How to Calculate and Solve for Thermal Stress | Thermal Properties
Last Updated on July 26, 2022
The thermal stress is illustrated by the image below.
To compute for 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
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 is 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;
σ = Thermal Stress = 40
αL = Linear Coefficient of Thermal Expansion = 8
ΔT = Change in Temperature = 2
E = σ / (αL)ΔT
E = 40 / (8)2
E = 40 / 16
E = 2.5
Therefore, the elastic modulus is 2.5.
Calculating the Linear Coefficient of Thermal Expansion when the Elastic Modulus, the Thermal Stress and the Change in Temperature is 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)
αL = 12 / 4(2)
αL = 12 / 8
αL = 1.5
Therefore, the linear coefficient of thermal expansion is 1.5.
Calculating the Change in Temperature when the Thermal Stress, the Elastic Modulus and the Linear Coefficient of Thermal Expansion is 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)
ΔT = 32 / 10(2)
ΔT = 32 / 20
ΔT = 1.6
Therefore, the change in temperature is 1.6.
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).
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.
Finally, Click on Calculate
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.