Radius of Kern for Hollow Square Calculator

✖The Length of Outer Side is the measurement of the inner side of a shape/object from its head to foot or from base to top.ⓘ Length of Outer Side [H]			+10% -10%
✖The Length of Inner Side is the measurement of the inner side of a shape/object from its head to foot or from base to top.ⓘ Length of Inner Side [h_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 Hollow Square [r_kern]

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Radius of Kern for Hollow Square

Formula

`"r"_{"kern"} = 0.1179*"H"*(1+("h"_{"i"}/"H")^2)`

Example

`"6.8382mm"=0.1179*"50.0mm"*(1+("20mm"/"50.0mm")^2)`

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Download Eccentric Loads on Columns Formulas PDF

Radius of Kern for Hollow Square Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Kern = 0.1179*Length of Outer Side*(1+(Length of Inner Side/Length of Outer Side)^2)
r_kern = 0.1179*H*(1+(h_i/H)^2)
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.
Length of Outer Side - (Measured in Meter) - The Length of Outer Side is the measurement of the inner side of a shape/object from its head to foot or from base to top.
Length of Inner Side - (Measured in Meter) - The Length of Inner Side is the measurement of the inner side of a shape/object from its head to foot or from base to top.

STEP 1: Convert Input(s) to Base Unit

Length of Outer Side: 50 Millimeter --> 0.05 Meter (Check conversion here)
Length of Inner Side: 20 Millimeter --> 0.02 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_kern = 0.1179*H*(1+(h_i/H)^2) --> 0.1179*0.05*(1+(0.02/0.05)^2)

Evaluating ... ...

r_kern = 0.0068382

STEP 3: Convert Result to Output's Unit

0.0068382 Meter -->6.8382 Millimeter (Check conversion here)

FINAL ANSWER

6.8382 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 Hollow Square Formula

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

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 Hollow Square?

Radius of Kern for Hollow Square calculator uses Radius of Kern = 0.1179*Length of Outer Side*(1+(Length of Inner Side/Length of Outer Side)^2) to calculate the Radius of Kern, The Radius of Kern for Hollow Square 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 Hollow Square using this online calculator? To use this online calculator for Radius of Kern for Hollow Square, enter Length of Outer Side (H) & Length of Inner Side (h_i) and hit the calculate button. Here is how the Radius of Kern for Hollow Square calculation can be explained with given input values -> 6838.2 = 0.1179*0.05*(1+(0.02/0.05)^2).

FAQ

What is Radius of Kern for Hollow Square?

The Radius of Kern for Hollow Square 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 = 0.1179*H*(1+(h_i/H)^2) or Radius of Kern = 0.1179*Length of Outer Side*(1+(Length of Inner Side/Length of Outer Side)^2). The Length of Outer Side is the measurement of the inner side of a shape/object from its head to foot or from base to top & The Length of Inner Side is the measurement of the inner side of a shape/object from its head to foot or from base to top.

How to calculate Radius of Kern for Hollow Square?

The Radius of Kern for Hollow Square 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 = 0.1179*Length of Outer Side*(1+(Length of Inner Side/Length of Outer Side)^2). To calculate Radius of Kern for Hollow Square, you need Length of Outer Side (H) & Length of Inner Side (h_i). With our tool, you need to enter the respective value for Length of Outer Side & Length of Inner Side 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 Length of Outer Side & Length of Inner Side. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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