Modulus of Elasticity 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%
✖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%

✖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 given Euler Load [ε_column]

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Modulus of Elasticity given Euler Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
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.

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)
Moment of Inertia: 1.125 Kilogram Square Meter --> 1.125 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_column = (P_E*(l^2))/(pi^2*I) --> (4000*(5^2))/(pi^2*1.125)

Evaluating ... ...

ε_column = 9006.32743487447

STEP 3: Convert Result to Output's Unit

9006.32743487447 Pascal -->0.00900632743487447 Megapascal (Check conversion here)

FINAL ANSWER

0.00900632743487447 ≈ 0.009006 Megapascal <-- Modulus of Elasticity of Column

(Calculation completed in 00.020 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)

Modulus of Elasticity given Euler Load Formula

LaTeX Go

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

What is Young Modulus of Elasticity?

The Young's Modulus of Elasticity (E), commonly referred to as Young's Modulus, is a fundamental mechanical property that measures the stiffness or elasticity of a material. It defines the relationship between stress (force per unit area) and strain (deformation in response to stress) in a material under tension or compression within the elastic limit (the range where the material returns to its original shape after the load is removed).

How to Calculate Modulus of Elasticity given Euler Load?

Modulus of Elasticity given Euler Load calculator uses Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/(pi^2*Moment of Inertia) to calculate 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 calculate Modulus of Elasticity given Euler Load using this online calculator? To use this online calculator 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. Here is how the Modulus of Elasticity given Euler Load calculation can be explained with given input values -> 9E-9 = (4000*(5^2))/(pi^2*1.125).

FAQ

What is Modulus of Elasticity given Euler Load?

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 and is represented as ε_column = (P_E*(l^2))/(pi^2*I) or Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/(pi^2*Moment of Inertia). 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 & Moment of Inertia is a physical quantity that describes how mass is distributed in relation to an axis of rotation.

How to calculate Modulus of Elasticity given Euler Load?

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 is calculated using Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/(pi^2*Moment of Inertia). To calculate Modulus of Elasticity given Euler Load, you need Euler Load (P_E), Length of Column (l) & Moment of Inertia (I). With our tool, you need to enter the respective value for Euler Load, Length of Column & Moment of Inertia 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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