How to Calculate and Solve for Modulus of Elasticity | Mechanical Properties

The image above represents modulus of elasticity. To calculate 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)
So, 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 are 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;

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E = Modulus of Elasticity = 40
V = Poisson’s Ratio = 3

G = E / 2(1 + V)
G = 40 / 2(1 + 3)
That is, 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 are 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
Then, V = (30 / 6) – 1
V = 5 – 1
V = 4

Therefore, the poisson’s ratio is 4.

How to Calculate Modulus of Elasticity With Nickzom Calculator

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).

How to Calculate and Solve for Modulus of Elasticity | Mechanical Properties

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.

How to Calculate and Solve for Modulus of Elasticity | Mechanical Properties

Finally, Click on Calculate

How to Calculate and Solve for Modulus of Elasticity | Mechanical Properties

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.

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