Section Modulus of Rectangular Shape Calculator

✖Width of Cross Section is the geometric measurement or extent of the member from side to side.ⓘ Width of Cross Section [b]			+10% -10%
✖Depth of Cross Section (Height), in (mm) defines the geometrical measure from head to foot or from base to top of the section considered.ⓘ Depth of Cross Section [d]			+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 Rectangular Shape [Z]

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Formula

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Section Modulus of Rectangular Shape

Formula

`"Z" = ("b"*"d"^2)/6`

Example

`"0.041405m³"=("300mm"*("910mm")^2)/6`

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Section Modulus of Rectangular Shape Solution

STEP 0: Pre-Calculation Summary

Formula Used

Section Modulus = (Width of Cross Section*Depth of Cross Section^2)/6
Z = (b*d^2)/6
This formula uses 3 Variables

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.
Width of Cross Section - (Measured in Meter) - Width of Cross Section is the geometric measurement or extent of the member from side to side.
Depth of Cross Section - (Measured in Meter) - Depth of Cross Section (Height), in (mm) defines the geometrical measure from head to foot or from base to top of the section considered.

STEP 1: Convert Input(s) to Base Unit

Width of Cross Section: 300 Millimeter --> 0.3 Meter (Check conversion here)
Depth of Cross Section: 910 Millimeter --> 0.91 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z = (b*d^2)/6 --> (0.3*0.91^2)/6

Evaluating ... ...

Z = 0.041405

STEP 3: Convert Result to Output's Unit

0.041405 Cubic Meter --> No Conversion Required

FINAL ANSWER

0.041405 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 Rectangular Shape

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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National Institute of Technology (NIT), Warangal

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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 Rectangular Shape Formula

Section Modulus = (Width of Cross Section*Depth of Cross Section^2)/6
Z = (b*d^2)/6

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 Rectangular Shape?

Section Modulus of Rectangular Shape calculator uses Section Modulus = (Width of Cross Section*Depth of Cross Section^2)/6 to calculate the Section Modulus, The Section Modulus of Rectangular Shape formula is defined as the section modulus for a rectangular section when cross-section details are known. Section Modulus is denoted by Z symbol.

How to calculate Section Modulus of Rectangular Shape using this online calculator? To use this online calculator for Section Modulus of Rectangular Shape, enter Width of Cross Section (b) & Depth of Cross Section (d) and hit the calculate button. Here is how the Section Modulus of Rectangular Shape calculation can be explained with given input values -> 0.041405 = (0.3*0.91^2)/6.

FAQ

What is Section Modulus of Rectangular Shape?

The Section Modulus of Rectangular Shape formula is defined as the section modulus for a rectangular section when cross-section details are known and is represented as Z = (b*d^2)/6 or Section Modulus = (Width of Cross Section*Depth of Cross Section^2)/6. Width of Cross Section is the geometric measurement or extent of the member from side to side & Depth of Cross Section (Height), in (mm) defines the geometrical measure from head to foot or from base to top of the section considered.

How to calculate Section Modulus of Rectangular Shape?

The Section Modulus of Rectangular Shape formula is defined as the section modulus for a rectangular section when cross-section details are known is calculated using Section Modulus = (Width of Cross Section*Depth of Cross Section^2)/6. To calculate Section Modulus of Rectangular Shape, you need Width of Cross Section (b) & Depth of Cross Section (d). With our tool, you need to enter the respective value for Width of Cross Section & Depth of Cross Section 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 Width of Cross Section & Depth of Cross Section. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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