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

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

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

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

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

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

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

Here is how the Moment of Inertia given Crippling Load by Euler's Formula equation looks like.

6.8E+6 = \frac{1491.407 \cdot 3000^{2}}{{3.1416}^{2} \cdot 200000}

6.8E+6mm⁴ = \frac{1491.407kN \cdot {3000mm}^{2}}{{3.1416}^{2} \cdot 200000MPa}

6.8E+6 = \frac{1491.407 \cdot 3000^{2}}{{3.1416}^{2} \cdot 200000}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

I = \frac{1491.407kN \cdot {3000mm}^{2}}{π^{2} \cdot 200000MPa}

Next Step Substitute values of Constants

∴

I = \frac{1491.407kN \cdot {3000mm}^{2}}{{3.1416}^{2} \cdot 200000MPa}

Next Step Convert Units

∴

I = \frac{1.5E+6N \cdot {3m}^{2}}{{3.1416}^{2} \cdot 2E+11Pa}

Next Step Prepare to Evaluate

∴

I = \frac{1.5E+6 \cdot 3^{2}}{{3.1416}^{2} \cdot 2E+11}

Next Step Evaluate

∴

I = 6.80000051396106E-06m⁴

Next Step Convert to Output's Unit

∴

I = 6800000.51396106mm⁴

LAST Step Rounding Answer

∴

I = 6.8E+6mm⁴

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

Variables

Constants

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

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

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 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 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}

How to Evaluate Moment of Inertia given Crippling Load by Euler's Formula?

Moment of Inertia given Crippling Load by Euler's Formula evaluator uses Moment of Inertia Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column) to evaluate the Moment of Inertia Column, The Moment of Inertia given Crippling Load by Euler's Formula is defined as a measure of an object's resistance to changes in its rotation, calculated based on the crippling load and effective length, providing valuable insights into the structural integrity of columns and beams in accordance with Euler's theory. Moment of Inertia Column is denoted by I symbol.

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

FAQs on Moment of Inertia given Crippling Load by Euler's Formula

What is the formula to find Moment of Inertia given Crippling Load by Euler's Formula?

The formula of Moment of Inertia given Crippling Load by Euler's Formula is expressed as Moment of Inertia Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column). Here is an example- 6.8E+18 = (1491407*3^2)/(pi^2*200000000000).

How to calculate Moment of Inertia given Crippling Load by Euler's Formula?

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

Can the Moment of Inertia given Crippling Load by Euler's Formula be negative?

No, the Moment of Inertia given Crippling Load by Euler's Formula, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia given Crippling Load by Euler's Formula?

Moment of Inertia given Crippling Load by Euler's Formula is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Moment of Inertia given Crippling Load by Euler's Formula can be measured.

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

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

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

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

Other formulas in Euler and Rankine's Theory category

How to Evaluate Moment of Inertia given Crippling Load by Euler's Formula?

FAQs on Moment of Inertia given Crippling Load by Euler's Formula

Variable Name