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

✖Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.ⓘ Column Crippling Load [P]			+10% -10%
✖Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.ⓘ Effective Column Length [L_eff]			+10% -10%
✖Modulus of Elasticity 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 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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Formula

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

Formula

`"I" = ("P"*"L"_{"eff"}^2)/(pi^2*"ε"_{"c"})`

Example

`"59967.56cm⁴"=("10000N"*("2500mm")^2)/(pi^2*"10.56MPa")`

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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 Column Length^2)/(pi^2*Modulus of Elasticity Column)
I = (P*L_eff^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 is the load over which a column prefers to deform laterally rather than compressing itself.
Effective Column Length - (Measured in Meter) - Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.
Modulus of Elasticity Column - (Measured in Pascal) - Modulus of Elasticity 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

Column Crippling Load: 10000 Newton --> 10000 Newton No Conversion Required
Effective Column Length: 2500 Millimeter --> 2.5 Meter (Check conversion here)
Modulus of Elasticity Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (P*L_eff^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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< 14 Estimation of Effective Length of Columns Calculators

Radius of Gyration given Effective Length and Crippling Load

Go Least Radius of Gyration Column = sqrt((Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column*Column Cross Sectional Area))

Effective Length of Column given Crippling Stress

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

Effective Length of Column given Crippling Load for any type of End Condition

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

Modulus of Elasticity of Column given Crippling Stress

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

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

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

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

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

Least Radius of Gyration given Slenderness Ratio

Go Least Radius of Gyration Column = Length of Column/Slenderness Ratio

Actual Length given Slenderness Ratio

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

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

Go Effective Column Length = Length of Column/(sqrt(2))

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

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

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

Go Length of Column = Effective Column Length/2

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

Go Effective Column Length = 2*Length of Column

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

Go Length of Column = 2*Effective Column Length

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

Go Effective Column Length = Length of Column/2

< 3 Modulus of elasticity Calculators

Modulus of Elasticity of Column given Crippling Stress

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

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

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

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

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

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

Moment of Inertia Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column)
I = (P*L_eff^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 Column Length^2)/(pi^2*Modulus of Elasticity Column) to calculate the Moment of Inertia Column, The Moment of Inertia given Crippling Load for any type of End Condition is defined as 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 torque (turning force). 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), Effective Column Length (L_eff) & Modulus of Elasticity 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?

The Moment of Inertia given Crippling Load for any type of End Condition is defined as 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 torque (turning force) and is represented as I = (P*L_eff^2)/(pi^2*ε_c) or Moment of Inertia Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column). Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself, Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration & Modulus of Elasticity 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 Crippling Load for any type of End Condition?

The Moment of Inertia given Crippling Load for any type of End Condition is defined as 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 torque (turning force) is calculated using Moment of Inertia Column = (Column Crippling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column). To calculate Moment of Inertia given Crippling Load for any type of End Condition, you need Column Crippling Load (P), Effective Column Length (L_eff) & Modulus of Elasticity Column (ε_c). With our tool, you need to enter the respective value for Column Crippling Load, Effective Column Length & Modulus of Elasticity 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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