Effective Length of Column given Crippling Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Least Radius of Gyration Column^2)/Crippling Stress)
Leff = sqrt((pi^2*εc*rL^2)/σcrippling stress)
This formula uses 1 Constants, 1 Functions, 4 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
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.
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.
Crippling Stress - (Measured in Pascal) - Crippling Stress is the stress in column due to crippling load.
STEP 1: Convert Input(s) to Base Unit
Modulus of Elasticity Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
Least Radius of Gyration Column: 50 Millimeter --> 0.05 Meter (Check conversion here)
Crippling Stress: 0.02 Megapascal --> 20000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Leff = sqrt((pi^2*εc*rL^2)/σcrippling stress) --> sqrt((pi^2*10560000*0.05^2)/20000)
Evaluating ... ...
Leff = 3.60941516169004
STEP 3: Convert Result to Output's Unit
3.60941516169004 Meter -->3609.41516169004 Millimeter (Check conversion here)
FINAL ANSWER
3609.41516169004 3609.415 Millimeter <-- Effective Column Length
(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

Effective Length of Column given Crippling Stress Formula

Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Least Radius of Gyration Column^2)/Crippling Stress)
Leff = sqrt((pi^2*εc*rL^2)/σcrippling stress)

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 Effective Length of Column given Crippling Stress?

Effective Length of Column given Crippling Stress calculator uses Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Least Radius of Gyration Column^2)/Crippling Stress) to calculate the Effective Column Length, The Effective length of column given crippling stress formula is defined as the distance between successive inflection points or points of zero moment. Effective Column Length is denoted by Leff symbol.

How to calculate Effective Length of Column given Crippling Stress using this online calculator? To use this online calculator for Effective Length of Column given Crippling Stress, enter Modulus of Elasticity Column c), Least Radius of Gyration Column (rL) & Crippling Stress crippling stress) and hit the calculate button. Here is how the Effective Length of Column given Crippling Stress calculation can be explained with given input values -> 55797.54 = sqrt((pi^2*10560000*0.05^2)/20000).

FAQ

What is Effective Length of Column given Crippling Stress?
The Effective length of column given crippling stress formula is defined as the distance between successive inflection points or points of zero moment and is represented as Leff = sqrt((pi^2*εc*rL^2)/σcrippling stress) or Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Least Radius of Gyration Column^2)/Crippling Stress). 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, Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations & Crippling Stress is the stress in column due to crippling load.
How to calculate Effective Length of Column given Crippling Stress?
The Effective length of column given crippling stress formula is defined as the distance between successive inflection points or points of zero moment is calculated using Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Least Radius of Gyration Column^2)/Crippling Stress). To calculate Effective Length of Column given Crippling Stress, you need Modulus of Elasticity Column c), Least Radius of Gyration Column (rL) & Crippling Stress crippling stress). With our tool, you need to enter the respective value for Modulus of Elasticity Column, Least Radius of Gyration Column & Crippling Stress 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 Effective Column Length?
In this formula, Effective Column Length uses Modulus of Elasticity Column, Least Radius of Gyration Column & Crippling Stress. We can use 8 other way(s) to calculate the same, which is/are as follows -
  • Effective Column Length = Length of Column/2
  • Effective Column Length = Length of Column/(sqrt(2))
  • Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Column Crippling Load))
  • Effective Column Length = 2*Length of Column
  • Effective Column Length = Length of Column/2
  • Effective Column Length = 2*Length of Column
  • Effective Column Length = Length of Column/(sqrt(2))
  • Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Column Crippling Load))
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