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%
✖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 [l]			+10% -10%

✖Euler load is the compressive load at which a slender column will suddenly bend or buckle.ⓘ Euler Load [P_E]

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Euler Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Euler Load - (Measured in Newton) - Euler load is the compressive load at which a slender column will suddenly bend or buckle.
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.
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.

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
Length of Column: 5000 Millimeter --> 5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_E = ((pi^2)*ε_column*I)/(l^2) --> ((pi^2)*9006*1.125)/(5^2)

Evaluating ... ...

P_E = 3999.85457562948

STEP 3: Convert Result to Output's Unit

3999.85457562948 Newton --> No Conversion Required

FINAL ANSWER

3999.85457562948 ≈ 3999.855 Newton <-- Euler Load

(Calculation completed in 00.004 seconds)

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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)

Euler Load Formula

LaTeX Go

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

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 Euler Load?

Euler Load calculator uses Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2) to calculate the Euler Load, The Euler Load formula is defined as the maximum load that a long, slender, ideal column can carry without buckling, taking into account the initial curvature of the column, and is a critical concept in structural engineering and architecture. Euler Load is denoted by P_E symbol.

How to calculate Euler Load using this online calculator? To use this online calculator for Euler Load, enter Modulus of Elasticity of Column (ε_column), Moment of Inertia (I) & Length of Column (l) and hit the calculate button. Here is how the Euler Load calculation can be explained with given input values -> 4.7E+6 = ((pi^2)*9006*1.125)/(5^2).

FAQ

What is Euler Load?

The Euler Load formula is defined as the maximum load that a long, slender, ideal column can carry without buckling, taking into account the initial curvature of the column, and is a critical concept in structural engineering and architecture and is represented as P_E = ((pi^2)*ε_column*I)/(l^2) or Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2). 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 & 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.

How to calculate Euler Load?

The Euler Load formula is defined as the maximum load that a long, slender, ideal column can carry without buckling, taking into account the initial curvature of the column, and is a critical concept in structural engineering and architecture is calculated using Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2). To calculate Euler Load, you need Modulus of Elasticity of Column (ε_column), Moment of Inertia (I) & Length of Column (l). With our tool, you need to enter the respective value for Modulus of Elasticity of Column, Moment of Inertia & Length of Column 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 Euler Load?

In this formula, Euler Load uses Modulus of Elasticity of Column, Moment of Inertia & Length of Column. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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