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Effective Length of Column given Crippling Load for any type of End Condition 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 I}{P cr}}

L_e - Effective Length of Column?ε_c - Modulus of Elasticity of Column?I - Moment of Inertia Column?P_cr - Column Crippling Load?π - Archimedes' constant?

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

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Here is how the Effective Length of Column given Crippling Load for any type of End Condition equation looks like with Values.

Here is how the Effective Length of Column given Crippling Load for any type of End Condition equation looks like with Units.

Here is how the Effective Length of Column given Crippling Load for any type of End Condition equation looks like.

2500.6762 = \sqrt{\frac{{3.1416}^{2} \cdot 10.56 \cdot 60000}{10000}}

2500.6762mm = \sqrt{\frac{{3.1416}^{2} \cdot 10.56MPa \cdot 60000cm⁴}{10000N}}

2500.6762 = \sqrt{\frac{{3.1416}^{2} \cdot 10.56 \cdot 60000}{10000}}

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

Follow our step by step solution on how to calculate Effective Length of Column given Crippling Load for any type of End Condition?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L e = \sqrt{\frac{π^{2} \cdot 10.56MPa \cdot 60000cm⁴}{10000N}}

Next Step Substitute values of Constants

∴

L e = \sqrt{\frac{{3.1416}^{2} \cdot 10.56MPa \cdot 60000cm⁴}{10000N}}

Next Step Convert Units

∴

L e = \sqrt{\frac{{3.1416}^{2} \cdot 1.1E+7Pa \cdot 0.0006m⁴}{10000N}}

Next Step Prepare to Evaluate

∴

L e = \sqrt{\frac{{3.1416}^{2} \cdot 1.1E+7 \cdot 0.0006}{10000}}

Next Step Evaluate

∴

L e = 2.50067617826263m

Next Step Convert to Output's Unit

∴

L e = 2500.67617826263mm

LAST Step Rounding Answer

∴

L e = 2500.6762mm

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

Moment of Inertia Column

Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.

Symbol: I

Measurement: Second Moment of AreaUnit: cm⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia Column

Column Crippling Load

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.

Symbol: P_cr

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Column Crippling Load

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 Stress

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

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 Load for any type of End Condition?

Effective Length of Column given Crippling Load for any type of End Condition evaluator uses Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load)) to evaluate 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 evaluate Effective Length of Column given Crippling Load for any type of End Condition using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Effective Length of Column given Crippling Load for any type of End Condition?

The formula of Effective Length of Column given Crippling Load for any type of End Condition is expressed as Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load)). Here is an example- 2.5E+6 = sqrt((pi^2*10560000*0.0006)/(10000)).

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

With Modulus of Elasticity of Column (ε_c), Moment of Inertia Column (I) & Column Crippling Load (P_cr) we can find Effective Length of Column given Crippling Load for any type of End Condition using the formula - Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load)). 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 Load for any type of End Condition be negative?

No, the Effective Length of Column given Crippling Load for any type of End Condition, measured in Length cannot be negative.

Which unit is used to measure 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 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 Load for any type of End Condition can be measured.

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

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

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

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

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