What is Stress?

Stress in physics is defined as the force exerted on the unit area of a substance. Stress affects the body as strain in which the shape of the body changes if the stress is applied and sometimes it gets permanently deformed. On the basis of the direction of force applied to the body, we can categorize stress into three categories that include,

• Longitudinal Stress
• Bulk Stress
• Shearing Stress

Apart from these three, there are also other types of stress that we will learn in this article. In this article, we will also learn about what is stress, the types of stress, the Formula for stress, the unit of stress, and others in detail.

What is Stress?

Stress in physics is defined as the force we apply to an object divided by the cross-section area of the object on which the force acts. 

The force applied to any object deformed the shape of the object and to restore the object to its original shape an internal restoring force is applied to the object. The internal force acting per unit area of the object is called the stress. Thus,

Stress is defined as “The restoring force per unit area of the material”.

• Stress is a Scalar Quantity, and it’s denoted by σ. 
• Stress is measured in Pascal or N/m².

Stress Formula

The formula to calculate the stress acting on a body is,

Stress = (Restoring Force) / (Area of Material)

We use σ notation to denote stress thus,

σ = F / A

where,

• F is the Restoring Force is measured in Newton,
• A is the Area of Cross-Section of Material is measured in m²

Units of Stress

There are various units in which stress is measured. Some of the most common units of stress are listed in the table below:

System	Unit of Stress
SI system	N/m2 or N/mm2
Fundamental system	kg.m-1.s-2
US unit	lbf/ft2

SI System for measuring larger values of stress.

• Kilo (10³): KN/m² or KN/mm²
• Mega (10⁶): MN/m² or MN/mm²
• Giga (10⁹): GN/m² or GN/mm²
• Tera (10¹²): TN/m² or TN/mm²

Types of Stress

In physics, there are many different types of stress, but the most common are Normal Stress and Tangential or Shearing Stress. In the following paragraphs, we’ll go through a few different sorts of stress.

Normal Stress

The normal force is the stress that arises when an axial force is applied to a component. In other words, when the stress imparted to the body is perpendicular. When the object’s length and volume are altered, the object’s stress level returns to normal. The symbol is represented by it. Normal stress is measured in millipascals (MPa) in the SI system.

Formula of Normal Stress

Normal Stress = Axial Force / Cross-sectional Area

When an object is in tension or compression, normal stress occurs. Normal Stress is further classified into two categories that are,

• Longitudinal Stress
• Bulk Stress

Now let’s learn about them in detail.

Longitudinal Stress

Longitudinal stress is defined as when the length of the body changes due to normal stress.

Formula of Longitudinal Stress

Longitudinal Stress = Deforming Force / Cross-Sectional Area

Longitudinal Stress stretches or compresses an object throughout its whole length. As a result, based on the direction of deforming force, it can be divided into two types – Tensile stress and Compressive stress

When a rod is stretched according to Newton’s third law of motion, tensile stress is visible. Tensile stress is commonly represented by a rubber band being stretched out. Compression is the polar opposite of tension. When it is acting on a rod that is pressed at both ends by opposing or equal forces. Compressive stress is what you get when you squeeze a rubber ball in your hands. Longitudinal Stress is further classified into two categories that include,

• Tensile Stress
• Compressive Stress

Now let’s learn about the same in detail.

Tensile Stress

Tensile stress is defined as stress that occurs when a deforming force or applied force causes an increase in the object’s length. When a rod or wire is stretched, for example, equal and opposite forces (outwards) are applied at both ends.

Compression Stress

The shape and volume of the body are altered when a tangential force is applied to it. The length of the body is reduced once compression load has been applied. Tensile stress and compression stress are diametrically opposed. Compression stress is created when you squeeze a pet’s squeak toy in your hand.

Bulk Stress

Volume stress is also known as Bulk Stress. The term “volume stress” refers to stress that causes the body’s volume to fluctuate. Normal stress causes a change in length or volume, while tangential stress causes a change in the shape of the body, which is referred to as volume stress. When a body is submerged in a liquid and is under the force of pressure p, the body encounters a force that is perpendicular to the body’s surface.

