Elastic Critical Buckling Load Calculator

✖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%
✖Column Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point.ⓘ Column Cross-Sectional Area [A]			+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 Radius of Gyration of Column about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass.ⓘ Radius of Gyration of Column [r_gyration]			+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.ⓘ Elastic Critical Buckling Load [P_{Buckling Load}]

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Formula

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Elastic Critical Buckling Load

Formula

`"P"_{"Buckling Load"} = (pi^2*"E"*"A")/("L"/"r"_{"gyration "})^2`

Example

`"25.94609N"=(pi^2*"50MPa"*"700mm²")/("3000mm"/"26mm")^2`

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Download Elastic Flexural Buckling of Columns Formulas PDF

Elastic Critical Buckling Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Buckling Load = (pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/(Effective Length of Column/Radius of Gyration of Column)^2
P_{Buckling Load} = (pi^2*E*A)/(L/r_gyration)^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.
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.
Column Cross-Sectional Area - (Measured in Square Millimeter) - Column Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point.
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.
Radius of Gyration of Column - (Measured in Millimeter) - The Radius of Gyration of Column about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass.

STEP 1: Convert Input(s) to Base Unit

Modulus of Elasticity: 50 Megapascal --> 50 Megapascal No Conversion Required
Column Cross-Sectional Area: 700 Square Millimeter --> 700 Square Millimeter No Conversion Required
Effective Length of Column: 3000 Millimeter --> 3000 Millimeter No Conversion Required
Radius of Gyration of Column: 26 Millimeter --> 26 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_{Buckling Load} = (pi^2*E*A)/(L/r_gyration)^2 --> (pi^2*50*700)/(3000/26)^2

Evaluating ... ...

P_{Buckling Load} = 25.9460933477527

STEP 3: Convert Result to Output's Unit

25.9460933477527 Newton --> No Conversion Required

FINAL ANSWER

25.9460933477527 ≈ 25.94609 Newton <-- Buckling Load

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Columns » Elastic Flexural Buckling of Columns » Slender Columns » Elastic Critical Buckling Load

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Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

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< 4 Slender Columns Calculators

Radius of Gyration of Column given Elastic Critical Buckling Load

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

Cross-Sectional Area given Elastic Critical Buckling Load

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

Elastic Critical Buckling Load

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

Slenderness Ratio given Elastic Critical Buckling Load

Go Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load)

Elastic Critical Buckling Load Formula

Buckling Load = (pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/(Effective Length of Column/Radius of Gyration of Column)^2
P_{Buckling Load} = (pi^2*E*A)/(L/r_gyration)^2

Column End Conditions for Effective Length of Column.

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 = 0.7;
when both ends are fixed, n = 0.5; and
when one end is fixed and the other is free, n = 2.

Define Buckling.

In structural engineering, buckling is the sudden change in shape (deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear.

How to Calculate Elastic Critical Buckling Load?

Elastic Critical Buckling Load calculator uses Buckling Load = (pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/(Effective Length of Column/Radius of Gyration of Column)^2 to calculate the Buckling Load, The Elastic Critical Buckling Load formula is defined as the greatest load applied on pin ended columns that cause lateral deflection i.e., failure due to buckling. Buckling Load is denoted by P_{Buckling Load} symbol.

How to calculate Elastic Critical Buckling Load using this online calculator? To use this online calculator for Elastic Critical Buckling Load, enter Modulus of Elasticity (E), Column Cross-Sectional Area (A), Effective Length of Column (L) & Radius of Gyration of Column (r_gyration) and hit the calculate button. Here is how the Elastic Critical Buckling Load calculation can be explained with given input values -> 2.6E+7 = (pi^2*50000000*0.0007)/(3/0.026)^2.

FAQ

What is Elastic Critical Buckling Load?

The Elastic Critical Buckling Load formula is defined as the greatest load applied on pin ended columns that cause lateral deflection i.e., failure due to buckling and is represented as P_{Buckling Load} = (pi^2*E*A)/(L/r_gyration)^2 or Buckling Load = (pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/(Effective Length of Column/Radius of Gyration of Column)^2. 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, Column Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point, 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 & The Radius of Gyration of Column about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass.

How to calculate Elastic Critical Buckling Load?

The Elastic Critical Buckling Load formula is defined as the greatest load applied on pin ended columns that cause lateral deflection i.e., failure due to buckling is calculated using Buckling Load = (pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/(Effective Length of Column/Radius of Gyration of Column)^2. To calculate Elastic Critical Buckling Load, you need Modulus of Elasticity (E), Column Cross-Sectional Area (A), Effective Length of Column (L) & Radius of Gyration of Column (r_gyration). With our tool, you need to enter the respective value for Modulus of Elasticity, Column Cross-Sectional Area, Effective Length of Column & Radius of Gyration 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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