Modulus of Elasticity – Definition, Young’s Modulus, Types

What is Modulus of Elasticity?

Within proportionality limit modulus of elasticity, the ratio is stress to strain. proportional limit. It measures the rigidity or stiffness of a material. If the material is greater in the modulus, the material will be stiffer, or smaller than the elastic strain that results from the application of a given stress.

The modulus of elasticity is the important design parameter used for computing elastic deflections. Elastic modulus is called modulus of elasticity. The modulus of elasticity is also known as Young’s modulus.

Types of Modulus of Elasticity

Depending upon the type of force applied to the body and change in deformation. Modulus of elasticity is divided into the following types.

• Young’s Modulus
• Shear Modulus
• Bulk Modulus of Elasticity

Young’s Modulus

Elastic modulus is explained only for one axis of the substance. Young’s modulus of a material is an important attribute to understanding how the material will behave when applied to a force. It is represented by E.

The Dimensional formula of E is [M¹L^-1T^-2].

Shear Modulus

The shear modulus of the material is the ratio of shear stress to shear strain in a body. When the shear force is increased, the value of the shear modulus also increases. It is represented by G or C.

The Dimensional formula of G is [M¹L^-1T^-2].

Bulk Modulus of Elasticity

Bulk modulus is defined when uniform pressure is applied from all directions to the change in volume. The bulk modulus is the measure of the ability of a substance which changes in volume when under compression on all sides. It is represented by K.

Bulk modulus of elasticity,

K= – P/ (ΔV/V)

Dimensions of K are [M¹L^-1T^-2].

Relationship Between Modulus of Elasticity

The different types of Modulus of elasticity can be related to each other with the following equations:

Modulus of Elasticity Formula

E = 3K(1-2μ)

E = 2G(1+μ)

E = 9KG/(G+3K)

Where μ = Poisson’s ratio

Analysis of Modulus of Elasticity

As per Hooke’s law, The modulus of elasticity is the slope of the stress-strain curve up to the linear proportionality of stress to strain. In the Stress-Strain Curve of steel, the area under the curve up to the yield point represents the modulus of resilience and from the yield point to the fracture of material represents the modulus of toughness.

E = stress/strain = (P/A)/(ΔL/L)

E = modulus of elasticity or young’s modulus within proportionality limit.

Unit of Young’s Modulus

The elastic modulus is a material property that elaborates its stiffness and is, therefore, one of the most important properties of solid materials. It is the ratio of stress to strain when deformation is elastic in any direction.

• SI unit: Pascal (or) N/mm²
• CGS unit: Dyne/cm²
• MKS unit: Kg/cm²

Different materials with their value of Young’s modulus as per the elastic in nature. Higher the value of Young’s modulus refers to high elasticity in nature when a load is applied to that material.

Material	Young’s Modulus (GPa)
Diamond	1000
Mild Steel	200
Copper	120
Aluminum	69
Concrete	30
Glass	65
Bone	18
Plastic	3
Rubber	0.02
Wood	15

Note: Usually 2 materials (concrete and steel) we use in the design of RCC structure. The concrete young’s modulus depends on the grade of concrete.

Modulus of Elasticity of Concrete

In the stress-strain curve of concrete, The tangent modulus is the slope of the stress-strain curve at any specified stress or strain. Below the proportional limit (the limit of linear elastic regime), the tangent modulus is equivalent to Young’s modulus.

Young’s modulus of concrete, E_c= 5000√f_ck for a short-term period

E_c= 5000√f_ck/1+Θ for long-term period

Where

• Θ= creep coefficient depends on the age of concrete
• f_ck= characteristic strength of concrete after 28 days.

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