Euler's Formula for Critical Buckling Load Calculator

✖Coefficient for Column End Conditions is defined as the multiplicative factor for different column end conditions.ⓘ Coefficient for Column End Conditions [n]			+10% -10%
✖The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.ⓘ Modulus of Elasticity [E]			+10% -10%
✖The Area Moment of Inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or second moment of inertia.ⓘ Area Moment of Inertia [I]			+10% -10%
✖The Effective Length of Column 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 [L]			+10% -10%

✖The Buckling Load is the load at which the column starts buckling. The buckling load of a given material depends on the Slenderness ratio, Area of a cross-section, and Modulus of Elasticity.ⓘ Euler's Formula for Critical Buckling Load [P_{Buckling Load}]

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Euler's Formula for Critical Buckling Load

Formula

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

Example

`"10.96623N"="2.0"*(pi^2)*"50MPa"*"100000mm⁴"/("3000mm")^2`

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Euler's Formula for Critical Buckling Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Buckling Load = Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity*Area Moment of Inertia/Effective Length of Column^2
P_{Buckling Load} = n*(pi^2)*E*I/L^2
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Buckling Load - (Measured in Newton) - The Buckling Load is the load at which the column starts buckling. The buckling load of a given material depends on the Slenderness ratio, Area of a cross-section, and Modulus of Elasticity.
Coefficient for Column End Conditions - Coefficient for Column End Conditions is defined as the multiplicative factor for different column end conditions.
Modulus of Elasticity - (Measured in Megapascal) - The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.
Area Moment of Inertia - (Measured in Millimeter⁴) - The Area Moment of Inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or second moment of inertia.
Effective Length of Column - (Measured in Millimeter) - The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

STEP 1: Convert Input(s) to Base Unit

Coefficient for Column End Conditions: 2 --> No Conversion Required
Modulus of Elasticity: 50 Megapascal --> 50 Megapascal No Conversion Required
Area Moment of Inertia: 100000 Millimeter⁴ --> 100000 Millimeter⁴ No Conversion Required
Effective Length of Column: 3000 Millimeter --> 3000 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_{Buckling Load} = n*(pi^2)*E*I/L^2 --> 2*(pi^2)*50*100000/3000^2

Evaluating ... ...

P_{Buckling Load} = 10.9662271123215

STEP 3: Convert Result to Output's Unit

10.9662271123215 Newton --> No Conversion Required

FINAL ANSWER

10.9662271123215 ≈ 10.96623 Newton <-- Buckling Load

(Calculation completed in 00.004 seconds)

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Euler's Formula for Critical Buckling Load given Area

Go Buckling Load = (Coefficient for Column End Conditions*pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/((Effective Length of Column/Radius of Gyration of Column)^2)

Euler's Formula for Critical Buckling Load

Go Buckling Load = Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity*Area Moment of Inertia/Effective Length of Column^2

Euler's Formula for Critical Buckling Load Formula

Buckling Load = Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity*Area Moment of Inertia/Effective Length of Column^2
P_{Buckling Load} = n*(pi^2)*E*I/L^2

Column End Conditions

In this formula, the coefficient n accounts for end conditions. When the column
is pivoted at both ends, n = 1; when one end is fixed and the other end is rounded, n = 2; when both ends are fixed, n = 4; and when one end is fixed and the other is free, n = 0.25. The slenderness ratio separating long columns from short columns depends on the modulus of elasticity and the yield strength of the column material.

How to Calculate Euler's Formula for Critical Buckling Load?

Euler's Formula for Critical Buckling Load calculator uses Buckling Load = Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity*Area Moment of Inertia/Effective Length of Column^2 to calculate the Buckling Load, The Euler's Formula for Critical Buckling Load formula is defined as the compressive load at which a slender column will suddenly bend or buckle. Buckling Load is denoted by P_{Buckling Load} symbol.

How to calculate Euler's Formula for Critical Buckling Load using this online calculator? To use this online calculator for Euler's Formula for Critical Buckling Load, enter Coefficient for Column End Conditions (n), Modulus of Elasticity (E), Area Moment of Inertia (I) & Effective Length of Column (L) and hit the calculate button. Here is how the Euler's Formula for Critical Buckling Load calculation can be explained with given input values -> 10.96623 = 2*(pi^2)*50000000*1E-07/3^2.

FAQ

What is Euler's Formula for Critical Buckling Load?

The Euler's Formula for Critical Buckling Load formula is defined as the compressive load at which a slender column will suddenly bend or buckle and is represented as P_{Buckling Load} = n*(pi^2)*E*I/L^2 or Buckling Load = Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity*Area Moment of Inertia/Effective Length of Column^2. Coefficient for Column End Conditions is defined as the multiplicative factor for different column end conditions, The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality, The Area Moment of Inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or second moment of inertia & The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

How to calculate Euler's Formula for Critical Buckling Load?

The Euler's Formula for Critical Buckling Load formula is defined as the compressive load at which a slender column will suddenly bend or buckle is calculated using Buckling Load = Coefficient for Column End Conditions*(pi^2)*Modulus of Elasticity*Area Moment of Inertia/Effective Length of Column^2. To calculate Euler's Formula for Critical Buckling Load, you need Coefficient for Column End Conditions (n), Modulus of Elasticity (E), Area Moment of Inertia (I) & Effective Length of Column (L). With our tool, you need to enter the respective value for Coefficient for Column End Conditions, Modulus of Elasticity, Area Moment of Inertia & Effective Length of Column 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 Buckling Load?

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

Buckling Load = (Coefficient for Column End Conditions*pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/((Effective Length of Column/Radius of Gyration of Column)^2)

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