How to Calculate and Solve for Modulus of Elasticity | Mechanical Properties
Last Updated on January 5, 2023
The image above represents modulus of elasticity.
To compute for modulus of elasticity, two essential parameters are needed and these parameters are Shear Modulus (G) and Poisson’s Ratio (V).
The formula for calculating modulus of elasticity:
E = 2G(1 + V)
Where:
E = Modulus of Elasticity
G = Shear Modulus
V = Poisson’s Ratio
Given an example;
Find the modulus of elasticity when the shear modulus is 28 and the poisson’s ratio is 4.
This implies that;
G = Shear Modulus = 28
V = Poisson’s Ratio = 4
E = 2G(1 + V)
E = 2(28)(1 + 4)
E = 2(28)(5)
E = (56)(5)
E = 280
Therefore, the modulus of elasticity is 280 Pa.
Calculating the Shear Modulus when the Modulus of Elasticity and the Poisson’s Ratio is Given.
G = E / 2(1 + V)
Where:
G = Shear Modulus
E = Modulus of Elasticity
V = Poisson’s Ratio
Let’s solve an example;
Find the shear modulus when the modulus of elasticity is 40 and the poisson’s ratio is 3.
This implies that;
E = Modulus of Elasticity = 40
V = Poisson’s Ratio = 3
G = E / 2(1 + V)
G = 40 / 2(1 + 3)
G = 40 / 2(4)
G = 40 / 8
G = 5
Therefore, the shear modulus is 5.
Calculating the Poisson’s Ratio when the Modulus of Elasticity and the Shear Modulus is Given.
V = (E / 2G) – 1
Where:
V = Poisson’s Ratio
E = Modulus of Elasticity
G = Shear Modulus
Let’s solve an example;
Find the poisson’s ratio when the modulus of elasticity is 30 and the shear modulus is 3.
This implies that;
E = Modulus of Elasticity = 30
G = Shear Modulus = 3
V = (E / 2G) – 1
V = (30 / 2(3)) – 1
V = (30 / 6) – 1
V = 5 – 1
V = 4
Therefore, the poisson’s ratio is 4.
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the modulus of elasticity.
To get the answer and workings of the modulus of elasticity 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 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 Materials and Metallurgical under Engineering.
Now, Click on Mechanical Properties under Materials and Metallurgical
Now, Click on Modulus of Elasticity under Mechanical Properties
The screenshot below displays the page or activity to enter your values, to get the answer for the modulus of elasticity according to the respective parameter which is the Shear Modulus (G) and Poisson’s Ratio (V).
Now, enter the values appropriately and accordingly for the parameters as required by the Shear Modulus (G) is 28 and Poisson’s Ratio (V) is 4.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the modulus of elasticity and presents the formula, workings and steps too.