Section Modulus of Hollow Circular Shape Calculator

✖Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft [d_o]			+10% -10%
✖The Inner Diameter of Shaft is the length of the longest chord inside the hollow shaft.ⓘ Inner Diameter of Shaft [d_i]			+10% -10%

✖The Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.ⓘ Section Modulus of Hollow Circular Shape [Z]

⎘ Copy

👎

Formula

✖

Section Modulus of Hollow Circular Shape

Formula

`"Z" = (pi*("d"_{"o"}^4-"d"_{"i"}^4))/(32*"d"_{"o"})`

Example

`"0.022608m³"=(pi*(("700mm")^4-("530mm")^4))/(32*"700mm")`

Calculator

LaTeX

Reset

👍

Download Bending Stress Formulas PDF PDF Image

Section Modulus of Hollow Circular Shape Solution

STEP 0: Pre-Calculation Summary

Formula Used

Section Modulus = (pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4))/(32*Outer Diameter of Shaft)
Z = (pi*(d_o^4-d_i^4))/(32*d_o)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Section Modulus - (Measured in Cubic Meter) - The Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.
Outer Diameter of Shaft - (Measured in Meter) - Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.
Inner Diameter of Shaft - (Measured in Meter) - The Inner Diameter of Shaft is the length of the longest chord inside the hollow shaft.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Shaft: 700 Millimeter --> 0.7 Meter (Check conversion here)
Inner Diameter of Shaft: 530 Millimeter --> 0.53 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z = (pi*(d_o^4-d_i^4))/(32*d_o) --> (pi*(0.7^4-0.53^4))/(32*0.7)

Evaluating ... ...

Z = 0.0226075725311612

STEP 3: Convert Result to Output's Unit

0.0226075725311612 Cubic Meter --> No Conversion Required

FINAL ANSWER

0.0226075725311612 ≈ 0.022608 Cubic Meter <-- Section Modulus

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Strength of Materials » Bending Stress » Section Modulus for Various Shapes » Section Modulus of Hollow Circular Shape

Credits

Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Calculator and 1300+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< 15 Section Modulus for Various Shapes Calculators

Inner Depth of Hollow Rectangular Shape

Go Inner Depth of Hollow Rectangular Section = (((6*Section Modulus*Outer Depth of Hollow Rectangular Section)+(Outer Breadth of Hollow Rectangular Section*Outer Depth of Hollow Rectangular Section^3))/(Inner Breadth of Hollow Rectangular Section))^(1/3)

Outer Breadth of Hollow Rectangular Shape

Go Outer Breadth of Hollow Rectangular Section = ((6*Section Modulus*Outer Depth of Hollow Rectangular Section)+(Inner Breadth of Hollow Rectangular Section*Inner Depth of Hollow Rectangular Section^3))/(Outer Depth of Hollow Rectangular Section^(3))

Section Modulus of Hollow Rectangular Shape

Go Section Modulus = ((Outer Breadth of Hollow Rectangular Section*Outer Depth of Hollow Rectangular Section^3)-(Inner Breadth of Hollow Rectangular Section*Inner Depth of Hollow Rectangular Section^3))/(6*Outer Depth of Hollow Rectangular Section)

Inner Breadth of Hollow Rectangular Shape

Go Inner Breadth of Hollow Rectangular Section = ((6*Section Modulus*Outer Depth of Hollow Rectangular Section)+(Outer Breadth of Hollow Rectangular Section*Outer Depth of Hollow Rectangular Section^3))/(Inner Depth of Hollow Rectangular Section^3)

Depth of Beam for Uniform Strength in Bending Stress

Go Depth of Beam = sqrt((3*Load on Beam*Length of Beam)/(Allowable Bending Stress*2*Width of Beam))

Inner Diameter of Hollow Circular Shape in Bending Stress

Go Inner Diameter of Shaft = ((Outer Diameter of Shaft^4)-(32*Section Modulus*Outer Diameter of Shaft/pi))^(1/4)

