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Moment of Inertia given Euler Load Formula

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

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

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

Moment of Inertia given Euler Load Example

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Here is how the Moment of Inertia given Euler Load equation looks like with Values.

Here is how the Moment of Inertia given Euler Load equation looks like with Units.

Here is how the Moment of Inertia given Euler Load equation looks like.

0.001 = \frac{4 \cdot (5000^{2})}{({3.1416}^{2}) \cdot 10.56}

0.001kg·m² = \frac{4kN \cdot ({5000mm}^{2})}{({3.1416}^{2}) \cdot 10.56MPa}

0.001 = \frac{4 \cdot (5000^{2})}{({3.1416}^{2}) \cdot 10.56}

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Moment of Inertia given Euler Load Solution

Follow our step by step solution on how to calculate Moment of Inertia given Euler Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

I = \frac{4kN \cdot ({5000mm}^{2})}{(π^{2}) \cdot 10.56MPa}

Next Step Substitute values of Constants

∴

I = \frac{4kN \cdot ({5000mm}^{2})}{({3.1416}^{2}) \cdot 10.56MPa}

Next Step Convert Units

∴

I = \frac{4000N \cdot ({5m}^{2})}{({3.1416}^{2}) \cdot 1.1E+7Pa}

Next Step Prepare to Evaluate

∴

I = \frac{4000 \cdot (5^{2})}{({3.1416}^{2}) \cdot 1.1E+7}

Next Step Evaluate

∴

I = 0.000959480905703956kg·m²

LAST Step Rounding Answer

∴

I = 0.001kg·m²

Moment of Inertia given Euler Load Formula Elements

Variables

Constants

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

Euler Load

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

Symbol: P_E

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Euler Load

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

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

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 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 Euler Load

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

Go Modulus of Elasticity given Euler Load

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

How to Evaluate Moment of Inertia given Euler Load?

Moment of Inertia given Euler Load evaluator uses Moment of Inertia = (Euler Load*(Length of Column^2))/((pi^2)*Modulus of Elasticity of Column) to evaluate the Moment of Inertia, The Moment of Inertia given Euler Load formula is defined as a measure of the resistance of a column to bending, considering the initial curvature of the column and the Euler load, which is the critical load at which the column will buckle. Moment of Inertia is denoted by I symbol.

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

FAQs on Moment of Inertia given Euler Load

What is the formula to find Moment of Inertia given Euler Load?

The formula of Moment of Inertia given Euler Load is expressed as Moment of Inertia = (Euler Load*(Length of Column^2))/((pi^2)*Modulus of Elasticity of Column). Here is an example- 0.000959 = (4000*(5^2))/((pi^2)*10560000).

How to calculate Moment of Inertia given Euler Load?

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

Can the Moment of Inertia given Euler Load be negative?

No, the Moment of Inertia given Euler Load, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Moment of Inertia given Euler Load?

Moment of Inertia given Euler Load is usually measured using the Kilogram Square Meter[kg·m²] for Moment of Inertia. Kilogram Square Centimeter[kg·m²], Kilogram Square Millimeter[kg·m²], Gram Square Centimeter[kg·m²] are the few other units in which Moment of Inertia given Euler Load can be measured.

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Moment of Inertia given Euler Load Formula

Moment of Inertia given Euler Load Example

Moment of Inertia given Euler Load Solution

Moment of Inertia given Euler Load Formula Elements

Other formulas in Columns With Initial Curvature category

How to Evaluate Moment of Inertia given Euler Load?

FAQs on Moment of Inertia given Euler Load

Variable Name