What are the units of stress and strain?

Short Answer:

The unit of stress in the SI system is Pascal (Pa), which is equal to one Newton per square meter (N/m²). Sometimes, larger units like kiloPascal (kPa), MegaPascal (MPa), or GigaPascal (GPa) are used depending on the magnitude of stress.

The unit of strain is dimensionless because it is a ratio of two similar quantities (change in length/original length). Strain has no unit, but it is often expressed as a pure number or in microstrain (×10⁻⁶) for very small deformations.

Detailed Explanation:

Units of Stress and Strain

In the study of mechanics of materials, the concepts of stress and strain are fundamental to understanding how materials behave under external forces. When a force is applied to a material, it develops an internal resistance (stress) and undergoes deformation (strain). To measure and compare these quantities scientifically, proper units are assigned.

The unit of stress indicates how much force acts on a given area, while the unit of strain shows how much the material has deformed relative to its original size. Both play a key role in designing safe and reliable mechanical components.

Unit of Stress

Definition of Stress:
Stress is defined as the internal resisting force developed per unit area of a material when an external force acts on it. Mathematically,

where,

  •  = Stress
  •  = Force (in Newton, N)
  •  = Area (in square meters, m²)

From this equation, the unit of stress can be derived easily.

Unit of Stress in SI System:
Since force is measured in Newtons (N) and area is measured in square meters (m²), the unit of stress becomes:

This unit is called a Pascal (Pa).

However, because the value of a Pascal is very small, engineers generally use larger multiples:

  • 1 kPa = 10³ N/m²
  • 1 MPa = 10⁶ N/m²
  • 1 GPa = 10⁹ N/m²

Example:
If a force of 1000 N acts on an area of 0.01 m², then the stress is:

Other Unit Systems for Stress

While the SI unit (Pascal) is most widely used, stress can also be expressed in other unit systems:

  1. CGS System:
    • Force = dyne
    • Area = cm²
    • Therefore, the unit of stress = dyne/cm².
    • 1 N/m² = 10 dyne/cm²
  2. FPS System (British Units):
    • Force = pound-force (lbf)
    • Area = square inch (in²)
    • Unit of stress = psi (pound per square inch)
    • 1 psi = 6894.76 Pa

Thus,

  • In SI → Pascal (Pa)
  • In FPS → psi (pound per square inch)

Common Stress Ranges:

  • For structural steel: about 250 MPa
  • For concrete: about 30 MPa
  • For aluminum: about 100 MPa

This shows why the use of MPa or GPa is more practical in engineering applications.

Unit of Strain

Definition of Strain:
Strain is defined as the ratio of the change in dimension to the original dimension of a material when subjected to stress.

where,

  •  = Strain
  •  = Change in length
  •  = Original length

Since both the numerator and denominator represent lengths (meters), strain is a ratio of similar quantities. Hence, it has no unit and is dimensionless.

However, because the amount of strain produced is usually very small, it is expressed in convenient forms such as:

  • Microstrain (µε):
  • Millistrain (mε):

For example, if a steel rod of length 1 meter elongates by 0.0005 meters, then:

Thus, strain is represented as a pure number, but for small deformations, engineers use microstrain or percentage strain for clarity.

Comparison of Units

  1. Stress:
    • Derived unit = N/m²
    • Dimension = [M¹L⁻¹T⁻²]
    • Unit name = Pascal (Pa)
    • Common engineering use = MPa or GPa
  2. Strain:
    • Derived from ratio (change/original)
    • Dimensionless (no unit)
    • Represented in small values such as microstrain (µε)

This comparison helps in understanding that stress has both magnitude and dimension, while strain only represents the proportional change in dimension.

Significance of Units of Stress and Strain

  1. Standardization:
    Using SI units like Pascal and dimensionless strain ensures uniformity and easy comparison of results globally.
  2. Design and Safety:
    Stress and strain units help engineers determine whether materials can safely resist applied loads.
  3. Material Testing:
    In tensile, compression, and torsion tests, stress and strain values (in Pa and dimensionless form) are used to plot stress-strain diagrams.
  4. Elastic and Plastic Behavior:
    By analyzing stress (Pa) and strain (dimensionless), engineers can determine the elastic limit, yield point, and failure point of materials.
  5. Practical Applications:
    Used in analyzing bridges, building frames, machine components, and aircraft structures to ensure durability and safety.

Example Application

Suppose a steel bar with a cross-sectional area of 1000 mm² is subjected to a load of 50,000 N, causing an elongation of 0.25 mm in a 500 mm long bar.

  • Stress:
  • Strain:

Thus, the stress is 50 MPa and the strain is 500 microstrain.

Conclusion

The unit of stress in the SI system is Pascal (Pa) or N/m², which measures the intensity of internal resistance developed in a material. The unit of strain is dimensionless, as it represents a ratio of change in dimension to original dimension. In practical applications, stress is usually expressed in MPa or GPa, while strain is expressed in microstrain (µε). Understanding these units is essential for analyzing material behavior, designing structures, and ensuring the safety and efficiency of engineering systems.