Longitudinal Strain, Definition of Longitudinal Strain, Longitudinal Strain Meaning (For CBSE, ICSE, IAS, NET, NRA 2022)

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Longitudinal Strain

Strain

  • According to the strain definition, it is defined as the amount of deformation experienced by the body in the direction of force applied, divided by initial dimensions of the body.
  • The relation for deformation in terms of length of a solid is given below.

where,

  • = the strain due to stress applied
  • = the change in length
  • L = original length of the material.
  • The strain is a dimensionless quantity as it just defines the relative change in shape.
  • There are two types of strain and they are:
    • Longitudinal strain
    • Lateral strain

Definition of Longitudinal Strain

  • A longitudinal strain is defined as Change in the length to the original length of an object
  • If there is a change in the length of a body due to the applied force, then the strain is called longitudinal strain.
  • It is the ratio of the change in length of a body to the original length of the body. It is measured by the change in length per unit length. This kind of strain is also called torsion strain.
  • It is caused due to longitudinal stress and is denoted by the Greek letter epsilon .

Longitudinal Strain Formula

Longitudinal Strain Formula
  • Let the initial length of a body = L
  • The change in length due to applied force (Figure)

Longitudinal strain

  • If the length increases due to tensile stress, the corresponding strain is called tensile strain.
  • If the length decreases due to compressive stress, the strain is called compressive strain.
  • The longitudinal strain, e, is measured in terms of the changes in the lengths of lines.

Longitudinal Strain Unit

They cancel each other, making it unit less or dimensionless quantity.

Longitudinal Strain Meaning

  • Stress and strain are like two sides of a coin.
  • It is important to know their behaviour at microscopic scales.
  • All solids are elastic by nature. Atoms or molecules constitute them. Each atom or molecule is surrounded by neighboring atoms or molecules.
  • Each atom or molecule surrounded by neighboring atoms or molecules are bonded together by intermolecular forces and stay in equilibrium.
  • When a deforming force or external force is applied, their intermolecular or inter atomic distances vary.
  • By conclusion, a restoring force will be generated to attain back the equilibrium, thereby regaining original size and shape.
  • When a body is under load, it will extend in the direction of the stress (longitudinal strain) and contract in the transverse or lateral direction (lateral strain) , in case of longitudinal tensile stress. As a result, a restoring force will be generated to attain back the equilibrium, thereby regaining the original size and shape.

Cylinder with L as Length and D as the Diameter

Cylinder with L as Length and D as the Diameter
  • What happens to the cylinder when an equal force is applied such that it is perpendicular to the cross-sectional area? The answer is there will be a change in its length as well as in diameter.
  • The length will increase from L to and Diameter will reduce from D to D-.
  • So, the change in dimension to the original dimension is defined as strain. It tells the amount of stress an object is experiencing.
  • When the object is stretched, the restoring force is known as tensile stress. When the object is compressed, the restoring force is known as compressive stress.
  • So, in both ways, there will be a considerable change in the length of the object, say, cylinder.
  • So, we can define “longitudinal strain as Change in the Length to Original Length L.”

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