Section Modulus of Hollow Circular Shape

Go Section Modulus = (pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4))/(32*Outer Diameter of Shaft)

Load on Beam for Uniform Strength in Bending Stress

Go Load on Beam = (Allowable Bending Stress*(2*Width of Beam*Depth of Beam^2))/(3*Length of Beam)

Beam Width for Uniform Strength in Bending Stress

Go Width of Beam = 3*Load on Beam*Length of Beam/(2*Allowable Bending Stress*Depth of Beam^2)

Allowable Bending Stress

Go Allowable Bending Stress = 3*Load on Beam*Length of Beam/(2*Width of Beam*Depth of Beam^2)

Depth of Rectangular Shape given Section Modulus

Go Depth of Cross Section = sqrt((6*Section Modulus)/Width of Cross Section)

Breadth of Rectangular Shape given Section Modulus

Go Width of Cross Section = (6*Section Modulus)/Depth of Cross Section^2

Section Modulus of Rectangular Shape

Go Section Modulus = (Width of Cross Section*Depth of Cross Section^2)/6

Diameter of Circular Shape given Section Modulus

Go Diameter of Circular Shaft = ((32*Section Modulus)/pi)^(1/3)

Section Modulus of Circular Shape

Go Section Modulus = (pi*Diameter of Circular Shaft^3)/32

Section Modulus of Hollow Circular Shape Formula

Section Modulus = (pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4))/(32*Outer Diameter of Shaft)
Z = (pi*(d_o^4-d_i^4))/(32*d_o)

What is Section Modulus?

The Section Modulus is a geometric property for a given cross-section used in the design of beams or flexural members.

How to Calculate Section Modulus of Hollow Circular Shape?

Section Modulus of Hollow Circular Shape calculator uses Section Modulus = (pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4))/(32*Outer Diameter of Shaft) to calculate the Section Modulus, The Section Modulus of Hollow Circular Shape formula is defined as section modulus when the cross-sectional properties are known. Section Modulus is denoted by Z symbol.

How to calculate Section Modulus of Hollow Circular Shape using this online calculator? To use this online calculator for Section Modulus of Hollow Circular Shape, enter Outer Diameter of Shaft (d_o) & Inner Diameter of Shaft (d_i) and hit the calculate button. Here is how the Section Modulus of Hollow Circular Shape calculation can be explained with given input values -> 0.022608 = (pi*(0.7^4-0.53^4))/(32*0.7).

FAQ

What is Section Modulus of Hollow Circular Shape?

The Section Modulus of Hollow Circular Shape formula is defined as section modulus when the cross-sectional properties are known and is represented as Z = (pi*(d_o^4-d_i^4))/(32*d_o) or Section Modulus = (pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4))/(32*Outer Diameter of Shaft). Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft & The Inner Diameter of Shaft is the length of the longest chord inside the hollow shaft.

How to calculate Section Modulus of Hollow Circular Shape?

The Section Modulus of Hollow Circular Shape formula is defined as section modulus when the cross-sectional properties are known is calculated using Section Modulus = (pi*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4))/(32*Outer Diameter of Shaft). To calculate Section Modulus of Hollow Circular Shape, you need Outer Diameter of Shaft (d_o) & Inner Diameter of Shaft (d_i). With our tool, you need to enter the respective value for Outer Diameter of Shaft & Inner Diameter of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Section Modulus?

In this formula, Section Modulus uses Outer Diameter of Shaft & Inner Diameter of Shaft. We can use 3 other way(s) to calculate the same, which is/are as follows -

Section Modulus = (Width of Cross Section*Depth of Cross Section^2)/6
Section Modulus = ((Outer Breadth of Hollow Rectangular Section*Outer Depth of Hollow Rectangular Section^3)-(Inner Breadth of Hollow Rectangular Section*Inner Depth of Hollow Rectangular Section^3))/(6*Outer Depth of Hollow Rectangular Section)
Section Modulus = (pi*Diameter of Circular Shaft^3)/32

Home

FREE PDFs

🔍 Search