Radius of Gyration given Effective Length and Crippling Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Least Radius of Gyration Column = sqrt((Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column*Column Cross Sectional Area))
rleast = sqrt((P*Leff^2)/(pi^2*εc*Asectional))
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
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.
Column Crippling Load - (Measured in Newton) - Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.
Effective Column Length - (Measured in Meter) - Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.
Modulus of Elasticity Column - (Measured in Pascal) - Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Column Cross Sectional Area - (Measured in Square Meter) - Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.
STEP 1: Convert Input(s) to Base Unit
Column Crippling Load: 10000 Newton --> 10000 Newton No Conversion Required
Effective Column Length: 2500 Millimeter --> 2.5 Meter (Check conversion here)
Modulus of Elasticity Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
Column Cross Sectional Area: 6.25 Square Meter --> 6.25 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rleast = sqrt((P*Leff^2)/(pi^2*εc*Asectional)) --> sqrt((10000*2.5^2)/(pi^2*10560000*6.25))
Evaluating ... ...
rleast = 0.00979530962095613
STEP 3: Convert Result to Output's Unit
0.00979530962095613 Meter -->9.79530962095613 Millimeter (Check conversion here)
FINAL ANSWER
9.79530962095613 9.79531 Millimeter <-- Least Radius of Gyration Column
(Calculation completed in 00.004 seconds)

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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

6 Effective Length 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))
Effective Length of Column given Actual Length if One End is Fixed Other is Hinged
Go Effective Column Length = Length of Column/(sqrt(2))
Effective Length of Column given Actual Length if One End is Fixed Other is Free
Go Effective Column Length = 2*Length of Column
Effective Length of Column given Actual Length if Both Ends of Column are Fixed
Go Effective Column Length = Length of Column/2

Radius of Gyration given Effective Length and Crippling Load Formula

Least Radius of Gyration Column = sqrt((Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column*Column Cross Sectional Area))
rleast = sqrt((P*Leff^2)/(pi^2*εc*Asectional))

What is meant by Effective Length of a Column also define Slenderness Ratio?

The effective length of the column is the length of an equivalent column of the same material and cross sectional area with hinged ends and having the value of the crippling load equal to that of the given column. The least radius of gyration is the radius of gyration where the least moment of inertia is considered.

How to Calculate Radius of Gyration given Effective Length and Crippling Load?

Radius of Gyration given Effective Length and Crippling Load calculator uses Least Radius of Gyration Column = sqrt((Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column*Column Cross Sectional Area)) to calculate the Least Radius of Gyration Column, The Radius of Gyration given Effective Length and Crippling Load is defined as the radial distance to a point which 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 Radius of Gyration given Effective Length and Crippling Load using this online calculator? To use this online calculator for Radius of Gyration given Effective Length and Crippling Load, enter Column Crippling Load (P), Effective Column Length (Leff), Modulus of Elasticity Column c) & Column Cross Sectional Area (Asectional) and hit the calculate button. Here is how the Radius of Gyration given Effective Length and Crippling Load calculation can be explained with given input values -> 9795.31 = sqrt((10000*2.5^2)/(pi^2*10560000*6.25)).

FAQ

What is Radius of Gyration given Effective Length and Crippling Load?
The Radius of Gyration given Effective Length and Crippling Load is defined as the radial distance to a point which 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 rleast = sqrt((P*Leff^2)/(pi^2*εc*Asectional)) or Least Radius of Gyration Column = sqrt((Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column*Column Cross Sectional Area)). Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself, Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration, Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it & Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.
How to calculate Radius of Gyration given Effective Length and Crippling Load?
The Radius of Gyration given Effective Length and Crippling Load is defined as the radial distance to a point which 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 = sqrt((Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column*Column Cross Sectional Area)). To calculate Radius of Gyration given Effective Length and Crippling Load, you need Column Crippling Load (P), Effective Column Length (Leff), Modulus of Elasticity Column c) & Column Cross Sectional Area (Asectional). With our tool, you need to enter the respective value for Column Crippling Load, Effective Column Length, Modulus of Elasticity Column & Column Cross Sectional Area 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 Column Crippling Load, Effective Column Length, Modulus of Elasticity Column & Column Cross Sectional Area. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Least Radius of Gyration Column = Length of Column/Slenderness Ratio
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