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Euler's Formula for Critical Buckling Load Formula

GoEuler's Formula for Critical Buckling Load given Area Formula

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The Buckling Load is the load at which the column starts buckling. The buckling load of a given material depends on the Slenderness ratio, Area of a cross-section, and Modulus of Elasticity. Check FAQs

P Buckling Load = n \cdot (π^{2}) \cdot E \cdot \frac{I}{L^{2}}

P_{Buckling Load} - Buckling Load?n - Coefficient for Column End Conditions?E - Modulus of Elasticity?I - Area Moment of Inertia?L - Effective Length of Column?π - Archimedes' constant?

Euler's Formula for Critical Buckling Load Example

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Here is how the Euler's Formula for Critical Buckling Load equation looks like with Values.

Here is how the Euler's Formula for Critical Buckling Load equation looks like with Units.

Here is how the Euler's Formula for Critical Buckling Load equation looks like.

10.9662 = 2 \cdot ({3.1416}^{2}) \cdot 50 \cdot \frac{100000}{3000^{2}}

10.9662N = 2 \cdot ({3.1416}^{2}) \cdot 50MPa \cdot \frac{100000mm⁴}{{3000mm}^{2}}

10.9662 = 2 \cdot ({3.1416}^{2}) \cdot 50 \cdot \frac{100000}{3000^{2}}

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Euler's Formula for Critical Buckling Load Solution

Follow our step by step solution on how to calculate Euler's Formula for Critical Buckling Load?

FIRST Step Consider the formula

P Buckling Load = n \cdot (π^{2}) \cdot E \cdot \frac{I}{L^{2}}

Next Step Substitute values of Variables

∴

P Buckling Load = 2 \cdot (π^{2}) \cdot 50MPa \cdot \frac{100000mm⁴}{{3000mm}^{2}}

Next Step Substitute values of Constants

∴

P Buckling Load = 2 \cdot ({3.1416}^{2}) \cdot 50MPa \cdot \frac{100000mm⁴}{{3000mm}^{2}}

Next Step Prepare to Evaluate

∴

P Buckling Load = 2 \cdot ({3.1416}^{2}) \cdot 50 \cdot \frac{100000}{3000^{2}}

Next Step Evaluate

∴

P Buckling Load = 10.9662271123215N

LAST Step Rounding Answer

∴

P Buckling Load = 10.9662N

Euler's Formula for Critical Buckling Load Formula Elements

Variables

Constants

Buckling Load

The Buckling Load is the load at which the column starts buckling. The buckling load of a given material depends on the Slenderness ratio, Area of a cross-section, and Modulus of Elasticity.

Symbol: P_{Buckling Load}

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Buckling Load

Coefficient for Column End Conditions

Coefficient for Column End Conditions is defined as the multiplicative factor for different column end conditions.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Coefficient for Column End Conditions

Modulus of Elasticity

The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.

Symbol: E

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

Area Moment of Inertia

The Area Moment of Inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or second moment of inertia.

Symbol: I

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Effective Length of Column

The Effective Length of Column 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

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective 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 Buckling Load

Go Euler's Formula for Critical Buckling Load given Area

P Buckling Load = \frac{n \cdot π^{2} \cdot E \cdot A}{{(\frac{L}{r gyration})}^{2}}

How to Evaluate Euler's Formula for Critical Buckling Load?

Euler's Formula for Critical Buckling Load evaluator uses Buckling Load = Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity*Area Moment of Inertia/Effective Length of Column^2 to evaluate the Buckling Load, The Euler's Formula for Critical Buckling Load formula is defined as the compressive load at which a slender column will suddenly bend or buckle. Buckling Load is denoted by P_{Buckling Load} symbol.

How to evaluate Euler's Formula for Critical Buckling Load using this online evaluator? To use this online evaluator for Euler's Formula for Critical Buckling Load, enter Coefficient for Column End Conditions (n), Modulus of Elasticity (E), Area Moment of Inertia (I) & Effective Length of Column (L) and hit the calculate button.

FAQs on Euler's Formula for Critical Buckling Load

What is the formula to find Euler's Formula for Critical Buckling Load?

The formula of Euler's Formula for Critical Buckling Load is expressed as Buckling Load = Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity*Area Moment of Inertia/Effective Length of Column^2. Here is an example- 10.96623 = 2*(pi^2)*50000000*1E-07/3^2.

How to calculate Euler's Formula for Critical Buckling Load?

With Coefficient for Column End Conditions (n), Modulus of Elasticity (E), Area Moment of Inertia (I) & Effective Length of Column (L) we can find Euler's Formula for Critical Buckling Load using the formula - Buckling Load = Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity*Area Moment of Inertia/Effective Length of Column^2. This formula also uses Archimedes' constant .

What are the other ways to Calculate Buckling Load?

Here are the different ways to Calculate Buckling Load-

Buckling Load=(Coefficient for Column End Conditions*pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/((Effective Length of Column/Radius of Gyration of Column)^2)

Can the Euler's Formula for Critical Buckling Load be negative?

No, the Euler's Formula for Critical Buckling Load, measured in Force cannot be negative.

Which unit is used to measure Euler's Formula for Critical Buckling Load?

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

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Euler's Formula for Critical Buckling Load Formula

​GoEuler's Formula for Critical Buckling Load given Area Formula

Euler's Formula for Critical Buckling Load Example

Euler's Formula for Critical Buckling Load Solution

Euler's Formula for Critical Buckling Load Formula Elements

Other Formulas to find Buckling Load

How to Evaluate Euler's Formula for Critical Buckling Load?

FAQs on Euler's Formula for Critical Buckling Load

Variable Name

GoEuler's Formula for Critical Buckling Load given Area Formula