Euler's Formula for Critical Buckling Load given Area 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%
✖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.ⓘ Euler's Formula for Critical Buckling Load given Area [P_{Buckling Load}]

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Euler's Formula for Critical Buckling Load given Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
P_{Buckling Load} = (n*pi^2*E*A)/((L/r_gyration)^2)
This formula uses 1 Constants, 6 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.
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

Coefficient for Column End Conditions: 2 --> No Conversion Required
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} = (n*pi^2*E*A)/((L/r_gyration)^2) --> (2*pi^2*50*700)/((3000/26)^2)

Evaluating ... ...

P_{Buckling Load} = 51.8921866955054

STEP 3: Convert Result to Output's Unit

51.8921866955054 Newton --> No Conversion Required

FINAL ANSWER

51.8921866955054 ≈ 51.89219 Newton <-- Buckling Load

(Calculation completed in 00.020 seconds)

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Euler's Formula for Critical Buckling Load given Area

LaTeX 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

LaTeX 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 given Area Formula

LaTeX Go

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 given Area?

Euler's Formula for Critical Buckling Load given Area calculator uses 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) to calculate the Buckling Load, The Euler's Formula for Critical Buckling Load given Area 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 given Area using this online calculator? To use this online calculator for Euler's Formula for Critical Buckling Load given Area, enter Coefficient for Column End Conditions (n), 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 Euler's Formula for Critical Buckling Load given Area calculation can be explained with given input values -> 51.89219 = (2*pi^2*50000000*0.0007)/((3/0.026)^2).

FAQ

What is Euler's Formula for Critical Buckling Load given Area?

The Euler's Formula for Critical Buckling Load given Area 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*A)/((L/r_gyration)^2) or 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). 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, 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 Euler's Formula for Critical Buckling Load given Area?

The Euler's Formula for Critical Buckling Load given Area 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*Column Cross-Sectional Area)/((Effective Length of Column/Radius of Gyration of Column)^2). To calculate Euler's Formula for Critical Buckling Load given Area, you need Coefficient for Column End Conditions (n), 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 Coefficient for Column End Conditions, 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.

How many ways are there to calculate Buckling Load?

In this formula, Buckling Load uses Coefficient for Column End Conditions, Modulus of Elasticity, Column Cross-Sectional Area, Effective Length of Column & Radius of Gyration 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*Area Moment of Inertia/Effective Length of Column^2

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