**Compressive strength** is the capacity of a

materialMaterial is anything made of matter, constituted of one or more substances. Wood, cement, hydrogen, air and water are all examples of materials. Sometimes the term "material" is used more narrowly to refer to substances or components with certain physical properties that are used as inputs to...

or structure to withstand axially directed pushing forces. When the limit of compressive strength is reached, materials are crushed.

ConcreteConcrete is a composite construction material, composed of cement and other cementitious materials such as fly ash and slag cement, aggregate , water and chemical admixtures.The word concrete comes from the Latin word...

can be made to have high compressive strength, e.g. many concrete structures have compressive strengths in excess of 50

MPa-Academic degrees:* Master of Professional Accountancy* Master of Public Administration* Master of Public Affairs* Master of Physician's Assistant-Chemicals:* Medroxyprogesterone acetate, also known by the brand name Depo-Provera* Morpholide of pelargonic acid...

, whereas a material such as soft

sandstoneSandstone is a sedimentary rock composed mainly of sand-sized minerals or rock grains.Most sandstone is composed of quartz and/or feldspar because these are the most common minerals in the Earth's crust. Like sand, sandstone may be any colour, but the most common colours are tan, brown, yellow,...

may have a compressive strength as low as 5 or 10 MPa.

Compressive strength is often measured on a

universal testing machineA universal testing machine, also known as a universal tester, materials testing machine or materials test frame, is used to test the tensile stress and compressive strength of materials...

; these range from very small table top systems to ones with over 53 MN capacity. Measurements of compressive strength are affected by the specific

test methodA test method is a definitive procedure that produces a test result.A test can be considered as technical operation that consists of determination of one or more characteristics of a given product, process or service according to a specified procedure. Often a test is part of an experiment.The test...

and conditions of measurement. Compressive strengths are usually reported in relationship to a specific technical standard that may, or may not, relate to end-use performance.

Compare

tensile strengthUltimate tensile strength , often shortened to tensile strength or ultimate strength, is the maximum stress that a material can withstand while being stretched or pulled before necking, which is when the specimen's cross-section starts to significantly contract...

.

## 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. On a macroscopic scale, these aspects are also reflected in the fact that the properties of most common materials in tension and compression are quite similar.

The major difference between the two types of loading is the strain which would have opposite signs for tension (positive—it gets longer) and compression (negative—it gets shorter).

Another major difference is tension tends to pull small sideways deflections back into alignment, while compression tends to amplify such deflection into

bucklingIn science, buckling is a mathematical instability, leading to a failure mode.Theoretically, buckling is caused by a bifurcation in the solution to the equations of static equilibrium...

.

## Compressive Strength

By definition, the 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:

The compressive strength of the material would correspond to the stress at the red point shown on the curve. Even in a compression test, there is a linear region where the material follows

Hooke's LawIn mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law...

. Hence for this region

where this time E refers to the Young's Modulus for compression.

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:

where,

F = Load applied [N],

A = Area [m

^{2}]

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,

A

_{0}=Original specimen area [m

^{2}]

Correspondingly, the engineering

strainIn continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal deformations of a continuum body...

would be defined by:

where

l = current specimen length [m] and l

_{0} = original specimen length [m]

The compressive stress would therefore correspond to the point on the engineering stress strain curve

defined by

where

F

^{*} = load applied just before crushing and l

^{*} = specimen length just before crushing.

## Deviation of engineering stress from true stress

In engineering design practice we mostly rely on the engineering stress. In reality, the

**true stress** is different from the engineering stress. Hence calculating the compressive strength of a material from the given equations will not yield an accurate result. This is of course because the cross sectional area A

_{0} changes and is some function of load A = φ(F).

The difference in values may therefore be summarized as follows:

- On compression, the specimen will shorten. The material will tend to spread in the lateral direction and hence increase the cross sectional
In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc...

area.

- In a compression test the specimen is clamped at the edges. For this reason, a frictional force arises which will oppose the lateral spread. This means that work has to be done to oppose this frictional force hence increasing the energy consumed during the process. This results in a slightly inaccurate value of stress which is obtained from the experiment.

As a final note, it should be mentioned that the frictional force mentioned in the second point is not constant for the entire cross section of the specimen. It varies from a minimum at the centre to a maximum at the edges. Due to this a phenomenon known as

**barrelling** occurs where the specimen attains a barrel shape.

## Comparison of compressive and tensile strengths

An example of a material with a much higher compressive strength than tensile strength is concrete. Ceramics typically have a much higher compressive strength than tensile strength. Composite materials tend to have higher tensile strengths than compressive strengths. One such example is glass fiber epoxy matrix composite.

## See also

- Compression (physical)
- Box compression test
The container compression test measures the compressive strength of packages such as boxes, drums, and cans. It usually provides a plot of deformation vs compressive force....

- Buckling
In science, buckling is a mathematical instability, leading to a failure mode.Theoretically, buckling is caused by a bifurcation in the solution to the equations of static equilibrium...

- Deformation (engineering)
- Schmidt hammer
A Schmidt hammer, also known as a Swiss hammer or a rebound hammer, is a device to measure the elastic properties or strength of concrete or rock, mainly surface hardness and penetration resistance.It was invented by Ernst Schmidt, a Swiss engineer....

(measuring compressive strength of concrete)
- Strength of materials
In materials science, the strength of a material is its ability to withstand an applied stress without failure. The applied stress may be tensile, compressive, or shear. Strength of materials is a subject which deals with loads, deformations and the forces acting on a material. A load applied to a...