Compressive Stress

Compressive stress, denoted by the Greek symbol sigma σ, is given by:

σ_C = F/A

Where:

– F: Applied compressive force

– A: Area over which the force is applied

This formula quantifies the force applied per unit area of a material. The larger the applied force, the greater the compressive stress. However, if the area over which the force is distributed increases, the stress decreases.

Units

The SI unit of compressive stress is the Pascal (Pa), which is defined as one Newton per square meter (N/m²). This means that if a force of 1 Newton is applied uniformly over an area of 1 square meter, the resulting compressive stress is 1 Pascal. However, since the Pascal is a very small unit, larger units like megaPascals (MPa, 10⁶ Pa) and gigaPascals (GPa, 10⁹) are commonly used in engineering and materials science.

When materials experience stress, they undergo deformation, which is termed strain.

When a material is subjected to compressive stress, it deforms by reducing its length. This deformation is measured using compressive strain, which tells us how much a material shortens compared to its original length.

Compressive strain is denoted by the Greek symbol epsilon, ε, and is given by:

ε_C = ΔL/L

Where:

– ΔL: Change in length

– L: Original length of the material

Since strain is the ratio of two lengths, it is dimensionless and indicates how much material has compressed relative to its original size.

Compressive Strain and Material Behavior

Different materials respond differently to compressive stress. Some materials, like rubber and soft metals, can undergo large compressive strains without breaking, while brittle materials like ceramics and concrete may crack or fail under high compression. Hooke’s Law describes the relationship between compressive stress and compressive strain for elastic materials:

σ_C = E⋅ε_C

Where E is Young’s modulus, a measure of a material’s stiffness. A higher Young’s modulus indicates greater resistance to deformation.

Comparison Factor	Compressive Stress	Tensile Stress
Definition	Occurs when a material is subjected to a pushing or squeezing	Occurs when a material is subjected to a pulling or stretching
Formula	σC = F/A	σT = F/A
Effect on Material	Causes shortening or compression	Causes elongation or stretching
Failure Mode	Materials may crack, buckle, or crush under excessive compression	Materials may fracture or break under excessive tension
Real-World Examples	Bridges and Buildings: Concrete pillars support compressive loads.Human Body: Bones experience compressive stress when supporting weight.	Suspension Bridges: Steel cables are under tensile stress.Tendons in the Body: Stretching exerts tensile stress on tendons and muscles.
Stress-Strain Curve	Compressive stress-strain curves often show buckling in slender materials and crushing in brittle materials.	Tensile stress-strain curves show elastic deformation followed by necking and fracture in ductile materials.