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Moment of Inertia given Crippling Load with Both Ends of Column Hinged Formula

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

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

I - Moment of Inertia Column?P - Column Crippling Load?l - Column Length?E - Modulus of Elasticity of Column?π - Archimedes' constant?

Moment of Inertia given Crippling Load with Both Ends of Column Hinged Example

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Here is how the Moment of Inertia given Crippling Load with Both Ends of Column Hinged equation looks like with Values.

Here is how the Moment of Inertia given Crippling Load with Both Ends of Column Hinged equation looks like with Units.

Here is how the Moment of Inertia given Crippling Load with Both Ends of Column Hinged equation looks like.

71961.0679 = \frac{3 \cdot 5000^{2}}{{3.1416}^{2} \cdot 10.56}

71961.0679cm⁴ = \frac{3kN \cdot {5000mm}^{2}}{{3.1416}^{2} \cdot 10.56MPa}

71961.0679 = \frac{3 \cdot 5000^{2}}{{3.1416}^{2} \cdot 10.56}

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Moment of Inertia given Crippling Load with Both Ends of Column Hinged Solution

Follow our step by step solution on how to calculate Moment of Inertia given Crippling Load with Both Ends of Column Hinged?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

I = \frac{3kN \cdot {5000mm}^{2}}{π^{2} \cdot 10.56MPa}

Next Step Substitute values of Constants

∴

I = \frac{3kN \cdot {5000mm}^{2}}{{3.1416}^{2} \cdot 10.56MPa}

Next Step Convert Units

∴

I = \frac{3000N \cdot {5m}^{2}}{{3.1416}^{2} \cdot 1.1E+7Pa}

Next Step Prepare to Evaluate

∴

I = \frac{3000 \cdot 5^{2}}{{3.1416}^{2} \cdot 1.1E+7}

Next Step Evaluate

∴

I = 0.000719610679277967m⁴

Next Step Convert to Output's Unit

∴

I = 71961.0679277967cm⁴

LAST Step Rounding Answer

∴

I = 71961.0679cm⁴

Moment of Inertia given Crippling Load with Both Ends of Column Hinged Formula Elements

Variables

Constants

Moment of Inertia Column

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

Symbol: I

Measurement: Second Moment of AreaUnit: cm⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia Column

Column Crippling Load

Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

Symbol: P

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Column Crippling Load

Column Length

Column Length 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 Column Length

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: E

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 Both Ends of Columns are Hinged category

Go Moment due to Crippling Load at Section if Both Ends of Column are Hinged

M t = - P \cdot δ

Go Crippling Load given Moment at Section if Both Ends of Column are Hinged

P = - \frac{M t}{δ}

Go Deflection at Section given Moment at Section if Both Ends of Column are Hinged

δ = - \frac{M t}{P}

Go Crippling Load when Both Ends of Column are Hinged

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

How to Evaluate Moment of Inertia given Crippling Load with Both Ends of Column Hinged?

Moment of Inertia given Crippling Load with Both Ends of Column Hinged evaluator uses Moment of Inertia Column = (Column Crippling Load*Column Length^2)/(pi^2*Modulus of Elasticity of Column) to evaluate the Moment of Inertia Column, Moment of Inertia given Crippling Load with Both Ends of Column Hinged formula is defined as a measure of the tendency of an object to resist changes in its rotation, providing a critical value for the maximum load a column can withstand before collapsing, with both ends of the column being hinged. Moment of Inertia Column is denoted by I symbol.

How to evaluate Moment of Inertia given Crippling Load with Both Ends of Column Hinged using this online evaluator? To use this online evaluator for Moment of Inertia given Crippling Load with Both Ends of Column Hinged, enter Column Crippling Load (P), Column Length (l) & Modulus of Elasticity of Column (E) and hit the calculate button.

FAQs on Moment of Inertia given Crippling Load with Both Ends of Column Hinged

What is the formula to find Moment of Inertia given Crippling Load with Both Ends of Column Hinged?

The formula of Moment of Inertia given Crippling Load with Both Ends of Column Hinged is expressed as Moment of Inertia Column = (Column Crippling Load*Column Length^2)/(pi^2*Modulus of Elasticity of Column). Here is an example- 7.2E+12 = (3000*5^2)/(pi^2*10560000).

How to calculate Moment of Inertia given Crippling Load with Both Ends of Column Hinged?

With Column Crippling Load (P), Column Length (l) & Modulus of Elasticity of Column (E) we can find Moment of Inertia given Crippling Load with Both Ends of Column Hinged using the formula - Moment of Inertia Column = (Column Crippling Load*Column Length^2)/(pi^2*Modulus of Elasticity of Column). This formula also uses Archimedes' constant .

Can the Moment of Inertia given Crippling Load with Both Ends of Column Hinged be negative?

No, the Moment of Inertia given Crippling Load with Both Ends of Column Hinged, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia given Crippling Load with Both Ends of Column Hinged?

Moment of Inertia given Crippling Load with Both Ends of Column Hinged is usually measured using the Centimeter⁴[cm⁴] for Second Moment of Area. Meter⁴[cm⁴], Millimeter⁴[cm⁴] are the few other units in which Moment of Inertia given Crippling Load with Both Ends of Column Hinged can be measured.

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Moment of Inertia given Crippling Load with Both Ends of Column Hinged Formula

Moment of Inertia given Crippling Load with Both Ends of Column Hinged Example

Moment of Inertia given Crippling Load with Both Ends of Column Hinged Solution

Moment of Inertia given Crippling Load with Both Ends of Column Hinged Formula Elements

Other formulas in Both Ends of Columns are Hinged category

How to Evaluate Moment of Inertia given Crippling Load with Both Ends of Column Hinged?

FAQs on Moment of Inertia given Crippling Load with Both Ends of Column Hinged

Variable Name