over 53 MN capacity.[1] Measurements of compressive strength are affected by the specific test method and conditions of measurement. Compressive strengths are usually reported in relationship to a specific technical standard.

## Introduction

When a specimen of material is loaded in such a way that it extends it is said to be in tension. On the other hand, if the material compresses and shortens it is said to be in compression.

On an atomic level, the molecules or atoms are forced apart when in tension whereas in compression they are forced together. Since atoms in solids always try to find an equilibrium position, and distance between other atoms, forces arise throughout the entire material which oppose both tension or compression. The phenomena prevailing on an atomic level are therefore similar.

The "strain" is the relative change in length under applied stress; positive strain characterises an object under tension load which tends to lengthen it, and a compressive stress that shortens an object gives negative strain. Tension tends to pull small sideways deflections back into alignment, while compression tends to amplify such deflection into buckling.

Compressive strength is measured on materials, components,[2] and structures.[3]

By definition, the ultimate compressive strength of a material is that value of uniaxial compressive stress reached when the material fails completely. The compressive strength is usually obtained experimentally by means of a compressive test. The apparatus used for this experiment is the same as that used in a tensile test. However, rather than applying a uniaxial tensile load, a uniaxial compressive load is applied. As can be imagined, the specimen (usually cylindrical) is shortened as well as spread laterally. A stress–strain curve is plotted by the instrument and would look similar to the following:

True Stress-Strain curve for a typical specimen

The compressive strength of the material would correspond to the stress at the red point shown on the curve. In a compression test, there is a linear region where the material follows Hooke's law. Hence, for this region, ${\displaystyle \sigma =E\epsilon }$, where, this time, E refers to the Young's Modulus for compression. In this region, the material deforms elastically and returns to its original length when the stress is removed.

This linear region terminates at what is known as the yield point. Above this point the material behaves plastically and will not return to its original length once the load is removed.

There is a difference between the engineering stress and the true stress. By its basic definition the uniaxial stress is given by:

${\displaystyle \sigma ={\frac {F}{A}}}$

where, F = Load applied [N], A = Area [m2]

As stated, the area of the specimen varies on compression. In reality therefore the area is some function of the applied load i.e. A = f(F). Indeed, stress is defined as the force divided by the area at the start of the experiment. This is known as the engineering stress and is defined by,

${\displaystyle \sigma _{e}={\frac {F}{A_{0}}}}$

A0=Original specimen area [m2]

Correspondingly, the engineering strain would be defined by:

${\displaystyle \epsilon _{e}={\frac {l-l_{0}}{l_{0}}}}$

where l = current specimen length [m] and l0 = original specimen length [m]

The compressive strength would therefore correspond to the point on the engineering stress strain curve ${\displaystyle (\epsilon _{e}^{*},\sigma _{e}^{*})}$ defined by

${\displaystyle \sigma _{e}^{*}={\frac {F^{*}}{A_{0}}}}$

${\displaystyle \epsilon _{e}^{*}={\frac {l^{*}-l_{0}}{l_{0}}}}$

where F* = load applied just before crushing and l* = specimen length just before crushing.

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Simple English: Compressive strength