What is Compressive Strength?- Definition, Formula

What is Compressive Strength?

In mechanics, compressive strength—sometimes called compression strength—describes how well a material or structure can handle forces that try to squash or shorten it. It’s essentially a measure of a material’s resistance to being compressed.

To put it simply, compressive strength is about how much squeezing a material can take, while tensile strength deals with how much pulling it can withstand. When we study the strength of materials, we often look at tensile, compressive, and shear strength separately, since each tells us something unique about how a material will behave under different conditions.

Compressive strength specifically refers to a material’s ability to hold up under loads that aim to make it smaller. In a standard test, a sample is placed between two plates and squeezed from the top and bottom until it either breaks or deforms.

Materials like concrete and rock are typically tested this way, and they usually fracture when the compressive limit is reached. On the other hand, if you test a ductile material like steel, you’ll notice it tends to deform rather than crack. Ductile materials handle the load by subtly rearranging their internal structure, a process known as plastic flow.

However, once this deformation becomes focused in one spot, the material stops flowing and eventually breaks. That’s one reason why, for ductile metals, we often use tensile strength as a benchmark instead—tensile tests are better at capturing the way these materials stretch and eventually fail, which is more in line with how plastic flow works.

For compressive strength, the test usually involves applying a steadily increasing load and then using a specific equation to calculate the material’s maximum resistance to compression.

Compressive Strength Formula

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

• F=The compressive strength (MPa)
• P=Maximum load (or load until failure) to the material (N)
• A=A cross-section of the area of the material resisting the load (mm2)

Introduction Of Compressive Strength

Compressive strength refers to the level of compressive stress a material can withstand before it fails. This failure can present itself as ductile—where the material seems to stretch its limits without actually breaking—or as brittle, where cracks spread rapidly or the material simply slides apart along a weak layer.

We commonly measure compressive strength not just in materials, but also in components and entire structures. The ultimate compressive strength is defined as the maximum uniaxial compressive stress a material can endure before it is completely compromised.

It’s important to recognize that how we test for compressive strength—and the exact procedures or standards followed—can influence the results. For that reason, compressive strength values are usually tied to specific testing standards to ensure clarity and consistency.

When comparing different materials, concrete and ceramics typically stand out for their high compressive strengths—much higher than their tensile strengths. On the other hand, composite materials like glass fiber epoxy composites generally offer greater strength under tension than compression.

With concrete, the situation is unique: while it excels under compression, it doesn’t perform well under tension. This is why engineers reinforce concrete with materials that handle tensile forces better.

In fact, compressive strength is a primary criterion for specifying and quality-checking concrete in construction. Engineers often know the tensile or flexural strength targets for a project and express those needs in terms of compressive strength.

Depending on the application, the required compressive strength of concrete can range quite a bit. Residential projects might require around 2,500 psi, while commercial structures often call for 4,000 psi or more. For specialized applications, strengths above 10,000 psi are sometimes necessary.

Generally, for both ductile and brittle materials, compressive strength tends to be much greater than tensile strength. However, there are exceptions—fiber-reinforced composites like fiberglass are strong under tension but can be crushed more easily.

Concrete, as a particle-reinforced composite, is a classic case: it’s vastly superior in compression, and whenever it must face tensile forces, reinforcing it with steel rods becomes essential.

Which materials have the highest/lowest compressive strengths?

Among brittle materials, substances like rock generally exhibit higher compressive strengths, often reaching approximately 140 MPa. In contrast, softer types, such as sandstone, typically display lower compressive strengths, usually around 60 MPa.

On the other hand, ductile materials—take mild steel for instance, which is commonly chosen for structural applications—tend to have compressive strengths in the range of 250 MPa.

Which applications require high/low compressive strength?

When it comes to construction, the choice of concrete strength really depends on what the structure is expected to handle. For instance, ultra-high-strength concrete is essential for projects like highway bridges, where the material needs to bear significant loads and ongoing stress.

On the other hand, for more everyday applications like paving around the house, a standard concrete mix with a compressive strength of about 30 MPa is usually sufficient.

Deviation of engineering stress from true stress

In the field of engineering design, it’s common for professionals to base calculations on engineering stress. However, it’s important to recognize that true stress behaves differently from engineering stress in real-world scenarios.

When it comes to determining the compressive strength of a material, relying solely on standard equations doesn’t always provide an accurate picture. The reason lies in the way the cross-sectional area—initially represented as A₀—actually changes as the load is applied. In practice, the area becomes a function of the load, expressed as A = φ(F).

This difference in approach has practical implications. During compression, a test specimen naturally shortens and, at the same time, tends to expand laterally. As a result, the cross-sectional area increases.

There’s another key point to consider during a compression test: the specimen is typically clamped at its edges. This setup introduces friction at the contact surfaces, which resists the material’s lateral spread. The energy required to overcome this friction means the process consumes more energy than it would otherwise, leading to a slight inaccuracy in the measured stress values.

It’s also worth noting that this frictional force isn’t uniform across the entire cross-section. It’s generally weakest at the center—furthest from the clamps—and strongest near the edges. This uneven distribution of friction gives rise to a phenomenon known as barreling, where the specimen starts to take on a barrel-like shape as the test progresses.

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