Young’s Modulus Formula

Young’s Modulus or Elastic Modulus or Tensile Modulus, is the measurement of mechanical properties of linear elastic solids like rods, wires, etc. There are some other numbers exists which provide us a measure of elastic properties of a material. Some of these are Bulk modulus and Shear modulus etc. But the value of Young’s Modulus is mostly used. This is due to the reason that it gives information about the tensile elasticity of a material. In this article, we will discuss its concept and Young’s Modulus Formula with examples. Let us learn the interesting concept!

Young’s Modulus Formula

What is Young’s Modulus?

Young’s modulus, used as a numerical constant. It was named for the 18th-century English physician and physicist Thomas Young. It describes the elastic properties of a solid undergoing tension or compression in only one direction. For example as in the case of a metal rod that after being stretched or compressed lengthwise returns to its original length.

It is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression. Often we refer to it as the modulus of elasticity. We compute it by dividing It is computed as the longitudinal stress divided by the strain. Stress and strain both may be described in the case of a metal bar under tension.

Young’s modulus is defined as the mechanical property of a material to withstand the compression or the elongation with respect to its original length. It is denoted as E or Y.

It is also a fact that many materials are not linear and elastic beyond a small amount of deformation. Therefore the constant Young’s modulus applies only to linear elastic substances. Its values in the factor of 10^9 Nm^{-2} of different material are:

• Steel – 200
• Glass – 65
• Wood – 13
• Plastic – 3

Young’s Modulus Factors

We can claim that Steel is a lot more rigid in nature than wood or plastic, as in its tendency to experience deformation under applied load is less. Also, Young’s modulus is used to find how much a material will deform under a certain load.

Also, we must remember that the lower the value of Young’s Modulus in materials, the more is the deformation experienced by such a body. As we know that one part of the clay sample deforms more than the other whereas a steel bar will experience an equal deformation throughout.

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The formula for Young’s Modulus

Formula is as follows according to the definition:

E = \( \frac{\sigma} {\varepsilon} \)

We can also write Young’s Modulus Formula by using other quantities, as below:

E = \( \frac{FL_0}{A \Delta L} \)

Notations Used in the Young’s Modulus Formula

Where,

E	Young’s modulus in Pa
\(\sigma \)	The uniaxial stress in Pa
\(\varepsilon\)	The strain or proportional deformation
F	The force exerted by the object under tension
A	It is the actual cross-sectional area
\(\Delta L\)	It is the change in the length
\(L_0\)	It is the actual length

Solved Examples

Q.1: Find out Young’s modulus value of a material whose elastic stress and strains are 4 N/m² and 0.30 respectively?

Solution:

Stress,

\(\sigma = 4 N m^{-2} \)

Strain,

\(\varepsilon = 0.30 \)

So, Young’s modulus is:

E = \( \frac{\sigma }{\varepsilon } \)

Substituting values, we get

E = \( \frac{4}{0.30} \)

E = 13.33 Nm{-2}

Thus young’s modulus is 13.33 Nm{-2}.