Least Radius of Gyration given Slenderness Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Least Radius of Gyration Column = Length of Column/Slenderness Ratio
rL = l/λ
This formula uses 3 Variables
Variables Used
Least Radius of Gyration Column - (Measured in Meter) - Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.
Length of Column - (Measured in Meter) - Length of Column is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.
Slenderness Ratio - The Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
STEP 1: Convert Input(s) to Base Unit
Length of Column: 5000 Millimeter --> 5 Meter (Check conversion here)
Slenderness Ratio: 100 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rL = l/λ --> 5/100
Evaluating ... ...
rL = 0.05
STEP 3: Convert Result to Output's Unit
0.05 Meter -->50 Millimeter (Check conversion here)
FINAL ANSWER
50 Millimeter <-- Least Radius of Gyration Column
(Calculation completed in 00.020 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Payal Priya
Birsa Institute of Technology (BIT), Sindri
Payal Priya has verified this Calculator and 1900+ more calculators!

14 Estimation of Effective Length of Columns Calculators

Radius of Gyration given Effective Length and Crippling Load
Go Least Radius of Gyration Column = sqrt((Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column*Column Cross Sectional Area))
Effective Length of Column given Crippling Stress
Go Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Least Radius of Gyration Column^2)/Crippling Stress)
Effective Length of Column given Crippling Load for any type of End Condition
Go Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Column Crippling Load))
Modulus of Elasticity of Column given Crippling Stress
Go Modulus of Elasticity Column = (Crippling Stress*Effective Column Length^2)/(pi^2*Least Radius of Gyration Column^2)
Modulus of Elasticity given Crippling Load for any type of End Condition
Go Modulus of Elasticity Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Moment of Inertia Column)
Moment of Inertia given Crippling Load for any type of End Condition
Go Moment of Inertia Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column)
Least Radius of Gyration given Slenderness Ratio
Go Least Radius of Gyration Column = Length of Column/Slenderness Ratio
Actual Length given Slenderness Ratio
Go Length of Column = Slenderness Ratio*Least Radius of Gyration Column
Effective Length of Column given Actual Length if One End is Fixed Other is Hinged
Go Effective Column Length = Length of Column/(sqrt(2))
Actual Length of Column given Effective Length if One End is Fixed Other is Hinged
Go Length of Column = sqrt(2)*Effective Column Length
Actual Length of Column given Effective Length if One End is Fixed Other is Free
Go Length of Column = Effective Column Length/2
Effective Length of Column given Actual Length if One End is Fixed Other is Free
Go Effective Column Length = 2*Length of Column
Actual Length of Column given Effective Length if Both Ends of Column are Fixed
Go Length of Column = 2*Effective Column Length
Effective Length of Column given Actual Length if Both Ends of Column are Fixed
Go Effective Column Length = Length of Column/2

1 Radius of Gyration Calculators

Least Radius of Gyration given Slenderness Ratio
Go Least Radius of Gyration Column = Length of Column/Slenderness Ratio

Least Radius of Gyration given Slenderness Ratio Formula

Least Radius of Gyration Column = Length of Column/Slenderness Ratio
rL = l/λ

What is Ultimate Compressive Strength?

Ultimate Compressive Strength is defined as the force at which a specimen with a certain cross-section, and consisting of a particular fracturing material, fails when it is subjected to compression. The ultimate compressive strength is normally measured in N/mm2 (force per area) and is thus stress.

How to Calculate Least Radius of Gyration given Slenderness Ratio?

Least Radius of Gyration given Slenderness Ratio calculator uses Least Radius of Gyration Column = Length of Column/Slenderness Ratio to calculate the Least Radius of Gyration Column, The Least Radius of Gyration given Slenderness Ratio is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass if the total mass of the body were concentrated there. Least Radius of Gyration Column is denoted by rL symbol.

How to calculate Least Radius of Gyration given Slenderness Ratio using this online calculator? To use this online calculator for Least Radius of Gyration given Slenderness Ratio, enter Length of Column (l) & Slenderness Ratio (λ) and hit the calculate button. Here is how the Least Radius of Gyration given Slenderness Ratio calculation can be explained with given input values -> 50000 = 5/100.

FAQ

What is Least Radius of Gyration given Slenderness Ratio?
The Least Radius of Gyration given Slenderness Ratio is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass if the total mass of the body were concentrated there and is represented as rL = l/λ or Least Radius of Gyration Column = Length of Column/Slenderness Ratio. Length of Column is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions & The Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
How to calculate Least Radius of Gyration given Slenderness Ratio?
The Least Radius of Gyration given Slenderness Ratio is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass if the total mass of the body were concentrated there is calculated using Least Radius of Gyration Column = Length of Column/Slenderness Ratio. To calculate Least Radius of Gyration given Slenderness Ratio, you need Length of Column (l) & Slenderness Ratio (λ). With our tool, you need to enter the respective value for Length of Column & Slenderness Ratio 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 Least Radius of Gyration Column?
In this formula, Least Radius of Gyration Column uses Length of Column & Slenderness Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Least Radius of Gyration Column = sqrt((Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column*Column Cross Sectional Area))
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!