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 the measure of the resistance of a body to angular acceleration about a given axis.ⓘ 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

Formula

`"ε"_{"column"} = ("P"_{"E"}*("l"^2))/((pi^2)*"I")`

Example

`"0.009006MPa"=("4kN"*(("5000mm")^2))/((pi^2)*"1.125kg·m²")`

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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 the measure of the resistance of a body to angular acceleration about a given axis.

STEP 1: Convert Input(s) to Base Unit

Euler Load: 4 Kilonewton --> 4000 Newton (Check conversion here)
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 00.004 seconds)

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

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< 19 Columns With Initial Curvature Calculators

Radius of Gyration given Maximum Stress for Columns with Initial Curvature

Go Radius of Gyration = sqrt((Maximum initial deflection*Distance from Neutral Axis to Extreme Point)/(1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1))

Euler Stress given Maximum Stress for Columns with Initial Curvature

Go Euler Stress = Direct stress/(1-((Maximum initial deflection*Distance from Neutral Axis to Extreme Point/(Least Radius of Gyration Column^2))/((Maximum Stress at Crack Tip/Direct stress)-1)))

Maximum Stress for Columns with Initial Curvature

Go Maximum Stress at Crack Tip = (((Maximum initial deflection*Distance from Neutral Axis to Extreme Point/(Least Radius of Gyration Column^2))/(1-(Direct stress/Euler Stress)))+1)*Direct stress

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

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

Value of Distance 'X' given Final Deflection at Distance X from end A of Column

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

Distance from Neutral Axis of Extreme Layer given Maximum Stress for Columns

Go Distance from Neutral Axis to Extreme Point = (1-(Direct stress/Euler Stress))*((Maximum Stress at Crack Tip/Direct stress)-1)*(Radius of Gyration^2)/Maximum initial deflection

Crippling Load given Final Deflection at Distance X from end A of Column

Go Crippling Load = (1-(Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)/Deflection of Column))*Euler Load

Euler Load given Final Deflection at Distance X from end A of Column

Go Euler Load = Crippling Load/(1-(Maximum initial deflection*sin((pi*Distance of deflection from end A)/Length of column)/Deflection of Column))

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

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

Go Distance of deflection from end A = (asin(Initial Deflection/Maximum initial deflection))*Length of column/pi

Length of Column given Euler Load

Go Length of column = sqrt(((pi^2)*Modulus of elasticity of column*Moment of Inertia)/(Euler Load))

Modulus of Elasticity given Euler Load

Go Modulus of elasticity of column = (Euler Load*(Length of column^2))/((pi^2)*Moment of Inertia)

Moment of Inertia given Euler Load

Go Moment of Inertia = (Euler Load*(Length of column^2))/((pi^2)*Modulus of elasticity of column)

Euler Load

Go Euler Load = ((pi^2)*Modulus of elasticity of column*Moment of Inertia)/(Length of column^2)

Crippling Load given Maximum Deflection for Columns with Initial Curvature

Go Crippling Load = (1-(Maximum initial deflection/Deflection of Column))*Euler Load

Euler Load given Maximum Deflection for Columns with Initial Curvature

Go Euler Load = Crippling Load/(1-(Maximum initial deflection/Deflection of Column))

Crippling Load given Factor of Safety

Go Crippling Load = (1-(1/Factor of Safety))*Euler Load

Factor of Safety given Euler Load

Go Factor of Safety = 1/(1-(Crippling Load/Euler Load))

Euler Load given Factor of Safety

Go Euler Load = Crippling Load/(1-(1/Factor of Safety))

Modulus of Elasticity given Euler Load Formula

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 buckling or crippling load?

Buckling Load is the highest load at which the column will buckle. Crippling load is the max load beyond that load, it cant use further it becomes disable to use.

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 quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when stress is applied to it. 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 quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when stress is applied to it 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 the measure of the resistance of a body to angular acceleration about a given axis.

How to calculate Modulus of Elasticity given Euler Load?

The Modulus of elasticity given Euler load formula is defined as a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when stress is applied to it 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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