Moment of Inertia given Euler Load Calculator

✖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 [l]			+10% -10%
✖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 given Euler Load [I]

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Moment of Inertia given Euler Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Euler Load: 4000 Newton --> 4000 Newton No Conversion Required
Length of Column: 5000 Millimeter --> 5 Meter (Check conversion here)
Modulus of Elasticity of Column: 0.009006 Megapascal --> 9006 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (P_E*(l^2))/((pi^2)*ε_column) --> (4000*(5^2))/((pi^2)*9006)

Evaluating ... ...

I = 1.12504090209125

STEP 3: Convert Result to Output's Unit

1.12504090209125 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

1.12504090209125 ≈ 1.125041 Kilogram Square Meter <-- Moment of Inertia

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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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)

Moment of Inertia given Euler Load Formula

LaTeX Go

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

What is Moment of Inertia?

The Moment of Inertia (I), also known as the second moment of area, is a geometric property of a cross-section that quantifies its resistance to bending and torsion. It plays a crucial role in structural and mechanical engineering, particularly in analyzing beams and other load-bearing structures.

How to Calculate Moment of Inertia given Euler Load?

Moment of Inertia given Euler Load calculator uses Moment of Inertia = (Euler Load*(Length of Column^2))/((pi^2)*Modulus of Elasticity of Column) to calculate the Moment of Inertia, The Moment of Inertia given Euler Load formula is defined as a measure of the resistance of a column to bending, considering the initial curvature of the column and the Euler load, which is the critical load at which the column will buckle. Moment of Inertia is denoted by I symbol.

How to calculate Moment of Inertia given Euler Load using this online calculator? To use this online calculator for Moment of Inertia given Euler Load, enter Euler Load (P_E), Length of Column (l) & Modulus of Elasticity of Column (ε_column) and hit the calculate button. Here is how the Moment of Inertia given Euler Load calculation can be explained with given input values -> 0.000959 = (4000*(5^2))/((pi^2)*9006).

FAQ

What is Moment of Inertia given Euler Load?

The Moment of Inertia given Euler Load formula is defined as a measure of the resistance of a column to bending, considering the initial curvature of the column and the Euler load, which is the critical load at which the column will buckle and is represented as I = (P_E*(l^2))/((pi^2)*ε_column) or Moment of Inertia = (Euler Load*(Length of Column^2))/((pi^2)*Modulus of Elasticity of Column). Euler load is the compressive load at which a slender column will suddenly bend or buckle, 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 is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

How to calculate Moment of Inertia given Euler Load?

The Moment of Inertia given Euler Load formula is defined as a measure of the resistance of a column to bending, considering the initial curvature of the column and the Euler load, which is the critical load at which the column will buckle is calculated using Moment of Inertia = (Euler Load*(Length of Column^2))/((pi^2)*Modulus of Elasticity of Column). To calculate Moment of Inertia given Euler Load, you need Euler Load (P_E), Length of Column (l) & Modulus of Elasticity of Column (ε_column). With our tool, you need to enter the respective value for Euler Load, Length of Column & Modulus of Elasticity of Column and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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