Inner Diameter of Hollow Circular Shape in Bending Stress 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 Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.ⓘ Section Modulus [Z]			+10% -10%

✖The Inner Diameter of Shaft is the length of the longest chord inside the hollow shaft.ⓘ Inner Diameter of Hollow Circular Shape in Bending Stress [d_i]

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Formula

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Inner Diameter of Hollow Circular Shape in Bending Stress

Formula

`"d"_{"i"} = (("d"_{"o"}^4)-(32*"Z"*"d"_{"o"}/pi))^(1/4)`

Example

`"700mm"=((("700mm")^4)-(32*"0.04141m³"*"700mm"/pi))^(1/4)`

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Inner Diameter of Hollow Circular Shape in Bending Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Inner Diameter of Shaft - (Measured in Millimeter) - The Inner Diameter of Shaft is the length of the longest chord inside the hollow shaft.
Outer Diameter of Shaft - (Measured in Millimeter) - Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.
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.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Shaft: 700 Millimeter --> 700 Millimeter No Conversion Required
Section Modulus: 0.04141 Cubic Meter --> 0.04141 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_i = ((d_o^4)-(32*Z*d_o/pi))^(1/4) --> ((700^4)-(32*0.04141*700/pi))^(1/4)

Evaluating ... ...

d_i = 699.999999784797

STEP 3: Convert Result to Output's Unit

0.699999999784797 Meter -->699.999999784797 Millimeter (Check conversion here)

FINAL ANSWER

699.999999784797 ≈ 700 Millimeter <-- Inner Diameter of Shaft

(Calculation completed in 00.004 seconds)

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

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Created by Rachana B V

The National Institute of Engineering (NIE), Mysuru

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Gautam Buddha University (GBU), Greater Noida

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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

Inner Diameter of Hollow Circular Shape in Bending Stress Formula

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

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 Inner Diameter of Hollow Circular Shape in Bending Stress?

Inner Diameter of Hollow Circular Shape in Bending Stress calculator uses Inner Diameter of Shaft = ((Outer Diameter of Shaft^4)-(32*Section Modulus*Outer Diameter of Shaft/pi))^(1/4) to calculate the Inner Diameter of Shaft, The Inner Diameter of Hollow Circular Shape in Bending Stress formula is defined as the inner diameter which can result in the specified section modulus. Inner Diameter of Shaft is denoted by d_i symbol.

How to calculate Inner Diameter of Hollow Circular Shape in Bending Stress using this online calculator? To use this online calculator for Inner Diameter of Hollow Circular Shape in Bending Stress, enter Outer Diameter of Shaft (d_o) & Section Modulus (Z) and hit the calculate button. Here is how the Inner Diameter of Hollow Circular Shape in Bending Stress calculation can be explained with given input values -> 700000 = ((0.7^4)-(32*0.04141*0.7/pi))^(1/4).

FAQ

What is Inner Diameter of Hollow Circular Shape in Bending Stress?

The Inner Diameter of Hollow Circular Shape in Bending Stress formula is defined as the inner diameter which can result in the specified section modulus and is represented as d_i = ((d_o^4)-(32*Z*d_o/pi))^(1/4) or Inner Diameter of Shaft = ((Outer Diameter of Shaft^4)-(32*Section Modulus*Outer Diameter of Shaft/pi))^(1/4). Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft & The Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.

How to calculate Inner Diameter of Hollow Circular Shape in Bending Stress?

The Inner Diameter of Hollow Circular Shape in Bending Stress formula is defined as the inner diameter which can result in the specified section modulus is calculated using Inner Diameter of Shaft = ((Outer Diameter of Shaft^4)-(32*Section Modulus*Outer Diameter of Shaft/pi))^(1/4). To calculate Inner Diameter of Hollow Circular Shape in Bending Stress, you need Outer Diameter of Shaft (d_o) & Section Modulus (Z). With our tool, you need to enter the respective value for Outer Diameter of Shaft & Section Modulus and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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