Moment of Inertia given Crippling Load for any type of End Condition Calculator

✖Column crippling load also known as the buckling load, is the maximum axial compressive load that a column can withstand before it buckles or fails due to instability.ⓘ Column Crippling Load [P_cr]			+10% -10%
✖Effective length of column is the length of an equivalent pin-ended column that has the same load-carrying capacity as the actual column under consideration.ⓘ Effective Length of Column [L_e]			+10% -10%
✖Modulus of elasticity of column also known as Young’s modulus, is a measure of a material’s stiffness or rigidity which quantifies the relationship between stress and strain.ⓘ Modulus of Elasticity of Column [ε_c]			+10% -10%

✖Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia given Crippling Load for any type of End Condition [I]

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Moment of Inertia given Crippling Load for any type of End Condition Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column)
I = (P_cr*L_e^2)/(pi^2*ε_c)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Moment of Inertia Column - (Measured in Meter⁴) - Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.
Column Crippling Load - (Measured in Newton) - Column crippling load also known as the buckling load, is the maximum axial compressive load that a column can withstand before it buckles or fails due to instability.
Effective Length of Column - (Measured in Meter) - Effective length of column is the length of an equivalent pin-ended column that has the same load-carrying capacity as the actual column under consideration.
Modulus of Elasticity of Column - (Measured in Pascal) - Modulus of elasticity of column also known as Young’s modulus, is a measure of a material’s stiffness or rigidity which quantifies the relationship between stress and strain.

STEP 1: Convert Input(s) to Base Unit

Column Crippling Load: 10000 Newton --> 10000 Newton No Conversion Required
Effective Length of Column: 2500 Millimeter --> 2.5 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 = (P_cr*L_e^2)/(pi^2*ε_c) --> (10000*2.5^2)/(pi^2*10560000)

Evaluating ... ...

I = 0.000599675566064973

STEP 3: Convert Result to Output's Unit

0.000599675566064973 Meter⁴ -->59967.5566064973 Centimeter⁴ (Check conversion here)

FINAL ANSWER

59967.5566064973 ≈ 59967.56 Centimeter⁴ <-- Moment of Inertia Column

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Estimation of Effective Length of Columns Calculators

Actual Length given Slenderness Ratio

LaTeX Go Length of Column = Slenderness Ratio*Least Radius of Gyration of Column

Actual Length of Column given Effective Length if One End is Fixed Other is Hinged

LaTeX Go Length of Column = sqrt(2)*Effective Length of Column

Actual Length of Column given Effective Length if One End is Fixed Other is Free

LaTeX Go Length of Column = Effective Length of Column/2

Actual Length of Column given Effective Length if Both Ends of Column are Fixed

LaTeX Go Length of Column = 2*Effective Length of Column

< Modulus of elasticity Calculators

Modulus of Elasticity of Column given Crippling Stress

LaTeX Go Modulus of Elasticity of Column = (Crippling Stress*Effective Length of Column^2)/(pi^2*Least Radius of Gyration of Column^2)

Modulus of Elasticity given Crippling Load for any type of End Condition

LaTeX Go Modulus of Elasticity of Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Moment of Inertia Column)

Moment of Inertia given Crippling Load for any type of End Condition

LaTeX Go Moment of Inertia Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column)

Moment of Inertia given Crippling Load for any type of End Condition Formula

LaTeX Go

Moment of Inertia Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column)
I = (P_cr*L_e^2)/(pi^2*ε_c)

What is meant by Effective Length of a Column also define Slenderness Ratio?

The effective length of the column is the length of an equivalent column of the same material and cross-sectional area with hinged ends and having the value of the crippling load equal to that of the given column. The least radius of gyration is the radius of gyration where the least moment of inertia is considered.

How to Calculate Moment of Inertia given Crippling Load for any type of End Condition?

Moment of Inertia given Crippling Load for any type of End Condition calculator uses Moment of Inertia Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column) to calculate the Moment of Inertia Column, Moment of Inertia given Crippling Load for any type of End Condition formula is defined as a measure of an object's resistance to changes in its rotation, providing a critical value for structural integrity in columns under various end conditions, essential for safe and efficient design in engineering applications. Moment of Inertia Column is denoted by I symbol.

How to calculate Moment of Inertia given Crippling Load for any type of End Condition using this online calculator? To use this online calculator for Moment of Inertia given Crippling Load for any type of End Condition, enter Column Crippling Load (P_cr), Effective Length of Column (L_e) & Modulus of Elasticity of Column (ε_c) and hit the calculate button. Here is how the Moment of Inertia given Crippling Load for any type of End Condition calculation can be explained with given input values -> 6E+12 = (10000*2.5^2)/(pi^2*10560000).

FAQ

What is Moment of Inertia given Crippling Load for any type of End Condition?

Moment of Inertia given Crippling Load for any type of End Condition formula is defined as a measure of an object's resistance to changes in its rotation, providing a critical value for structural integrity in columns under various end conditions, essential for safe and efficient design in engineering applications and is represented as I = (P_cr*L_e^2)/(pi^2*ε_c) or Moment of Inertia Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column). Column crippling load also known as the buckling load, is the maximum axial compressive load that a column can withstand before it buckles or fails due to instability, Effective length of column is the length of an equivalent pin-ended column that has the same load-carrying capacity as the actual column under consideration & Modulus of elasticity of column also known as Young’s modulus, is a measure of a material’s stiffness or rigidity which quantifies the relationship between stress and strain.

How to calculate Moment of Inertia given Crippling Load for any type of End Condition?

Moment of Inertia given Crippling Load for any type of End Condition formula is defined as a measure of an object's resistance to changes in its rotation, providing a critical value for structural integrity in columns under various end conditions, essential for safe and efficient design in engineering applications is calculated using Moment of Inertia Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column). To calculate Moment of Inertia given Crippling Load for any type of End Condition, you need Column Crippling Load (P_cr), Effective Length of Column (L_e) & Modulus of Elasticity of Column (ε_c). With our tool, you need to enter the respective value for Column Crippling Load, Effective 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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