How to Calculate and Solve for Flexural Strength for Rectangular Cross-section in Defects | Ceramics
Last Updated on March 31, 2024
The image above represents flexural strength for rectangular cross-section in defects in ceramics. To calculate flexural strength for rectangular cross-section in defect, four essential parameters are needed and these parameters are Load at fracture (Ff), Length of the cross-section (b), Width of the cross-section (d) and Distance between support points (L).
The formula for calculating flexural strength for rectangular cross-section in defects:
σfs = 3FfL / 2bd²
Where:
σfs = Flexural Strength
Ff = Load at Fracture
L = Distance between Support Points
b = Length of Cross-section
d = Width of Cross-section
Let’s solve an example;
Find the flexural strength when the load at fracture is 10, the length of cross-section is 7, width of cross-section is 9 and the distance between support points is 21.
This implies that;
Ff = Load at Fracture = 10
L = Distance between Support Points = 21
b = Length of Cross-section = 7
d = Width of Cross-section = 9
σfs = 3FfL / 2bd²
σfr = 3(10)(21) / 2(7)(9)²
Then, σfr = (630) / 2(7)(81)
σfr = (630) / (1134)
σfr = 0.55
Therefore, the flexural strength for rectangular cross-section in defect is 0.55 Pa.
Read more: How to Calculate and Solve for Flexural Strength for Circular Cross-section in Defects | Ceramics
Calculating the Distance Between Support Points when the Flexural Strength for Rectangular Cross-Section in Defects, Load at Fracture, length of the cross-section and width of cross-section are Given.
L = σfs x 2bd2 / 3Ff
Where;
L = Distance between Support Points
σfs = Flexural Strength
Ff = Load at Fracture
b = Length of Cross-section
d = Width of Cross-section
Let’s solve an example;
Find the distance between support points when the flexural strength is 20, the load at fracture is 12, the length of cross-section is 7 and the width of cross-section is 9.
This implies that;
σfs = Flexural Strength = 20
Ff = Load at Fracture = 12
b = Length of Cross-section = 7
d = Width of Cross-section = 9
L = σfs x 2bd2 / 3Ff
L = 20 x 2 x 7 x 92 / 3 x 12
That is, L = 280 x 81 / 36
L = 22680 / 36
L = 630
Therefore, the distance between support points is 630.
Read more: How to Calculate and Solve for Flexural Strength with Relation to Volume Fraction | Ceramics
Calculating the Load at Fracture when the Flexural Strength for Rectangular Cross-Section in Defects, Distance Between Support Points, Length of Cross-section and Width of Cross-section are Given
Ff = σfs x 2bd2 / 3L
Where;
Ff = Load at Fracture
σfs = Flexural Strength
L = Distance between Support Points
b = Length of Cross-section
d = Width of Cross-section
Let’s solve an example;
Find the load at fracture when the flexural strength is 40, the distance between support points is 22, the length of cross-section is 15 and the width of cross-section is 12.
This implies that;
σfs = Flexural Strength = 40
L = Distance between Support Points = 22
b = Length of Cross-section = 15
d = Width of Cross-section = 12
Ff = σfs x 2bd2 / 3L
Ff = 40 x 2 x 15 x 122 / 3 x 22
That is, Ff = 1200 x 144 / 66
Ff = 172800 / 66
Ff = 2618.1
Therefore, the load at fracture is 2618.1.
Calculating the Length of Cross-Section when the Flexural Strength for Rectangular Cross-Section in Defects, Distance Between Support Points, Load at Fracture and Width of Cross-section are Given
b = 3Ff / σfs x 1 / 2d2
Where;
b = Length of Cross-section
σfs = Flexural Strength
Ff = Load at Fracture
L = Distance between Support Points
d = Width of Cross-section
Let’s solve an example;
Find the lenght of cross-section when the flexural strength is 24, the load at fracture is 10, the distance between support points is 8 and the width of cross-section is 3.
This implies that;
σfs = Flexural Strength = 24
Ff = Load at Fracture = 10
L = Distance between Support Points = 8
d = Width of Cross-section = 3
b = 3Ff / σfs x 1 / 2d2
Then, b = 3 x 10 / 24 x 1 / 2 x 32
b = 30 / 24 x 1 / 2 x 9
b = 1.25 x 1 / 18
So, b = 1.25 x 0.05
b = 0.0625
Therefore, the length of cross-section is 0.0625.
Read more: How to Calculate and Solve for Frenkel Defect | Ceramics
Calculating the Width of Cross-Section when the Flexural Strength for Rectangular Cross-Section in Defects, Distance Between Support Points, Load at Fracture and Length of Cross-Section are Given
d = √(3Ff / σfs x 1 / 2b)
Where;
d = Width of Cross-section
σfs = Flexural Strength
Ff = Load at Fracture
L = Distance between Support Points
b = Length of Cross-section
Let’s solve an example;
Find the width of cross-section when the flexural strength is 14, load at fracture is 6, distance between support points is 4 and length of cross-section is 2.
This implies that;
σfs = Flexural Strength = 14
Ff = Load at Fracture = 6
L = Distance between Support Points = 4
b = Length of Cross-section = 2
d = √(3Ff / σfs x 1 / 2b)
That is,d = √(3 x 6 / 14 x 1 / 2 x 2)
d = √(18 / 14 x 1 / 4)
d = √(1.28 x 0.25)
So, d = √(0.32)
d = 0.56
Therefore, the width of cross-section is 0.56.
How to Calculate Flexural Strength for Rectangular Cross-section in Defects in Ceramics With Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the flexural strength for rectangular cross-section in defects.
To get the answer and workings of the flexural strength for rectangular cross-section in defects 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 Materials & Metallurgical under Engineering.
Now, Click on Ceramics under Material & Metallurgical
Now, Click on Flexural Strength for Rectangular Cross-Section in Defects under Ceramics
The screenshot below displays the page or activity to enter your values, to get the answer for the flexural strength for rectangular cross-section in defects according to the respective parameters which are the Load at fracture (Ff), Length of the cross-section (b), Width of the cross-section (d) and Distance between support points (L).
Now, enter the values appropriately and accordingly for the parameters as required by the Load at fracture (Ff) is 10, Length of the cross-section (b) is 7, Width of the cross-section (d) is 9 and Distance between support points (L) is 21.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the flexural strength for rectangular cross-section in defects and presents the formula, workings and steps too.