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Modulus of Elasticity given Euler Load Formula

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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. Check FAQs

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

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

Modulus of Elasticity given Euler Load Example

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Here is how the Modulus of Elasticity given Euler Load equation looks like with Values.

Here is how the Modulus of Elasticity given Euler Load equation looks like with Units.

Here is how the Modulus of Elasticity given Euler Load equation looks like.

0.009 = \frac{4 \cdot (5000^{2})}{({3.1416}^{2}) \cdot 1.125}

0.009MPa = \frac{4kN \cdot ({5000mm}^{2})}{({3.1416}^{2}) \cdot 1.125kg·m²}

0.009 = \frac{4 \cdot (5000^{2})}{({3.1416}^{2}) \cdot 1.125}

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Modulus of Elasticity given Euler Load Solution

Follow our step by step solution on how to calculate Modulus of Elasticity given Euler Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ε column = \frac{4kN \cdot ({5000mm}^{2})}{(π^{2}) \cdot 1.125kg·m²}

Next Step Substitute values of Constants

∴

ε column = \frac{4kN \cdot ({5000mm}^{2})}{({3.1416}^{2}) \cdot 1.125kg·m²}

Next Step Convert Units

∴

ε column = \frac{4000N \cdot ({5m}^{2})}{({3.1416}^{2}) \cdot 1.125kg·m²}

Next Step Prepare to Evaluate

∴

ε column = \frac{4000 \cdot (5^{2})}{({3.1416}^{2}) \cdot 1.125}

Next Step Evaluate

∴

ε column = 9006.32743487447Pa

Next Step Convert to Output's Unit

∴

ε column = 0.00900632743487447MPa

LAST Step Rounding Answer

∴

ε column = 0.009MPa

Modulus of Elasticity given Euler Load Formula Elements

Variables

Constants

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

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

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

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 Moment of Inertia given Euler Load

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

How to Evaluate Modulus of Elasticity given Euler Load?

Modulus of Elasticity given Euler Load evaluator uses Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/((pi^2)*Moment of Inertia) to evaluate the Modulus of Elasticity of Column, The Modulus of Elasticity given Euler Load formula is defined as a measure of the stiffness of a material and the load at which a column will buckle, considering the initial curvature of the column, which is essential in structural analysis and design. Modulus of Elasticity of Column is denoted by ε_column symbol.

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

FAQs on Modulus of Elasticity given Euler Load

What is the formula to find Modulus of Elasticity given Euler Load?

The formula of Modulus of Elasticity given Euler Load is expressed as Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/((pi^2)*Moment of Inertia). Here is an example- 9E-9 = (4000*(5^2))/((pi^2)*1.125).

How to calculate Modulus of Elasticity given Euler Load?

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

Can the Modulus of Elasticity given Euler Load be negative?

No, the Modulus of Elasticity given Euler Load, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of Elasticity given Euler Load?

Modulus of Elasticity given Euler Load is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Modulus of Elasticity given Euler Load can be measured.

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Modulus of Elasticity given Euler Load Formula

Modulus of Elasticity given Euler Load Example

Modulus of Elasticity given Euler Load Solution

Modulus of Elasticity given Euler Load Formula Elements

Other formulas in Columns With Initial Curvature category

How to Evaluate Modulus of Elasticity given Euler Load?

FAQs on Modulus of Elasticity given Euler Load

Variable Name