Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula [A]

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Formula

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Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula

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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Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 » Pin-Ended Columns » Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula

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< 4 Pin-Ended Columns Calculators

Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula

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 Critical Buckling Load for Pin Ended Columns by Euler's Formula

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

Critical Buckling Load for Pin Ended Columns by Euler's Formula

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 Critical Buckling Load for Pin Ended Columns by Euler's Formula

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

Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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)

What is Critical Buckling Load?

Buckling is a sudden lateral failure of an axially loaded member in compression, under a load value less than the compressive load-carrying capacity of that member. The axial compression load corresponding to this mode of failure is referred to as critical buckling load.

What does Buckling mean?

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 Critical Buckling Load for Pin Ended Columns by Euler's Formula?

Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula is defined as the area of a two-dimensional shape obtained when a Pin Ended 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula using this online calculator? To use this online calculator for Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula, 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula?

The Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula is defined as the area of a two-dimensional shape obtained when a Pin Ended 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula?

The Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula is defined as the area of a two-dimensional shape obtained when a Pin Ended 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula, 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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