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Effective Length of Column given Crippling Load by Euler's Formula Formula

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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. Check FAQs

L eff = \sqrt{\frac{π^{2} \cdot E \cdot I}{P E}}

L_eff - Effective Column Length?E - Modulus of Elasticity Column?I - Moment of Inertia Column?P_E - Euler’s Buckling Load?π - Archimedes' constant?

Effective Length of Column given Crippling Load by Euler's Formula Example

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Here is how the Effective Length of Column given Crippling Load by Euler's Formula equation looks like with Values.

Here is how the Effective Length of Column given Crippling Load by Euler's Formula equation looks like with Units.

Here is how the Effective Length of Column given Crippling Load by Euler's Formula equation looks like.

2999.9999 = \sqrt{\frac{{3.1416}^{2} \cdot 200000 \cdot 6.8E+6}{1491.407}}

2999.9999mm = \sqrt{\frac{{3.1416}^{2} \cdot 200000MPa \cdot 6.8E+6mm⁴}{1491.407kN}}

2999.9999 = \sqrt{\frac{{3.1416}^{2} \cdot 200000 \cdot 6.8E+6}{1491.407}}

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Effective Length of Column given Crippling Load by Euler's Formula Solution

Follow our step by step solution on how to calculate Effective Length of Column given Crippling Load by Euler's Formula?

FIRST Step Consider the formula

L eff = \sqrt{\frac{π^{2} \cdot E \cdot I}{P E}}

Next Step Substitute values of Variables

∴

L eff = \sqrt{\frac{π^{2} \cdot 200000MPa \cdot 6.8E+6mm⁴}{1491.407kN}}

Next Step Substitute values of Constants

∴

L eff = \sqrt{\frac{{3.1416}^{2} \cdot 200000MPa \cdot 6.8E+6mm⁴}{1491.407kN}}

Next Step Convert Units

∴

L eff = \sqrt{\frac{{3.1416}^{2} \cdot 2E+11Pa \cdot 6.8E-6m⁴}{1.5E+6N}}

Next Step Prepare to Evaluate

∴

L eff = \sqrt{\frac{{3.1416}^{2} \cdot 2E+11 \cdot 6.8E-6}{1.5E+6}}

Next Step Evaluate

∴

L eff = 2.99999988662624m

Next Step Convert to Output's Unit

∴

L eff = 2999.99988662624mm

LAST Step Rounding Answer

∴

L eff = 2999.9999mm

Effective Length of Column given Crippling Load by Euler's Formula Formula Elements

Variables

Constants

Functions

Effective Column Length

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.

Symbol: L_eff

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Column Length

Modulus of Elasticity Column

Modulus of Elasticity Column is a quantity that measures column's resistance to being deformed elastically when stress is applied to it.

Symbol: E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity Column

Moment of Inertia Column

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

Symbol: I

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia Column

Euler’s Buckling Load

The Euler’s Buckling Load is the axial load at which a perfectly straight column or structural member starts to bend.

Symbol: P_E

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Euler’s Buckling 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 in Euler and Rankine's Theory category

Go Crippling Load by Euler's Formula

P E = \frac{π^{2} \cdot E \cdot I}{{L eff}^{2}}

Go Crippling Load by Euler's Formula given Crippling Load by Rankine's

P E = \frac{P c \cdot P r}{P c - P r}

Go Modulus of Elasticity given Crippling Load by Euler's Formula

E = \frac{P E \cdot {L eff}^{2}}{π^{2} \cdot I}

Go Moment of Inertia given Crippling Load by Euler's Formula

I = \frac{P E \cdot {L eff}^{2}}{π^{2} \cdot E}

How to Evaluate Effective Length of Column given Crippling Load by Euler's Formula?

Effective Length of Column given Crippling Load by Euler's Formula evaluator uses Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load)) to evaluate the Effective Column Length, The Effective Length of Column given Crippling Load by Euler's Formula is defined as the maximum length of a column that can withstand a given crippling load without buckling, providing a critical load value for structural design and analysis in accordance with Euler's theory. Effective Column Length is denoted by L_eff symbol.

How to evaluate Effective Length of Column given Crippling Load by Euler's Formula using this online evaluator? To use this online evaluator for Effective Length of Column given Crippling Load by Euler's Formula, enter Modulus of Elasticity Column (E), Moment of Inertia Column (I) & Euler’s Buckling Load (P_E) and hit the calculate button.

FAQs on Effective Length of Column given Crippling Load by Euler's Formula

What is the formula to find Effective Length of Column given Crippling Load by Euler's Formula?

The formula of Effective Length of Column given Crippling Load by Euler's Formula is expressed as Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load)). Here is an example- 3E+6 = sqrt((pi^2*200000000000*6.8E-06)/(1491407)).

How to calculate Effective Length of Column given Crippling Load by Euler's Formula?

With Modulus of Elasticity Column (E), Moment of Inertia Column (I) & Euler’s Buckling Load (P_E) we can find Effective Length of Column given Crippling Load by Euler's Formula using the formula - Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Effective Length of Column given Crippling Load by Euler's Formula be negative?

No, the Effective Length of Column given Crippling Load by Euler's Formula, measured in Length cannot be negative.

Which unit is used to measure Effective Length of Column given Crippling Load by Euler's Formula?

Effective Length of Column given Crippling Load by Euler's Formula 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 by Euler's Formula can be measured.

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Effective Length of Column given Crippling Load by Euler's Formula Formula

Effective Length of Column given Crippling Load by Euler's Formula Example

Effective Length of Column given Crippling Load by Euler's Formula Solution

Effective Length of Column given Crippling Load by Euler's Formula Formula Elements

Other formulas in Euler and Rankine's Theory category

How to Evaluate Effective Length of Column given Crippling Load by Euler's Formula?

FAQs on Effective Length of Column given Crippling Load by Euler's Formula

Variable Name