We were
discussing the concept of stress and strain and also we have discussed the
different types of stress and also different types of strain in our previous
posts. We have also seen the concept of Hook’s Law in our recent post.

Now we are
going further to start our discussion to understand the “Types of modulus of
elasticity”, in subject of strength of material, with the help of this post.

###
**Let us see here the various types of
modulus of elasticity**

On the basis of types of applied stress
and resulting strain, we will have three types of modulus of elasticity as
mentioned here

1. Young’s modulus of elasticity

2. Modulus of rigidity

3. Bulk modulus of elasticity

Let us first recall the concept of
modulus of elasticity and after that we will see each type of modulus of
elasticity in detail.

As we have already discussed that within
elastic limit, stress applied over an elastic material will be directionally
proportional to the strain produced due to external loading. Mathematically we
can say as displayed here.

Let us remove the proportionality sign
and therefore we will have to use one constant value in order to remove the
proportionality sign.

Where E is basically Modulus of
elasticity and we can define modulus of elasticity as the ratio of stress to
strain. Modulus of elasticity will have same unit as that for stress because
strain is unit less parameter and therefore Modulus of elasticity unit in S.I.
system will be N/m2.

###
**Young’s modulus of elasticity**

Young’s modulus of elasticity is
basically defined as the ratio of longitudinal stress to longitudinal strain.
Young’s modulus of elasticity will be indicated by Y or E.

Young’s modulus of elasticity is
basically defined as the property of material which will describe the stiffness
of the material and therefore Young’s modulus of elasticity is very important
property of a solid material.

Let we have one cylindrical solid bar of
length L and cross sectional area is A. Let tensile force F is applied as shown
in figure. Change in length of the bar will be Î”L due to external applied
tensile force F. Young's modulus of elasticity is calculated above in figure.

###
**Modulus of rigidity**

Modulus of rigidity is also termed as
shear modulus and we can define it as ratio of shear stress to shear strain.
Modulus of rigidity will be indicated by G.

Modulus of rigidity measures the
resistance to the shear deformation

Where,

G, Modulus of rigidity

E, Modulus of elasticity

V, Poisson’s ratio

###
**Bulk Modulus **

Bulk modulus of elasticity is usually
referred as the property of material (solid and fluid) in order to determine the
compressibility of material or we can say that bulk modulus of elasticity will
represent that how much material will be compressed under a certain amount of pressure.

Let we have a solid body with volume V and
it is subjected with same stress Ïƒ in three mutually perpendicular directions
as shown in figure, body will have uniform changes in three directions and
there will not be any distortion in the shape of the body.

Bulk modulus will be defined as the
ratio of normal stress to volumetric strain and it will be indicated by K. Reciprocal of Bulk modulus (K) will be
termed as compressibility of the material.

###
**Relationship between Young’s modulus
of elasticity (E), modulus of rigidity (G) and Bulk modulus (K)**

Do you
have any suggestions? Please write in comment box

### Reference:

Strength of material, By R. K. Bansal

Image Courtesy: Google

We will see another important topic i.e. types of
strain in the category of strength of material.

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