Short Answer:

Strain is defined as the ratio of the change in dimension of a body to its original dimension when an external force is applied. It is a measure of deformation produced in a material due to stress. Strain has no unit because it is a ratio of two similar quantities (lengths).

In simple words, when a material is stretched or compressed under load, it changes its shape or size. The amount of this change compared to the original size is called strain. It helps engineers understand how much deformation occurs in a material before failure.

Detailed Explanation:

Strain

When a body is subjected to an external force, internal resistance called stress develops within the body. This stress causes the body to deform — either by elongating, compressing, twisting, or shearing. The measure of this deformation with respect to the original dimension is called strain.

Mathematically, strain is expressed as:

If the length of a bar changes from L to (L + δL) when subjected to load, then:

Where,

= Strain (no unit, dimensionless)
= Change in length (m or mm)
= Original length (m or mm)

Strain helps in determining how flexible or stiff a material is under a given load. It is a key parameter used along with stress to understand a material’s mechanical behavior.

Types of Strain

Depending on the type of load and nature of deformation, strain can be classified into three main types:

Tensile Strain
Compressive Strain
Shear Strain

Let’s understand each type in simple terms:

Tensile Strain

When a body is subjected to tensile stress (pulling or stretching force), it elongates in the direction of the applied load. The ratio of the increase in length to the original length is called tensile strain.

Example:
A steel rod under a pulling force that increases its length by a small amount develops tensile strain.

Important Note:
Tensile strain is always positive, as it results in an increase in dimension.

Compressive Strain

When a body is subjected to compressive stress (pushing force), it shortens in the direction of the applied load. The ratio of the decrease in length to the original length is called compressive strain.

Example:
A concrete column under the weight of a building shortens slightly, producing compressive strain.

Important Note:
Compressive strain is generally negative, as it results in a decrease in length.

Shear Strain

When a body is acted upon by tangential (parallel) forces on opposite faces, it deforms such that one layer slides over another. The angular distortion produced between two perpendicular faces of the body is known as shear strain.

(where is the angle of deformation in radians.)

Example:
When a book kept on a table is pushed sideways, the top layer moves while the bottom remains fixed. The angular change produced in the shape of the book represents shear strain.

Volumetric Strain

When a body is subjected to uniform pressure in all directions, its volume changes but the shape remains the same. The ratio of the change in volume to the original volume is called volumetric strain.

where,

= Change in volume
= Original volume

This type of strain is important in studying fluids, pressure vessels, and materials subjected to hydrostatic pressure.

Lateral and Longitudinal Strain

When a material is subjected to a uniaxial load (load along one axis), it undergoes two types of strain:

Longitudinal Strain:
- The strain in the direction of the applied load.
- Example: A rod elongates or shortens along its length.
Lateral Strain:
- The strain perpendicular to the applied load direction.
- Example: When a rod elongates in length, it becomes thinner in diameter.

These two strains are related through Poisson’s ratio (ν), defined as:

Poisson’s ratio helps in understanding the deformation behavior of materials under load.

Graphical Representation (Stress-Strain Curve)

In a stress-strain diagram, the strain is plotted along the horizontal axis (X-axis), and stress along the vertical axis (Y-axis). The initial straight portion of the curve represents the elastic region, where strain is proportional to stress (Hooke’s Law). Beyond the elastic limit, the material enters the plastic region, where permanent deformation occurs.

This relationship helps engineers determine the limits of elastic behavior and the material’s ductility, strength, and toughness.

Characteristics of Strain

Dimensionless Quantity:
Strain has no unit because it is a ratio of two similar dimensions (length to length).
Proportional Limit:
Within the elastic range, strain is directly proportional to stress, i.e.,

where E is Young’s modulus of elasticity.

Very Small in Magnitude:
Strain values are usually very small, often expressed in microstrain (1 microstrain = 10⁻⁶).
Depends on Material Property:
Different materials have different abilities to deform under stress — ductile materials show large strains, while brittle materials show very little strain.
Reversible and Irreversible:
- In the elastic region, strain is reversible — the material returns to its original shape.
- In the plastic region, strain is irreversible — permanent deformation occurs.

Applications of Strain

Design of Structural Members:
Helps determine allowable deformation in beams, columns, and shafts.
Material Testing:
Used to evaluate elasticity, ductility, and strength of materials.
Machine Component Design:
Ensures machine parts can safely deform without failure.
Civil and Mechanical Engineering:
Used in analyzing building materials, bridges, and automotive components.
Strain Gauges:
Strain is measured using electrical strain gauges to detect deformation in structures and machines.

Conclusion

In conclusion, strain is the ratio of deformation (change in dimension) to the original dimension of a material under load. It indicates how much a material deforms when subjected to stress. Strain is a dimensionless quantity that plays a vital role in mechanical and structural design. Understanding different types of strain — tensile, compressive, and shear — helps engineers predict material behavior, ensure safety, and design components that can withstand external loads effectively.