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Length of Column given Euler Load Formula

GoLength of Column given Initial Deflection at Distance X from end A Formula

GoLength of Column given Final Deflection at Distance X from End A of Column Formula

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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. Check FAQs

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

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

Length of Column given Euler Load Example

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Here is how the Length of Column given Euler Load equation looks like with Values.

Here is how the Length of Column given Euler Load equation looks like with Units.

Here is how the Length of Column given Euler Load equation looks like.

4999.9091 = \sqrt{\frac{({3.1416}^{2}) \cdot 0.009 \cdot 1.125}{4000}}

4999.9091mm = \sqrt{\frac{({3.1416}^{2}) \cdot 0.009MPa \cdot 1.125kg·m²}{4000N}}

4999.9091 = \sqrt{\frac{({3.1416}^{2}) \cdot 0.009 \cdot 1.125}{4000}}

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Length of Column given Euler Load Solution

Follow our step by step solution on how to calculate Length of Column given Euler Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

l = \sqrt{\frac{(π^{2}) \cdot 0.009MPa \cdot 1.125kg·m²}{4000N}}

Next Step Substitute values of Constants

∴

l = \sqrt{\frac{({3.1416}^{2}) \cdot 0.009MPa \cdot 1.125kg·m²}{4000N}}

Next Step Convert Units

∴

l = \sqrt{\frac{({3.1416}^{2}) \cdot 9006Pa \cdot 1.125kg·m²}{4000N}}

Next Step Prepare to Evaluate

∴

l = \sqrt{\frac{({3.1416}^{2}) \cdot 9006 \cdot 1.125}{4000}}

Next Step Evaluate

∴

l = 4.99990910894231m

Next Step Convert to Output's Unit

∴

l = 4999.90910894231mm

LAST Step Rounding Answer

∴

l = 4999.9091mm

Length of Column given Euler Load Formula Elements

Variables

Constants

Functions

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

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: N

Note: Value can be positive or negative.

Formulas to find Euler Load

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Length of Column

Go Length of Column given Initial Deflection at Distance X from end A

l = \frac{π \cdot x}{a \sin (\frac{y'}{C})}

Go Length of Column given Final Deflection at Distance X from End A of Column

l = \frac{π \cdot x}{a \sin (\frac{δ c}{(\frac{1}{1 - (\frac{P}{P E})}) \cdot C})}

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 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}

Go Moment of Inertia given Euler Load

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

How to Evaluate Length of Column given Euler Load?

Length of Column given Euler Load evaluator uses Length of Column = sqrt(((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Euler Load)) to evaluate the Length of Column, The Length of Column given Euler Load formula is defined as a measure of the maximum axial load that a long, slender column can support without buckling, taking into account the initial curvature of the column and its material properties, providing a critical value for structural engineers to ensure the stability of their designs. Length of Column is denoted by l symbol.

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

FAQs on Length of Column given Euler Load

What is the formula to find Length of Column given Euler Load?

The formula of Length of Column given Euler Load is expressed as Length of Column = sqrt(((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Euler Load)). Here is an example- 1.7E+8 = sqrt(((pi^2)*9006*1.125)/(4000)).

How to calculate Length of Column given Euler Load?

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

What are the other ways to Calculate Length of Column?

Here are the different ways to Calculate Length of Column-

Length of Column=(pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection))
Length of Column=(pi*Distance of Deflection from end A)/(asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection)))

Can the Length of Column given Euler Load be negative?

No, the Length of Column given Euler Load, measured in Length cannot be negative.

Which unit is used to measure Length of Column given Euler Load?

Length of Column given Euler Load is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Column given Euler Load can be measured.

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Length of Column given Euler Load Formula

​GoLength of Column given Initial Deflection at Distance X from end A Formula

​GoLength of Column given Final Deflection at Distance X from End A of Column Formula

Length of Column given Euler Load Example

Length of Column given Euler Load Solution

Length of Column given Euler Load Formula Elements

Other Formulas to find Length of Column

Other formulas in Columns With Initial Curvature category

How to Evaluate Length of Column given Euler Load?

FAQs on Length of Column given Euler Load

Variable Name

GoLength of Column given Initial Deflection at Distance X from end A Formula

GoLength of Column given Final Deflection at Distance X from End A of Column Formula