Cross-Sectional Area given Elastic Critical Buckling Load Calculator

✖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.ⓘ Buckling Load [P_{Buckling Load}]			+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 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.ⓘ Cross-Sectional Area given Elastic Critical Buckling Load [A]

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Formula

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Cross-Sectional Area given Elastic Critical Buckling Load

Formula

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

Example

`"134.8951mm²"=("5N"*("3000mm"/"26mm")^2)/(pi^2*"50MPa")`

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Download Elastic Flexural Buckling of Columns Formulas PDF

Cross-Sectional Area given Elastic Critical Buckling Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Column Cross-Sectional Area = (Buckling Load*(Effective Length of Column/Radius of Gyration of Column)^2)/(pi^2*Modulus of Elasticity)
A = (P_{Buckling Load}*(L/r_gyration)^2)/(pi^2*E)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Buckling Load: 5 Newton --> 5 Newton 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
Modulus of Elasticity: 50 Megapascal --> 50 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (P_{Buckling Load}*(L/r_gyration)^2)/(pi^2*E) --> (5*(3000/26)^2)/(pi^2*50)

Evaluating ... ...

A = 134.895066979444

STEP 3: Convert Result to Output's Unit

0.000134895066979444 Square Meter -->134.895066979444 Square Millimeter (Check conversion here)

FINAL ANSWER

134.895066979444 ≈ 134.8951 Square Millimeter <-- Column Cross-Sectional Area

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Columns » Elastic Flexural Buckling of Columns » Slender Columns » Cross-Sectional Area given 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)

Cross-Sectional Area given Elastic Critical Buckling Load Formula

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

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 Cross-Sectional Area given Elastic Critical Buckling Load?

Cross-Sectional Area given Elastic Critical Buckling Load calculator uses Column Cross-Sectional Area = (Buckling Load*(Effective Length of Column/Radius of Gyration of Column)^2)/(pi^2*Modulus of Elasticity) to calculate the Column Cross-Sectional Area, The Cross-Sectional Area given Elastic Critical Buckling Load is defined as the area of a two-dimensional shape obtained when a Column is sliced perpendicular to its length axis at a point. Column Cross-Sectional Area is denoted by A symbol.

How to calculate Cross-Sectional Area given Elastic Critical Buckling Load using this online calculator? To use this online calculator for Cross-Sectional Area given Elastic Critical Buckling Load, enter Buckling Load (P_{Buckling Load}), Effective Length of Column (L), Radius of Gyration of Column (r_gyration) & Modulus of Elasticity (E) and hit the calculate button. Here is how the Cross-Sectional Area given Elastic Critical Buckling Load calculation can be explained with given input values -> 134.8951 = (5*(3/0.026)^2)/(pi^2*50000000).

FAQ

What is Cross-Sectional Area given Elastic Critical Buckling Load?

The Cross-Sectional Area given Elastic Critical Buckling Load is defined as the area of a two-dimensional shape obtained when a Column is sliced perpendicular to its length axis at a point and is represented as A = (P_{Buckling Load}*(L/r_gyration)^2)/(pi^2*E) or Column Cross-Sectional Area = (Buckling Load*(Effective Length of Column/Radius of Gyration of Column)^2)/(pi^2*Modulus of Elasticity). 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, 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 & 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.

How to calculate Cross-Sectional Area given Elastic Critical Buckling Load?

The Cross-Sectional Area given Elastic Critical Buckling Load is defined as the area of a two-dimensional shape obtained when a Column is sliced perpendicular to its length axis at a point is calculated using Column Cross-Sectional Area = (Buckling Load*(Effective Length of Column/Radius of Gyration of Column)^2)/(pi^2*Modulus of Elasticity). To calculate Cross-Sectional Area given Elastic Critical Buckling Load, you need Buckling Load (P_{Buckling Load}), Effective Length of Column (L), Radius of Gyration of Column (r_gyration) & Modulus of Elasticity (E). With our tool, you need to enter the respective value for Buckling Load, Effective Length of Column, Radius of Gyration of Column & Modulus of Elasticity 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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