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Euler Load Formula

GoEuler Load given Factor of Safety Formula

GoEuler Load given Final Deflection at Distance X from end A of Column Formula

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Euler load is the compressive load at which a slender column will suddenly bend or buckle. Check FAQs

P E = \frac{(π^{2}) \cdot ε column \cdot I}{l^{2}}

P_E - Euler Load?ε_column - Modulus of Elasticity of Column?I - Moment of Inertia?l - Length of Column?π - Archimedes' constant?

Euler Load Example

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Here is how the Euler Load equation looks like with Values.

Here is how the Euler Load equation looks like with Units.

Here is how the Euler Load equation looks like.

3999.8546 = \frac{({3.1416}^{2}) \cdot 0.009 \cdot 1.125}{5000^{2}}

3999.8546N = \frac{({3.1416}^{2}) \cdot 0.009MPa \cdot 1.125kg·m²}{{5000mm}^{2}}

3999.8546 = \frac{({3.1416}^{2}) \cdot 0.009 \cdot 1.125}{5000^{2}}

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Euler Load Solution

Follow our step by step solution on how to calculate Euler Load?

FIRST Step Consider the formula

P E = \frac{(π^{2}) \cdot ε column \cdot I}{l^{2}}

Next Step Substitute values of Variables

∴

P E = \frac{(π^{2}) \cdot 0.009MPa \cdot 1.125kg·m²}{{5000mm}^{2}}

Next Step Substitute values of Constants

∴

P E = \frac{({3.1416}^{2}) \cdot 0.009MPa \cdot 1.125kg·m²}{{5000mm}^{2}}

Next Step Convert Units

∴

P E = \frac{({3.1416}^{2}) \cdot 9006Pa \cdot 1.125kg·m²}{{5m}^{2}}

Next Step Prepare to Evaluate

∴

P E = \frac{({3.1416}^{2}) \cdot 9006 \cdot 1.125}{5^{2}}

Next Step Evaluate

∴

P E = 3999.85457562948N

LAST Step Rounding Answer

∴

P E = 3999.8546N

Euler Load Formula Elements

Variables

Constants

Euler Load

Euler load is the compressive load at which a slender column will suddenly bend or buckle.

Symbol: P_E

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Euler Load

Modulus of Elasticity of Column

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

Symbol: ε_column

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Column

Moment of Inertia

Moment of Inertia is a physical quantity that describes how mass is distributed in relation to an axis of rotation.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia

Length of Column

Length of Column is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Column

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

Other Formulas to find Euler Load

Go Euler Load given Factor of Safety

P E = \frac{P}{1 - (\frac{1}{f s})}

Go Euler Load given Final Deflection at Distance X from end A of Column

P E = \frac{P}{1 - (C \cdot \frac{\sin (\frac{π \cdot x}{l})}{δ c})}

Go Euler Load given Maximum Deflection for Columns with Initial Curvature

P E = \frac{P}{1 - (\frac{C}{δ c})}

Other formulas in Columns With Initial Curvature category

Go Value of Distance 'X' given Initial Deflection at Distance X from end A

x = (a \sin (\frac{y'}{C})) \cdot \frac{l}{π}

Go Length of Column given Initial Deflection at Distance X from end A

l = \frac{π \cdot x}{a \sin (\frac{y'}{C})}

Go Modulus of Elasticity given Euler Load

ε column = \frac{P E \cdot (l^{2})}{π^{2} \cdot I}

Go Moment of Inertia given Euler Load

I = \frac{P E \cdot (l^{2})}{(π^{2}) \cdot ε column}

How to Evaluate Euler Load?

Euler Load evaluator uses Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2) to evaluate the Euler Load, The Euler Load formula is defined as the maximum load that a long, slender, ideal column can carry without buckling, taking into account the initial curvature of the column, and is a critical concept in structural engineering and architecture. Euler Load is denoted by P_E symbol.

How to evaluate Euler Load using this online evaluator? To use this online evaluator for Euler Load, enter Modulus of Elasticity of Column (ε_column), Moment of Inertia (I) & Length of Column (l) and hit the calculate button.

FAQs on Euler Load

What is the formula to find Euler Load?

The formula of Euler Load is expressed as Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2). Here is an example- 4.7E+6 = ((pi^2)*9006*1.125)/(5^2).

How to calculate Euler Load?

With Modulus of Elasticity of Column (ε_column), Moment of Inertia (I) & Length of Column (l) we can find Euler Load using the formula - Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2). This formula also uses Archimedes' constant .

What are the other ways to Calculate Euler Load?

Here are the different ways to Calculate Euler Load-

Euler Load=Crippling Load/(1-(1/Factor of Safety))
Euler Load=Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column))
Euler Load=Crippling Load/(1-(Maximum Initial Deflection/Deflection of Column))

Can the Euler Load be negative?

Yes, the Euler Load, measured in Force can be negative.

Which unit is used to measure Euler Load?

Euler Load is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Euler Load can be measured.

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Euler Load Formula

​GoEuler Load given Factor of Safety Formula

​GoEuler Load given Final Deflection at Distance X from end A of Column Formula

Euler Load Example

Euler Load Solution

Euler Load Formula Elements

Other Formulas to find Euler Load

Other formulas in Columns With Initial Curvature category

How to Evaluate Euler Load?

FAQs on Euler Load

Variable Name

GoEuler Load given Factor of Safety Formula

GoEuler Load given Final Deflection at Distance X from end A of Column Formula