Formula of Volume Stress

Volume Stress = Force / Area 

Shearing Stress

A force applied tangentially across the plane’s surface area is known as shearing stress. When the forces operating on the surface are parallel to it and the stress acting on the surface traces a tangent, the surface is said to be tangent. Shearing stress is the term for this type of anxiety.

Formula of Shearing Stress

Shearing Stress = Force / Surface Area

Hydraulic Stress

The internal force per unit area acting on liquids is referred to as hydraulic stress. When a force is applied to the body by a fluid, hydraulic stress is the restoring force per unit area. Stress differs from pressure in that it considers the internal force per unit area rather than the outward force per unit area. Hydraulic stress is characterized in a similar way in the case of liquids.

Real-Life Example of Stress

Various examples in which the concept of stress is applied in our daily life are,

• In architecture, the idea of stress is utilized to plan a building’s structure. The concept of stress and how it affects the different components of the building is integrated into everything from the foundations to the support beams to the columns.
• The concept of stress is used to design the parts of an automobile, spacecraft, Areoplanes, Fighter planes, etc.
• Concept of stress is used to made various day to day tools used in our daily life, etc.

Stress and Strain

Stress is the defined as the restoring force acting on an object and strain is the change in the dimension of object with respect to the original dimension. We can say that stress is the cause and strain is the effect. The formula for strain is given as follows

Strain = (l_f – l_i)/l_i

where,

l_f is the final length

l_i is the initial length

Since, strain is ration of change is dimension to the original dimension, hence it has no units. We can also convert strain into percentage by multiplying the above formula with 100.

In the case of tensile stress, the strain will be positive as the body will elongate and the difference between the final and initial length will be positive from the above formula. But in case of compressive stress the strain will be negative as the body will get compressed and the final length will reduce making the difference of length in the above formula negative.

Strain is not only in terms of length, it cam also be in terms of area and volume. To calculate are and volume strain we just need to replace length by area or volume as per our need in the above formula. The relation between Stress and Strain is determined by Hooke’s Law which is discussed below:

Hooke’s Law

Hooke’s Law states that within elastic limit of a material, the strain resulted in the material is directly proportional to the stress applied. In this limit, the graph between stress and strain is linear in nature and from the yield point the nature of the graph changes. The mathematical expression for Hooke’s Law is given as

σ = Yε

where,

σ is Stress

Y is Young’s Modulus

ε is Strain

The Graph for Hooke’s Law is shown in the image below:

Examples on Stress Formula

Example 1: Find the stress of an item with a 60 Newtons (N) operating force and a 4 mm² cross-section area.

Solution:

Given,

• Restoring Force = 60 N
• Area of Cross-Section = 4 mm²

Stress = (Restoring Force) / (Area of Cross-Section)

Stress = 60 N / 4 × 10^-6

Stress = 15 × 10⁶ Nm

Stress of an item is 15 × 10⁶ Nm

Example 2: Find the stress on an object if 100 Nm force is applied to 5 cm² area of cross-section.

Solution:

Given,

• Restoring Force = 100 N
• Area of Cross-Section = 5 cm² = 5×10^-4 m²

Stress = (Restoring Force) / (Area of Cross-Section)

Stress = 100 / 5×10^-4

Stress = 20 × 10⁴ Nm

Stress of an item is 2 × 10⁵ Nm

FAQs on Stress

1. Define Stress.

Stress is defined as “Restoring force per unit area of the material”.

2. What is Formula for Stress?

The Formula of Stress is,

Stress = (Restoring Force) / (Cross-Section Area of Material)

3. What is Shearing Stress?

A force applied tangentially across the plane’s surface area is known as shearing stress. When the forces operating on the surface are parallel to it and the stress acting on the surface traces a tangent, the surface is said to be tangent. Shearing stress is the term for this type of anxiety.

4. What is the SI Unit of Stress?

SI unit of Stress is Pascal or N/m² or N/mm²

5. What is Longitudional Stress?

The stress experienced by the object over its length is called the Longitudional Stress.

6. What are types of Longitudional Stress?

The two types of Longitudional Stress are,

• Tensile Stress
• Compressive Stress

7. What is Tangential Stress?

Tangential Stress is also called the Shearing stress, it is the stress that acts upon the tangential direction to the object. It changes the shape of the object.