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 = (PE*(l^2))/((pi^2)*εcolumn)
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 the measure of the resistance of a body to angular acceleration about a given axis.
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: 4 Kilonewton --> 4000 Newton (Check conversion here)
Length of column: 5000 Millimeter --> 5 Meter (Check conversion here)
Modulus of elasticity of column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = (PE*(l^2))/((pi^2)*εcolumn) --> (4000*(5^2))/((pi^2)*10560000)
Evaluating ... ...
I = 0.000959480905703956
STEP 3: Convert Result to Output's Unit
0.000959480905703956 Kilogram Square Meter --> No Conversion Required
FINAL ANSWER
0.000959480905703956 0.000959 Kilogram Square Meter <-- Moment of Inertia
(Calculation completed in 00.004 seconds)

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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))

Moment of Inertia given Euler Load Formula

Moment of Inertia = (Euler Load*(Length of column^2))/((pi^2)*Modulus of elasticity of column)
I = (PE*(l^2))/((pi^2)*εcolumn)

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 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 quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque (turning force). 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 (PE), Length of column (l) & Modulus of elasticity of column 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)*10560000).

FAQ

What is Moment of Inertia given Euler Load?
The Moment of inertia given Euler load formula is defined as quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque (turning force) and is represented as I = (PE*(l^2))/((pi^2)*εcolumn) 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 quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque (turning force) 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 (PE), Length of column (l) & Modulus of elasticity of column 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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