How to Calculate and Solve for Flexural Strength for Rectangular Cross-section in Defects | Ceramics

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 (F_f), 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:

σ_fs = ^3F_fL / _2bd²

Where:

σ_fs = Flexural Strength
F_f = 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;

F_f = Load at Fracture = 10
L = Distance between Support Points = 21
b = Length of Cross-section = 7
d = Width of Cross-section = 9

σ_fs = ^3F_fL / _2bd²
σ_fr = ^3(10)(21) / _2(7)(9)²
Then, σ_fr = ⁽⁶³⁰⁾ / _2(7)(81)
σ_fr = ⁽⁶³⁰⁾ / ₍₁₁₃₄₎
σ_fr = 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 = ^{σ_fs x 2bd2} / _3Ff

Where;

L = Distance between Support Points
σ_fs = Flexural Strength
F_f = 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;

σ_fs = Flexural Strength = 20
F_f = Load at Fracture = 12
b = Length of Cross-section = 7
d = Width of Cross-section = 9

L = ^{σ_fs 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

F_f = ^{σ_fs x 2bd2} / _3L

Where;

F_f = Load at Fracture
σ_fs = 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;

σ_fs = Flexural Strength = 40
L = Distance between Support Points = 22
b = Length of Cross-section = 15
d = Width of Cross-section = 12

F_f = ^{σ_fs x 2bd2} / _3L
F_f = ^{40 x 2 x 15 x 122} / _{3 x 22}
That is, F_f = ^{1200 x 144} / ₆₆
F_f = ¹⁷²⁸⁰⁰ / ₆₆
F_f = 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 = ^3F_f / _σfs x ¹ / _2d²

Where;

b = Length of Cross-section
σ_fs = Flexural Strength
F_f = 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;

σ_fs = Flexural Strength = 24
F_f = Load at Fracture = 10
L = Distance between Support Points = 8
d = Width of Cross-section = 3

b = ^3F_f / _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 = √(^3F_f / _σfs x ¹ / _2b)

Where;

d = Width of Cross-section
σ_fs = Flexural Strength
F_f = 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;

σ_fs = Flexural Strength = 14
F_f = Load at Fracture = 6
L = Distance between Support Points = 4
b = Length of Cross-section = 2

d = √(^3F_f / _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 (F_f), 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 (F_f) 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.