Effective Length of Column given Crippling Load for any type of End Condition Calculator

✖Modulus of elasticity of column also known as Young’s modulus, is a measure of a material’s stiffness or rigidity which quantifies the relationship between stress and strain.ⓘ Modulus of Elasticity of Column [ε_c]			+10% -10%
✖Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia Column [I]			+10% -10%
✖Column crippling load also known as the buckling load, is the maximum axial compressive load that a column can withstand before it buckles or fails due to instability.ⓘ Column Crippling Load [P_cr]			+10% -10%

✖Effective length of column is the length of an equivalent pin-ended column that has the same load-carrying capacity as the actual column under consideration.ⓘ Effective Length of Column given Crippling Load for any type of End Condition [L_e]

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Effective Length of Column given Crippling Load for any type of End Condition Solution

STEP 0: Pre-Calculation Summary

Formula Used

Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load))
L_e = sqrt((pi^2*ε_c*I)/(P_cr))
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 Length of Column - (Measured in Meter) - Effective length of column is the length of an equivalent pin-ended column that has the same load-carrying capacity as the actual column under consideration.
Modulus of Elasticity of Column - (Measured in Pascal) - Modulus of elasticity of column also known as Young’s modulus, is a measure of a material’s stiffness or rigidity which quantifies the relationship between stress and strain.
Moment of Inertia Column - (Measured in Meter⁴) - Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.
Column Crippling Load - (Measured in Newton) - Column crippling load also known as the buckling load, is the maximum axial compressive load that a column can withstand before it buckles or fails due to instability.

STEP 1: Convert Input(s) to Base Unit

Modulus of Elasticity of Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
Moment of Inertia Column: 60000 Centimeter⁴ --> 0.0006 Meter⁴ (Check conversion here)
Column Crippling Load: 10000 Newton --> 10000 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_e = sqrt((pi^2*ε_c*I)/(P_cr)) --> sqrt((pi^2*10560000*0.0006)/(10000))

Evaluating ... ...

L_e = 2.50067617826263

STEP 3: Convert Result to Output's Unit

2.50067617826263 Meter -->2500.67617826263 Millimeter (Check conversion here)

FINAL ANSWER

2500.67617826263 ≈ 2500.676 Millimeter <-- Effective Length of Column

(Calculation completed in 00.020 seconds)

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< Estimation of Effective Length of Columns Calculators

Actual Length given Slenderness Ratio

LaTeX Go Length of Column = Slenderness Ratio*Least Radius of Gyration of Column

Actual Length of Column given Effective Length if One End is Fixed Other is Hinged

LaTeX Go Length of Column = sqrt(2)*Effective Length of Column

Actual Length of Column given Effective Length if One End is Fixed Other is Free

LaTeX Go Length of Column = Effective Length of Column/2

Actual Length of Column given Effective Length if Both Ends of Column are Fixed

LaTeX Go Length of Column = 2*Effective Length of Column

< Effective Length Calculators

Effective Length of Column given Crippling Load for any type of End Condition

LaTeX Go Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load))

Effective Length of Column given Actual Length if One End is Fixed Other is Hinged

LaTeX Go Effective Length of Column = Length of Column/(sqrt(2))

Effective Length of Column given Actual Length if One End is Fixed Other is Free

LaTeX Go Effective Length of Column = 2*Length of Column

Effective Length of Column given Actual Length if Both Ends of Column are Fixed

LaTeX Go Effective Length of Column = Length of Column/2

Effective Length of Column given Crippling Load for any type of End Condition Formula

LaTeX Go

Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load))
L_e = sqrt((pi^2*ε_c*I)/(P_cr))

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 Load for any type of End Condition?

Effective Length of Column given Crippling Load for any type of End Condition calculator uses Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load)) to calculate the Effective Length of Column, Effective Length of Column given Crippling Load for any type of End Condition formula is defined as the length of a column that takes into account the crippling load and end conditions, providing a more accurate representation of the column's behavior under various loads, and is essential in structural engineering design and analysis. Effective Length of Column is denoted by L_e symbol.

How to calculate Effective Length of Column given Crippling Load for any type of End Condition using this online calculator? To use this online calculator for Effective Length of Column given Crippling Load for any type of End Condition, enter Modulus of Elasticity of Column (ε_c), Moment of Inertia Column (I) & Column Crippling Load (P_cr) and hit the calculate button. Here is how the Effective Length of Column given Crippling Load for any type of End Condition calculation can be explained with given input values -> 2.5E+6 = sqrt((pi^2*10560000*0.0006)/(10000)).

FAQ

What is Effective Length of Column given Crippling Load for any type of End Condition?

Effective Length of Column given Crippling Load for any type of End Condition formula is defined as the length of a column that takes into account the crippling load and end conditions, providing a more accurate representation of the column's behavior under various loads, and is essential in structural engineering design and analysis and is represented as L_e = sqrt((pi^2*ε_c*I)/(P_cr)) or Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load)). Modulus of elasticity of column also known as Young’s modulus, is a measure of a material’s stiffness or rigidity which quantifies the relationship between stress and strain, Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis & Column crippling load also known as the buckling load, is the maximum axial compressive load that a column can withstand before it buckles or fails due to instability.

How to calculate Effective Length of Column given Crippling Load for any type of End Condition?

Effective Length of Column given Crippling Load for any type of End Condition formula is defined as the length of a column that takes into account the crippling load and end conditions, providing a more accurate representation of the column's behavior under various loads, and is essential in structural engineering design and analysis is calculated using Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load)). To calculate Effective Length of Column given Crippling Load for any type of End Condition, you need Modulus of Elasticity of Column (ε_c), Moment of Inertia Column (I) & Column Crippling Load (P_cr). With our tool, you need to enter the respective value for Modulus of Elasticity of Column, Moment of Inertia Column & Column Crippling Load 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 Length of Column?

In this formula, Effective Length of Column uses Modulus of Elasticity of Column, Moment of Inertia Column & Column Crippling Load. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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