Radius of Kern for Circular Ring Calculator

✖Outer Diameter of Hollow Circular Section is the measure of the smallest diameter of a 2D concentric circular cross-section.ⓘ Outer Diameter of Hollow Circular Section [D]			+10% -10%
✖Inner Diameter of Hollow Circular Section is the measure of the smallest diameter of a 2D concentric circular cross-section.ⓘ Inner Diameter of Hollow Circular Section [d_i]			+10% -10%

✖Radius of Kern is the radius of area around the center of gravity of a cross section i.e. kern area.ⓘ Radius of Kern for Circular Ring [r_kern]

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Radius of Kern for Circular Ring

Formula

`"r"_{"kern"} = ("D"*(1+("d"_{"i"}/"D")^2))/8`

Example

`"5.416667mm"=("30mm"*(1+("20.0mm"/"30mm")^2))/8`

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Download Eccentric Loads on Columns Formulas PDF

Radius of Kern for Circular Ring Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Kern = (Outer Diameter of Hollow Circular Section*(1+(Inner Diameter of Hollow Circular Section/Outer Diameter of Hollow Circular Section)^2))/8
r_kern = (D*(1+(d_i/D)^2))/8
This formula uses 3 Variables

Variables Used

Radius of Kern - (Measured in Meter) - Radius of Kern is the radius of area around the center of gravity of a cross section i.e. kern area.
Outer Diameter of Hollow Circular Section - (Measured in Meter) - Outer Diameter of Hollow Circular Section is the measure of the smallest diameter of a 2D concentric circular cross-section.
Inner Diameter of Hollow Circular Section - (Measured in Meter) - Inner Diameter of Hollow Circular Section is the measure of the smallest diameter of a 2D concentric circular cross-section.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Hollow Circular Section: 30 Millimeter --> 0.03 Meter (Check conversion here)
Inner Diameter of Hollow Circular Section: 20 Millimeter --> 0.02 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_kern = (D*(1+(d_i/D)^2))/8 --> (0.03*(1+(0.02/0.03)^2))/8

Evaluating ... ...

r_kern = 0.00541666666666667

STEP 3: Convert Result to Output's Unit

0.00541666666666667 Meter -->5.41666666666667 Millimeter (Check conversion here)

FINAL ANSWER

5.41666666666667 ≈ 5.416667 Millimeter <-- Radius of Kern

(Calculation completed in 00.020 seconds)

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Cummins College of Engineering for Women (CCEW), Pune

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< 7 Eccentric Loads on Columns Calculators

Maximum Stress for Circular Section Column under Compression

Go Maximum Stress for Section = (0.372+0.056*(Distance from Nearest Edge/Radius of Circular Cross-Section)*(Concentrated Load/Distance from Nearest Edge)*sqrt(Radius of Circular Cross-Section*Distance from Nearest Edge))

Radius of Kern for Circular Ring

Go Radius of Kern = (Outer Diameter of Hollow Circular Section*(1+(Inner Diameter of Hollow Circular Section/Outer Diameter of Hollow Circular Section)^2))/8

Maximum Stress for Rectangular Section Column under Compression

Go Maximum Stress for Section = (2/3)*Concentrated Load/(Height of Cross-Section*Distance from Nearest Edge)

Maximum Stress for Circular Cross-Section Columns

Go Maximum Stress for Section = Unit Stress*(1+8*Eccentricity of Column/Diameter of Circular Cross-Section)

Maximum Stress for Rectangular Cross-Section Column

Go Maximum Stress for Section = Unit Stress*(1+6*Eccentricity of Column/Rectangular Cross-Section Width)

Radius of Kern for Hollow Square

Go Radius of Kern = 0.1179*Length of Outer Side*(1+(Length of Inner Side/Length of Outer Side)^2)

Thickness of Wall for Hollow Octagon

Go Thickness of Wall = 0.9239*(Radii of Circle Circumscribing Outer Side-Radii of Circle Circumscribing Inner Side)

Radius of Kern for Circular Ring Formula

Radius of Kern = (Outer Diameter of Hollow Circular Section*(1+(Inner Diameter of Hollow Circular Section/Outer Diameter of Hollow Circular Section)^2))/8
r_kern = (D*(1+(d_i/D)^2))/8

What is Kern?

The kern is the area around the center of gravity of a cross section within which any load applied produces stress of only one sign throughout the entire cross section. Outside the kern, a load produces stresses of different sign

How to Calculate Radius of Kern for Circular Ring?

Radius of Kern for Circular Ring calculator uses Radius of Kern = (Outer Diameter of Hollow Circular Section*(1+(Inner Diameter of Hollow Circular Section/Outer Diameter of Hollow Circular Section)^2))/8 to calculate the Radius of Kern, The Radius of Kern for Circular Ring formula is defined as the radius of area around the center of gravity of a cross-section within which any load applied produces stress of only one sign throughout the entire cross-section. Radius of Kern is denoted by r_kern symbol.

How to calculate Radius of Kern for Circular Ring using this online calculator? To use this online calculator for Radius of Kern for Circular Ring, enter Outer Diameter of Hollow Circular Section (D) & Inner Diameter of Hollow Circular Section (d_i) and hit the calculate button. Here is how the Radius of Kern for Circular Ring calculation can be explained with given input values -> 5416.667 = (0.03*(1+(0.02/0.03)^2))/8.

FAQ

What is Radius of Kern for Circular Ring?

The Radius of Kern for Circular Ring formula is defined as the radius of area around the center of gravity of a cross-section within which any load applied produces stress of only one sign throughout the entire cross-section and is represented as r_kern = (D*(1+(d_i/D)^2))/8 or Radius of Kern = (Outer Diameter of Hollow Circular Section*(1+(Inner Diameter of Hollow Circular Section/Outer Diameter of Hollow Circular Section)^2))/8. Outer Diameter of Hollow Circular Section is the measure of the smallest diameter of a 2D concentric circular cross-section & Inner Diameter of Hollow Circular Section is the measure of the smallest diameter of a 2D concentric circular cross-section.

How to calculate Radius of Kern for Circular Ring?

The Radius of Kern for Circular Ring formula is defined as the radius of area around the center of gravity of a cross-section within which any load applied produces stress of only one sign throughout the entire cross-section is calculated using Radius of Kern = (Outer Diameter of Hollow Circular Section*(1+(Inner Diameter of Hollow Circular Section/Outer Diameter of Hollow Circular Section)^2))/8. To calculate Radius of Kern for Circular Ring, you need Outer Diameter of Hollow Circular Section (D) & Inner Diameter of Hollow Circular Section (d_i). With our tool, you need to enter the respective value for Outer Diameter of Hollow Circular Section & Inner Diameter of Hollow Circular 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 Radius of Kern?

In this formula, Radius of Kern uses Outer Diameter of Hollow Circular Section & Inner Diameter of Hollow Circular Section. We can use 1 other way(s) to calculate the same, which is/are as follows -

Radius of Kern = 0.1179*Length of Outer Side*(1+(Length of Inner Side/Length of Outer Side)^2)

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