Saturday, 15 April 2017

STRAIN ENERGY, RESILIENCE, PROOF RESILIENCE AND MODULUS OF RESILIENCE

STRAIN ENERGY, RESILIENCE, PROOF RESILIENCE AND MODULUS OF RESILIENCE


We were discussing meaning and importance of shear force and bending moment and basics of shear force and bending moment diagram and also some basic concepts of strength of materials in our recent posts. 
Today we will start here new topic i.e. Strain energy and impact loading in strength of materials with the help of this post. Let us first deal with strain energy here.
 
First we will understand here the basic concept of strain energy and its various engineering terms such as Resilience, Proof resilience and Modulus of resilience with the help of this post. Further we will discuss strain energy stored in a body when load will be applied gradually.

Strain energy

When a body will be loaded then there will be deformation in the body and due to this deformation, energy will be stored in the body and that energy will be termed as strain energy.

Let us see the basic definition of the strain energy

Strain energy is basically defined as the internal energy stored in the body when body will be subjected with a load within its elastic limit. 

We must have to be ensuring that load applied over the body must be within its elastic limit i.e. after removal of load; body must secure its original dimensions.

When a body will be loaded within its elastic limit, the work done by the load in deforming the body will be equal to the strain energy stored in the body.

Unit of strain energy
As we have studied above that strain energy stored in the body will be equal to the work done by the load in deforming the body and therefore unit of strain energy will be equal to the unit of work energy.

Unit of strain energy = Unit of work energy
Unit of strain energy = Unit of force x Unit of displacement
Unit of strain energy = N-m

 
As we have seen above that strain energy stored in the body will be equal to the work done by the load in deforming the body and therefore we can say that strain energy will be directionally proportional to the applied load within elastic limit of body.

Applied load might be gradually applied load, sudden applied load or impact load. We will see expression for strain energy stored in the body when body will be loaded with following three cases.
  1. Strain energy stored in the body when body will be loaded with gradually applied load
  2. Strain energy stored in the body when body will be loaded with sudden applied load
  3. Strain energy stored in the body when body will be loaded with impact load
Before going ahead for determining the strain energy stored in the body for above three situations, we must have to recall here the following technical terms in respect of strain energy.

Resilience

Resilience is basically defined as the total strain energy stored in the body.

Proof resilience

Proof resilience is basically defined as the maximum strain energy stored in the body. As we know that strain energy stored in the body will be maximum when body will be loaded up to its elastic limit, therefore we can also express the term proof resilience as the strain energy stored in the body when body will be loaded up to its elastic limit.

 

Modulus of resilience

Modulus of resilience is a property of the material which is defined as the proof resilience per unit volume of the body and we can express as

Modulus of resilience = Proof resilience/Volume of the body

Reference:

Strength of material, By R. K. Bansal
Image Courtesy: Google

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