How to Calculate and Solve for Thermal Stress | Thermal Properties

The thermal stress is illustrated by the image below. To calculate thermal stress, three essential parameters are needed and these parameters are Elastic Modulus (E), Linear Coefficient of Thermal Expansion (αL) and Change in Temperature (ΔT).

The formula for calculating thermal stress:

σ = EαLΔT

Where:

σ = Thermal Stress
E = Elastic Modulus
αL = Linear Coefficient of Thermal Expansion
ΔT = Change in Temperature

Given an example;
Find the thermal stress when the elastic modulus is 28, the linear coefficient of thermal expansion is 8 and the change in temperature is 2.

This implies that;

E = Elastic Modulus = 28
αL = Linear Coefficient of Thermal Expansion = 8
ΔT = Change in Temperature = 2

σ = EαLΔT
That is, σ = (28)(8)(2)
σ = 448

Therefore, the thermal stress is 448 Pa.

Calculating the Elastic Modulus when the Linear Coefficient of Thermal Expansion, the Thermal Stress and the Change in Temperature are Given

E = σ / (αL)ΔT

Where:

E = Elastic Modulus
σ = Thermal Stress
αL = Linear Coefficient of Thermal Expansion
ΔT = Change in Temperature

Let’s solve an example;
Find the elastic modulus when the thermal stress is 40, the linear coefficient of thermal expansion is 8 and the change in temperature is 2.

This implies that;

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σ = Thermal Stress = 40
αL = Linear Coefficient of Thermal Expansion = 8
ΔT = Change in Temperature = 2

E = σ / (αL)ΔT
Then, E = 40 / (8)2
E = 40 / 16
E = 2.5

Therefore, the elastic modulus is 2.5.

Read more: How to Calculate and Solve for Thermal Shock Resistance | Thermal Properties

Calculating the Linear Coefficient of Thermal Expansion when the Elastic Modulus, the Thermal Stress and the Change in Temperature are Given

αL = σ / E(ΔT)

Where:

αL = Linear Coefficient of Thermal Expansion
σ = Thermal Stress
E = Elastic Modulus
ΔT = Change in Temperature

Let’s solve an example;
Find the linear coefficient of thermal expansion when the thermal stress is 12, the elastic modulus is 4 and the change in temperature is 2.

This implies that;

σ = Thermal Stress = 12
E = Elastic Modulus = 4
ΔT = Change in Temperature = 2

αL = σ / E(ΔT)
Then, αL = 12 / 4(2)
αL = 12 / 8
αL = 1.5

Therefore, the linear coefficient of thermal expansion is 1.5.

Read more: How to Calculate and Solve for Linear Expansivity | Thermal Properties

Calculating the Change in Temperature when the Thermal Stress, the Elastic Modulus and the Linear Coefficient of Thermal Expansion are Given

ΔT = σ / E(αL)

Where:

ΔT = Change in Temperature
σ = Thermal Stress
E = Elastic Modulus
αL = Linear Coefficient of Thermal Expansion

Let’s solve an example;
Find the change in temperature when the thermal stress is 32, the elastic modulus is 10 and the linear coefficient of thermal expansion is 2.

This implies that;

σ = Thermal Stress = 32
E = Elastic Modulus = 10
αL = Linear Coefficient of Thermal Expansion = 2

ΔT = σ / E(αL)
So, ΔT = 32 / 10(2)
ΔT = 32 / 20
ΔT = 1.6

Therefore, the change in temperature is 1.6.

How to Calculate Thermal Stress With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the thermal stress.

To get the answer and workings of the thermal stress 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 Thermal Properities under Materials and Metallurgical

Now, Click on Thermal Stress under Thermal Properities

The screenshot below displays the page or activity to enter your values, to get the answer for the thermal stress according to the respective parameter which is the Elastic Modulus (E), Linear Coefficient of Thermal Expansion (αL) and Change in Temperature (ΔT).

How to Calculate and Solve for Thermal Stress | Thermal Properties

Now, enter the values appropriately and accordingly for the parameters as required by the Elastic Modulus (E) is 28, Linear Coefficient of Thermal Expansion (αL) is 8 and Change in Temperature (ΔT) is 2.

How to Calculate and Solve for Thermal Stress | Thermal Properties

Finally, Click on Calculate

How to Calculate and Solve for Thermal Stress | Thermal Properties

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the thermal stress and presents the formula, workings and steps too.

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