Elasticity

3. Strain

• When a body is under a system of forces or couples in equilibrium then a change is produced in the dimensions of the body.
  
• This fractional change or deformation produced in the body is called strain.
  
• Strain is a dimensionless quantity.
  
• Strain is of three types
  (a) Longitudinal strain:- It is defined as the ratio of the change in length to the original length. If l is the original length and Δl is the change in length then,
  
  

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  (b) Volume strain:-It is defined as the ratio of change in volume to the original volume
  
  (c) Shearing strain:- If the deforming forces produce change in shape of the body then the strain is called shear strain. Considering Figure 2. it can also be defined as the ratio of displacement x of corner b to the transverse dimension l. Thus
  
  or,
  Shear strain = tanθ
  In practice since x is much smaller than l so, tanθ ≅ θ and the strain is simply the angle θ(measured in radians). Thus, shear strain is pure number without units as it is ratio of two lengths.
  

4. Hook's Law

• Hook's law is the fundamental law of elasticity and is stated as " for small deformations stress is proportional to strain".
  Thus,
  stress ∝ strain
  or,
  $\frac{stress}{strain}=constant$
  This constant is known as modulus of elasticity of a given material, which depends upon the nature of the material of the body and the manner in which body is deformed.
  
• Hook's law is not valid for plastic materials.
  
• Units and dimension of the modulus of elasticity are same as those of stress.