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Moment of Inertia given Crippling Load for any type of End Condition 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 cr \cdot {L e}^{2}}{π^{2} \cdot ε c}

I - Moment of Inertia Column?P_cr - Column Crippling Load?L_e - Effective Length of Column?ε_c - Modulus of Elasticity of Column?π - Archimedes' constant?

Moment of Inertia given Crippling Load for any type of End Condition Example

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Here is how the Moment of Inertia given Crippling Load for any type of End Condition equation looks like with Values.

Here is how the Moment of Inertia given Crippling Load for any type of End Condition equation looks like with Units.

Here is how the Moment of Inertia given Crippling Load for any type of End Condition equation looks like.

59967.5566 = \frac{10000 \cdot 2500^{2}}{{3.1416}^{2} \cdot 10.56}

59967.5566cm⁴ = \frac{10000N \cdot {2500mm}^{2}}{{3.1416}^{2} \cdot 10.56MPa}

59967.5566 = \frac{10000 \cdot 2500^{2}}{{3.1416}^{2} \cdot 10.56}

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Moment of Inertia given Crippling Load for any type of End Condition Solution

Follow our step by step solution on how to calculate Moment of Inertia given Crippling Load for any type of End Condition?

FIRST Step Consider the formula

I = \frac{P cr \cdot {L e}^{2}}{π^{2} \cdot ε c}

Next Step Substitute values of Variables

∴

I = \frac{10000N \cdot {2500mm}^{2}}{π^{2} \cdot 10.56MPa}

Next Step Substitute values of Constants

∴

I = \frac{10000N \cdot {2500mm}^{2}}{{3.1416}^{2} \cdot 10.56MPa}

Next Step Convert Units

∴

I = \frac{10000N \cdot {2.5m}^{2}}{{3.1416}^{2} \cdot 1.1E+7Pa}

Next Step Prepare to Evaluate

∴

I = \frac{10000 \cdot {2.5}^{2}}{{3.1416}^{2} \cdot 1.1E+7}

Next Step Evaluate

∴

I = 0.000599675566064973m⁴

Next Step Convert to Output's Unit

∴

I = 59967.5566064973cm⁴

LAST Step Rounding Answer

∴

I = 59967.5566cm⁴

Moment of Inertia given Crippling Load for any type of End Condition 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 also known as the buckling load, is the maximum axial compressive load that a column can withstand before it buckles or fails due to instability.

Symbol: P_cr

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Column Crippling Load

Effective Length of Column

Effective length of column is the length of an equivalent pin-ended column that has the same load-carrying capacity as the actual column under consideration.

Symbol: L_e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Length of Column

Modulus of Elasticity of Column

Modulus of elasticity of column also known as Young’s modulus, is a measure of a material’s stiffness or rigidity which quantifies the relationship between stress and strain.

Symbol: ε_c

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 Estimation of Effective Length of Columns category

Go Modulus of Elasticity given Crippling Load for any type of End Condition

ε c = \frac{P cr \cdot {L e}^{2}}{π^{2} \cdot I}

Go Modulus of Elasticity of Column given Crippling Stress

ε c = \frac{σ crippling \cdot {L e}^{2}}{π^{2} \cdot r^{2}}

How to Evaluate Moment of Inertia given Crippling Load for any type of End Condition?

Moment of Inertia given Crippling Load for any type of End Condition evaluator uses Moment of Inertia Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column) to evaluate the Moment of Inertia Column, Moment of Inertia given Crippling Load for any type of End Condition formula is defined as a measure of an object's resistance to changes in its rotation, providing a critical value for structural integrity in columns under various end conditions, essential for safe and efficient design in engineering applications. Moment of Inertia Column is denoted by I symbol.

How to evaluate Moment of Inertia given Crippling Load for any type of End Condition using this online evaluator? To use this online evaluator for Moment of Inertia given Crippling Load for any type of End Condition, enter Column Crippling Load (P_cr), Effective Length of Column (L_e) & Modulus of Elasticity of Column (ε_c) and hit the calculate button.

FAQs on Moment of Inertia given Crippling Load for any type of End Condition

What is the formula to find Moment of Inertia given Crippling Load for any type of End Condition?

The formula of Moment of Inertia given Crippling Load for any type of End Condition is expressed as Moment of Inertia Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column). Here is an example- 6E+12 = (10000*2.5^2)/(pi^2*10560000).

How to calculate Moment of Inertia given Crippling Load for any type of End Condition?

With Column Crippling Load (P_cr), Effective Length of Column (L_e) & Modulus of Elasticity of Column (ε_c) we can find Moment of Inertia given Crippling Load for any type of End Condition using the formula - Moment of Inertia Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column). This formula also uses Archimedes' constant .

Can the Moment of Inertia given Crippling Load for any type of End Condition be negative?

No, the Moment of Inertia given Crippling Load for any type of End Condition, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia given Crippling Load for any type of End Condition?

Moment of Inertia given Crippling Load for any type of End Condition 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 for any type of End Condition can be measured.

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Moment of Inertia given Crippling Load for any type of End Condition Formula

Moment of Inertia given Crippling Load for any type of End Condition Example

Moment of Inertia given Crippling Load for any type of End Condition Solution

Moment of Inertia given Crippling Load for any type of End Condition Formula Elements

Other formulas in Estimation of Effective Length of Columns category

How to Evaluate Moment of Inertia given Crippling Load for any type of End Condition?

FAQs on Moment of Inertia given Crippling Load for any type of End Condition

Variable Name