What is the Stress Formula?

Stress is a key term in physics and engineering that defines the internal forces per unit area of a material caused by external loads. Understanding stress is vital for developing and assessing buildings, materials, and mechanical systems in many domains. The symbol for stress is σ and it is measured in N/m². Learn more about Stress formula and examples based on them in this article.

In physics and engineering, stress is defined as the internal force per unit area that acts on a material. It is a measure of the intensity of internal forces within a material that arise in reaction to external loads or applied forces. Stress denotes a material’s deformation or shape change in response to external forces.

Stress is equal to force acting per unit area. The stress formula can be defined as,

σ = F / A

where,

• σ = Stress
• F = Force applied
• A = Area on the surface

The unit of stress is N/m². The other unit of measurement for stress is Pascal, denoted as Pa. The commonly used units of stress are gigapascal, denoted as GPa, and megapascal, denoted as MPa.

Dimension of Stress

The dimension formula of stress is ML^-1T^-2

Related Articles

• Stress and Strain
• Stress Strain Curve
• Hooke’s Law
• Mechanical Properties of Solid

Example 1: Find stress if a force of 40 N is acted upon an object with area 4mm².

Solution:

Given,

• Force (F) = 40N
• Area (A) = 4mm²

According to the formula for stress,

σ = F / A

σ = 40N / 4mm² 

σ = 10 ×10⁶ N/m² 

Thus the stress on the surface is 10×10⁶ N/m²

Example 2: Find the stress on a rubber band with an area of 0.35m² which is pulled with a force of 500 N.

Solution:

Given,

• Force (F) = 500N
• Area (A) = 0.35mm2

According to the formula for stress,

σ = F / A

σ = 600N / 0.3mm² 

σ = 2000 N/m²

Thus the stress on the surface is 2000 N/m²

Example 3: Find area if stress is 1000N/m² and force is 500 N. 

Solution:

Given,

• Stress (σ) = 1000N/m²
• Force (F) = 500 N

According to the formula for stress,

σ = F / A

Rearranging the formula for stress,

A = F / σ

A = 500/1000 

A = 0.5

Thus area is 0.5 m² 

Example 4: Find force if stress is 800N/m² and area of 0.2m².

Solution:

Given,

• Stress (σ) = 800N/m²
• Area (A) = 0.2 m²

According to the formula for stress,

σ = F / A

Rearranging the formula for stress,

F = σ×A

F = 800×0.2

F = 160 N

Thus force is 160 N. 

Q1. A force of 800 N is applied to a steel rod with a cross-sectional area of 0.005m². Calculate the tensile stress experienced by the rod.

Q2. A concrete column with a cross-sectional area of 0.2m² experiences a compressive force of 500 kN. Determine the compressive stress exerted on the column.

Q3. A steel beam with a cross-sectional area of 0.01m² is subjected to a bending moment of 10 kNm. Determine the bending stress experienced by the beam.

Q4. An aluminum wire with a cross-sectional area of 2mm² experiences a tensile force of 50 N. Determine the tensile stress developed in the wire.

What is stress?

Stress is the restoring force per unit area of the material.

What are the units used to define stress?

The units used are,

• N/m²
• Pascal

What are types of stress?

The different types of stress are Tensile stress, Normal Stress, Tangential or Shearing Stress and Bulk stress

How is stress related to force and area?

Stress is directly proportional to the force exerted to the material, and inversely proportional to its cross-sectional area. In simple terms, increasing the applied force or decreasing the area causes higher stress levels.

What is the difference between stress and strain?

Stress measures the internal force per unit area exerted on a material, whereas strain measures the material’s deformation or shape change in reaction to stress. Strain is a dimensionless number that is often stated as a percentage or as the change in length divided by the original length.