Stress and Strain: Introduction and Types

February 6, 2025

Introduction of Stress

The restoring force is developed inside the body when deforming force is applied on it. This restoring force per unit area of the body is known as stress. The restoring force is equal and opposite with deforming force. Therefore, stress may also be defined as the deforming force per unit area of the body.

Thus,

Stress = external force or deforming force/ area of the body

or, Stress = F/A

In SI units, the unit of stress is newton per meter square (Nm^-2) and in CGS system its unit is dyne cm^-2. The dimensional formula for stress is written as [ML^-1T^-2].

Types of Stress

The stress developed in a body depends upon the way on which the external forces are applied over it. On this basis, there are following types of stress.

a) Normal Stress

When the deforming force is applied normally to the surface of the body, then the force applied per unit area is called normal stress. Normal stress has two categories. They are:

i) Tensile stress

It is the stress which is set up when there is an increase in the length or when there is extension of the body in the direction of the force applied.

ii) Compression stress

It is the stress which is set up when there is a decrease in length of the wire or compression of the body occurs due to the force applied.

b) Tangential stress or shearing stress

When two equal but opposite forces act tangent to the surface of the opposite faces of an object, then one face of the object is displaced with respect to the other face as in diagram below. In this case, the body is under the stress which is called tangential or shearing stress. Therefore, tangential stress or shearing stress is defined as the ratio of the force acting tangentially on the surface to the area of the surface.

i.e., Tangential stress = F/A

c) Bulk stress or volume stress or hydraulic stress

When a body is immersed in a fluid (liquid or gas), the fluid exerts force on the surface of the body. As a result, the volume of the body decreases and the body is under a stress known as bulk stress or volume stress or hydraulic stress. Thus, it can also be defined as the force acting perpendicular to the surface of the object per unit area of the object.

i.e., bulk stress = force /area = F/A

Image source: study.com Image source: libretext

Definition of Strain

When a deforming force is applied on a body, there is change in the configuration of the body. The body is thus said to be strained or deformed. Therefore, the ratio of the change in configuration (i.e. shape, length or volume) to the original configuration of the body is called strain.

i.e., Strain = change in configuration/original configuration

Since, strain is a ratio of similar quantities, it has no unit and dimensions.

Types of Strain

The change in configuration involves a change either in length, volume or shape of the body. Hence, there are three types of strain.

1. Longitudinal Strain

It is the strain which is defined as the change in length per unit original length produced under the action of the deforming force. Therefore, if L is the original length of the body and ΔL is the change in length, then,

Longitudinal strain = change in length/original length

= ΔL/L

Image source: keyence

2. Volumetric strain

It is also called bulk strain. It is the change in volume per unit original volume of the body produced under the action of the deforming force. Thus, if V is the original volume of the spherical ball and ΔV is the change in volume, then,

Volumetric strain = Change in volume/ original volume

= ΔV/V

Image source: themechanical

3. Shear strain

It is the strain which is produced when the body is under the tangential stress or hearing stress. It is defined as the angle, θ through which the face of the body originally perpendicular to the fixed face is turned when it is under the shearing stress. Then,

tan θ = x/L

or, θ = x/L (if θ is small tan θ is nearly equal to θ)