Strain: Definition, Types, Formula, Unit

In this article, you will learn a complete overview of strain such as its definition, types, formula, unit, and many more. 

Strain is a major contributor to physics and mechanics, without which the modulus of elasticity, bulk modulus, shear modulus, Poisson's ratio, etc. cannot be defined. 

So without wasting time let's get started.

What is Strain?

When an elastic body is subjected to an external deformation force then there is a change in dimensions of the body, the ratio of change in dimension to original dimension is called strain. 

It is represented by ' ε '. 

It has no unit.

It is also known as deformation.

Strain is the change in the dimensions of a body due to the effect of stress.

ε =Change in Dimension/Orginal Dimension

Formula of Strain

Let a spring of length x be fixed at one end and a load of 250 g is suspended at the other end, due to which the spring is deflected from x to x'.

strain formula
So,

Change in length, Δx = x' - x

As we know,

ε =Change in Dimension/Orginal Dimension

ε = Δx/x

Types of Strain

The strain can be divided into the following four types:
  • Linear Strain 
  • Lateral Strain
  • Volumetric Strain
  • Shear Strain

Linear Strain 

When an elastic body is subjected to an external deforming force then there is a change in the dimension of the body, the dimension along the direction of force is called a linear dimension and the ratio of change in linear dimension to original dimension is called linear strain. 

It is also called a longitudinal strain.

It is denoted by εₗₒₙ₉.

There are two types of linear strain 
  • Tensile Strain
  • Compressive Strain

Tensile Strain

When a member is subjected to axial pull on its cross-sectional area then its length increases.

The ratio of increase in the length to the original length of the member is termed a tensile strain.

It is denoted by εₜ.

εₜ = Increase in length/Original length

Compressive Strain

When a member is subjected to axial push on its cross-sectional area then its length decreases.

The ratio of decrease in the length to the original length of the member is termed a compressive strain.

It is denoted by ε꜀.

ε꜀ = Decrease in length/Original length

Lateral Strain

When an elastic body is subjected to external deforming force then there is a change in the dimension of the body, the dimension perpendicular to the direction of force is called lateral dimension, and the ratio of change in lateral dimension to original dimension is called lateral strain.

It is denoted by εₗₐₜ.

Formula of Linear and Lateral Strain

Let the length of a cylinder be l and the diameter d.  

Whose bottom part is fixed, now this cylinder is pulled out by applying an external force, due to which its length increases to l' and diameter decreases to d'.

lateral and linear strain formula
So,

Longitudinal change in length,

Δl = l' - l

Lateral change in length,

Δd = d' - d

So,

εₗₒₙ₉ = Δl/l

εₗₐₜ = Δd/d


Where,

εₗₒₙ₉ = Linear Strain

εₗₐₜ = Longitudinal Strain

Volumetric strain

When an elastic body is subjected to external deforming forces such that there is a change in volume of the body, then the ratio of change in volume to original volume is called volumetric strain.

It is denoted by εᵥ.

Formula of Volumetric Strain

Let the volume of the cylinder be V and its volume changes from V to V' after applying a force.

volumetric strain formula
So,

Change in volume

ΔV = V' - V

As we know,

εᵥ = Change in volume/Original volume

So,

εᵥ = ΔV/V

Shear Strain

Shear strain is the deformation of a material in response to an applied shear force.  

It is measured in terms of the angle by which the material has been displaced.

When two equal and opposite forces are applied parallel to the cross-sectional area of the body such that, one layer moves relative to the other, then the ratio of relative displacement to the distance between the two layers is called the Shear strain.

It is denoted by Φ.

Φ = Displacement of a top layer/Its distance from a fixed surface

Formula of Shear Strain

Let an object which is fixed at the bottom and a tangential force is applied to the top layer of the object then this tangential force develops shear stress in the object.

Due to this tangential force, the top of the object is deformed by changing its shape, causing the top layer of the object to be displaced by x distance.

shear strain formula
So,

Shear strain, Φ = x/l = tanθ

If θ is very small then,

tan θ = θ

So,

Φ = x/l = θ


So here you have to know all aspects related to strain. If you have any doubt then you are free to ask me by mail or on the contact us page.

Thank You.

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