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Crippling Load by Euler's Formula Formula

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

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

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

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

Crippling Load by Euler's Formula Example

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With units

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Here is how the Crippling Load by Euler's Formula equation looks like with Values.

Here is how the Crippling Load by Euler's Formula equation looks like with Units.

Here is how the Crippling Load by Euler's Formula equation looks like.

1491.4069 = \frac{{3.1416}^{2} \cdot 200000 \cdot 6.8E+6}{3000^{2}}

1491.4069kN = \frac{{3.1416}^{2} \cdot 200000MPa \cdot 6.8E+6mm⁴}{{3000mm}^{2}}

1491.4069 = \frac{{3.1416}^{2} \cdot 200000 \cdot 6.8E+6}{3000^{2}}

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Crippling Load by Euler's Formula Solution

Follow our step by step solution on how to calculate Crippling Load by Euler's Formula?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

P E = \frac{π^{2} \cdot 200000MPa \cdot 6.8E+6mm⁴}{{3000mm}^{2}}

Next Step Substitute values of Constants

∴

P E = \frac{{3.1416}^{2} \cdot 200000MPa \cdot 6.8E+6mm⁴}{{3000mm}^{2}}

Next Step Convert Units

∴

P E = \frac{{3.1416}^{2} \cdot 2E+11Pa \cdot 6.8E-6m⁴}{{3m}^{2}}

Next Step Prepare to Evaluate

∴

P E = \frac{{3.1416}^{2} \cdot 2E+11 \cdot 6.8E-6}{3^{2}}

Next Step Evaluate

∴

P E = 1491406.88727573N

Next Step Convert to Output's Unit

∴

P E = 1491.40688727573kN

LAST Step Rounding Answer

∴

P E = 1491.4069kN

Crippling Load by Euler's Formula Formula Elements

Variables

Constants

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

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

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

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’s Buckling Load

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}

Other formulas in Euler and Rankine's Theory category

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

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

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 Crippling Load by Euler's Formula?

Crippling Load by Euler's Formula evaluator uses Euler’s Buckling Load = (pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Effective Column Length^2) to evaluate the Euler’s Buckling Load, The Crippling Load by Euler's formula is defined as the maximum load that a long, slender column can withstand without buckling, considering the column's effective length, modulus of elasticity, and moment of inertia, providing a critical load value for structural analysis and design. Euler’s Buckling Load is denoted by P_E symbol.

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

FAQs on Crippling Load by Euler's Formula

What is the formula to find Crippling Load by Euler's Formula?

The formula of Crippling Load by Euler's Formula is expressed as Euler’s Buckling Load = (pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Effective Column Length^2). Here is an example- 1.491407 = (pi^2*200000000000*6.8E-06)/(3^2).

How to calculate Crippling Load by Euler's Formula?

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

What are the other ways to Calculate Euler’s Buckling Load?

Here are the different ways to Calculate Euler’s Buckling Load-

Euler’s Buckling Load=(Crushing Load*Rankine’s Critical Load)/(Crushing Load-Rankine’s Critical Load)

Can the Crippling Load by Euler's Formula be negative?

No, the Crippling Load by Euler's Formula, measured in Force cannot be negative.

Which unit is used to measure Crippling Load by Euler's Formula?

Crippling Load by Euler's Formula is usually measured using the Kilonewton[kN] for Force. Newton[kN], Exanewton[kN], Meganewton[kN] are the few other units in which Crippling Load by Euler's Formula can be measured.

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Crippling Load by Euler's Formula Formula

​GoCrippling Load by Euler's Formula given Crippling Load by Rankine's Formula

Crippling Load by Euler's Formula Example

Crippling Load by Euler's Formula Solution

Crippling Load by Euler's Formula Formula Elements

Other Formulas to find Euler’s Buckling Load

Other formulas in Euler and Rankine's Theory category

How to Evaluate Crippling Load by Euler's Formula?

FAQs on Crippling Load by Euler's Formula

Variable Name

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