What is the unit of stress?

Short Answer:

The unit of stress is Pascal (Pa) in the International System of Units (SI). One Pascal is defined as one Newton of force acting on an area of one square meter. Thus, 1 Pa = 1 N/m². Stress can also be expressed in larger units such as kilo Pascal (kPa), mega Pascal (MPa), or giga Pascal (GPa) depending on the magnitude of the stress involved.

In mechanical engineering, these larger units are often used because stresses in machine parts and structures are usually very high. Therefore, stress gives a clear idea of how much internal force a material can resist per unit area.

Detailed Explanation :

Unit of Stress

Stress is the internal resisting force per unit area developed in a material when an external load or force acts on it. The strength or intensity of this internal force is measured using specific units so that engineers can compare and design materials properly. The standard unit of stress in the SI system is the Pascal (Pa).

Mathematically, stress (σ) is given by the formula:

where,
σ = Stress,
F = Applied force,
A = Cross-sectional area.

From this equation, it is clear that stress is the ratio of force (F) to area (A). Therefore, its unit depends on the units of these two quantities. In the SI system:

  • The unit of force (F) is Newton (N).
  • The unit of area (A) is square meter (m²).

So, the unit of stress becomes:

This means that 1 Pascal is equal to one Newton of force acting uniformly over an area of one square meter.

However, the value of 1 Pascal is very small for practical engineering use. Therefore, larger units are commonly used:

  • 1 kPa (kilo Pascal) = 1,000 Pa = 10³ N/m²
  • 1 MPa (mega Pascal) = 1,000,000 Pa = 10⁶ N/m²
  • 1 GPa (giga Pascal) = 1,000,000,000 Pa = 10⁹ N/m²

For example, the typical stress in steel materials is often in the range of 200 to 400 MPa, which is equal to 200 to 400 million Pascals.

Other Common Units of Stress

In addition to the SI system, other unit systems are also used in different countries and industries.

  • In the CGS (Centimeter-Gram-Second) system, stress is measured in dyne/cm².
    1 N = 10⁵ dyne and 1 m² = 10⁴ cm². Therefore,
  • In the FPS (Foot-Pound-Second) system, which is used in some countries like the United States, stress is measured in pounds per square inch (psi).

Conversion between these units is also important in engineering:

and

Dimensional Formula of Stress

The dimensional formula of stress helps in verifying its physical relationship with other quantities.
Stress = Force / Area

Force has the dimensional formula [M¹ L¹ T⁻²]
Area has the dimensional formula [L²]
Therefore, the dimensional formula of stress becomes:

This shows that stress has the same dimensions as pressure, since both are defined as force per unit area.

Difference Between Stress and Pressure (by Meaning)

Although stress and pressure have the same unit (N/m² or Pa), they differ in meaning:

  • Stress acts internally within a body and can be tensile, compressive, or shear.
  • Pressure acts externally on a surface and is always compressive in nature.

Hence, while both have the same unit, they represent different physical effects.

Engineering Relevance of Stress Units

In engineering design, stress units are extremely important for calculations related to:

  • Material selection: Materials are compared based on their strength measured in MPa or GPa.
  • Structural safety: The safe limit of stress is known as allowable stress, and it ensures that structures and components do not fail under load.
  • Testing and analysis: Stress units are used in tensile tests, compression tests, and fatigue analysis to determine material properties.

For example, the yield strength of mild steel is approximately 250 MPa, while that of aluminum is around 100 MPa. This shows that steel can withstand higher internal forces before deforming compared to aluminum.

Understanding and using the correct unit of stress ensures accuracy and consistency in mechanical design calculations.

Practical Example:

If a force of 500 N acts on a steel rod having a cross-sectional area of 0.002 m²,

This means the stress developed in the rod is 0.25 MPa. Such calculations help engineers evaluate the strength and performance of materials.

Conclusion:

The SI unit of stress is Pascal (Pa), which represents one Newton of force acting on one square meter of area. In engineering practice, larger units like kPa, MPa, and GPa are commonly used because stress values are often large. Understanding the unit of stress is essential for comparing material strengths, ensuring structural safety, and performing accurate design calculations in mechanical engineering.