# What is Compressive Strength?- Definition, Formula

## What is Compressive Strength?

In mechanics, compressive strength or compression strength is the capacity of a material or structure to withstand loads tending to reduce size. In other words, compressive strength resists compression, whereas tensile strength resists tension. In the study of the strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.

Compressive strength refers to the ability of a certain material or structural element to withstand loads that reduce the size of that material, or structural element when applied. A force is applied to the top and bottom of a test sample, until the sample fractures or is deformed.

Materials such as concrete and rock are often evaluated using a compressive strength test and, in these cases, fracturing occurs.

Materials such as steel can also be tested for compressive strength, and in the case of ductile materials, deformation tends to occur. Initially, a ductile material will accommodate the applied load by adjusting its internal structure– a process referred to as plastic flow.

Once the deformation is concentrated in one area, the plastic flow stops, and the material breaks. For ductile metals, tensile strength is usually the preferred indicator for measurement and comparison. This is because tensile stress measures the forces needed to pull a material apart, which is better suited to the plastic flow phenomenon.

Compressive strength tests the compressive strength is calculated by using the equation,

## Compressive Strength Formula

The formula to calculate compressive strength is F = P/A, where:

• F=The compressive strength (MPa)
• A=A cross-section of the area of the material resisting the load (mm2)

## Introduction Of Compressive Strength

Compressive strength is a limited state of compressive stress that leads to failure in a material in the manner of ductile failure (infinite theoretical yield) or brittle failure (rupture as the result of crack propagation, or sliding along a weak plane).

Compressive strength is measured on materials, components, and structures. By definition, the ultimate compressive strength of a material is the value of uniaxial compressive stress reached when the material fails completely.

Measurements of compressive strength are affected by the specific test methods and conditions of measurement. Compressive strengths are usually reported in relationship to a specific technical standard.

Concrete and ceramics typically have much higher compressive strengths than those with high tensile strengths. Composite materials, such as glass fiber epoxy matrix composite, tend to have higher tensile strengths than compressive strengths.

Concrete is usually reinforced with materials that are strong in tension. Compressive strength is widely used for specification requirements and quality control of concrete. Engineers know their target tensile (flexural) requirements, and express these in terms of compressive strength.

Concrete compressive strength requirements can vary from 2,500 psi for residential concrete to 4,000 psi and higher in commercial structures. Higher strengths up to and exceeding 10,000 psi are specified for certain applications.

For both ductile and brittle materials, the compressive strength is usually significantly higher than the tensile strength. Exceptions to this include fiber-reinforced composites such as fiberglass, which are strong in tension but are easily crushed.

Concrete, however, which is a particle-reinforced composite, is far stronger in compression than tension to the extent that if it is going to be exposed to tensile forces, it needs to be reinforced with steel rods.

## Which materials have the highest/lowest compressive strengths?

Within the brittle material group, materials such as rock tend to have higher compressive strengths of 140 MPa. Softer variations such as sandstone tend to have lower compressive strengths of around 60 MPa.

The compressive strength of ductile materials such as mild steel used for most structural purposes is around 250 MPa.

## Which applications require high/low compressive strength?

In terms of concrete, ultra-high-strength concrete can be used to construct structures that have to be able to withstand heavy loads and stresses such as highway bridges, whereas for standard, domestic paving use, the concrete can have a lower compressive strength of 30 MPa.

## Deviation of engineering stress from true stress

In engineering design practice, professionals mostly rely on engineering stress. In reality, true stress is different from engineering stress. Hence calculating the compressive strength of the material from the given equations will not yield an accurate result. This is because the cross-sectional area A0 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 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 obtained from the experiment.

The frictional force is not constant for the entire cross-section of the specimen. It varies from a minimum at the center, away from the clamps, to a maximum at the edges where it is clamped. Due to this, a phenomenon known as barreling occurs where the specimen attains a barrel shape.