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

✖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 Column [I]			+10% -10%
✖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 Length of Column given Crippling Load by Euler's Formula [L_eff]

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

Formula

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

Example

`"3000mm"=sqrt((pi^2*"200000MPa"*"6800000mm⁴")/("1491.407kN"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load))
L_eff = sqrt((pi^2*E*I)/(P_E))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Modulus of Elasticity Column: 200000 Megapascal --> 200000000000 Pascal (Check conversion here)
Moment of Inertia Column: 6800000 Millimeter⁴ --> 6.8E-06 Meter⁴ (Check conversion here)
Euler’s Buckling Load: 1491.407 Kilonewton --> 1491407 Newton (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_eff = sqrt((pi^2*E*I)/(P_E)) --> sqrt((pi^2*200000000000*6.8E-06)/(1491407))

Evaluating ... ...

L_eff = 2.99999988662624

STEP 3: Convert Result to Output's Unit

2.99999988662624 Meter -->2999.99988662624 Millimeter (Check conversion here)

FINAL ANSWER

2999.99988662624 ≈ 3000 Millimeter <-- Effective Column Length

(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)

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

Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load))
L_eff = sqrt((pi^2*E*I)/(P_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 Effective Length of Column given Crippling Load by Euler's Formula?

Effective Length of Column given Crippling Load by Euler's Formula calculator uses Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load)) to calculate the Effective Column Length, The Effective Length of Column given Crippling Load by Euler's Formula is defined as the distance between successive inflection points or points of zero moment. Effective Column Length is denoted by L_eff symbol.

How to calculate Effective Length of Column given Crippling Load by Euler's Formula using this online calculator? To use this online calculator for Effective Length of Column given Crippling Load by Euler's Formula, enter Modulus of Elasticity Column (E), Moment of Inertia Column (I) & Euler’s Buckling Load (P_E) and hit the calculate button. Here is how the Effective Length of Column given Crippling Load by Euler's Formula calculation can be explained with given input values -> 3E+6 = sqrt((pi^2*200000000000*6.8E-06)/(1491407)).

FAQ

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

The Effective Length of Column given Crippling Load by Euler's Formula is defined as the distance between successive inflection points or points of zero moment and is represented as L_eff = sqrt((pi^2*E*I)/(P_E)) or Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load)). 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, Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis & The Euler’s Buckling Load is the axial load at which a perfectly straight column or structural member starts to bend.

How to calculate Effective Length of Column given Crippling Load by Euler's Formula?

The Effective Length of Column given Crippling Load by Euler's Formula is defined as the distance between successive inflection points or points of zero moment is calculated using Effective Column Length = sqrt((pi^2*Modulus of Elasticity Column*Moment of Inertia Column)/(Euler’s Buckling Load)). To calculate Effective Length of Column given Crippling Load by Euler's Formula, you need Modulus of Elasticity Column (E), Moment of Inertia Column (I) & Euler’s Buckling Load (P_E). With our tool, you need to enter the respective value for Modulus of Elasticity Column, Moment of Inertia Column & Euler’s Buckling Load and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Effective Column Length?

In this formula, Effective Column Length uses Modulus of Elasticity Column, Moment of Inertia Column & Euler’s Buckling Load. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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