Effective Length of Column given Crippling Stress 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%
✖Least radius of gyration of column is a critical parameter in structural engineering, representing the smallest radius of gyration among all possible axes of the column’s cross-section.ⓘ Least Radius of Gyration of Column [r]			+10% -10%
✖Crippling stress refers to the stress level at which a structural element, such as a column, experiences local instability or failure due to buckling, particularly relevant for thin-walled columns.ⓘ Crippling Stress [σ_crippling]			+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 Stress [L_e]

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Effective Length of Column given Crippling Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Least Radius of Gyration of Column^2)/Crippling Stress)
L_e = sqrt((pi^2*ε_c*r^2)/σ_crippling)
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.
Least Radius of Gyration of Column - (Measured in Meter) - Least radius of gyration of column is a critical parameter in structural engineering, representing the smallest radius of gyration among all possible axes of the column’s cross-section.
Crippling Stress - (Measured in Pascal) - Crippling stress refers to the stress level at which a structural element, such as a column, experiences local instability or failure due to buckling, particularly relevant for thin-walled columns.

STEP 1: Convert Input(s) to Base Unit

Modulus of Elasticity of Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
Least Radius of Gyration of 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

L_e = sqrt((pi^2*ε_c*r^2)/σ_crippling) --> sqrt((pi^2*10560000*0.05^2)/20000)

Evaluating ... ...

L_e = 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 Length of Column

(Calculation completed in 00.021 seconds)

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National Institute Of Technology (NIT), Hamirpur

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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 Stress Formula

LaTeX Go

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

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 Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Least Radius of Gyration of Column^2)/Crippling Stress) to calculate the Effective Length of Column, Effective Length of Column given Crippling Stress formula is defined as a measure of the reduced length of a column that takes into account the crippling stress, which is the maximum stress a column can withstand without buckling, and is used to determine the load-carrying capacity of a column in various structural systems. Effective Length of Column is denoted by L_e 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 of Column (ε_c), Least Radius of Gyration of Column (r) & Crippling Stress (σ_crippling) and hit the calculate button. Here is how the Effective Length of Column given Crippling Stress calculation can be explained with given input values -> 3.6E+6 = sqrt((pi^2*10560000*0.05^2)/20000).

FAQ

What is Effective Length of Column given Crippling Stress?

Effective Length of Column given Crippling Stress formula is defined as a measure of the reduced length of a column that takes into account the crippling stress, which is the maximum stress a column can withstand without buckling, and is used to determine the load-carrying capacity of a column in various structural systems and is represented as L_e = sqrt((pi^2*ε_c*r^2)/σ_crippling) or Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Least Radius of Gyration of Column^2)/Crippling Stress). 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, Least radius of gyration of column is a critical parameter in structural engineering, representing the smallest radius of gyration among all possible axes of the column’s cross-section & Crippling stress refers to the stress level at which a structural element, such as a column, experiences local instability or failure due to buckling, particularly relevant for thin-walled columns.

How to calculate Effective Length of Column given Crippling Stress?

Effective Length of Column given Crippling Stress formula is defined as a measure of the reduced length of a column that takes into account the crippling stress, which is the maximum stress a column can withstand without buckling, and is used to determine the load-carrying capacity of a column in various structural systems is calculated using Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Least Radius of Gyration of Column^2)/Crippling Stress). To calculate Effective Length of Column given Crippling Stress, you need Modulus of Elasticity of Column (ε_c), Least Radius of Gyration of Column (r) & Crippling Stress (σ_crippling). With our tool, you need to enter the respective value for Modulus of Elasticity of Column, Least Radius of Gyration of 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 Length of Column?

In this formula, Effective Length of Column uses Modulus of Elasticity of Column, Least Radius of Gyration of Column & Crippling Stress. 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*Moment of Inertia Column)/(Column Crippling Load))

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