How to Calculate and Solve for Young’s Modulus | Rock Mechanics

September 25, 2019March 8, 2024 Loveth Idoko

Last Updated on March 8, 2024

The image above represents young’s modulus. To calculate young’s modulus, two essential parameters are needed and these parameters are axial stress (σ_a) and axial strain (ε_a).

The formula for calculating the young’s modulus:

E = ^σ_a / _εa

Where:

E = Young’s Modulus
σ_a = Axial Stress
ε_a = Axial Strain

Let’s solve an example;
Given that the axial stress is 65 and the axial strain is 45, calculate for the young’s modulus.

This implies that;

σ_a = Axial Stress = 65
ε_a = Axial Strain = 45

Then, E = ^σ_a / _εa
E = ⁶⁵ / ₄₅
E = 1.44

Therefore, the young’s modulus is 1.44.

Calculating the Axial Stress when the Young’s Modulus and the Axial Strain are Given

σ_a = E x ε_a

Where;

σ_a = Axial Stress
E = Young’s Modulus
ε_a = Axial Strain

Let’s solve an example;
Given that the young’s modulus is 25 and the axial strain is 10, calculate the axial stress.

This implies that;

E = Young’s Modulus = 25
ε_a = Axial Strain = 10

So, σ_a = E x ε_a
σ_a = 25 x 10
σ_a = 250

Therefore, the axial stress is 250.

Calculating the Axial Strain when the Young’s Modulus and the Axial Stress are Given

ε_a = ^σ_a / _E

Where;

ε_a = Axial Strain
E = Young’s Modulus
σ_a = Axial Stress

Let’s solve an example;
Given that the young’s modulus is 7 and the axial stress is 35, calculate the axial strain.

This implies that;

E = Young’s Modulus = 7
σ_a = Axial Stress = 35

Then, ε_a = ^σ_a / _E
ε_a = ³⁵ / ₇
ε_a = 5

Therefore, the axial strain is 5.

How to Calculate and Solve for Young’s Modulus Using the Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the young’s modulus.

To get the answer and workings of young’s modulus using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Geology under Add-on.

Now, Click on Rock Mechanics under Geology

Now, Click on Young’s Modulus under Rock Mechanics

The screenshot below displays the page or activity to enter your values, to get the answer for the young’s modulus according to the respective parameters which are the axial stress (σ_a) and axial strain (ε_a).

Now, enter the values appropriately and accordingly for the parameters as required by the axial stress (σ_a) is 65 and axial strain (ε_a) is 45.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the Young’s modulus and presents the formula, workings and steps too.