Strain

We know that, when external forces are applied on given surface area of substance stress is produced. This stress produces deformation in the given substance in terms of its length, volume or shape. The change in the dimension that takes place can be studied with the help of the concept termed as strain.

Let’s define the concept now….!

The ratio of change in dimensions per unit original dimensions is called as strain.

Strain = (Change in dimensions)/(Original dimensions)

Strain is ratio of similar quantities hence it is unit less and dimensionless.

It is pure number.

As there are three types

Tensile stress (Longitudinal stress)

When the deformation consists of a change in the length of the body, the strain is called tensile strain or longitudinal strain.

Consider the uniform metal wire of length ‘L is subjected to a load F=mg, so that its length increases by l, then the final length of wire is L+l

Increase in length= L+l-L = l

    The ratio of change in length per unit original length is called tensile strain.

∴ Tensile strain = (Change in length )/(original length) = ∆l/L

Volume strain

When the deformation consists of a change in volume of the body, the strain in it is called Volume strain.

Suppose that the cube of volume ‘V’ is subjected to external load F, then the volume is shrinks by ‘dV’

Hence, change in volume= V-dV-V= -V

Negative sign indicates that the volume is decreased.

The ratio of change volume to original volume.

Volume Strain= (Change in volume)/(Original volume) = dv/V

Shearing strain

When the deformation consists of a change in the shape of the body the strain in it is called shearing strain or shear.”

Consider the cube of volume ‘V’ is subjected to tangential force ‘F’ so that the upper face of cube is displaced ‘x’ or by angle θ as shown below,

The ratio of change in shape to the original shape.

Or Ratio of lateral displacement of layer to the distance of that layer from the fixed layer.

∴ Shearing strain = (lateral displacement of layer)/(distance of layer from fix layer)

∴ Shearing strain = x/h

∴ Shearing strain = tanθ ≈ θ (θ in radian)

Some important points to note……!

  1. Strain is unit less and dimensionless quantity.
  2. Shearing strain is also known as shear
  3. Strain gives us details about the deformation.

Updated: December 9, 2021 — 2:30 am

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