Section Modulus of Hollow Rectangular Shape Calculator

✖Outer Breadth of Hollow Rectangular Section is the exterior width of rectangle in a hollow rectangular section.ⓘ Outer Breadth of Hollow Rectangular Section [B_o]			+10% -10%
✖Outer Depth of Hollow Rectangular Section is the exterior Depth of rectangle in a hollow rectangular section.ⓘ Outer Depth of Hollow Rectangular Section [D_o]			+10% -10%
✖Inner Breadth of Hollow Rectangular Section is the interior width of rectangle in a hollow rectangular section.ⓘ Inner Breadth of Hollow Rectangular Section [B_i]			+10% -10%
✖Inner Depth of Hollow Rectangular Section is the interior Depth of rectangle in a hollow rectangular section.ⓘ Inner Depth of Hollow Rectangular Section [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 Rectangular Shape [Z]

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Formula

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Section Modulus of Hollow Rectangular Shape

Formula

`"Z" = (("B"_{"o"}*"D"_{"o"}^3)-("B"_{"i"}*"D"_{"i"}^3))/(6*"D"_{"o"})`

Example

`"0.141375m³"=(("800mm"*("1200mm")^3)-("500mm"*("900mm")^3))/(6*"1200mm")`

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Section Modulus of Hollow Rectangular Shape Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
Z = ((B_o*D_o^3)-(B_i*D_i^3))/(6*D_o)
This formula uses 5 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.
Outer Breadth of Hollow Rectangular Section - (Measured in Meter) - Outer Breadth of Hollow Rectangular Section is the exterior width of rectangle in a hollow rectangular section.
Outer Depth of Hollow Rectangular Section - (Measured in Meter) - Outer Depth of Hollow Rectangular Section is the exterior Depth of rectangle in a hollow rectangular section.
Inner Breadth of Hollow Rectangular Section - (Measured in Meter) - Inner Breadth of Hollow Rectangular Section is the interior width of rectangle in a hollow rectangular section.
Inner Depth of Hollow Rectangular Section - (Measured in Meter) - Inner Depth of Hollow Rectangular Section is the interior Depth of rectangle in a hollow rectangular section.

STEP 1: Convert Input(s) to Base Unit

Outer Breadth of Hollow Rectangular Section: 800 Millimeter --> 0.8 Meter (Check conversion here)
Outer Depth of Hollow Rectangular Section: 1200 Millimeter --> 1.2 Meter (Check conversion here)
Inner Breadth of Hollow Rectangular Section: 500 Millimeter --> 0.5 Meter (Check conversion here)
Inner Depth of Hollow Rectangular Section: 900 Millimeter --> 0.9 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z = ((B_o*D_o^3)-(B_i*D_i^3))/(6*D_o) --> ((0.8*1.2^3)-(0.5*0.9^3))/(6*1.2)

Evaluating ... ...

Z = 0.141375

STEP 3: Convert Result to Output's Unit

0.141375 Cubic Meter --> No Conversion Required

FINAL ANSWER

0.141375 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 Hollow Rectangular Shape

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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 Hollow Rectangular Shape Formula

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 Rectangular Shape?

Section Modulus of Hollow Rectangular Shape calculator uses 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) to calculate the Section Modulus, The Section Modulus of Hollow Rectangular 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 Rectangular Shape using this online calculator? To use this online calculator for Section Modulus of Hollow Rectangular Shape, enter Outer Breadth of Hollow Rectangular Section (B_o), Outer Depth of Hollow Rectangular Section (D_o), Inner Breadth of Hollow Rectangular Section (B_i) & Inner Depth of Hollow Rectangular Section (D_i) and hit the calculate button. Here is how the Section Modulus of Hollow Rectangular Shape calculation can be explained with given input values -> 0.141375 = ((0.8*1.2^3)-(0.5*0.9^3))/(6*1.2).

FAQ

What is Section Modulus of Hollow Rectangular Shape?

The Section Modulus of Hollow Rectangular Shape formula is defined as section modulus when the cross-sectional properties are known and is represented as Z = ((B_o*D_o^3)-(B_i*D_i^3))/(6*D_o) or 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). Outer Breadth of Hollow Rectangular Section is the exterior width of rectangle in a hollow rectangular section, Outer Depth of Hollow Rectangular Section is the exterior Depth of rectangle in a hollow rectangular section, Inner Breadth of Hollow Rectangular Section is the interior width of rectangle in a hollow rectangular section & Inner Depth of Hollow Rectangular Section is the interior Depth of rectangle in a hollow rectangular section.

How to calculate Section Modulus of Hollow Rectangular Shape?

The Section Modulus of Hollow Rectangular Shape formula is defined as section modulus when the cross-sectional properties are known is calculated using 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). To calculate Section Modulus of Hollow Rectangular Shape, you need Outer Breadth of Hollow Rectangular Section (B_o), Outer Depth of Hollow Rectangular Section (D_o), Inner Breadth of Hollow Rectangular Section (B_i) & Inner Depth of Hollow Rectangular Section (D_i). With our tool, you need to enter the respective value for Outer Breadth of Hollow Rectangular Section, Outer Depth of Hollow Rectangular Section, Inner Breadth of Hollow Rectangular Section & Inner Depth of Hollow Rectangular 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 Outer Breadth of Hollow Rectangular Section, Outer Depth of Hollow Rectangular Section, Inner Breadth of Hollow Rectangular Section & Inner Depth of Hollow Rectangular Section. 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 = (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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