Moment of Inertia given Crippling Load by Euler's Formula Calculator

✖The Euler’s Buckling Load is the axial load at which a perfectly straight column or structural member starts to bend.ⓘ Euler’s Buckling Load [P_E]			+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 [E]			+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 by Euler's Formula [I]

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Moment of Inertia given Crippling Load by Euler's Formula

Formula

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

Example

`"6.8E^6mm⁴"=("1491.407kN"*("3000mm")^2)/(pi^2*"200000MPa")`

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Download Euler and Rankine's Theory Formulas PDF

Moment of Inertia given Crippling Load by Euler's Formula Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column)
I = (P_E*L_eff^2)/(pi^2*E)
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.
Euler’s Buckling Load - (Measured in Newton) - The Euler’s Buckling Load is the axial load at which a perfectly straight column or structural member starts to bend.
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

Euler’s Buckling Load: 1491.407 Kilonewton --> 1491407 Newton (Check conversion here)
Effective Column Length: 3000 Millimeter --> 3 Meter (Check conversion here)
Modulus of Elasticity Column: 200000 Megapascal --> 200000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (P_E*L_eff^2)/(pi^2*E) --> (1491407*3^2)/(pi^2*200000000000)

Evaluating ... ...

I = 6.80000051396106E-06

STEP 3: Convert Result to Output's Unit

6.80000051396106E-06 Meter⁴ -->6800000.51396106 Millimeter⁴ (Check conversion here)

FINAL ANSWER

6800000.51396106 ≈ 6.8E+6 Millimeter⁴ <-- Moment of Inertia Column

(Calculation completed in 00.004 seconds)

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< 19 Euler and Rankine's Theory Calculators

Effective Length of Column given Crippling Load and Rankine's Constant

Go Effective Column Length = sqrt((Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)*(Least Radius of Gyration Column^2)/Rankine's Constant)

Least Radius of Gyration given Crippling Load and Rankine's Constant

Go Least Radius of Gyration Column = sqrt((Rankine's Constant*Effective Column Length^2)/(Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1))

Rankine's Constant given Crippling Load

Go Rankine's Constant = ((Column Crushing Stress*Column Cross Sectional Area)/Crippling Load-1)*((Least Radius of Gyration Column)/Effective Column Length)^2

Cross-Sectional Area of Column given Crippling Load and Rankine's Constant

Go Column Cross Sectional Area = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Crushing Stress

Ultimate Crushing Stress given Crippling Load and Rankine's Constant

Go Column Crushing Stress = (Crippling Load*(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2))/Column Cross Sectional Area

Crippling Load given Rankine's Constant

Go Crippling Load = (Column Crushing Stress*Column Cross Sectional Area)/(1+Rankine's Constant*(Effective Column Length/Least Radius of Gyration Column)^2)

Effective Length of Column given Crippling Load by Euler's Formula

Go Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load))

Crushing Load by Rankine's Formula

Go Crushing Load = (Rankine’s Critical Load*Euler’s Buckling Load)/(Euler’s Buckling Load-Rankine’s Critical Load)

Crippling Load by Euler's Formula given Crippling Load by Rankine's Formula

Go Euler’s Buckling Load = (Crushing Load*Rankine’s Critical Load)/(Crushing Load-Rankine’s Critical Load)

Crippling Load by Rankine's Formula

Go Rankine’s Critical Load = (Crushing Load*Euler’s Buckling Load)/(Crushing Load+Euler’s Buckling Load)

Modulus of Elasticity given Crippling Load by Euler's Formula

Go Modulus of Elasticity Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Moment of Inertia Column)

Moment of Inertia given Crippling Load by Euler's Formula

Go Moment of Inertia Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column)

Crippling Load by Euler's Formula

Go Euler’s Buckling Load = (pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Effective Column Length^2)

Modulus of Elasticity given Rankine's Constant

Go Modulus of Elasticity Column = Column Crushing Stress/(pi^2*Rankine's Constant)

Rankine's Constant

Go Rankine's Constant = Column Crushing Stress/(pi^2*Modulus of Elasticity Column)

Ultimate Crushing Stress given Rankine's Constant

Go Column Crushing Stress = Rankine's Constant*pi^2*Modulus of Elasticity Column

Cross-Sectional Area of Column given Crushing Load

Go Column Cross Sectional Area = Crushing Load/Column Crushing Stress

Crushing Load given Ultimate Crushing Stress

Go Crushing Load = Column Crushing Stress*Column Cross Sectional Area

Ultimate Crushing Stress given Crushing Load

Go Column Crushing Stress = Crushing Load/Column Cross Sectional Area

< 5 Crippling Load by Euler's Formula Calculators

Effective Length of Column given Crippling Load by Euler's Formula

Go Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load))

Crippling Load by Euler's Formula given Crippling Load by Rankine's Formula

Go Euler’s Buckling Load = (Crushing Load*Rankine’s Critical Load)/(Crushing Load-Rankine’s Critical Load)

Modulus of Elasticity given Crippling Load by Euler's Formula

Go Modulus of Elasticity Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Moment of Inertia Column)

Moment of Inertia given Crippling Load by Euler's Formula

Go Moment of Inertia Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column)

Crippling Load by Euler's Formula

Go Euler’s Buckling Load = (pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Effective Column Length^2)

Moment of Inertia given Crippling Load by Euler's Formula Formula

Moment of Inertia Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column)
I = (P_E*L_eff^2)/(pi^2*E)

What is Ultimate Compressive Strength?

Ultimate Compressive Strength is defined as the force at which a specimen with a certain cross-section, and consisting of a particular fracturing material, fails when it is subjected to compression. The ultimate compressive strength is normally measured in N/mm2 (force per area) and is thus stress.

How to Calculate Moment of Inertia given Crippling Load by Euler's Formula?

Moment of Inertia given Crippling Load by Euler's Formula calculator uses Moment of Inertia Column = (Euler’s Buckling 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 by Euler's formula 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 by Euler's Formula using this online calculator? To use this online calculator for Moment of Inertia given Crippling Load by Euler's Formula, enter Euler’s Buckling Load (P_E), Effective Column Length (L_eff) & Modulus of Elasticity Column (E) and hit the calculate button. Here is how the Moment of Inertia given Crippling Load by Euler's Formula calculation can be explained with given input values -> 6.8E+18 = (1491407*3^2)/(pi^2*200000000000).

FAQ

What is Moment of Inertia given Crippling Load by Euler's Formula?

The Moment of Inertia given Crippling Load by Euler's formula 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_E*L_eff^2)/(pi^2*E) or Moment of Inertia Column = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column). The Euler’s Buckling Load is the axial load at which a perfectly straight column or structural member starts to bend, 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 by Euler's Formula?

The Moment of Inertia given Crippling Load by Euler's formula 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 = (Euler’s Buckling Load*Effective Column Length^2)/(pi^2*Modulus of Elasticity Column). To calculate Moment of Inertia given Crippling Load by Euler's Formula, you need Euler’s Buckling Load (P_E), Effective Column Length (L_eff) & Modulus of Elasticity Column (E). With our tool, you need to enter the respective value for Euler’s Buckling 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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