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Effective Length of Column given Crippling Stress Formula

GoEffective Length of Column given Actual Length if Both Ends of Column are Fixed Formula

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

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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. Check FAQs

L e = \sqrt{\frac{π^{2} \cdot ε c \cdot r^{2}}{σ crippling}}

L_e - Effective Length of Column?ε_c - Modulus of Elasticity of Column?r - Least Radius of Gyration of Column?σ_crippling - Crippling Stress?π - Archimedes' constant?

Effective Length of Column given Crippling Stress Example

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Here is how the Effective Length of Column given Crippling Stress equation looks like with Values.

Here is how the Effective Length of Column given Crippling Stress equation looks like with Units.

Here is how the Effective Length of Column given Crippling Stress equation looks like.

3609.4152 = \sqrt{\frac{{3.1416}^{2} \cdot 10.56 \cdot 50^{2}}{0.02}}

3609.4152mm = \sqrt{\frac{{3.1416}^{2} \cdot 10.56MPa \cdot {50mm}^{2}}{0.02MPa}}

3609.4152 = \sqrt{\frac{{3.1416}^{2} \cdot 10.56 \cdot 50^{2}}{0.02}}

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Effective Length of Column given Crippling Stress Solution

Follow our step by step solution on how to calculate Effective Length of Column given Crippling Stress?

FIRST Step Consider the formula

L e = \sqrt{\frac{π^{2} \cdot ε c \cdot r^{2}}{σ crippling}}

Next Step Substitute values of Variables

∴

L e = \sqrt{\frac{π^{2} \cdot 10.56MPa \cdot {50mm}^{2}}{0.02MPa}}

Next Step Substitute values of Constants

∴

L e = \sqrt{\frac{{3.1416}^{2} \cdot 10.56MPa \cdot {50mm}^{2}}{0.02MPa}}

Next Step Convert Units

∴

L e = \sqrt{\frac{{3.1416}^{2} \cdot 1.1E+7Pa \cdot {0.05m}^{2}}{20000Pa}}

Next Step Prepare to Evaluate

∴

L e = \sqrt{\frac{{3.1416}^{2} \cdot 1.1E+7 \cdot {0.05}^{2}}{20000}}

Next Step Evaluate

∴

L e = 3.60941516169004m

Next Step Convert to Output's Unit

∴

L e = 3609.41516169004mm

LAST Step Rounding Answer

∴

L e = 3609.4152mm

Effective Length of Column given Crippling Stress Formula Elements

Variables

Constants

Functions

Effective Length of Column

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.

Symbol: L_e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Length of Column

Modulus of Elasticity of Column

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.

Symbol: ε_c

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Column

Least Radius of Gyration of Column

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.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Least Radius of Gyration of Column

Crippling Stress

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.

Symbol: σ_crippling

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Crippling Stress

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Effective Length of Column

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

L e = \frac{L}{2}

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

L e = 2 \cdot L

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

L e = \frac{L}{\sqrt{2}}

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

L e = \sqrt{\frac{π^{2} \cdot ε c \cdot I}{P cr}}

Other formulas in Estimation of Effective Length of Columns category

Go Radius of Gyration given Effective Length and Crippling Load

r = \sqrt{\frac{P cr \cdot {L e}^{2}}{π^{2} \cdot ε c \cdot A}}

How to Evaluate Effective Length of Column given Crippling Stress?

Effective Length of Column given Crippling Stress evaluator uses Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Least Radius of Gyration of Column^2)/Crippling Stress) to evaluate 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 evaluate Effective Length of Column given Crippling Stress using this online evaluator? To use this online evaluator 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.

FAQs on Effective Length of Column given Crippling Stress

What is the formula to find Effective Length of Column given Crippling Stress?

The formula of Effective Length of Column given Crippling Stress is expressed as Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Least Radius of Gyration of Column^2)/Crippling Stress). Here is an example- 3.6E+6 = sqrt((pi^2*10560000*0.05^2)/20000).

How to calculate Effective Length of Column given Crippling Stress?

With Modulus of Elasticity of Column (ε_c), Least Radius of Gyration of Column (r) & Crippling Stress (σ_crippling) we can find Effective Length of Column given Crippling Stress using the formula - Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Least Radius of Gyration of Column^2)/Crippling Stress). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Effective Length of Column?

Here are the different ways to Calculate Effective Length of Column-

Effective Length of Column=Length of Column/2
Effective Length of Column=2*Length of Column
Effective Length of Column=Length of Column/(sqrt(2))

Can the Effective Length of Column given Crippling Stress be negative?

No, the Effective Length of Column given Crippling Stress, measured in Length cannot be negative.

Which unit is used to measure Effective Length of Column given Crippling Stress?

Effective Length of Column given Crippling Stress is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Effective Length of Column given Crippling Stress can be measured.

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Effective Length of Column given Crippling Stress Formula

​GoEffective Length of Column given Actual Length if Both Ends of Column are Fixed Formula

​GoEffective Length of Column given Actual Length if One End is Fixed Other is Free Formula

Effective Length of Column given Crippling Stress Example

Effective Length of Column given Crippling Stress Solution

Effective Length of Column given Crippling Stress Formula Elements

Other Formulas to find Effective Length of Column

Other formulas in Estimation of Effective Length of Columns category

How to Evaluate Effective Length of Column given Crippling Stress?

FAQs on Effective Length of Column given Crippling Stress

Variable Name

GoEffective Length of Column given Actual Length if Both Ends of Column are Fixed Formula

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