Elastic Constant

  Welcome to “The Civil Engineer”.  About myself, I am a Civil Engineer with 9+ Years of Experience and I write articles about Civil Engineering on this website on a regular basis. In this article, I explained Elastic Constants.

Elasticity

    Objects are subject to change in dimension when a force is applied, up to a certain limit when the force is removed the object returns to its original shape. Hence the ability of the object to return to its original shape is known as the elastic property or elasticity of an object. It differs from object to object based on its material properties.

Elastic Limit 

    An elastic limit is nothing but the maximum load or forces up to which the object return to its original shape when the force is removed beyond the limit if the load is increased the object losses its elastic property and don't come back to its original shape, such limit is known as the Elastic limit of an Object.

Example

    Let me explain with you an example, 

Case 1 :

    Take a plastic Scale/Ruler now try to apply some little force with your hands on both ends of the scale the scale bends a little bit now stop applying the force the scale comes to its original position.

Case 2 :

    Take the same Scale now and apply the force as directed before, this time give force as max a can so that the scale brittle into two pieces.

What Happened :

Case 1 - In this case, the force that you applied is within the elastic limit of the Object(Scale). Hence after removing the applied form the scale returns to its original position without losing its elastic property(Elasticity).

Case 2 - In this case, the force applied is greater than the elastic limit of the object(Scale). Hence the scale lost its elastic property and brittle into two pieces.

Note:  The maximum load up to which the scale doesn't lose its elasticity is the elastic limit of the Scale.

Hooke's Law

About Robert Hooke

    Robert Hooke's an English scientist credited with Hooke's law. He did his work both in Physics and Biology. Apart from Hooke's law, his contributions were in the development of steam engines and also the discovery of micro-organisms and the coining of the term "Cell".

What Hooke's Law Says

    Within the Elastic Limit of an object, the stress is directly proportional to the strain produced in the object by the stress. This means, that the ratio of the stress to the corresponding strain is a constant and is known as the Elastic Modulus.

Types of Modulus

1. Young's Modulus
2. Shear Modulus

Young's Modulus

    The constant is known as the Modulus of Elasticity(E), when the stress is Tensile Stress or Compresstive stress then, the constant created from the ratio of the Stress and Strain is known as the Modulus of Elasticity of Young's Modulus. Mathematically Expressing

Young's Modulus or MOE (E) = Tensile Stress/ Tensile Strain or Compressive Stress/Compressive Strain = σ /ε

Shear Modulus or Modulus of Rigidity

    The constant is known as the Modulus of Rigidity(C or G or N), when the stress is Shear Stress then, the constant created from the ratio of the Shear Stress and Shear Strain is known as the Modulus of Rigidity or Shear Modulus. Mathematically Expressing

Shear Modulus or MOR (C or G or N) = Shear Stress / Shear Strain = τ/φ

Longitudinal Strain and Lateral Strain

Longitudinal Strain

    Let us take a Rectangular bar with dimensions Lenght(L), Breadth(B) and Depth(D), and now apply tensile force on both ends of the bar. There will be an increase in the length(L) of the bar, along the direction of the applied force which is known as the Longitudinal Strain.

Longitudinal Strain(φ) = Longitudinal Stress(σ)/Young's Modulus(E) = σ/E

Lateral Strain

    In the other two dimensions of the above case, there is also a decrease in the dimension of Breadth(B) and Depth(D), but this is not due to the tensile force that is applied but due to the compressive force that is created as a counter force due to the applied tensile force. This dimensional change in the other direction of the object instead of the force applied direction is known as the Lateral Strain.

Lateral Strain = - Poisson's Ratio x Longitudinal Strain = -μ / φ

Note: The Lateral strain and the Longitudinal strain were always in Opposite directions, hence the negative sign is given.

Poisson's Ratio

    The ratio of the Lateral strain to the Longitudinal Strain of an object, due to the applied stress within the elastic limit of the object is a constant which is known as the Poisson's ratio. It is denoted by the greek letter Mu (μ). Mathematically Expressing,

Poisson's Ratio (μ) = Lateral strain / Longitudinal Strain

    The Main use of Poisson's ratio is to find the lateral strain of an object for the given stress, hence,

Lateral Strain = - Poisson's Ratio x Longitudinal Strain = -μ / φ

Note: The Lateral strain and the Longitudinal strain were always in Opposite directions, hence the negative sign is given.