Section Modulus of Circular Shape Calculator

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

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Section Modulus of Circular Shape

Formula

`"Z" = (pi*"Φ"^3)/32`

Example

`"0.041417m³"=(pi*("750mm")^3)/32`

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Section Modulus of Circular Shape Solution

STEP 0: Pre-Calculation Summary

Formula Used

Section Modulus = (pi*Diameter of Circular Shaft^3)/32
Z = (pi*Φ^3)/32
This formula uses 1 Constants, 2 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.
Diameter of Circular Shaft - (Measured in Meter) - Diameter of circular shaft is denoted by d.

STEP 1: Convert Input(s) to Base Unit

Diameter of Circular Shaft: 750 Millimeter --> 0.75 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z = (pi*Φ^3)/32 --> (pi*0.75^3)/32

Evaluating ... ...

Z = 0.0414174812729123

STEP 3: Convert Result to Output's Unit

0.0414174812729123 Cubic Meter --> No Conversion Required

FINAL ANSWER

0.0414174812729123 ≈ 0.041417 Cubic Meter <-- Section Modulus

(Calculation completed in 00.004 seconds)

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

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 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 Circular Shape Formula

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

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 Circular Shape?

Section Modulus of Circular Shape calculator uses Section Modulus = (pi*Diameter of Circular Shaft^3)/32 to calculate the Section Modulus, The Section Modulus of 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 Circular Shape using this online calculator? To use this online calculator for Section Modulus of Circular Shape, enter Diameter of Circular Shaft (Φ) and hit the calculate button. Here is how the Section Modulus of Circular Shape calculation can be explained with given input values -> 0.041417 = (pi*0.75^3)/32.

FAQ

What is Section Modulus of Circular Shape?

The Section Modulus of Circular Shape formula is defined as section modulus when the cross-sectional properties are known and is represented as Z = (pi*Φ^3)/32 or Section Modulus = (pi*Diameter of Circular Shaft^3)/32. Diameter of circular shaft is denoted by d.

How to calculate Section Modulus of Circular Shape?

The Section Modulus of Circular Shape formula is defined as section modulus when the cross-sectional properties are known is calculated using Section Modulus = (pi*Diameter of Circular Shaft^3)/32. To calculate Section Modulus of Circular Shape, you need Diameter of Circular Shaft (Φ). With our tool, you need to enter the respective value for Diameter of Circular 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 Diameter of Circular 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*(Outer Diameter of Shaft^4-Inner Diameter of Shaft^4))/(32*Outer Diameter of Shaft)

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