Length of Column given Euler Load Calculator

✖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.ⓘ Modulus of Elasticity of Column [ε_column]			+10% -10%
✖Moment of Inertia is a physical quantity that describes how mass is distributed in relation to an axis of rotation.ⓘ Moment of Inertia [I]			+10% -10%
✖Euler load is the compressive load at which a slender column will suddenly bend or buckle.ⓘ Euler Load [P_E]			+10% -10%

✖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.ⓘ Length of Column given Euler Load [l]

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Length of Column given Euler Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Column = sqrt(((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Euler Load))
l = sqrt(((pi^2)*ε_column*I)/(P_E))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Length of Column - (Measured in Meter) - 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.
Modulus of Elasticity of Column - (Measured in Pascal) - 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.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is a physical quantity that describes how mass is distributed in relation to an axis of rotation.
Euler Load - (Measured in Newton) - Euler load is the compressive load at which a slender column will suddenly bend or buckle.

STEP 1: Convert Input(s) to Base Unit

Modulus of Elasticity of Column: 0.009006 Megapascal --> 9006 Pascal (Check conversion here)
Moment of Inertia: 1.125 Kilogram Square Meter --> 1.125 Kilogram Square Meter No Conversion Required
Euler Load: 4000 Newton --> 4000 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l = sqrt(((pi^2)*ε_column*I)/(P_E)) --> sqrt(((pi^2)*9006*1.125)/(4000))

Evaluating ... ...

l = 4.99990910894231

STEP 3: Convert Result to Output's Unit

4.99990910894231 Meter -->4999.90910894231 Millimeter (Check conversion here)

FINAL ANSWER

4999.90910894231 ≈ 4999.909 Millimeter <-- Length of Column

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Initial Curvature » Length of Column given Euler Load

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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< Columns With Initial Curvature Calculators

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

LaTeX Go Length of Column = (pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection))

Value of Distance 'X' given Initial Deflection at Distance X from end A

LaTeX Go Distance of Deflection from end A = (asin(Initial Deflection/Maximum Initial Deflection))*Length of Column/pi

Modulus of Elasticity given Euler Load

LaTeX Go Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/(pi^2*Moment of Inertia)

Euler Load

LaTeX Go Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2)

Length of Column given Euler Load Formula

LaTeX Go

Length of Column = sqrt(((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Euler Load))
l = sqrt(((pi^2)*ε_column*I)/(P_E))

What is Euler Load?

The Euler Load (or Euler’s Critical Load) refers to the maximum axial load a slender column can bear before it buckles. It was derived by Swiss mathematician Leonhard Euler and is a key concept in structural engineering when analyzing column stability. Buckling occurs when a column under compressive load becomes unstable and deflects laterally, potentially leading to failure even if the material hasn’t reached its compressive strength limit.

How to Calculate Length of Column given Euler Load?

Length of Column given Euler Load calculator uses Length of Column = sqrt(((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Euler Load)) to calculate 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 calculate Length of Column given Euler Load using this online calculator? To use this online calculator 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. Here is how the Length of Column given Euler Load calculation can be explained with given input values -> 1.7E+8 = sqrt(((pi^2)*9006*1.125)/(4000)).

FAQ

What is Length of Column given Euler Load?

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 and is represented as l = sqrt(((pi^2)*ε_column*I)/(P_E)) or Length of Column = sqrt(((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Euler Load)). 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, Moment of Inertia is a physical quantity that describes how mass is distributed in relation to an axis of rotation & Euler load is the compressive load at which a slender column will suddenly bend or buckle.

How to calculate Length of Column given Euler Load?

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 is calculated using Length of Column = sqrt(((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Euler Load)). To calculate Length of Column given Euler Load, you need Modulus of Elasticity of Column (ε_column), Moment of Inertia (I) & Euler Load (P_E). With our tool, you need to enter the respective value for Modulus of Elasticity of Column, Moment of Inertia & Euler Load and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Length of Column?

In this formula, Length of Column uses Modulus of Elasticity of Column, Moment of Inertia & Euler Load. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)))

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